+2019-02-25 Sam Weinig <sam@webkit.org>
+
+ Update double-conversion to the latest version
+ https://bugs.webkit.org/show_bug.cgi?id=194994
+
+ Import the latest version of the double-conversion library based on
+ https://github.com/google/double-conversion/commit/990c44707c70832dc1ce1578048c2198bafd3307
+
+ In additon to importing the code, the following changes were applied (or re-applied) to maintain
+ parity with what we had previously:
+ - Add #include "config.h" to each cpp file.
+ - Put everything inside the WTF namespace.
+ - Changed all in library includes to be of the form #include <wtf/dtoa/FILE.h>.
+ - Renamed double_conversion::Vector<> to double_conversion::BufferReference<>.
+ - Replaced duplicated functions with ASCIICType.h variants
+ - Made CachedPower table a constexpr.
+ - Exported (via WTF_EXPORT_PRIVATE) several functions in double-conversion.h.
+ - Made substantial changes to StringToDoubleConverter to avoid unnecessary overhead of
+ parameterization, as we only ever want one configuration. Instead of constructing a
+ configured class and calling StringToDouble on it, StringToDouble is now a static
+ function. This allows a bunch of now dead code (hex support, octal support, etc.) to
+ be eliminated. As StringToDoubleConverter now supports single precision floats, some
+ additional templating of StringToIeee was added to avoid extra unnecessary branching.
+ - Added RemoveCharacters function to double_conversion::StringBuilder.
+
+ Reviewed by Darin Adler.
+
+ * WTF.xcodeproj/project.pbxproj:
+ * wtf/CMakeLists.txt:
+ * wtf/dtoa/AUTHORS: Added.
+ * wtf/dtoa/README: Removed.
+ * wtf/dtoa/README.md: Added.
+ * wtf/dtoa/bignum-dtoa.cc:
+ * wtf/dtoa/bignum-dtoa.h:
+ * wtf/dtoa/bignum.cc:
+ * wtf/dtoa/bignum.h:
+ (WTF::double_conversion::Bignum::Times10):
+ (WTF::double_conversion::Bignum::Equal):
+ (WTF::double_conversion::Bignum::LessEqual):
+ (WTF::double_conversion::Bignum::Less):
+ (WTF::double_conversion::Bignum::PlusEqual):
+ (WTF::double_conversion::Bignum::PlusLessEqual):
+ (WTF::double_conversion::Bignum::PlusLess):
+ (WTF::double_conversion::Bignum::EnsureCapacity):
+ (WTF::double_conversion::Bignum::BigitLength const):
+ * wtf/dtoa/cached-powers.cc:
+ * wtf/dtoa/cached-powers.h:
+ * wtf/dtoa/diy-fp.cc:
+ * wtf/dtoa/diy-fp.h:
+ (WTF::double_conversion::DiyFp::DiyFp):
+ (WTF::double_conversion::DiyFp::Subtract):
+ (WTF::double_conversion::DiyFp::Minus):
+ (WTF::double_conversion::DiyFp::Times):
+ (WTF::double_conversion::DiyFp::Normalize):
+ (WTF::double_conversion::DiyFp::f const):
+ (WTF::double_conversion::DiyFp::e const):
+ (WTF::double_conversion::DiyFp::set_f):
+ (WTF::double_conversion::DiyFp::set_e):
+ * wtf/dtoa/double-conversion.cc:
+ * wtf/dtoa/double-conversion.h:
+ (WTF::double_conversion::DoubleToStringConverter::DoubleToStringConverter):
+ (WTF::double_conversion::DoubleToStringConverter::ToShortest const):
+ (WTF::double_conversion::DoubleToStringConverter::ToShortestSingle const):
+ (WTF::double_conversion::StringToDoubleConverter::StringToDoubleConverter):
+ * wtf/dtoa/double.h: Removed.
+ * wtf/dtoa/fast-dtoa.cc:
+ * wtf/dtoa/fast-dtoa.h:
+ * wtf/dtoa/fixed-dtoa.cc:
+ * wtf/dtoa/fixed-dtoa.h:
+ * wtf/dtoa/ieee.h: Added.
+ (WTF::double_conversion::double_to_uint64):
+ (WTF::double_conversion::uint64_to_double):
+ (WTF::double_conversion::float_to_uint32):
+ (WTF::double_conversion::uint32_to_float):
+ (WTF::double_conversion::Double::Double):
+ (WTF::double_conversion::Double::AsDiyFp const):
+ (WTF::double_conversion::Double::AsNormalizedDiyFp const):
+ (WTF::double_conversion::Double::AsUint64 const):
+ (WTF::double_conversion::Double::NextDouble const):
+ (WTF::double_conversion::Double::PreviousDouble const):
+ (WTF::double_conversion::Double::Exponent const):
+ (WTF::double_conversion::Double::Significand const):
+ (WTF::double_conversion::Double::IsDenormal const):
+ (WTF::double_conversion::Double::IsSpecial const):
+ (WTF::double_conversion::Double::IsNan const):
+ (WTF::double_conversion::Double::IsInfinite const):
+ (WTF::double_conversion::Double::Sign const):
+ (WTF::double_conversion::Double::UpperBoundary const):
+ (WTF::double_conversion::Double::NormalizedBoundaries const):
+ (WTF::double_conversion::Double::LowerBoundaryIsCloser const):
+ (WTF::double_conversion::Double::value const):
+ (WTF::double_conversion::Double::SignificandSizeForOrderOfMagnitude):
+ (WTF::double_conversion::Double::Infinity):
+ (WTF::double_conversion::Double::NaN):
+ (WTF::double_conversion::Double::DiyFpToUint64):
+ (WTF::double_conversion::Single::Single):
+ (WTF::double_conversion::Single::AsDiyFp const):
+ (WTF::double_conversion::Single::AsUint32 const):
+ (WTF::double_conversion::Single::Exponent const):
+ (WTF::double_conversion::Single::Significand const):
+ (WTF::double_conversion::Single::IsDenormal const):
+ (WTF::double_conversion::Single::IsSpecial const):
+ (WTF::double_conversion::Single::IsNan const):
+ (WTF::double_conversion::Single::IsInfinite const):
+ (WTF::double_conversion::Single::Sign const):
+ (WTF::double_conversion::Single::NormalizedBoundaries const):
+ (WTF::double_conversion::Single::UpperBoundary const):
+ (WTF::double_conversion::Single::LowerBoundaryIsCloser const):
+ (WTF::double_conversion::Single::value const):
+ (WTF::double_conversion::Single::Infinity):
+ (WTF::double_conversion::Single::NaN):
+ * wtf/dtoa/strtod.cc:
+ * wtf/dtoa/strtod.h:
+ * wtf/dtoa/utils.h:
+ (abort_noreturn):
+ (WTF::double_conversion::Max):
+ (WTF::double_conversion::Min):
+ (WTF::double_conversion::StrLength):
+ (WTF::double_conversion::BufferReference::BufferReference):
+ (WTF::double_conversion::BufferReference::SubVector):
+ (WTF::double_conversion::BufferReference::length const):
+ (WTF::double_conversion::BufferReference::is_empty const):
+ (WTF::double_conversion::BufferReference::start const):
+ (WTF::double_conversion::BufferReference::operator[] const):
+ (WTF::double_conversion::BufferReference::first):
+ (WTF::double_conversion::BufferReference::last):
+ (WTF::double_conversion::StringBuilder::StringBuilder):
+ (WTF::double_conversion::StringBuilder::~StringBuilder):
+ (WTF::double_conversion::StringBuilder::size const):
+ (WTF::double_conversion::StringBuilder::position const):
+ (WTF::double_conversion::StringBuilder::Reset):
+ (WTF::double_conversion::StringBuilder::AddCharacter):
+ (WTF::double_conversion::StringBuilder::AddString):
+ (WTF::double_conversion::StringBuilder::AddSubstring):
+ (WTF::double_conversion::StringBuilder::AddPadding):
+ (WTF::double_conversion::StringBuilder::RemoveCharacters):
+ (WTF::double_conversion::StringBuilder::Finalize):
+ (WTF::double_conversion::StringBuilder::is_finalized const):
+ (WTF::double_conversion::BitCast):
+ (WTF::double_conversion::BufferReference::SubBufferReference): Deleted.
+ (WTF::double_conversion::StringBuilder::SetPosition): Deleted.
+
2019-02-20 Darin Adler <darin@apple.com>
Finish removing String::format
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isa = PBXGroup;
children = (
+ 7C137941222326C700D7A824 /* AUTHORS */,
A8A47288151A825A004123FF /* COPYING */,
A8A47292151A825A004123FF /* LICENSE */,
- A8A47293151A825A004123FF /* README */,
+ 7C137943222326D500D7A824 /* README.md */,
A8A47282151A825A004123FF /* bignum-dtoa.cc */,
A8A47283151A825A004123FF /* bignum-dtoa.h */,
A8A47284151A825A004123FF /* bignum.cc */,
A8A4728A151A825A004123FF /* diy-fp.h */,
A8A4728B151A825A004123FF /* double-conversion.cc */,
A8A4728C151A825A004123FF /* double-conversion.h */,
- A8A4728D151A825A004123FF /* double.h */,
A8A4728E151A825A004123FF /* fast-dtoa.cc */,
A8A4728F151A825A004123FF /* fast-dtoa.h */,
A8A47290151A825A004123FF /* fixed-dtoa.cc */,
A8A47291151A825A004123FF /* fixed-dtoa.h */,
+ 7C137942222326D500D7A824 /* ieee.h */,
A8A47294151A825A004123FF /* strtod.cc */,
A8A47295151A825A004123FF /* strtod.h */,
A8A47296151A825A004123FF /* utils.h */,
dtoa/cached-powers.h
dtoa/diy-fp.h
dtoa/double-conversion.h
- dtoa/double.h
dtoa/fast-dtoa.h
dtoa/fixed-dtoa.h
+ dtoa/ieee.h
dtoa/strtod.h
dtoa/utils.h
--- /dev/null
+# Below is a list of people and organizations that have contributed
+# to the double-conversion project. Names should be added to the
+# list like so:
+#
+# Name/Organization <email address>
+
+Google Inc.
+Mozilla Foundation
+
+Jeff Muizelaar <jmuizelaar@mozilla.com>
+Mike Hommey <mhommey@mozilla.com>
+Martin Olsson <mnemo@minimum.se>
+Kent Williams <chaircrusher@gmail.com>
+Elan Ruusamäe <glen@delfi.ee>
+++ /dev/null
-http://code.google.com/p/double-conversion
-
-This project (double-conversion) provides binary-decimal and decimal-binary
-routines for IEEE doubles.
-
-The library consists of efficient conversion routines that have been extracted
-from the V8 JavaScript engine. The code has been refactored and improved so that
-it can be used more easily in other projects.
-
-There is extensive documentation in src/double-conversion.h. Other examples can
-be found in test/cctest/test-conversions.cc.
--- /dev/null
+https://github.com/google/double-conversion
+
+This project (double-conversion) provides binary-decimal and decimal-binary
+routines for IEEE doubles.
+
+The library consists of efficient conversion routines that have been extracted
+from the V8 JavaScript engine. The code has been refactored and improved so that
+it can be used more easily in other projects.
+
+There is extensive documentation in `double-conversion/double-conversion.h`. Other
+examples can be found in `test/cctest/test-conversions.cc`.
+
+
+Building
+========
+
+This library can be built with [scons][0] or [cmake][1].
+The checked-in Makefile simply forwards to scons, and provides a
+shortcut to run all tests:
+
+ make
+ make test
+
+Scons
+-----
+
+The easiest way to install this library is to use `scons`. It builds
+the static and shared library, and is set up to install those at the
+correct locations:
+
+ scons install
+
+Use the `DESTDIR` option to change the target directory:
+
+ scons DESTDIR=alternative_directory install
+
+Cmake
+-----
+
+To use cmake run `cmake .` in the root directory. This overwrites the
+existing Makefile.
+
+Use `-DBUILD_SHARED_LIBS=ON` to enable the compilation of shared libraries.
+Note that this disables static libraries. There is currently no way to
+build both libraries at the same time with cmake.
+
+Use `-DBUILD_TESTING=ON` to build the test executable.
+
+ cmake . -DBUILD_TESTING=ON
+ make
+ test/cctest/cctest --list | tr -d '<' | xargs test/cctest/cctest
+
+[0]: http://www.scons.org/
+[1]: https://cmake.org/
#include "config.h"
-#include <math.h>
+#include <cmath>
-#include "bignum-dtoa.h"
+#include <wtf/dtoa/bignum-dtoa.h>
-#include "bignum.h"
-#include "double.h"
+#include <wtf/dtoa/bignum.h>
+#include <wtf/dtoa/ieee.h>
namespace WTF {
-
namespace double_conversion {
-
- static int NormalizedExponent(uint64_t significand, int exponent) {
- ASSERT(significand != 0);
- while ((significand & Double::kHiddenBit) == 0) {
- significand = significand << 1;
- exponent = exponent - 1;
- }
- return exponent;
- }
-
-
- // Forward declarations:
- // Returns an estimation of k such that 10^(k-1) <= v < 10^k.
- static int EstimatePower(int exponent);
- // Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
- // and denominator.
- static void InitialScaledStartValues(double v,
- int estimated_power,
- bool need_boundary_deltas,
- Bignum* numerator,
- Bignum* denominator,
- Bignum* delta_minus,
- Bignum* delta_plus);
- // Multiplies numerator/denominator so that its values lies in the range 1-10.
- // Returns decimal_point s.t.
- // v = numerator'/denominator' * 10^(decimal_point-1)
- // where numerator' and denominator' are the values of numerator and
- // denominator after the call to this function.
- static void FixupMultiply10(int estimated_power, bool is_even,
- int* decimal_point,
- Bignum* numerator, Bignum* denominator,
- Bignum* delta_minus, Bignum* delta_plus);
- // Generates digits from the left to the right and stops when the generated
- // digits yield the shortest decimal representation of v.
- static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
- Bignum* delta_minus, Bignum* delta_plus,
- bool is_even,
- BufferReference<char> buffer, int* length);
- // Generates 'requested_digits' after the decimal point.
- static void BignumToFixed(int requested_digits, int* decimal_point,
- Bignum* numerator, Bignum* denominator,
- BufferReference<char>(buffer), int* length);
- // Generates 'count' digits of numerator/denominator.
- // Once 'count' digits have been produced rounds the result depending on the
- // remainder (remainders of exactly .5 round upwards). Might update the
- // decimal_point when rounding up (for example for 0.9999).
- static void GenerateCountedDigits(int count, int* decimal_point,
- Bignum* numerator, Bignum* denominator,
- BufferReference<char>(buffer), int* length);
-
-
- void BignumDtoa(double v, BignumDtoaMode mode, int requested_digits,
- BufferReference<char> buffer, int* length, int* decimal_point) {
- ASSERT(v > 0);
- ASSERT(!Double(v).IsSpecial());
- uint64_t significand = Double(v).Significand();
- bool is_even = (significand & 1) == 0;
- int exponent = Double(v).Exponent();
- int normalized_exponent = NormalizedExponent(significand, exponent);
- // estimated_power might be too low by 1.
- int estimated_power = EstimatePower(normalized_exponent);
-
- // Shortcut for Fixed.
- // The requested digits correspond to the digits after the point. If the
- // number is much too small, then there is no need in trying to get any
- // digits.
- if (mode == BIGNUM_DTOA_FIXED && -estimated_power - 1 > requested_digits) {
- buffer[0] = '\0';
- *length = 0;
- // Set decimal-point to -requested_digits. This is what Gay does.
- // Note that it should not have any effect anyways since the string is
- // empty.
- *decimal_point = -requested_digits;
- return;
- }
-
- Bignum numerator;
- Bignum denominator;
- Bignum delta_minus;
- Bignum delta_plus;
- // Make sure the bignum can grow large enough. The smallest double equals
- // 4e-324. In this case the denominator needs fewer than 324*4 binary digits.
- // The maximum double is 1.7976931348623157e308 which needs fewer than
- // 308*4 binary digits.
- ASSERT(Bignum::kMaxSignificantBits >= 324*4);
- bool need_boundary_deltas = (mode == BIGNUM_DTOA_SHORTEST);
- InitialScaledStartValues(v, estimated_power, need_boundary_deltas,
- &numerator, &denominator,
- &delta_minus, &delta_plus);
- // We now have v = (numerator / denominator) * 10^estimated_power.
- FixupMultiply10(estimated_power, is_even, decimal_point,
- &numerator, &denominator,
- &delta_minus, &delta_plus);
- // We now have v = (numerator / denominator) * 10^(decimal_point-1), and
- // 1 <= (numerator + delta_plus) / denominator < 10
- switch (mode) {
- case BIGNUM_DTOA_SHORTEST:
- GenerateShortestDigits(&numerator, &denominator,
- &delta_minus, &delta_plus,
- is_even, buffer, length);
- break;
- case BIGNUM_DTOA_FIXED:
- BignumToFixed(requested_digits, decimal_point,
- &numerator, &denominator,
- buffer, length);
- break;
- case BIGNUM_DTOA_PRECISION:
- GenerateCountedDigits(requested_digits, decimal_point,
- &numerator, &denominator,
- buffer, length);
- break;
- default:
- UNREACHABLE();
- }
- buffer[*length] = '\0';
+
+static int NormalizedExponent(uint64_t significand, int exponent) {
+ ASSERT(significand != 0);
+ while ((significand & Double::kHiddenBit) == 0) {
+ significand = significand << 1;
+ exponent = exponent - 1;
+ }
+ return exponent;
+}
+
+
+// Forward declarations:
+// Returns an estimation of k such that 10^(k-1) <= v < 10^k.
+static int EstimatePower(int exponent);
+// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
+// and denominator.
+static void InitialScaledStartValues(uint64_t significand,
+ int exponent,
+ bool lower_boundary_is_closer,
+ int estimated_power,
+ bool need_boundary_deltas,
+ Bignum* numerator,
+ Bignum* denominator,
+ Bignum* delta_minus,
+ Bignum* delta_plus);
+// Multiplies numerator/denominator so that its values lies in the range 1-10.
+// Returns decimal_point s.t.
+// v = numerator'/denominator' * 10^(decimal_point-1)
+// where numerator' and denominator' are the values of numerator and
+// denominator after the call to this function.
+static void FixupMultiply10(int estimated_power, bool is_even,
+ int* decimal_point,
+ Bignum* numerator, Bignum* denominator,
+ Bignum* delta_minus, Bignum* delta_plus);
+// Generates digits from the left to the right and stops when the generated
+// digits yield the shortest decimal representation of v.
+static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
+ Bignum* delta_minus, Bignum* delta_plus,
+ bool is_even,
+ BufferReference<char> buffer, int* length);
+// Generates 'requested_digits' after the decimal point.
+static void BignumToFixed(int requested_digits, int* decimal_point,
+ Bignum* numerator, Bignum* denominator,
+ BufferReference<char>(buffer), int* length);
+// Generates 'count' digits of numerator/denominator.
+// Once 'count' digits have been produced rounds the result depending on the
+// remainder (remainders of exactly .5 round upwards). Might update the
+// decimal_point when rounding up (for example for 0.9999).
+static void GenerateCountedDigits(int count, int* decimal_point,
+ Bignum* numerator, Bignum* denominator,
+ BufferReference<char>(buffer), int* length);
+
+
+void BignumDtoa(double v, BignumDtoaMode mode, int requested_digits,
+ BufferReference<char> buffer, int* length, int* decimal_point) {
+ ASSERT(v > 0);
+ ASSERT(!Double(v).IsSpecial());
+ uint64_t significand;
+ int exponent;
+ bool lower_boundary_is_closer;
+ if (mode == BIGNUM_DTOA_SHORTEST_SINGLE) {
+ float f = static_cast<float>(v);
+ ASSERT(f == v);
+ significand = Single(f).Significand();
+ exponent = Single(f).Exponent();
+ lower_boundary_is_closer = Single(f).LowerBoundaryIsCloser();
+ } else {
+ significand = Double(v).Significand();
+ exponent = Double(v).Exponent();
+ lower_boundary_is_closer = Double(v).LowerBoundaryIsCloser();
+ }
+ bool need_boundary_deltas =
+ (mode == BIGNUM_DTOA_SHORTEST || mode == BIGNUM_DTOA_SHORTEST_SINGLE);
+
+ bool is_even = (significand & 1) == 0;
+ int normalized_exponent = NormalizedExponent(significand, exponent);
+ // estimated_power might be too low by 1.
+ int estimated_power = EstimatePower(normalized_exponent);
+
+ // Shortcut for Fixed.
+ // The requested digits correspond to the digits after the point. If the
+ // number is much too small, then there is no need in trying to get any
+ // digits.
+ if (mode == BIGNUM_DTOA_FIXED && -estimated_power - 1 > requested_digits) {
+ buffer[0] = '\0';
+ *length = 0;
+ // Set decimal-point to -requested_digits. This is what Gay does.
+ // Note that it should not have any effect anyways since the string is
+ // empty.
+ *decimal_point = -requested_digits;
+ return;
+ }
+
+ Bignum numerator;
+ Bignum denominator;
+ Bignum delta_minus;
+ Bignum delta_plus;
+ // Make sure the bignum can grow large enough. The smallest double equals
+ // 4e-324. In this case the denominator needs fewer than 324*4 binary digits.
+ // The maximum double is 1.7976931348623157e308 which needs fewer than
+ // 308*4 binary digits.
+ ASSERT(Bignum::kMaxSignificantBits >= 324*4);
+ InitialScaledStartValues(significand, exponent, lower_boundary_is_closer,
+ estimated_power, need_boundary_deltas,
+ &numerator, &denominator,
+ &delta_minus, &delta_plus);
+ // We now have v = (numerator / denominator) * 10^estimated_power.
+ FixupMultiply10(estimated_power, is_even, decimal_point,
+ &numerator, &denominator,
+ &delta_minus, &delta_plus);
+ // We now have v = (numerator / denominator) * 10^(decimal_point-1), and
+ // 1 <= (numerator + delta_plus) / denominator < 10
+ switch (mode) {
+ case BIGNUM_DTOA_SHORTEST:
+ case BIGNUM_DTOA_SHORTEST_SINGLE:
+ GenerateShortestDigits(&numerator, &denominator,
+ &delta_minus, &delta_plus,
+ is_even, buffer, length);
+ break;
+ case BIGNUM_DTOA_FIXED:
+ BignumToFixed(requested_digits, decimal_point,
+ &numerator, &denominator,
+ buffer, length);
+ break;
+ case BIGNUM_DTOA_PRECISION:
+ GenerateCountedDigits(requested_digits, decimal_point,
+ &numerator, &denominator,
+ buffer, length);
+ break;
+ default:
+ UNREACHABLE();
+ }
+ buffer[*length] = '\0';
+}
+
+
+// The procedure starts generating digits from the left to the right and stops
+// when the generated digits yield the shortest decimal representation of v. A
+// decimal representation of v is a number lying closer to v than to any other
+// double, so it converts to v when read.
+//
+// This is true if d, the decimal representation, is between m- and m+, the
+// upper and lower boundaries. d must be strictly between them if !is_even.
+// m- := (numerator - delta_minus) / denominator
+// m+ := (numerator + delta_plus) / denominator
+//
+// Precondition: 0 <= (numerator+delta_plus) / denominator < 10.
+// If 1 <= (numerator+delta_plus) / denominator < 10 then no leading 0 digit
+// will be produced. This should be the standard precondition.
+static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
+ Bignum* delta_minus, Bignum* delta_plus,
+ bool is_even,
+ BufferReference<char> buffer, int* length) {
+ // Small optimization: if delta_minus and delta_plus are the same just reuse
+ // one of the two bignums.
+ if (Bignum::Equal(*delta_minus, *delta_plus)) {
+ delta_plus = delta_minus;
+ }
+ *length = 0;
+ for (;;) {
+ uint16_t digit;
+ digit = numerator->DivideModuloIntBignum(*denominator);
+ ASSERT(digit <= 9); // digit is a uint16_t and therefore always positive.
+ // digit = numerator / denominator (integer division).
+ // numerator = numerator % denominator.
+ buffer[(*length)++] = static_cast<char>(digit + '0');
+
+ // Can we stop already?
+ // If the remainder of the division is less than the distance to the lower
+ // boundary we can stop. In this case we simply round down (discarding the
+ // remainder).
+ // Similarly we test if we can round up (using the upper boundary).
+ bool in_delta_room_minus;
+ bool in_delta_room_plus;
+ if (is_even) {
+ in_delta_room_minus = Bignum::LessEqual(*numerator, *delta_minus);
+ } else {
+ in_delta_room_minus = Bignum::Less(*numerator, *delta_minus);
}
-
-
- // The procedure starts generating digits from the left to the right and stops
- // when the generated digits yield the shortest decimal representation of v. A
- // decimal representation of v is a number lying closer to v than to any other
- // double, so it converts to v when read.
- //
- // This is true if d, the decimal representation, is between m- and m+, the
- // upper and lower boundaries. d must be strictly between them if !is_even.
- // m- := (numerator - delta_minus) / denominator
- // m+ := (numerator + delta_plus) / denominator
- //
- // Precondition: 0 <= (numerator+delta_plus) / denominator < 10.
- // If 1 <= (numerator+delta_plus) / denominator < 10 then no leading 0 digit
- // will be produced. This should be the standard precondition.
- static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
- Bignum* delta_minus, Bignum* delta_plus,
- bool is_even,
- BufferReference<char> buffer, int* length) {
- // Small optimization: if delta_minus and delta_plus are the same just reuse
- // one of the two bignums.
- if (Bignum::Equal(*delta_minus, *delta_plus)) {
- delta_plus = delta_minus;
- }
- *length = 0;
- while (true) {
- uint16_t digit;
- digit = numerator->DivideModuloIntBignum(*denominator);
- ASSERT(digit <= 9); // digit is a uint16_t and therefore always positive.
- // digit = numerator / denominator (integer division).
- // numerator = numerator % denominator.
- buffer[(*length)++] = digit + '0';
-
- // Can we stop already?
- // If the remainder of the division is less than the distance to the lower
- // boundary we can stop. In this case we simply round down (discarding the
- // remainder).
- // Similarly we test if we can round up (using the upper boundary).
- bool in_delta_room_minus;
- bool in_delta_room_plus;
- if (is_even) {
- in_delta_room_minus = Bignum::LessEqual(*numerator, *delta_minus);
- } else {
- in_delta_room_minus = Bignum::Less(*numerator, *delta_minus);
- }
- if (is_even) {
- in_delta_room_plus =
- Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
- } else {
- in_delta_room_plus =
- Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
- }
- if (!in_delta_room_minus && !in_delta_room_plus) {
- // Prepare for next iteration.
- numerator->Times10();
- delta_minus->Times10();
- // We optimized delta_plus to be equal to delta_minus (if they share the
- // same value). So don't multiply delta_plus if they point to the same
- // object.
- if (delta_minus != delta_plus) {
- delta_plus->Times10();
- }
- } else if (in_delta_room_minus && in_delta_room_plus) {
- // Let's see if 2*numerator < denominator.
- // If yes, then the next digit would be < 5 and we can round down.
- int compare = Bignum::PlusCompare(*numerator, *numerator, *denominator);
- if (compare < 0) {
- // Remaining digits are less than .5. -> Round down (== do nothing).
- } else if (compare > 0) {
- // Remaining digits are more than .5 of denominator. -> Round up.
- // Note that the last digit could not be a '9' as otherwise the whole
- // loop would have stopped earlier.
- // We still have an assert here in case the preconditions were not
- // satisfied.
- ASSERT(buffer[(*length) - 1] != '9');
- buffer[(*length) - 1]++;
- } else {
- // Halfway case.
- // TODO(floitsch): need a way to solve half-way cases.
- // For now let's round towards even (since this is what Gay seems to
- // do).
-
- if ((buffer[(*length) - 1] - '0') % 2 == 0) {
- // Round down => Do nothing.
- } else {
- ASSERT(buffer[(*length) - 1] != '9');
- buffer[(*length) - 1]++;
- }
- }
- return;
- } else if (in_delta_room_minus) {
- // Round down (== do nothing).
- return;
- } else { // in_delta_room_plus
- // Round up.
- // Note again that the last digit could not be '9' since this would have
- // stopped the loop earlier.
- // We still have an ASSERT here, in case the preconditions were not
- // satisfied.
- ASSERT(buffer[(*length) -1] != '9');
- buffer[(*length) - 1]++;
- return;
- }
- }
+ if (is_even) {
+ in_delta_room_plus =
+ Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
+ } else {
+ in_delta_room_plus =
+ Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
}
-
-
- // Let v = numerator / denominator < 10.
- // Then we generate 'count' digits of d = x.xxxxx... (without the decimal point)
- // from left to right. Once 'count' digits have been produced we decide wether
- // to round up or down. Remainders of exactly .5 round upwards. Numbers such
- // as 9.999999 propagate a carry all the way, and change the
- // exponent (decimal_point), when rounding upwards.
- static void GenerateCountedDigits(int count, int* decimal_point,
- Bignum* numerator, Bignum* denominator,
- BufferReference<char>(buffer), int* length) {
- ASSERT(count >= 0);
- for (int i = 0; i < count - 1; ++i) {
- uint16_t digit;
- digit = numerator->DivideModuloIntBignum(*denominator);
- ASSERT(digit <= 9); // digit is a uint16_t and therefore always positive.
- // digit = numerator / denominator (integer division).
- // numerator = numerator % denominator.
- buffer[i] = digit + '0';
- // Prepare for next iteration.
- numerator->Times10();
- }
- // Generate the last digit.
- uint16_t digit;
- digit = numerator->DivideModuloIntBignum(*denominator);
- if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
- digit++;
- }
- buffer[count - 1] = digit + '0';
- // Correct bad digits (in case we had a sequence of '9's). Propagate the
- // carry until we hat a non-'9' or til we reach the first digit.
- for (int i = count - 1; i > 0; --i) {
- if (buffer[i] != '0' + 10) break;
- buffer[i] = '0';
- buffer[i - 1]++;
- }
- if (buffer[0] == '0' + 10) {
- // Propagate a carry past the top place.
- buffer[0] = '1';
- (*decimal_point)++;
- }
- *length = count;
- }
-
-
- // Generates 'requested_digits' after the decimal point. It might omit
- // trailing '0's. If the input number is too small then no digits at all are
- // generated (ex.: 2 fixed digits for 0.00001).
- //
- // Input verifies: 1 <= (numerator + delta) / denominator < 10.
- static void BignumToFixed(int requested_digits, int* decimal_point,
- Bignum* numerator, Bignum* denominator,
- BufferReference<char>(buffer), int* length) {
- // Note that we have to look at more than just the requested_digits, since
- // a number could be rounded up. Example: v=0.5 with requested_digits=0.
- // Even though the power of v equals 0 we can't just stop here.
- if (-(*decimal_point) > requested_digits) {
- // The number is definitively too small.
- // Ex: 0.001 with requested_digits == 1.
- // Set decimal-point to -requested_digits. This is what Gay does.
- // Note that it should not have any effect anyways since the string is
- // empty.
- *decimal_point = -requested_digits;
- *length = 0;
- return;
- } else if (-(*decimal_point) == requested_digits) {
- // We only need to verify if the number rounds down or up.
- // Ex: 0.04 and 0.06 with requested_digits == 1.
- ASSERT(*decimal_point == -requested_digits);
- // Initially the fraction lies in range (1, 10]. Multiply the denominator
- // by 10 so that we can compare more easily.
- denominator->Times10();
- if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
- // If the fraction is >= 0.5 then we have to include the rounded
- // digit.
- buffer[0] = '1';
- *length = 1;
- (*decimal_point)++;
- } else {
- // Note that we caught most of similar cases earlier.
- *length = 0;
- }
- return;
+ if (!in_delta_room_minus && !in_delta_room_plus) {
+ // Prepare for next iteration.
+ numerator->Times10();
+ delta_minus->Times10();
+ // We optimized delta_plus to be equal to delta_minus (if they share the
+ // same value). So don't multiply delta_plus if they point to the same
+ // object.
+ if (delta_minus != delta_plus) {
+ delta_plus->Times10();
+ }
+ } else if (in_delta_room_minus && in_delta_room_plus) {
+ // Let's see if 2*numerator < denominator.
+ // If yes, then the next digit would be < 5 and we can round down.
+ int compare = Bignum::PlusCompare(*numerator, *numerator, *denominator);
+ if (compare < 0) {
+ // Remaining digits are less than .5. -> Round down (== do nothing).
+ } else if (compare > 0) {
+ // Remaining digits are more than .5 of denominator. -> Round up.
+ // Note that the last digit could not be a '9' as otherwise the whole
+ // loop would have stopped earlier.
+ // We still have an assert here in case the preconditions were not
+ // satisfied.
+ ASSERT(buffer[(*length) - 1] != '9');
+ buffer[(*length) - 1]++;
+ } else {
+ // Halfway case.
+ // TODO(floitsch): need a way to solve half-way cases.
+ // For now let's round towards even (since this is what Gay seems to
+ // do).
+
+ if ((buffer[(*length) - 1] - '0') % 2 == 0) {
+ // Round down => Do nothing.
} else {
- // The requested digits correspond to the digits after the point.
- // The variable 'needed_digits' includes the digits before the point.
- int needed_digits = (*decimal_point) + requested_digits;
- GenerateCountedDigits(needed_digits, decimal_point,
- numerator, denominator,
- buffer, length);
- }
- }
-
-
- // Returns an estimation of k such that 10^(k-1) <= v < 10^k where
- // v = f * 2^exponent and 2^52 <= f < 2^53.
- // v is hence a normalized double with the given exponent. The output is an
- // approximation for the exponent of the decimal approimation .digits * 10^k.
- //
- // The result might undershoot by 1 in which case 10^k <= v < 10^k+1.
- // Note: this property holds for v's upper boundary m+ too.
- // 10^k <= m+ < 10^k+1.
- // (see explanation below).
- //
- // Examples:
- // EstimatePower(0) => 16
- // EstimatePower(-52) => 0
- //
- // Note: e >= 0 => EstimatedPower(e) > 0. No similar claim can be made for e<0.
- static int EstimatePower(int exponent) {
- // This function estimates log10 of v where v = f*2^e (with e == exponent).
- // Note that 10^floor(log10(v)) <= v, but v <= 10^ceil(log10(v)).
- // Note that f is bounded by its container size. Let p = 53 (the double's
- // significand size). Then 2^(p-1) <= f < 2^p.
- //
- // Given that log10(v) == log2(v)/log2(10) and e+(len(f)-1) is quite close
- // to log2(v) the function is simplified to (e+(len(f)-1)/log2(10)).
- // The computed number undershoots by less than 0.631 (when we compute log3
- // and not log10).
- //
- // Optimization: since we only need an approximated result this computation
- // can be performed on 64 bit integers. On x86/x64 architecture the speedup is
- // not really measurable, though.
- //
- // Since we want to avoid overshooting we decrement by 1e10 so that
- // floating-point imprecisions don't affect us.
- //
- // Explanation for v's boundary m+: the computation takes advantage of
- // the fact that 2^(p-1) <= f < 2^p. Boundaries still satisfy this requirement
- // (even for denormals where the delta can be much more important).
-
- const double k1Log10 = 0.30102999566398114; // 1/lg(10)
-
- // For doubles len(f) == 53 (don't forget the hidden bit).
- const int kSignificandSize = 53;
- double estimate = ceil((exponent + kSignificandSize - 1) * k1Log10 - 1e-10);
- return static_cast<int>(estimate);
- }
-
-
- // See comments for InitialScaledStartValues.
- static void InitialScaledStartValuesPositiveExponent(
- double v, int estimated_power, bool need_boundary_deltas,
- Bignum* numerator, Bignum* denominator,
- Bignum* delta_minus, Bignum* delta_plus) {
- // A positive exponent implies a positive power.
- ASSERT(estimated_power >= 0);
- // Since the estimated_power is positive we simply multiply the denominator
- // by 10^estimated_power.
-
- // numerator = v.
- numerator->AssignUInt64(Double(v).Significand());
- numerator->ShiftLeft(Double(v).Exponent());
- // denominator = 10^estimated_power.
- denominator->AssignPowerUInt16(10, estimated_power);
-
- if (need_boundary_deltas) {
- // Introduce a common denominator so that the deltas to the boundaries are
- // integers.
- denominator->ShiftLeft(1);
- numerator->ShiftLeft(1);
- // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
- // denominator (of 2) delta_plus equals 2^e.
- delta_plus->AssignUInt16(1);
- delta_plus->ShiftLeft(Double(v).Exponent());
- // Same for delta_minus (with adjustments below if f == 2^p-1).
- delta_minus->AssignUInt16(1);
- delta_minus->ShiftLeft(Double(v).Exponent());
-
- // If the significand (without the hidden bit) is 0, then the lower
- // boundary is closer than just half a ulp (unit in the last place).
- // There is only one exception: if the next lower number is a denormal then
- // the distance is 1 ulp. This cannot be the case for exponent >= 0 (but we
- // have to test it in the other function where exponent < 0).
- uint64_t v_bits = Double(v).AsUint64();
- if ((v_bits & Double::kSignificandMask) == 0) {
- // The lower boundary is closer at half the distance of "normal" numbers.
- // Increase the common denominator and adapt all but the delta_minus.
- denominator->ShiftLeft(1); // *2
- numerator->ShiftLeft(1); // *2
- delta_plus->ShiftLeft(1); // *2
- }
- }
- }
-
-
- // See comments for InitialScaledStartValues
- static void InitialScaledStartValuesNegativeExponentPositivePower(
- double v, int estimated_power, bool need_boundary_deltas,
- Bignum* numerator, Bignum* denominator,
- Bignum* delta_minus, Bignum* delta_plus) {
- uint64_t significand = Double(v).Significand();
- int exponent = Double(v).Exponent();
- // v = f * 2^e with e < 0, and with estimated_power >= 0.
- // This means that e is close to 0 (have a look at how estimated_power is
- // computed).
-
- // numerator = significand
- // since v = significand * 2^exponent this is equivalent to
- // numerator = v * / 2^-exponent
- numerator->AssignUInt64(significand);
- // denominator = 10^estimated_power * 2^-exponent (with exponent < 0)
- denominator->AssignPowerUInt16(10, estimated_power);
- denominator->ShiftLeft(-exponent);
-
- if (need_boundary_deltas) {
- // Introduce a common denominator so that the deltas to the boundaries are
- // integers.
- denominator->ShiftLeft(1);
- numerator->ShiftLeft(1);
- // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
- // denominator (of 2) delta_plus equals 2^e.
- // Given that the denominator already includes v's exponent the distance
- // to the boundaries is simply 1.
- delta_plus->AssignUInt16(1);
- // Same for delta_minus (with adjustments below if f == 2^p-1).
- delta_minus->AssignUInt16(1);
-
- // If the significand (without the hidden bit) is 0, then the lower
- // boundary is closer than just one ulp (unit in the last place).
- // There is only one exception: if the next lower number is a denormal
- // then the distance is 1 ulp. Since the exponent is close to zero
- // (otherwise estimated_power would have been negative) this cannot happen
- // here either.
- uint64_t v_bits = Double(v).AsUint64();
- if ((v_bits & Double::kSignificandMask) == 0) {
- // The lower boundary is closer at half the distance of "normal" numbers.
- // Increase the denominator and adapt all but the delta_minus.
- denominator->ShiftLeft(1); // *2
- numerator->ShiftLeft(1); // *2
- delta_plus->ShiftLeft(1); // *2
- }
+ ASSERT(buffer[(*length) - 1] != '9');
+ buffer[(*length) - 1]++;
}
+ }
+ return;
+ } else if (in_delta_room_minus) {
+ // Round down (== do nothing).
+ return;
+ } else { // in_delta_room_plus
+ // Round up.
+ // Note again that the last digit could not be '9' since this would have
+ // stopped the loop earlier.
+ // We still have an ASSERT here, in case the preconditions were not
+ // satisfied.
+ ASSERT(buffer[(*length) -1] != '9');
+ buffer[(*length) - 1]++;
+ return;
}
-
-
- // See comments for InitialScaledStartValues
- static void InitialScaledStartValuesNegativeExponentNegativePower(
- double v, int estimated_power, bool need_boundary_deltas,
- Bignum* numerator, Bignum* denominator,
- Bignum* delta_minus, Bignum* delta_plus) {
- const uint64_t kMinimalNormalizedExponent =
- UINT64_2PART_C(0x00100000, 00000000);
- uint64_t significand = Double(v).Significand();
- int exponent = Double(v).Exponent();
- // Instead of multiplying the denominator with 10^estimated_power we
- // multiply all values (numerator and deltas) by 10^-estimated_power.
-
- // Use numerator as temporary container for power_ten.
- Bignum* power_ten = numerator;
- power_ten->AssignPowerUInt16(10, -estimated_power);
-
- if (need_boundary_deltas) {
- // Since power_ten == numerator we must make a copy of 10^estimated_power
- // before we complete the computation of the numerator.
- // delta_plus = delta_minus = 10^estimated_power
- delta_plus->AssignBignum(*power_ten);
- delta_minus->AssignBignum(*power_ten);
- }
-
- // numerator = significand * 2 * 10^-estimated_power
- // since v = significand * 2^exponent this is equivalent to
- // numerator = v * 10^-estimated_power * 2 * 2^-exponent.
- // Remember: numerator has been abused as power_ten. So no need to assign it
- // to itself.
- ASSERT(numerator == power_ten);
- numerator->MultiplyByUInt64(significand);
-
- // denominator = 2 * 2^-exponent with exponent < 0.
- denominator->AssignUInt16(1);
- denominator->ShiftLeft(-exponent);
-
- if (need_boundary_deltas) {
- // Introduce a common denominator so that the deltas to the boundaries are
- // integers.
- numerator->ShiftLeft(1);
- denominator->ShiftLeft(1);
- // With this shift the boundaries have their correct value, since
- // delta_plus = 10^-estimated_power, and
- // delta_minus = 10^-estimated_power.
- // These assignments have been done earlier.
-
- // The special case where the lower boundary is twice as close.
- // This time we have to look out for the exception too.
- uint64_t v_bits = Double(v).AsUint64();
- if ((v_bits & Double::kSignificandMask) == 0 &&
- // The only exception where a significand == 0 has its boundaries at
- // "normal" distances:
- (v_bits & Double::kExponentMask) != kMinimalNormalizedExponent) {
- numerator->ShiftLeft(1); // *2
- denominator->ShiftLeft(1); // *2
- delta_plus->ShiftLeft(1); // *2
- }
- }
- }
-
-
- // Let v = significand * 2^exponent.
- // Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
- // and denominator. The functions GenerateShortestDigits and
- // GenerateCountedDigits will then convert this ratio to its decimal
- // representation d, with the required accuracy.
- // Then d * 10^estimated_power is the representation of v.
- // (Note: the fraction and the estimated_power might get adjusted before
- // generating the decimal representation.)
- //
- // The initial start values consist of:
- // - a scaled numerator: s.t. numerator/denominator == v / 10^estimated_power.
- // - a scaled (common) denominator.
- // optionally (used by GenerateShortestDigits to decide if it has the shortest
- // decimal converting back to v):
- // - v - m-: the distance to the lower boundary.
- // - m+ - v: the distance to the upper boundary.
- //
- // v, m+, m-, and therefore v - m- and m+ - v all share the same denominator.
- //
- // Let ep == estimated_power, then the returned values will satisfy:
- // v / 10^ep = numerator / denominator.
- // v's boundarys m- and m+:
- // m- / 10^ep == v / 10^ep - delta_minus / denominator
- // m+ / 10^ep == v / 10^ep + delta_plus / denominator
- // Or in other words:
- // m- == v - delta_minus * 10^ep / denominator;
- // m+ == v + delta_plus * 10^ep / denominator;
- //
- // Since 10^(k-1) <= v < 10^k (with k == estimated_power)
- // or 10^k <= v < 10^(k+1)
- // we then have 0.1 <= numerator/denominator < 1
- // or 1 <= numerator/denominator < 10
- //
- // It is then easy to kickstart the digit-generation routine.
- //
- // The boundary-deltas are only filled if need_boundary_deltas is set.
- static void InitialScaledStartValues(double v,
- int estimated_power,
- bool need_boundary_deltas,
- Bignum* numerator,
- Bignum* denominator,
- Bignum* delta_minus,
- Bignum* delta_plus) {
- if (Double(v).Exponent() >= 0) {
- InitialScaledStartValuesPositiveExponent(
- v, estimated_power, need_boundary_deltas,
- numerator, denominator, delta_minus, delta_plus);
- } else if (estimated_power >= 0) {
- InitialScaledStartValuesNegativeExponentPositivePower(
- v, estimated_power, need_boundary_deltas,
- numerator, denominator, delta_minus, delta_plus);
- } else {
- InitialScaledStartValuesNegativeExponentNegativePower(
- v, estimated_power, need_boundary_deltas,
- numerator, denominator, delta_minus, delta_plus);
- }
+ }
+}
+
+
+// Let v = numerator / denominator < 10.
+// Then we generate 'count' digits of d = x.xxxxx... (without the decimal point)
+// from left to right. Once 'count' digits have been produced we decide wether
+// to round up or down. Remainders of exactly .5 round upwards. Numbers such
+// as 9.999999 propagate a carry all the way, and change the
+// exponent (decimal_point), when rounding upwards.
+static void GenerateCountedDigits(int count, int* decimal_point,
+ Bignum* numerator, Bignum* denominator,
+ BufferReference<char> buffer, int* length) {
+ ASSERT(count >= 0);
+ for (int i = 0; i < count - 1; ++i) {
+ uint16_t digit;
+ digit = numerator->DivideModuloIntBignum(*denominator);
+ ASSERT(digit <= 9); // digit is a uint16_t and therefore always positive.
+ // digit = numerator / denominator (integer division).
+ // numerator = numerator % denominator.
+ buffer[i] = static_cast<char>(digit + '0');
+ // Prepare for next iteration.
+ numerator->Times10();
+ }
+ // Generate the last digit.
+ uint16_t digit;
+ digit = numerator->DivideModuloIntBignum(*denominator);
+ if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
+ digit++;
+ }
+ ASSERT(digit <= 10);
+ buffer[count - 1] = static_cast<char>(digit + '0');
+ // Correct bad digits (in case we had a sequence of '9's). Propagate the
+ // carry until we hat a non-'9' or til we reach the first digit.
+ for (int i = count - 1; i > 0; --i) {
+ if (buffer[i] != '0' + 10) break;
+ buffer[i] = '0';
+ buffer[i - 1]++;
+ }
+ if (buffer[0] == '0' + 10) {
+ // Propagate a carry past the top place.
+ buffer[0] = '1';
+ (*decimal_point)++;
+ }
+ *length = count;
+}
+
+
+// Generates 'requested_digits' after the decimal point. It might omit
+// trailing '0's. If the input number is too small then no digits at all are
+// generated (ex.: 2 fixed digits for 0.00001).
+//
+// Input verifies: 1 <= (numerator + delta) / denominator < 10.
+static void BignumToFixed(int requested_digits, int* decimal_point,
+ Bignum* numerator, Bignum* denominator,
+ BufferReference<char>(buffer), int* length) {
+ // Note that we have to look at more than just the requested_digits, since
+ // a number could be rounded up. Example: v=0.5 with requested_digits=0.
+ // Even though the power of v equals 0 we can't just stop here.
+ if (-(*decimal_point) > requested_digits) {
+ // The number is definitively too small.
+ // Ex: 0.001 with requested_digits == 1.
+ // Set decimal-point to -requested_digits. This is what Gay does.
+ // Note that it should not have any effect anyways since the string is
+ // empty.
+ *decimal_point = -requested_digits;
+ *length = 0;
+ return;
+ } else if (-(*decimal_point) == requested_digits) {
+ // We only need to verify if the number rounds down or up.
+ // Ex: 0.04 and 0.06 with requested_digits == 1.
+ ASSERT(*decimal_point == -requested_digits);
+ // Initially the fraction lies in range (1, 10]. Multiply the denominator
+ // by 10 so that we can compare more easily.
+ denominator->Times10();
+ if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
+ // If the fraction is >= 0.5 then we have to include the rounded
+ // digit.
+ buffer[0] = '1';
+ *length = 1;
+ (*decimal_point)++;
+ } else {
+ // Note that we caught most of similar cases earlier.
+ *length = 0;
}
-
-
- // This routine multiplies numerator/denominator so that its values lies in the
- // range 1-10. That is after a call to this function we have:
- // 1 <= (numerator + delta_plus) /denominator < 10.
- // Let numerator the input before modification and numerator' the argument
- // after modification, then the output-parameter decimal_point is such that
- // numerator / denominator * 10^estimated_power ==
- // numerator' / denominator' * 10^(decimal_point - 1)
- // In some cases estimated_power was too low, and this is already the case. We
- // then simply adjust the power so that 10^(k-1) <= v < 10^k (with k ==
- // estimated_power) but do not touch the numerator or denominator.
- // Otherwise the routine multiplies the numerator and the deltas by 10.
- static void FixupMultiply10(int estimated_power, bool is_even,
- int* decimal_point,
- Bignum* numerator, Bignum* denominator,
- Bignum* delta_minus, Bignum* delta_plus) {
- bool in_range;
- if (is_even) {
- // For IEEE doubles half-way cases (in decimal system numbers ending with 5)
- // are rounded to the closest floating-point number with even significand.
- in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
- } else {
- in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
- }
- if (in_range) {
- // Since numerator + delta_plus >= denominator we already have
- // 1 <= numerator/denominator < 10. Simply update the estimated_power.
- *decimal_point = estimated_power + 1;
- } else {
- *decimal_point = estimated_power;
- numerator->Times10();
- if (Bignum::Equal(*delta_minus, *delta_plus)) {
- delta_minus->Times10();
- delta_plus->AssignBignum(*delta_minus);
- } else {
- delta_minus->Times10();
- delta_plus->Times10();
- }
- }
+ return;
+ } else {
+ // The requested digits correspond to the digits after the point.
+ // The variable 'needed_digits' includes the digits before the point.
+ int needed_digits = (*decimal_point) + requested_digits;
+ GenerateCountedDigits(needed_digits, decimal_point,
+ numerator, denominator,
+ buffer, length);
+ }
+}
+
+
+// Returns an estimation of k such that 10^(k-1) <= v < 10^k where
+// v = f * 2^exponent and 2^52 <= f < 2^53.
+// v is hence a normalized double with the given exponent. The output is an
+// approximation for the exponent of the decimal approimation .digits * 10^k.
+//
+// The result might undershoot by 1 in which case 10^k <= v < 10^k+1.
+// Note: this property holds for v's upper boundary m+ too.
+// 10^k <= m+ < 10^k+1.
+// (see explanation below).
+//
+// Examples:
+// EstimatePower(0) => 16
+// EstimatePower(-52) => 0
+//
+// Note: e >= 0 => EstimatedPower(e) > 0. No similar claim can be made for e<0.
+static int EstimatePower(int exponent) {
+ // This function estimates log10 of v where v = f*2^e (with e == exponent).
+ // Note that 10^floor(log10(v)) <= v, but v <= 10^ceil(log10(v)).
+ // Note that f is bounded by its container size. Let p = 53 (the double's
+ // significand size). Then 2^(p-1) <= f < 2^p.
+ //
+ // Given that log10(v) == log2(v)/log2(10) and e+(len(f)-1) is quite close
+ // to log2(v) the function is simplified to (e+(len(f)-1)/log2(10)).
+ // The computed number undershoots by less than 0.631 (when we compute log3
+ // and not log10).
+ //
+ // Optimization: since we only need an approximated result this computation
+ // can be performed on 64 bit integers. On x86/x64 architecture the speedup is
+ // not really measurable, though.
+ //
+ // Since we want to avoid overshooting we decrement by 1e10 so that
+ // floating-point imprecisions don't affect us.
+ //
+ // Explanation for v's boundary m+: the computation takes advantage of
+ // the fact that 2^(p-1) <= f < 2^p. Boundaries still satisfy this requirement
+ // (even for denormals where the delta can be much more important).
+
+ const double k1Log10 = 0.30102999566398114; // 1/lg(10)
+
+ // For doubles len(f) == 53 (don't forget the hidden bit).
+ const int kSignificandSize = Double::kSignificandSize;
+ double estimate = ceil((exponent + kSignificandSize - 1) * k1Log10 - 1e-10);
+ return static_cast<int>(estimate);
+}
+
+
+// See comments for InitialScaledStartValues.
+static void InitialScaledStartValuesPositiveExponent(
+ uint64_t significand, int exponent,
+ int estimated_power, bool need_boundary_deltas,
+ Bignum* numerator, Bignum* denominator,
+ Bignum* delta_minus, Bignum* delta_plus) {
+ // A positive exponent implies a positive power.
+ ASSERT(estimated_power >= 0);
+ // Since the estimated_power is positive we simply multiply the denominator
+ // by 10^estimated_power.
+
+ // numerator = v.
+ numerator->AssignUInt64(significand);
+ numerator->ShiftLeft(exponent);
+ // denominator = 10^estimated_power.
+ denominator->AssignPowerUInt16(10, estimated_power);
+
+ if (need_boundary_deltas) {
+ // Introduce a common denominator so that the deltas to the boundaries are
+ // integers.
+ denominator->ShiftLeft(1);
+ numerator->ShiftLeft(1);
+ // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
+ // denominator (of 2) delta_plus equals 2^e.
+ delta_plus->AssignUInt16(1);
+ delta_plus->ShiftLeft(exponent);
+ // Same for delta_minus. The adjustments if f == 2^p-1 are done later.
+ delta_minus->AssignUInt16(1);
+ delta_minus->ShiftLeft(exponent);
+ }
+}
+
+
+// See comments for InitialScaledStartValues
+static void InitialScaledStartValuesNegativeExponentPositivePower(
+ uint64_t significand, int exponent,
+ int estimated_power, bool need_boundary_deltas,
+ Bignum* numerator, Bignum* denominator,
+ Bignum* delta_minus, Bignum* delta_plus) {
+ // v = f * 2^e with e < 0, and with estimated_power >= 0.
+ // This means that e is close to 0 (have a look at how estimated_power is
+ // computed).
+
+ // numerator = significand
+ // since v = significand * 2^exponent this is equivalent to
+ // numerator = v * / 2^-exponent
+ numerator->AssignUInt64(significand);
+ // denominator = 10^estimated_power * 2^-exponent (with exponent < 0)
+ denominator->AssignPowerUInt16(10, estimated_power);
+ denominator->ShiftLeft(-exponent);
+
+ if (need_boundary_deltas) {
+ // Introduce a common denominator so that the deltas to the boundaries are
+ // integers.
+ denominator->ShiftLeft(1);
+ numerator->ShiftLeft(1);
+ // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
+ // denominator (of 2) delta_plus equals 2^e.
+ // Given that the denominator already includes v's exponent the distance
+ // to the boundaries is simply 1.
+ delta_plus->AssignUInt16(1);
+ // Same for delta_minus. The adjustments if f == 2^p-1 are done later.
+ delta_minus->AssignUInt16(1);
+ }
+}
+
+
+// See comments for InitialScaledStartValues
+static void InitialScaledStartValuesNegativeExponentNegativePower(
+ uint64_t significand, int exponent,
+ int estimated_power, bool need_boundary_deltas,
+ Bignum* numerator, Bignum* denominator,
+ Bignum* delta_minus, Bignum* delta_plus) {
+ // Instead of multiplying the denominator with 10^estimated_power we
+ // multiply all values (numerator and deltas) by 10^-estimated_power.
+
+ // Use numerator as temporary container for power_ten.
+ Bignum* power_ten = numerator;
+ power_ten->AssignPowerUInt16(10, -estimated_power);
+
+ if (need_boundary_deltas) {
+ // Since power_ten == numerator we must make a copy of 10^estimated_power
+ // before we complete the computation of the numerator.
+ // delta_plus = delta_minus = 10^estimated_power
+ delta_plus->AssignBignum(*power_ten);
+ delta_minus->AssignBignum(*power_ten);
+ }
+
+ // numerator = significand * 2 * 10^-estimated_power
+ // since v = significand * 2^exponent this is equivalent to
+ // numerator = v * 10^-estimated_power * 2 * 2^-exponent.
+ // Remember: numerator has been abused as power_ten. So no need to assign it
+ // to itself.
+ ASSERT(numerator == power_ten);
+ numerator->MultiplyByUInt64(significand);
+
+ // denominator = 2 * 2^-exponent with exponent < 0.
+ denominator->AssignUInt16(1);
+ denominator->ShiftLeft(-exponent);
+
+ if (need_boundary_deltas) {
+ // Introduce a common denominator so that the deltas to the boundaries are
+ // integers.
+ numerator->ShiftLeft(1);
+ denominator->ShiftLeft(1);
+ // With this shift the boundaries have their correct value, since
+ // delta_plus = 10^-estimated_power, and
+ // delta_minus = 10^-estimated_power.
+ // These assignments have been done earlier.
+ // The adjustments if f == 2^p-1 (lower boundary is closer) are done later.
+ }
+}
+
+
+// Let v = significand * 2^exponent.
+// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
+// and denominator. The functions GenerateShortestDigits and
+// GenerateCountedDigits will then convert this ratio to its decimal
+// representation d, with the required accuracy.
+// Then d * 10^estimated_power is the representation of v.
+// (Note: the fraction and the estimated_power might get adjusted before
+// generating the decimal representation.)
+//
+// The initial start values consist of:
+// - a scaled numerator: s.t. numerator/denominator == v / 10^estimated_power.
+// - a scaled (common) denominator.
+// optionally (used by GenerateShortestDigits to decide if it has the shortest
+// decimal converting back to v):
+// - v - m-: the distance to the lower boundary.
+// - m+ - v: the distance to the upper boundary.
+//
+// v, m+, m-, and therefore v - m- and m+ - v all share the same denominator.
+//
+// Let ep == estimated_power, then the returned values will satisfy:
+// v / 10^ep = numerator / denominator.
+// v's boundarys m- and m+:
+// m- / 10^ep == v / 10^ep - delta_minus / denominator
+// m+ / 10^ep == v / 10^ep + delta_plus / denominator
+// Or in other words:
+// m- == v - delta_minus * 10^ep / denominator;
+// m+ == v + delta_plus * 10^ep / denominator;
+//
+// Since 10^(k-1) <= v < 10^k (with k == estimated_power)
+// or 10^k <= v < 10^(k+1)
+// we then have 0.1 <= numerator/denominator < 1
+// or 1 <= numerator/denominator < 10
+//
+// It is then easy to kickstart the digit-generation routine.
+//
+// The boundary-deltas are only filled if the mode equals BIGNUM_DTOA_SHORTEST
+// or BIGNUM_DTOA_SHORTEST_SINGLE.
+
+static void InitialScaledStartValues(uint64_t significand,
+ int exponent,
+ bool lower_boundary_is_closer,
+ int estimated_power,
+ bool need_boundary_deltas,
+ Bignum* numerator,
+ Bignum* denominator,
+ Bignum* delta_minus,
+ Bignum* delta_plus) {
+ if (exponent >= 0) {
+ InitialScaledStartValuesPositiveExponent(
+ significand, exponent, estimated_power, need_boundary_deltas,
+ numerator, denominator, delta_minus, delta_plus);
+ } else if (estimated_power >= 0) {
+ InitialScaledStartValuesNegativeExponentPositivePower(
+ significand, exponent, estimated_power, need_boundary_deltas,
+ numerator, denominator, delta_minus, delta_plus);
+ } else {
+ InitialScaledStartValuesNegativeExponentNegativePower(
+ significand, exponent, estimated_power, need_boundary_deltas,
+ numerator, denominator, delta_minus, delta_plus);
+ }
+
+ if (need_boundary_deltas && lower_boundary_is_closer) {
+ // The lower boundary is closer at half the distance of "normal" numbers.
+ // Increase the common denominator and adapt all but the delta_minus.
+ denominator->ShiftLeft(1); // *2
+ numerator->ShiftLeft(1); // *2
+ delta_plus->ShiftLeft(1); // *2
+ }
+}
+
+
+// This routine multiplies numerator/denominator so that its values lies in the
+// range 1-10. That is after a call to this function we have:
+// 1 <= (numerator + delta_plus) /denominator < 10.
+// Let numerator the input before modification and numerator' the argument
+// after modification, then the output-parameter decimal_point is such that
+// numerator / denominator * 10^estimated_power ==
+// numerator' / denominator' * 10^(decimal_point - 1)
+// In some cases estimated_power was too low, and this is already the case. We
+// then simply adjust the power so that 10^(k-1) <= v < 10^k (with k ==
+// estimated_power) but do not touch the numerator or denominator.
+// Otherwise the routine multiplies the numerator and the deltas by 10.
+static void FixupMultiply10(int estimated_power, bool is_even,
+ int* decimal_point,
+ Bignum* numerator, Bignum* denominator,
+ Bignum* delta_minus, Bignum* delta_plus) {
+ bool in_range;
+ if (is_even) {
+ // For IEEE doubles half-way cases (in decimal system numbers ending with 5)
+ // are rounded to the closest floating-point number with even significand.
+ in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
+ } else {
+ in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
+ }
+ if (in_range) {
+ // Since numerator + delta_plus >= denominator we already have
+ // 1 <= numerator/denominator < 10. Simply update the estimated_power.
+ *decimal_point = estimated_power + 1;
+ } else {
+ *decimal_point = estimated_power;
+ numerator->Times10();
+ if (Bignum::Equal(*delta_minus, *delta_plus)) {
+ delta_minus->Times10();
+ delta_plus->AssignBignum(*delta_minus);
+ } else {
+ delta_minus->Times10();
+ delta_plus->Times10();
}
-
-} // namespace double_conversion
+ }
+}
-} // namespace WTF
+} // namespace double_conversion
+} // namespace WTF
#ifndef DOUBLE_CONVERSION_BIGNUM_DTOA_H_
#define DOUBLE_CONVERSION_BIGNUM_DTOA_H_
-#include "utils.h"
+#include <wtf/dtoa/utils.h>
namespace WTF {
-
namespace double_conversion {
-
- enum BignumDtoaMode {
- // Return the shortest correct representation.
- // For example the output of 0.299999999999999988897 is (the less accurate but
- // correct) 0.3.
- BIGNUM_DTOA_SHORTEST,
- // Return a fixed number of digits after the decimal point.
- // For instance fixed(0.1, 4) becomes 0.1000
- // If the input number is big, the output will be big.
- BIGNUM_DTOA_FIXED,
- // Return a fixed number of digits, no matter what the exponent is.
- BIGNUM_DTOA_PRECISION
- };
-
- // Converts the given double 'v' to ascii.
- // The result should be interpreted as buffer * 10^(point-length).
- // The buffer will be null-terminated.
- //
- // The input v must be > 0 and different from NaN, and Infinity.
- //
- // The output depends on the given mode:
- // - SHORTEST: produce the least amount of digits for which the internal
- // identity requirement is still satisfied. If the digits are printed
- // (together with the correct exponent) then reading this number will give
- // 'v' again. The buffer will choose the representation that is closest to
- // 'v'. If there are two at the same distance, than the number is round up.
- // In this mode the 'requested_digits' parameter is ignored.
- // - FIXED: produces digits necessary to print a given number with
- // 'requested_digits' digits after the decimal point. The produced digits
- // might be too short in which case the caller has to fill the gaps with '0's.
- // Example: toFixed(0.001, 5) is allowed to return buffer="1", point=-2.
- // Halfway cases are rounded up. The call toFixed(0.15, 2) thus returns
- // buffer="2", point=0.
- // Note: the length of the returned buffer has no meaning wrt the significance
- // of its digits. That is, just because it contains '0's does not mean that
- // any other digit would not satisfy the internal identity requirement.
- // - PRECISION: produces 'requested_digits' where the first digit is not '0'.
- // Even though the length of produced digits usually equals
- // 'requested_digits', the function is allowed to return fewer digits, in
- // which case the caller has to fill the missing digits with '0's.
- // Halfway cases are again rounded up.
- // 'BignumDtoa' expects the given buffer to be big enough to hold all digits
- // and a terminating null-character.
- void BignumDtoa(double v, BignumDtoaMode mode, int requested_digits,
- BufferReference<char> buffer, int* length, int* point);
-
-} // namespace double_conversion
-} // namespace WTF
+enum BignumDtoaMode {
+ // Return the shortest correct representation.
+ // For example the output of 0.299999999999999988897 is (the less accurate but
+ // correct) 0.3.
+ BIGNUM_DTOA_SHORTEST,
+ // Same as BIGNUM_DTOA_SHORTEST but for single-precision floats.
+ BIGNUM_DTOA_SHORTEST_SINGLE,
+ // Return a fixed number of digits after the decimal point.
+ // For instance fixed(0.1, 4) becomes 0.1000
+ // If the input number is big, the output will be big.
+ BIGNUM_DTOA_FIXED,
+ // Return a fixed number of digits, no matter what the exponent is.
+ BIGNUM_DTOA_PRECISION
+};
+
+// Converts the given double 'v' to ascii.
+// The result should be interpreted as buffer * 10^(point-length).
+// The buffer will be null-terminated.
+//
+// The input v must be > 0 and different from NaN, and Infinity.
+//
+// The output depends on the given mode:
+// - SHORTEST: produce the least amount of digits for which the internal
+// identity requirement is still satisfied. If the digits are printed
+// (together with the correct exponent) then reading this number will give
+// 'v' again. The buffer will choose the representation that is closest to
+// 'v'. If there are two at the same distance, than the number is round up.
+// In this mode the 'requested_digits' parameter is ignored.
+// - FIXED: produces digits necessary to print a given number with
+// 'requested_digits' digits after the decimal point. The produced digits
+// might be too short in which case the caller has to fill the gaps with '0's.
+// Example: toFixed(0.001, 5) is allowed to return buffer="1", point=-2.
+// Halfway cases are rounded up. The call toFixed(0.15, 2) thus returns
+// buffer="2", point=0.
+// Note: the length of the returned buffer has no meaning wrt the significance
+// of its digits. That is, just because it contains '0's does not mean that
+// any other digit would not satisfy the internal identity requirement.
+// - PRECISION: produces 'requested_digits' where the first digit is not '0'.
+// Even though the length of produced digits usually equals
+// 'requested_digits', the function is allowed to return fewer digits, in
+// which case the caller has to fill the missing digits with '0's.
+// Halfway cases are again rounded up.
+// 'BignumDtoa' expects the given buffer to be big enough to hold all digits
+// and a terminating null-character.
+void BignumDtoa(double v, BignumDtoaMode mode, int requested_digits,
+ BufferReference<char> buffer, int* length, int* point);
+
+} // namespace double_conversion
+} // namespace WTF
#endif // DOUBLE_CONVERSION_BIGNUM_DTOA_H_
#include "config.h"
-#include "bignum.h"
-#include "utils.h"
+#include <wtf/dtoa/bignum.h>
+
+#include <wtf/dtoa/utils.h>
#include <wtf/ASCIICType.h>
namespace WTF {
-
namespace double_conversion {
-
- Bignum::Bignum()
- : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) {
- for (int i = 0; i < kBigitCapacity; ++i) {
- bigits_[i] = 0;
- }
- }
-
-
- template<typename S>
- static int BitSize(S value) {
- return 8 * sizeof(value);
- }
-
- // Guaranteed to lie in one Bigit.
- void Bignum::AssignUInt16(uint16_t value) {
- ASSERT(kBigitSize >= BitSize(value));
- Zero();
- if (value == 0) return;
-
- EnsureCapacity(1);
- bigits_[0] = value;
- used_digits_ = 1;
- }
-
-
- void Bignum::AssignUInt64(uint64_t value) {
- const int kUInt64Size = 64;
-
- Zero();
- if (value == 0) return;
-
- int needed_bigits = kUInt64Size / kBigitSize + 1;
- EnsureCapacity(needed_bigits);
- for (int i = 0; i < needed_bigits; ++i) {
- bigits_[i] = static_cast<Chunk>(value & kBigitMask);
- value = value >> kBigitSize;
- }
- used_digits_ = needed_bigits;
- Clamp();
- }
-
-
- void Bignum::AssignBignum(const Bignum& other) {
- exponent_ = other.exponent_;
- for (int i = 0; i < other.used_digits_; ++i) {
- bigits_[i] = other.bigits_[i];
- }
- // Clear the excess digits (if there were any).
- for (int i = other.used_digits_; i < used_digits_; ++i) {
- bigits_[i] = 0;
- }
- used_digits_ = other.used_digits_;
- }
-
-
- static uint64_t ReadUInt64(BufferReference<const char> buffer,
- int from,
- int digits_to_read) {
- uint64_t result = 0;
- for (int i = 0; i < digits_to_read; ++i) {
- int digit = buffer[from + i] - '0';
- ASSERT(0 <= digit && digit <= 9);
- result = result * 10 + digit;
- }
- return result;
- }
-
-
- void Bignum::AssignDecimalString(BufferReference<const char> value) {
- // 2^64 = 18446744073709551616 > 10^19
- const int kMaxUint64DecimalDigits = 19;
- Zero();
- int length = value.length();
- int pos = 0;
- // Let's just say that each digit needs 4 bits.
- while (length >= kMaxUint64DecimalDigits) {
- uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
- pos += kMaxUint64DecimalDigits;
- length -= kMaxUint64DecimalDigits;
- MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
- AddUInt64(digits);
- }
- uint64_t digits = ReadUInt64(value, pos, length);
- MultiplyByPowerOfTen(length);
- AddUInt64(digits);
- Clamp();
- }
-
-
- void Bignum::AssignHexString(BufferReference<const char> value) {
- Zero();
- int length = value.length();
-
- int needed_bigits = length * 4 / kBigitSize + 1;
- EnsureCapacity(needed_bigits);
- int string_index = length - 1;
- for (int i = 0; i < needed_bigits - 1; ++i) {
- // These bigits are guaranteed to be "full".
- Chunk current_bigit = 0;
- for (int j = 0; j < kBigitSize / 4; j++) {
- current_bigit += toASCIIHexValue(value[string_index--]) << (j * 4);
- }
- bigits_[i] = current_bigit;
- }
- used_digits_ = needed_bigits - 1;
-
- Chunk most_significant_bigit = 0; // Could be = 0;
- for (int j = 0; j <= string_index; ++j) {
- most_significant_bigit <<= 4;
- most_significant_bigit += toASCIIHexValue(value[j]);
- }
- if (most_significant_bigit != 0) {
- bigits_[used_digits_] = most_significant_bigit;
- used_digits_++;
- }
- Clamp();
- }
-
-
- void Bignum::AddUInt64(uint64_t operand) {
- if (operand == 0) return;
- Bignum other;
- other.AssignUInt64(operand);
- AddBignum(other);
- }
-
-
- void Bignum::AddBignum(const Bignum& other) {
- ASSERT(IsClamped());
- ASSERT(other.IsClamped());
-
- // If this has a greater exponent than other append zero-bigits to this.
- // After this call exponent_ <= other.exponent_.
- Align(other);
-
- // There are two possibilities:
- // aaaaaaaaaaa 0000 (where the 0s represent a's exponent)
- // bbbbb 00000000
- // ----------------
- // ccccccccccc 0000
- // or
- // aaaaaaaaaa 0000
- // bbbbbbbbb 0000000
- // -----------------
- // cccccccccccc 0000
- // In both cases we might need a carry bigit.
-
- EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_);
- Chunk carry = 0;
- int bigit_pos = other.exponent_ - exponent_;
- ASSERT(bigit_pos >= 0);
- for (int i = 0; i < other.used_digits_; ++i) {
- Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
- bigits_[bigit_pos] = sum & kBigitMask;
- carry = sum >> kBigitSize;
- bigit_pos++;
- }
-
- while (carry != 0) {
- Chunk sum = bigits_[bigit_pos] + carry;
- bigits_[bigit_pos] = sum & kBigitMask;
- carry = sum >> kBigitSize;
- bigit_pos++;
- }
- used_digits_ = Max(bigit_pos, used_digits_);
- ASSERT(IsClamped());
- }
-
-
- void Bignum::SubtractBignum(const Bignum& other) {
- ASSERT(IsClamped());
- ASSERT(other.IsClamped());
- // We require this to be bigger than other.
- ASSERT(LessEqual(other, *this));
-
- Align(other);
-
- int offset = other.exponent_ - exponent_;
- Chunk borrow = 0;
- int i;
- for (i = 0; i < other.used_digits_; ++i) {
- ASSERT((borrow == 0) || (borrow == 1));
- Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow;
- bigits_[i + offset] = difference & kBigitMask;
- borrow = difference >> (kChunkSize - 1);
- }
- while (borrow != 0) {
- Chunk difference = bigits_[i + offset] - borrow;
- bigits_[i + offset] = difference & kBigitMask;
- borrow = difference >> (kChunkSize - 1);
- ++i;
- }
- Clamp();
- }
-
-
- void Bignum::ShiftLeft(int shift_amount) {
- if (used_digits_ == 0) return;
- exponent_ += shift_amount / kBigitSize;
- int local_shift = shift_amount % kBigitSize;
- EnsureCapacity(used_digits_ + 1);
- BigitsShiftLeft(local_shift);
- }
-
-
- void Bignum::MultiplyByUInt32(uint32_t factor) {
- if (factor == 1) return;
- if (factor == 0) {
- Zero();
- return;
- }
- if (used_digits_ == 0) return;
-
- // The product of a bigit with the factor is of size kBigitSize + 32.
- // Assert that this number + 1 (for the carry) fits into double chunk.
- ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);
- DoubleChunk carry = 0;
- for (int i = 0; i < used_digits_; ++i) {
- DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;
- bigits_[i] = static_cast<Chunk>(product & kBigitMask);
- carry = (product >> kBigitSize);
- }
- while (carry != 0) {
- EnsureCapacity(used_digits_ + 1);
- bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask);
- used_digits_++;
- carry >>= kBigitSize;
- }
- }
-
-
- void Bignum::MultiplyByUInt64(uint64_t factor) {
- if (factor == 1) return;
- if (factor == 0) {
- Zero();
- return;
- }
- ASSERT(kBigitSize < 32);
- uint64_t carry = 0;
- uint64_t low = factor & 0xFFFFFFFF;
- uint64_t high = factor >> 32;
- for (int i = 0; i < used_digits_; ++i) {
- uint64_t product_low = low * bigits_[i];
- uint64_t product_high = high * bigits_[i];
- uint64_t tmp = (carry & kBigitMask) + product_low;
- bigits_[i] = static_cast<Chunk>(tmp & kBigitMask);
- carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
- (product_high << (32 - kBigitSize));
- }
- while (carry != 0) {
- EnsureCapacity(used_digits_ + 1);
- bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask);
- used_digits_++;
- carry >>= kBigitSize;
- }
- }
-
-
- void Bignum::MultiplyByPowerOfTen(int exponent) {
- const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d);
- const uint16_t kFive1 = 5;
- const uint16_t kFive2 = kFive1 * 5;
- const uint16_t kFive3 = kFive2 * 5;
- const uint16_t kFive4 = kFive3 * 5;
- const uint16_t kFive5 = kFive4 * 5;
- const uint16_t kFive6 = kFive5 * 5;
- const uint32_t kFive7 = kFive6 * 5;
- const uint32_t kFive8 = kFive7 * 5;
- const uint32_t kFive9 = kFive8 * 5;
- const uint32_t kFive10 = kFive9 * 5;
- const uint32_t kFive11 = kFive10 * 5;
- const uint32_t kFive12 = kFive11 * 5;
- const uint32_t kFive13 = kFive12 * 5;
- const uint32_t kFive1_to_12[] =
- { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
- kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
-
- ASSERT(exponent >= 0);
- if (exponent == 0) return;
- if (used_digits_ == 0) return;
-
- // We shift by exponent at the end just before returning.
- int remaining_exponent = exponent;
- while (remaining_exponent >= 27) {
- MultiplyByUInt64(kFive27);
- remaining_exponent -= 27;
- }
- while (remaining_exponent >= 13) {
- MultiplyByUInt32(kFive13);
- remaining_exponent -= 13;
- }
- if (remaining_exponent > 0) {
- MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
- }
- ShiftLeft(exponent);
- }
-
-
- void Bignum::Square() {
- ASSERT(IsClamped());
- int product_length = 2 * used_digits_;
- EnsureCapacity(product_length);
-
- // Comba multiplication: compute each column separately.
- // Example: r = a2a1a0 * b2b1b0.
- // r = 1 * a0b0 +
- // 10 * (a1b0 + a0b1) +
- // 100 * (a2b0 + a1b1 + a0b2) +
- // 1000 * (a2b1 + a1b2) +
- // 10000 * a2b2
- //
- // In the worst case we have to accumulate nb-digits products of digit*digit.
- //
- // Assert that the additional number of bits in a DoubleChunk are enough to
- // sum up used_digits of Bigit*Bigit.
- if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
- UNIMPLEMENTED();
- }
- DoubleChunk accumulator = 0;
- // First shift the digits so we don't overwrite them.
- int copy_offset = used_digits_;
- for (int i = 0; i < used_digits_; ++i) {
- bigits_[copy_offset + i] = bigits_[i];
- }
- // We have two loops to avoid some 'if's in the loop.
- for (int i = 0; i < used_digits_; ++i) {
- // Process temporary digit i with power i.
- // The sum of the two indices must be equal to i.
- int bigit_index1 = i;
- int bigit_index2 = 0;
- // Sum all of the sub-products.
- while (bigit_index1 >= 0) {
- Chunk chunk1 = bigits_[copy_offset + bigit_index1];
- Chunk chunk2 = bigits_[copy_offset + bigit_index2];
- accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
- bigit_index1--;
- bigit_index2++;
- }
- bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
- accumulator >>= kBigitSize;
- }
- for (int i = used_digits_; i < product_length; ++i) {
- int bigit_index1 = used_digits_ - 1;
- int bigit_index2 = i - bigit_index1;
- // Invariant: sum of both indices is again equal to i.
- // Inner loop runs 0 times on last iteration, emptying accumulator.
- while (bigit_index2 < used_digits_) {
- Chunk chunk1 = bigits_[copy_offset + bigit_index1];
- Chunk chunk2 = bigits_[copy_offset + bigit_index2];
- accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
- bigit_index1--;
- bigit_index2++;
- }
- // The overwritten bigits_[i] will never be read in further loop iterations,
- // because bigit_index1 and bigit_index2 are always greater
- // than i - used_digits_.
- bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
- accumulator >>= kBigitSize;
- }
- // Since the result was guaranteed to lie inside the number the
- // accumulator must be 0 now.
- ASSERT(accumulator == 0);
-
- // Don't forget to update the used_digits and the exponent.
- used_digits_ = product_length;
- exponent_ *= 2;
- Clamp();
- }
-
-
- void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
- ASSERT(base != 0);
- ASSERT(power_exponent >= 0);
- if (power_exponent == 0) {
- AssignUInt16(1);
- return;
- }
- Zero();
- int shifts = 0;
- // We expect base to be in range 2-32, and most often to be 10.
- // It does not make much sense to implement different algorithms for counting
- // the bits.
- while ((base & 1) == 0) {
- base >>= 1;
- shifts++;
- }
- int bit_size = 0;
- int tmp_base = base;
- while (tmp_base != 0) {
- tmp_base >>= 1;
- bit_size++;
- }
- int final_size = bit_size * power_exponent;
- // 1 extra bigit for the shifting, and one for rounded final_size.
- EnsureCapacity(final_size / kBigitSize + 2);
-
- // Left to Right exponentiation.
- int mask = 1;
- while (power_exponent >= mask) mask <<= 1;
-
- // The mask is now pointing to the bit above the most significant 1-bit of
- // power_exponent.
- // Get rid of first 1-bit;
- mask >>= 2;
- uint64_t this_value = base;
-
- bool delayed_multipliciation = false;
- const uint64_t max_32bits = 0xFFFFFFFF;
- while (mask != 0 && this_value <= max_32bits) {
- this_value = this_value * this_value;
- // Verify that there is enough space in this_value to perform the
- // multiplication. The first bit_size bits must be 0.
- if ((power_exponent & mask) != 0) {
- uint64_t base_bits_mask =
- ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
- bool high_bits_zero = (this_value & base_bits_mask) == 0;
- if (high_bits_zero) {
- this_value *= base;
- } else {
- delayed_multipliciation = true;
- }
- }
- mask >>= 1;
- }
- AssignUInt64(this_value);
- if (delayed_multipliciation) {
- MultiplyByUInt32(base);
- }
-
- // Now do the same thing as a bignum.
- while (mask != 0) {
- Square();
- if ((power_exponent & mask) != 0) {
- MultiplyByUInt32(base);
- }
- mask >>= 1;
- }
-
- // And finally add the saved shifts.
- ShiftLeft(shifts * power_exponent);
- }
-
-
- // Precondition: this/other < 16bit.
- uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
- ASSERT(IsClamped());
- ASSERT(other.IsClamped());
- ASSERT(other.used_digits_ > 0);
-
- // Easy case: if we have less digits than the divisor than the result is 0.
- // Note: this handles the case where this == 0, too.
- if (BigitLength() < other.BigitLength()) {
- return 0;
- }
-
- Align(other);
-
- uint16_t result = 0;
-
- // Start by removing multiples of 'other' until both numbers have the same
- // number of digits.
- while (BigitLength() > other.BigitLength()) {
- // This naive approach is extremely inefficient if the this divided other
- // might be big. This function is implemented for doubleToString where
- // the result should be small (less than 10).
- ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
- // Remove the multiples of the first digit.
- // Example this = 23 and other equals 9. -> Remove 2 multiples.
- result += bigits_[used_digits_ - 1];
- SubtractTimes(other, bigits_[used_digits_ - 1]);
- }
-
- ASSERT(BigitLength() == other.BigitLength());
-
- // Both bignums are at the same length now.
- // Since other has more than 0 digits we know that the access to
- // bigits_[used_digits_ - 1] is safe.
- Chunk this_bigit = bigits_[used_digits_ - 1];
- Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
-
- if (other.used_digits_ == 1) {
- // Shortcut for easy (and common) case.
- int quotient = this_bigit / other_bigit;
- bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
- result += quotient;
- Clamp();
- return result;
- }
-
- int division_estimate = this_bigit / (other_bigit + 1);
- result += division_estimate;
- SubtractTimes(other, division_estimate);
-
- if (other_bigit * (division_estimate + 1) > this_bigit) {
- // No need to even try to subtract. Even if other's remaining digits were 0
- // another subtraction would be too much.
- return result;
- }
-
- while (LessEqual(other, *this)) {
- SubtractBignum(other);
- result++;
- }
- return result;
- }
-
-
- template<typename S>
- static int SizeInHexChars(S number) {
- ASSERT(number > 0);
- int result = 0;
- while (number != 0) {
- number >>= 4;
- result++;
- }
- return result;
- }
-
-
- static char HexCharOfValue(int value) {
- ASSERT(0 <= value && value <= 16);
- if (value < 10) return value + '0';
- return value - 10 + 'A';
+
+Bignum::Bignum()
+ : bigits_buffer_(), bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) {
+ for (int i = 0; i < kBigitCapacity; ++i) {
+ bigits_[i] = 0;
+ }
+}
+
+
+template<typename S>
+static int BitSize(S value) {
+ (void) value; // Mark variable as used.
+ return 8 * sizeof(value);
+}
+
+// Guaranteed to lie in one Bigit.
+void Bignum::AssignUInt16(uint16_t value) {
+ ASSERT(kBigitSize >= BitSize(value));
+ Zero();
+ if (value == 0) return;
+
+ EnsureCapacity(1);
+ bigits_[0] = value;
+ used_digits_ = 1;
+}
+
+
+void Bignum::AssignUInt64(uint64_t value) {
+ const int kUInt64Size = 64;
+
+ Zero();
+ if (value == 0) return;
+
+ int needed_bigits = kUInt64Size / kBigitSize + 1;
+ EnsureCapacity(needed_bigits);
+ for (int i = 0; i < needed_bigits; ++i) {
+ bigits_[i] = value & kBigitMask;
+ value = value >> kBigitSize;
+ }
+ used_digits_ = needed_bigits;
+ Clamp();
+}
+
+
+void Bignum::AssignBignum(const Bignum& other) {
+ exponent_ = other.exponent_;
+ for (int i = 0; i < other.used_digits_; ++i) {
+ bigits_[i] = other.bigits_[i];
+ }
+ // Clear the excess digits (if there were any).
+ for (int i = other.used_digits_; i < used_digits_; ++i) {
+ bigits_[i] = 0;
+ }
+ used_digits_ = other.used_digits_;
+}
+
+
+static uint64_t ReadUInt64(BufferReference<const char> buffer,
+ int from,
+ int digits_to_read) {
+ uint64_t result = 0;
+ for (int i = from; i < from + digits_to_read; ++i) {
+ int digit = buffer[i] - '0';
+ ASSERT(0 <= digit && digit <= 9);
+ result = result * 10 + digit;
+ }
+ return result;
+}
+
+
+void Bignum::AssignDecimalString(BufferReference<const char> value) {
+ // 2^64 = 18446744073709551616 > 10^19
+ const int kMaxUint64DecimalDigits = 19;
+ Zero();
+ int length = value.length();
+ unsigned int pos = 0;
+ // Let's just say that each digit needs 4 bits.
+ while (length >= kMaxUint64DecimalDigits) {
+ uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
+ pos += kMaxUint64DecimalDigits;
+ length -= kMaxUint64DecimalDigits;
+ MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
+ AddUInt64(digits);
+ }
+ uint64_t digits = ReadUInt64(value, pos, length);
+ MultiplyByPowerOfTen(length);
+ AddUInt64(digits);
+ Clamp();
+}
+
+
+void Bignum::AssignHexString(BufferReference<const char> value) {
+ Zero();
+ int length = value.length();
+
+ int needed_bigits = length * 4 / kBigitSize + 1;
+ EnsureCapacity(needed_bigits);
+ int string_index = length - 1;
+ for (int i = 0; i < needed_bigits - 1; ++i) {
+ // These bigits are guaranteed to be "full".
+ Chunk current_bigit = 0;
+ for (int j = 0; j < kBigitSize / 4; j++) {
+ current_bigit += toASCIIHexValue(value[string_index--]) << (j * 4);
}
-
-
- bool Bignum::ToHexString(char* buffer, int buffer_size) const {
- ASSERT(IsClamped());
- // Each bigit must be printable as separate hex-character.
- ASSERT(kBigitSize % 4 == 0);
- const int kHexCharsPerBigit = kBigitSize / 4;
-
- if (used_digits_ == 0) {
- if (buffer_size < 2) return false;
- buffer[0] = '0';
- buffer[1] = '\0';
- return true;
- }
- // We add 1 for the terminating '\0' character.
- int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
- SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
- if (needed_chars > buffer_size) return false;
- int string_index = needed_chars - 1;
- buffer[string_index--] = '\0';
- for (int i = 0; i < exponent_; ++i) {
- for (int j = 0; j < kHexCharsPerBigit; ++j) {
- buffer[string_index--] = '0';
- }
- }
- for (int i = 0; i < used_digits_ - 1; ++i) {
- Chunk current_bigit = bigits_[i];
- for (int j = 0; j < kHexCharsPerBigit; ++j) {
- buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
- current_bigit >>= 4;
- }
- }
- // And finally the last bigit.
- Chunk most_significant_bigit = bigits_[used_digits_ - 1];
- while (most_significant_bigit != 0) {
- buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
- most_significant_bigit >>= 4;
- }
- return true;
+ bigits_[i] = current_bigit;
+ }
+ used_digits_ = needed_bigits - 1;
+
+ Chunk most_significant_bigit = 0; // Could be = 0;
+ for (int j = 0; j <= string_index; ++j) {
+ most_significant_bigit <<= 4;
+ most_significant_bigit += toASCIIHexValue(value[j]);
+ }
+ if (most_significant_bigit != 0) {
+ bigits_[used_digits_] = most_significant_bigit;
+ used_digits_++;
+ }
+ Clamp();
+}
+
+
+void Bignum::AddUInt64(uint64_t operand) {
+ if (operand == 0) return;
+ Bignum other;
+ other.AssignUInt64(operand);
+ AddBignum(other);
+}
+
+
+void Bignum::AddBignum(const Bignum& other) {
+ ASSERT(IsClamped());
+ ASSERT(other.IsClamped());
+
+ // If this has a greater exponent than other append zero-bigits to this.
+ // After this call exponent_ <= other.exponent_.
+ Align(other);
+
+ // There are two possibilities:
+ // aaaaaaaaaaa 0000 (where the 0s represent a's exponent)
+ // bbbbb 00000000
+ // ----------------
+ // ccccccccccc 0000
+ // or
+ // aaaaaaaaaa 0000
+ // bbbbbbbbb 0000000
+ // -----------------
+ // cccccccccccc 0000
+ // In both cases we might need a carry bigit.
+
+ EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_);
+ Chunk carry = 0;
+ int bigit_pos = other.exponent_ - exponent_;
+ ASSERT(bigit_pos >= 0);
+ for (int i = 0; i < other.used_digits_; ++i) {
+ Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
+ bigits_[bigit_pos] = sum & kBigitMask;
+ carry = sum >> kBigitSize;
+ bigit_pos++;
+ }
+
+ while (carry != 0) {
+ Chunk sum = bigits_[bigit_pos] + carry;
+ bigits_[bigit_pos] = sum & kBigitMask;
+ carry = sum >> kBigitSize;
+ bigit_pos++;
+ }
+ used_digits_ = Max(bigit_pos, used_digits_);
+ ASSERT(IsClamped());
+}
+
+
+void Bignum::SubtractBignum(const Bignum& other) {
+ ASSERT(IsClamped());
+ ASSERT(other.IsClamped());
+ // We require this to be bigger than other.
+ ASSERT(LessEqual(other, *this));
+
+ Align(other);
+
+ int offset = other.exponent_ - exponent_;
+ Chunk borrow = 0;
+ int i;
+ for (i = 0; i < other.used_digits_; ++i) {
+ ASSERT((borrow == 0) || (borrow == 1));
+ Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow;
+ bigits_[i + offset] = difference & kBigitMask;
+ borrow = difference >> (kChunkSize - 1);
+ }
+ while (borrow != 0) {
+ Chunk difference = bigits_[i + offset] - borrow;
+ bigits_[i + offset] = difference & kBigitMask;
+ borrow = difference >> (kChunkSize - 1);
+ ++i;
+ }
+ Clamp();
+}
+
+
+void Bignum::ShiftLeft(int shift_amount) {
+ if (used_digits_ == 0) return;
+ exponent_ += shift_amount / kBigitSize;
+ int local_shift = shift_amount % kBigitSize;
+ EnsureCapacity(used_digits_ + 1);
+ BigitsShiftLeft(local_shift);
+}
+
+
+void Bignum::MultiplyByUInt32(uint32_t factor) {
+ if (factor == 1) return;
+ if (factor == 0) {
+ Zero();
+ return;
+ }
+ if (used_digits_ == 0) return;
+
+ // The product of a bigit with the factor is of size kBigitSize + 32.
+ // Assert that this number + 1 (for the carry) fits into double chunk.
+ ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);
+ DoubleChunk carry = 0;
+ for (int i = 0; i < used_digits_; ++i) {
+ DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;
+ bigits_[i] = static_cast<Chunk>(product & kBigitMask);
+ carry = (product >> kBigitSize);
+ }
+ while (carry != 0) {
+ EnsureCapacity(used_digits_ + 1);
+ bigits_[used_digits_] = carry & kBigitMask;
+ used_digits_++;
+ carry >>= kBigitSize;
+ }
+}
+
+
+void Bignum::MultiplyByUInt64(uint64_t factor) {
+ if (factor == 1) return;
+ if (factor == 0) {
+ Zero();
+ return;
+ }
+ ASSERT(kBigitSize < 32);
+ uint64_t carry = 0;
+ uint64_t low = factor & 0xFFFFFFFF;
+ uint64_t high = factor >> 32;
+ for (int i = 0; i < used_digits_; ++i) {
+ uint64_t product_low = low * bigits_[i];
+ uint64_t product_high = high * bigits_[i];
+ uint64_t tmp = (carry & kBigitMask) + product_low;
+ bigits_[i] = tmp & kBigitMask;
+ carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
+ (product_high << (32 - kBigitSize));
+ }
+ while (carry != 0) {
+ EnsureCapacity(used_digits_ + 1);
+ bigits_[used_digits_] = carry & kBigitMask;
+ used_digits_++;
+ carry >>= kBigitSize;
+ }
+}
+
+
+void Bignum::MultiplyByPowerOfTen(int exponent) {
+ const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d);
+ const uint16_t kFive1 = 5;
+ const uint16_t kFive2 = kFive1 * 5;
+ const uint16_t kFive3 = kFive2 * 5;
+ const uint16_t kFive4 = kFive3 * 5;
+ const uint16_t kFive5 = kFive4 * 5;
+ const uint16_t kFive6 = kFive5 * 5;
+ const uint32_t kFive7 = kFive6 * 5;
+ const uint32_t kFive8 = kFive7 * 5;
+ const uint32_t kFive9 = kFive8 * 5;
+ const uint32_t kFive10 = kFive9 * 5;
+ const uint32_t kFive11 = kFive10 * 5;
+ const uint32_t kFive12 = kFive11 * 5;
+ const uint32_t kFive13 = kFive12 * 5;
+ const uint32_t kFive1_to_12[] =
+ { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
+ kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
+
+ ASSERT(exponent >= 0);
+ if (exponent == 0) return;
+ if (used_digits_ == 0) return;
+
+ // We shift by exponent at the end just before returning.
+ int remaining_exponent = exponent;
+ while (remaining_exponent >= 27) {
+ MultiplyByUInt64(kFive27);
+ remaining_exponent -= 27;
+ }
+ while (remaining_exponent >= 13) {
+ MultiplyByUInt32(kFive13);
+ remaining_exponent -= 13;
+ }
+ if (remaining_exponent > 0) {
+ MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
+ }
+ ShiftLeft(exponent);
+}
+
+
+void Bignum::Square() {
+ ASSERT(IsClamped());
+ int product_length = 2 * used_digits_;
+ EnsureCapacity(product_length);
+
+ // Comba multiplication: compute each column separately.
+ // Example: r = a2a1a0 * b2b1b0.
+ // r = 1 * a0b0 +
+ // 10 * (a1b0 + a0b1) +
+ // 100 * (a2b0 + a1b1 + a0b2) +
+ // 1000 * (a2b1 + a1b2) +
+ // 10000 * a2b2
+ //
+ // In the worst case we have to accumulate nb-digits products of digit*digit.
+ //
+ // Assert that the additional number of bits in a DoubleChunk are enough to
+ // sum up used_digits of Bigit*Bigit.
+ if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
+ UNIMPLEMENTED();
+ }
+ DoubleChunk accumulator = 0;
+ // First shift the digits so we don't overwrite them.
+ int copy_offset = used_digits_;
+ for (int i = 0; i < used_digits_; ++i) {
+ bigits_[copy_offset + i] = bigits_[i];
+ }
+ // We have two loops to avoid some 'if's in the loop.
+ for (int i = 0; i < used_digits_; ++i) {
+ // Process temporary digit i with power i.
+ // The sum of the two indices must be equal to i.
+ int bigit_index1 = i;
+ int bigit_index2 = 0;
+ // Sum all of the sub-products.
+ while (bigit_index1 >= 0) {
+ Chunk chunk1 = bigits_[copy_offset + bigit_index1];
+ Chunk chunk2 = bigits_[copy_offset + bigit_index2];
+ accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
+ bigit_index1--;
+ bigit_index2++;
}
-
-
- Bignum::Chunk Bignum::BigitAt(int index) const {
- if (index >= BigitLength()) return 0;
- if (index < exponent_) return 0;
- return bigits_[index - exponent_];
+ bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
+ accumulator >>= kBigitSize;
+ }
+ for (int i = used_digits_; i < product_length; ++i) {
+ int bigit_index1 = used_digits_ - 1;
+ int bigit_index2 = i - bigit_index1;
+ // Invariant: sum of both indices is again equal to i.
+ // Inner loop runs 0 times on last iteration, emptying accumulator.
+ while (bigit_index2 < used_digits_) {
+ Chunk chunk1 = bigits_[copy_offset + bigit_index1];
+ Chunk chunk2 = bigits_[copy_offset + bigit_index2];
+ accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
+ bigit_index1--;
+ bigit_index2++;
}
-
-
- int Bignum::Compare(const Bignum& a, const Bignum& b) {
- ASSERT(a.IsClamped());
- ASSERT(b.IsClamped());
- int bigit_length_a = a.BigitLength();
- int bigit_length_b = b.BigitLength();
- if (bigit_length_a < bigit_length_b) return -1;
- if (bigit_length_a > bigit_length_b) return +1;
- for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) {
- Chunk bigit_a = a.BigitAt(i);
- Chunk bigit_b = b.BigitAt(i);
- if (bigit_a < bigit_b) return -1;
- if (bigit_a > bigit_b) return +1;
- // Otherwise they are equal up to this digit. Try the next digit.
- }
- return 0;
+ // The overwritten bigits_[i] will never be read in further loop iterations,
+ // because bigit_index1 and bigit_index2 are always greater
+ // than i - used_digits_.
+ bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
+ accumulator >>= kBigitSize;
+ }
+ // Since the result was guaranteed to lie inside the number the
+ // accumulator must be 0 now.
+ ASSERT(accumulator == 0);
+
+ // Don't forget to update the used_digits and the exponent.
+ used_digits_ = product_length;
+ exponent_ *= 2;
+ Clamp();
+}
+
+
+void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
+ ASSERT(base != 0);
+ ASSERT(power_exponent >= 0);
+ if (power_exponent == 0) {
+ AssignUInt16(1);
+ return;
+ }
+ Zero();
+ int shifts = 0;
+ // We expect base to be in range 2-32, and most often to be 10.
+ // It does not make much sense to implement different algorithms for counting
+ // the bits.
+ while ((base & 1) == 0) {
+ base >>= 1;
+ shifts++;
+ }
+ int bit_size = 0;
+ int tmp_base = base;
+ while (tmp_base != 0) {
+ tmp_base >>= 1;
+ bit_size++;
+ }
+ int final_size = bit_size * power_exponent;
+ // 1 extra bigit for the shifting, and one for rounded final_size.
+ EnsureCapacity(final_size / kBigitSize + 2);
+
+ // Left to Right exponentiation.
+ int mask = 1;
+ while (power_exponent >= mask) mask <<= 1;
+
+ // The mask is now pointing to the bit above the most significant 1-bit of
+ // power_exponent.
+ // Get rid of first 1-bit;
+ mask >>= 2;
+ uint64_t this_value = base;
+
+ bool delayed_multiplication = false;
+ const uint64_t max_32bits = 0xFFFFFFFF;
+ while (mask != 0 && this_value <= max_32bits) {
+ this_value = this_value * this_value;
+ // Verify that there is enough space in this_value to perform the
+ // multiplication. The first bit_size bits must be 0.
+ if ((power_exponent & mask) != 0) {
+ ASSERT(bit_size > 0);
+ uint64_t base_bits_mask =
+ ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
+ bool high_bits_zero = (this_value & base_bits_mask) == 0;
+ if (high_bits_zero) {
+ this_value *= base;
+ } else {
+ delayed_multiplication = true;
+ }
}
-
-
- int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
- ASSERT(a.IsClamped());
- ASSERT(b.IsClamped());
- ASSERT(c.IsClamped());
- if (a.BigitLength() < b.BigitLength()) {
- return PlusCompare(b, a, c);
- }
- if (a.BigitLength() + 1 < c.BigitLength()) return -1;
- if (a.BigitLength() > c.BigitLength()) return +1;
- // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
- // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
- // of 'a'.
- if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
- return -1;
- }
-
- Chunk borrow = 0;
- // Starting at min_exponent all digits are == 0. So no need to compare them.
- int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
- for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
- Chunk chunk_a = a.BigitAt(i);
- Chunk chunk_b = b.BigitAt(i);
- Chunk chunk_c = c.BigitAt(i);
- Chunk sum = chunk_a + chunk_b;
- if (sum > chunk_c + borrow) {
- return +1;
- } else {
- borrow = chunk_c + borrow - sum;
- if (borrow > 1) return -1;
- borrow <<= kBigitSize;
- }
- }
- if (borrow == 0) return 0;
- return -1;
+ mask >>= 1;
+ }
+ AssignUInt64(this_value);
+ if (delayed_multiplication) {
+ MultiplyByUInt32(base);
+ }
+
+ // Now do the same thing as a bignum.
+ while (mask != 0) {
+ Square();
+ if ((power_exponent & mask) != 0) {
+ MultiplyByUInt32(base);
}
-
-
- void Bignum::Clamp() {
- while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
- used_digits_--;
- }
- if (used_digits_ == 0) {
- // Zero.
- exponent_ = 0;
- }
+ mask >>= 1;
+ }
+
+ // And finally add the saved shifts.
+ ShiftLeft(shifts * power_exponent);
+}
+
+
+// Precondition: this/other < 16bit.
+uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
+ ASSERT(IsClamped());
+ ASSERT(other.IsClamped());
+ ASSERT(other.used_digits_ > 0);
+
+ // Easy case: if we have less digits than the divisor than the result is 0.
+ // Note: this handles the case where this == 0, too.
+ if (BigitLength() < other.BigitLength()) {
+ return 0;
+ }
+
+ Align(other);
+
+ uint16_t result = 0;
+
+ // Start by removing multiples of 'other' until both numbers have the same
+ // number of digits.
+ while (BigitLength() > other.BigitLength()) {
+ // This naive approach is extremely inefficient if `this` divided by other
+ // is big. This function is implemented for doubleToString where
+ // the result should be small (less than 10).
+ ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
+ ASSERT(bigits_[used_digits_ - 1] < 0x10000);
+ // Remove the multiples of the first digit.
+ // Example this = 23 and other equals 9. -> Remove 2 multiples.
+ result += static_cast<uint16_t>(bigits_[used_digits_ - 1]);
+ SubtractTimes(other, bigits_[used_digits_ - 1]);
+ }
+
+ ASSERT(BigitLength() == other.BigitLength());
+
+ // Both bignums are at the same length now.
+ // Since other has more than 0 digits we know that the access to
+ // bigits_[used_digits_ - 1] is safe.
+ Chunk this_bigit = bigits_[used_digits_ - 1];
+ Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
+
+ if (other.used_digits_ == 1) {
+ // Shortcut for easy (and common) case.
+ int quotient = this_bigit / other_bigit;
+ bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
+ ASSERT(quotient < 0x10000);
+ result += static_cast<uint16_t>(quotient);
+ Clamp();
+ return result;
+ }
+
+ int division_estimate = this_bigit / (other_bigit + 1);
+ ASSERT(division_estimate < 0x10000);
+ result += static_cast<uint16_t>(division_estimate);
+ SubtractTimes(other, division_estimate);
+
+ if (other_bigit * (division_estimate + 1) > this_bigit) {
+ // No need to even try to subtract. Even if other's remaining digits were 0
+ // another subtraction would be too much.
+ return result;
+ }
+
+ while (LessEqual(other, *this)) {
+ SubtractBignum(other);
+ result++;
+ }
+ return result;
+}
+
+
+template<typename S>
+static int SizeInHexChars(S number) {
+ ASSERT(number > 0);
+ int result = 0;
+ while (number != 0) {
+ number >>= 4;
+ result++;
+ }
+ return result;
+}
+
+
+static char HexCharOfValue(int value) {
+ ASSERT(0 <= value && value <= 16);
+ if (value < 10) return static_cast<char>(value + '0');
+ return static_cast<char>(value - 10 + 'A');
+}
+
+
+bool Bignum::ToHexString(char* buffer, int buffer_size) const {
+ ASSERT(IsClamped());
+ // Each bigit must be printable as separate hex-character.
+ ASSERT(kBigitSize % 4 == 0);
+ const int kHexCharsPerBigit = kBigitSize / 4;
+
+ if (used_digits_ == 0) {
+ if (buffer_size < 2) return false;
+ buffer[0] = '0';
+ buffer[1] = '\0';
+ return true;
+ }
+ // We add 1 for the terminating '\0' character.
+ int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
+ SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
+ if (needed_chars > buffer_size) return false;
+ int string_index = needed_chars - 1;
+ buffer[string_index--] = '\0';
+ for (int i = 0; i < exponent_; ++i) {
+ for (int j = 0; j < kHexCharsPerBigit; ++j) {
+ buffer[string_index--] = '0';
}
-
-
- bool Bignum::IsClamped() const {
- return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
+ }
+ for (int i = 0; i < used_digits_ - 1; ++i) {
+ Chunk current_bigit = bigits_[i];
+ for (int j = 0; j < kHexCharsPerBigit; ++j) {
+ buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
+ current_bigit >>= 4;
}
-
-
- void Bignum::Zero() {
- for (int i = 0; i < used_digits_; ++i) {
- bigits_[i] = 0;
- }
- used_digits_ = 0;
- exponent_ = 0;
+ }
+ // And finally the last bigit.
+ Chunk most_significant_bigit = bigits_[used_digits_ - 1];
+ while (most_significant_bigit != 0) {
+ buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
+ most_significant_bigit >>= 4;
+ }
+ return true;
+}
+
+
+Bignum::Chunk Bignum::BigitAt(int index) const {
+ if (index >= BigitLength()) return 0;
+ if (index < exponent_) return 0;
+ return bigits_[index - exponent_];
+}
+
+
+int Bignum::Compare(const Bignum& a, const Bignum& b) {
+ ASSERT(a.IsClamped());
+ ASSERT(b.IsClamped());
+ int bigit_length_a = a.BigitLength();
+ int bigit_length_b = b.BigitLength();
+ if (bigit_length_a < bigit_length_b) return -1;
+ if (bigit_length_a > bigit_length_b) return +1;
+ for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) {
+ Chunk bigit_a = a.BigitAt(i);
+ Chunk bigit_b = b.BigitAt(i);
+ if (bigit_a < bigit_b) return -1;
+ if (bigit_a > bigit_b) return +1;
+ // Otherwise they are equal up to this digit. Try the next digit.
+ }
+ return 0;
+}
+
+
+int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
+ ASSERT(a.IsClamped());
+ ASSERT(b.IsClamped());
+ ASSERT(c.IsClamped());
+ if (a.BigitLength() < b.BigitLength()) {
+ return PlusCompare(b, a, c);
+ }
+ if (a.BigitLength() + 1 < c.BigitLength()) return -1;
+ if (a.BigitLength() > c.BigitLength()) return +1;
+ // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
+ // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
+ // of 'a'.
+ if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
+ return -1;
+ }
+
+ Chunk borrow = 0;
+ // Starting at min_exponent all digits are == 0. So no need to compare them.
+ int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
+ for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
+ Chunk chunk_a = a.BigitAt(i);
+ Chunk chunk_b = b.BigitAt(i);
+ Chunk chunk_c = c.BigitAt(i);
+ Chunk sum = chunk_a + chunk_b;
+ if (sum > chunk_c + borrow) {
+ return +1;
+ } else {
+ borrow = chunk_c + borrow - sum;
+ if (borrow > 1) return -1;
+ borrow <<= kBigitSize;
}
-
-
- void Bignum::Align(const Bignum& other) {
- if (exponent_ > other.exponent_) {
- // If "X" represents a "hidden" digit (by the exponent) then we are in the
- // following case (a == this, b == other):
- // a: aaaaaaXXXX or a: aaaaaXXX
- // b: bbbbbbX b: bbbbbbbbXX
- // We replace some of the hidden digits (X) of a with 0 digits.
- // a: aaaaaa000X or a: aaaaa0XX
- int zero_digits = exponent_ - other.exponent_;
- EnsureCapacity(used_digits_ + zero_digits);
- for (int i = used_digits_ - 1; i >= 0; --i) {
- bigits_[i + zero_digits] = bigits_[i];
- }
- for (int i = 0; i < zero_digits; ++i) {
- bigits_[i] = 0;
- }
- used_digits_ += zero_digits;
- exponent_ -= zero_digits;
- ASSERT(used_digits_ >= 0);
- ASSERT(exponent_ >= 0);
- }
+ }
+ if (borrow == 0) return 0;
+ return -1;
+}
+
+
+void Bignum::Clamp() {
+ while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
+ used_digits_--;
+ }
+ if (used_digits_ == 0) {
+ // Zero.
+ exponent_ = 0;
+ }
+}
+
+
+bool Bignum::IsClamped() const {
+ return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
+}
+
+
+void Bignum::Zero() {
+ for (int i = 0; i < used_digits_; ++i) {
+ bigits_[i] = 0;
+ }
+ used_digits_ = 0;
+ exponent_ = 0;
+}
+
+
+void Bignum::Align(const Bignum& other) {
+ if (exponent_ > other.exponent_) {
+ // If "X" represents a "hidden" digit (by the exponent) then we are in the
+ // following case (a == this, b == other):
+ // a: aaaaaaXXXX or a: aaaaaXXX
+ // b: bbbbbbX b: bbbbbbbbXX
+ // We replace some of the hidden digits (X) of a with 0 digits.
+ // a: aaaaaa000X or a: aaaaa0XX
+ int zero_digits = exponent_ - other.exponent_;
+ EnsureCapacity(used_digits_ + zero_digits);
+ for (int i = used_digits_ - 1; i >= 0; --i) {
+ bigits_[i + zero_digits] = bigits_[i];
}
-
-
- void Bignum::BigitsShiftLeft(int shift_amount) {
- ASSERT(shift_amount < kBigitSize);
- ASSERT(shift_amount >= 0);
- Chunk carry = 0;
- for (int i = 0; i < used_digits_; ++i) {
- Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
- bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
- carry = new_carry;
- }
- if (carry != 0) {
- bigits_[used_digits_] = carry;
- used_digits_++;
- }
+ for (int i = 0; i < zero_digits; ++i) {
+ bigits_[i] = 0;
}
-
-
- void Bignum::SubtractTimes(const Bignum& other, int factor) {
-#ifndef NDEBUG
- Bignum a, b;
- a.AssignBignum(*this);
- b.AssignBignum(other);
- b.MultiplyByUInt32(factor);
- a.SubtractBignum(b);
-#endif
- ASSERT(exponent_ <= other.exponent_);
- if (factor < 3) {
- for (int i = 0; i < factor; ++i) {
- SubtractBignum(other);
- }
- return;
- }
- Chunk borrow = 0;
- int exponent_diff = other.exponent_ - exponent_;
- for (int i = 0; i < other.used_digits_; ++i) {
- DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
- DoubleChunk remove = borrow + product;
- Chunk difference =
- bigits_[i + exponent_diff] - static_cast<Chunk>(remove & kBigitMask);
- bigits_[i + exponent_diff] = difference & kBigitMask;
- borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
- (remove >> kBigitSize));
- }
- for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
- if (borrow == 0) return;
- Chunk difference = bigits_[i] - borrow;
- bigits_[i] = difference & kBigitMask;
- borrow = difference >> (kChunkSize - 1);
- }
- Clamp();
- ASSERT(Bignum::Equal(a, *this));
+ used_digits_ += zero_digits;
+ exponent_ -= zero_digits;
+ ASSERT(used_digits_ >= 0);
+ ASSERT(exponent_ >= 0);
+ }
+}
+
+
+void Bignum::BigitsShiftLeft(int shift_amount) {
+ ASSERT(shift_amount < kBigitSize);
+ ASSERT(shift_amount >= 0);
+ Chunk carry = 0;
+ for (int i = 0; i < used_digits_; ++i) {
+ Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
+ bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
+ carry = new_carry;
+ }
+ if (carry != 0) {
+ bigits_[used_digits_] = carry;
+ used_digits_++;
+ }
+}
+
+
+void Bignum::SubtractTimes(const Bignum& other, int factor) {
+ ASSERT(exponent_ <= other.exponent_);
+ if (factor < 3) {
+ for (int i = 0; i < factor; ++i) {
+ SubtractBignum(other);
}
-
-
-} // namespace double_conversion
+ return;
+ }
+ Chunk borrow = 0;
+ int exponent_diff = other.exponent_ - exponent_;
+ for (int i = 0; i < other.used_digits_; ++i) {
+ DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
+ DoubleChunk remove = borrow + product;
+ Chunk difference = bigits_[i + exponent_diff] - (remove & kBigitMask);
+ bigits_[i + exponent_diff] = difference & kBigitMask;
+ borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
+ (remove >> kBigitSize));
+ }
+ for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
+ if (borrow == 0) return;
+ Chunk difference = bigits_[i] - borrow;
+ bigits_[i] = difference & kBigitMask;
+ borrow = difference >> (kChunkSize - 1);
+ }
+ Clamp();
+}
+
-} // namespace WTF
+} // namespace double_conversion
+} // namespace WTF
#ifndef DOUBLE_CONVERSION_BIGNUM_H_
#define DOUBLE_CONVERSION_BIGNUM_H_
-#include "utils.h"
+#include <wtf/dtoa/utils.h>
namespace WTF {
-
namespace double_conversion {
-
- class Bignum {
- public:
- // 3584 = 128 * 28. We can represent 2^3584 > 10^1000 accurately.
- // This bignum can encode much bigger numbers, since it contains an
- // exponent.
- static const int kMaxSignificantBits = 3584;
-
- Bignum();
- void AssignUInt16(uint16_t value);
- void AssignUInt64(uint64_t value);
- void AssignBignum(const Bignum& other);
-
- void AssignDecimalString(BufferReference<const char> value);
- void AssignHexString(BufferReference<const char> value);
-
- void AssignPowerUInt16(uint16_t base, int exponent);
-
- void AddUInt16(uint16_t operand);
- void AddUInt64(uint64_t operand);
- void AddBignum(const Bignum& other);
- // Precondition: this >= other.
- void SubtractBignum(const Bignum& other);
-
- void Square();
- void ShiftLeft(int shift_amount);
- void MultiplyByUInt32(uint32_t factor);
- void MultiplyByUInt64(uint64_t factor);
- void MultiplyByPowerOfTen(int exponent);
- void Times10() { return MultiplyByUInt32(10); }
- // Pseudocode:
- // int result = this / other;
- // this = this % other;
- // In the worst case this function is in O(this/other).
- uint16_t DivideModuloIntBignum(const Bignum& other);
-
- bool ToHexString(char* buffer, int buffer_size) const;
-
- static int Compare(const Bignum& a, const Bignum& b);
- static bool Equal(const Bignum& a, const Bignum& b) {
- return Compare(a, b) == 0;
- }
- static bool LessEqual(const Bignum& a, const Bignum& b) {
- return Compare(a, b) <= 0;
- }
- static bool Less(const Bignum& a, const Bignum& b) {
- return Compare(a, b) < 0;
- }
- // Returns Compare(a + b, c);
- static int PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c);
- // Returns a + b == c
- static bool PlusEqual(const Bignum& a, const Bignum& b, const Bignum& c) {
- return PlusCompare(a, b, c) == 0;
- }
- // Returns a + b <= c
- static bool PlusLessEqual(const Bignum& a, const Bignum& b, const Bignum& c) {
- return PlusCompare(a, b, c) <= 0;
- }
- // Returns a + b < c
- static bool PlusLess(const Bignum& a, const Bignum& b, const Bignum& c) {
- return PlusCompare(a, b, c) < 0;
- }
- private:
- typedef uint32_t Chunk;
- typedef uint64_t DoubleChunk;
-
- static const int kChunkSize = sizeof(Chunk) * 8;
- static const int kDoubleChunkSize = sizeof(DoubleChunk) * 8;
- // With bigit size of 28 we loose some bits, but a double still fits easily
- // into two chunks, and more importantly we can use the Comba multiplication.
- static const int kBigitSize = 28;
- static const Chunk kBigitMask = (1 << kBigitSize) - 1;
- // Every instance allocates kBigitLength chunks on the stack. Bignums cannot
- // grow. There are no checks if the stack-allocated space is sufficient.
- static const int kBigitCapacity = kMaxSignificantBits / kBigitSize;
-
- void EnsureCapacity(int size) {
- if (size > kBigitCapacity) {
- UNREACHABLE();
- }
- }
- void Align(const Bignum& other);
- void Clamp();
- bool IsClamped() const;
- void Zero();
- // Requires this to have enough capacity (no tests done).
- // Updates used_digits_ if necessary.
- // shift_amount must be < kBigitSize.
- void BigitsShiftLeft(int shift_amount);
- // BigitLength includes the "hidden" digits encoded in the exponent.
- int BigitLength() const { return used_digits_ + exponent_; }
- Chunk BigitAt(int index) const;
- void SubtractTimes(const Bignum& other, int factor);
-
- Chunk bigits_buffer_[kBigitCapacity];
- // A vector backed by bigits_buffer_. This way accesses to the array are
- // checked for out-of-bounds errors.
- BufferReference<Chunk> bigits_;
- int used_digits_;
- // The Bignum's value equals value(bigits_) * 2^(exponent_ * kBigitSize).
- int exponent_;
-
- DISALLOW_COPY_AND_ASSIGN(Bignum);
- };
-
-} // namespace double_conversion
-} // namespace WTF
+class Bignum {
+ public:
+ // 3584 = 128 * 28. We can represent 2^3584 > 10^1000 accurately.
+ // This bignum can encode much bigger numbers, since it contains an
+ // exponent.
+ static const int kMaxSignificantBits = 3584;
+
+ Bignum();
+ void AssignUInt16(uint16_t value);
+ void AssignUInt64(uint64_t value);
+ void AssignBignum(const Bignum& other);
+
+ void AssignDecimalString(BufferReference<const char> value);
+ void AssignHexString(BufferReference<const char> value);
+
+ void AssignPowerUInt16(uint16_t base, int exponent);
+
+ void AddUInt64(uint64_t operand);
+ void AddBignum(const Bignum& other);
+ // Precondition: this >= other.
+ void SubtractBignum(const Bignum& other);
+
+ void Square();
+ void ShiftLeft(int shift_amount);
+ void MultiplyByUInt32(uint32_t factor);
+ void MultiplyByUInt64(uint64_t factor);
+ void MultiplyByPowerOfTen(int exponent);
+ void Times10() { return MultiplyByUInt32(10); }
+ // Pseudocode:
+ // int result = this / other;
+ // this = this % other;
+ // In the worst case this function is in O(this/other).
+ uint16_t DivideModuloIntBignum(const Bignum& other);
+
+ bool ToHexString(char* buffer, int buffer_size) const;
+
+ // Returns
+ // -1 if a < b,
+ // 0 if a == b, and
+ // +1 if a > b.
+ static int Compare(const Bignum& a, const Bignum& b);
+ static bool Equal(const Bignum& a, const Bignum& b) {
+ return Compare(a, b) == 0;
+ }
+ static bool LessEqual(const Bignum& a, const Bignum& b) {
+ return Compare(a, b) <= 0;
+ }
+ static bool Less(const Bignum& a, const Bignum& b) {
+ return Compare(a, b) < 0;
+ }
+ // Returns Compare(a + b, c);
+ static int PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c);
+ // Returns a + b == c
+ static bool PlusEqual(const Bignum& a, const Bignum& b, const Bignum& c) {
+ return PlusCompare(a, b, c) == 0;
+ }
+ // Returns a + b <= c
+ static bool PlusLessEqual(const Bignum& a, const Bignum& b, const Bignum& c) {
+ return PlusCompare(a, b, c) <= 0;
+ }
+ // Returns a + b < c
+ static bool PlusLess(const Bignum& a, const Bignum& b, const Bignum& c) {
+ return PlusCompare(a, b, c) < 0;
+ }
+ private:
+ typedef uint32_t Chunk;
+ typedef uint64_t DoubleChunk;
+
+ static const int kChunkSize = sizeof(Chunk) * 8;
+ static const int kDoubleChunkSize = sizeof(DoubleChunk) * 8;
+ // With bigit size of 28 we loose some bits, but a double still fits easily
+ // into two chunks, and more importantly we can use the Comba multiplication.
+ static const int kBigitSize = 28;
+ static const Chunk kBigitMask = (1 << kBigitSize) - 1;
+ // Every instance allocates kBigitLength chunks on the stack. Bignums cannot
+ // grow. There are no checks if the stack-allocated space is sufficient.
+ static const int kBigitCapacity = kMaxSignificantBits / kBigitSize;
+
+ void EnsureCapacity(int size) {
+ if (size > kBigitCapacity) {
+ UNREACHABLE();
+ }
+ }
+ void Align(const Bignum& other);
+ void Clamp();
+ bool IsClamped() const;
+ void Zero();
+ // Requires this to have enough capacity (no tests done).
+ // Updates used_digits_ if necessary.
+ // shift_amount must be < kBigitSize.
+ void BigitsShiftLeft(int shift_amount);
+ // BigitLength includes the "hidden" digits encoded in the exponent.
+ int BigitLength() const { return used_digits_ + exponent_; }
+ Chunk BigitAt(int index) const;
+ void SubtractTimes(const Bignum& other, int factor);
+
+ Chunk bigits_buffer_[kBigitCapacity];
+ // A BufferReference backed by bigits_buffer_. This way accesses to the array are
+ // checked for out-of-bounds errors.
+ BufferReference<Chunk> bigits_;
+ int used_digits_;
+ // The Bignum's value equals value(bigits_) * 2^(exponent_ * kBigitSize).
+ int exponent_;
+
+ DC_DISALLOW_COPY_AND_ASSIGN(Bignum);
+};
+
+} // namespace double_conversion
+} // namespace WTF
#endif // DOUBLE_CONVERSION_BIGNUM_H_
#include "config.h"
-#include <stdarg.h>
-#include <limits.h>
-#include <math.h>
+#include <climits>
+#include <cmath>
+#include <cstdarg>
-#include "utils.h"
-#include "cached-powers.h"
+#include <wtf/dtoa/utils.h>
-namespace WTF {
+#include <wtf/dtoa/cached-powers.h>
+namespace WTF {
namespace double_conversion {
-
- struct CachedPower {
- uint64_t significand;
- int16_t binary_exponent;
- int16_t decimal_exponent;
- };
-
- constexpr static const double kD_1_LOG2_10 = 0.30102999566398114; // 1 / lg(10)
- constexpr static const CachedPower kCachedPowers[] = {
- {UINT64_2PART_C(0xfa8fd5a0, 081c0288), -1220, -348},
- {UINT64_2PART_C(0xbaaee17f, a23ebf76), -1193, -340},
- {UINT64_2PART_C(0x8b16fb20, 3055ac76), -1166, -332},
- {UINT64_2PART_C(0xcf42894a, 5dce35ea), -1140, -324},
- {UINT64_2PART_C(0x9a6bb0aa, 55653b2d), -1113, -316},
- {UINT64_2PART_C(0xe61acf03, 3d1a45df), -1087, -308},
- {UINT64_2PART_C(0xab70fe17, c79ac6ca), -1060, -300},
- {UINT64_2PART_C(0xff77b1fc, bebcdc4f), -1034, -292},
- {UINT64_2PART_C(0xbe5691ef, 416bd60c), -1007, -284},
- {UINT64_2PART_C(0x8dd01fad, 907ffc3c), -980, -276},
- {UINT64_2PART_C(0xd3515c28, 31559a83), -954, -268},
- {UINT64_2PART_C(0x9d71ac8f, ada6c9b5), -927, -260},
- {UINT64_2PART_C(0xea9c2277, 23ee8bcb), -901, -252},
- {UINT64_2PART_C(0xaecc4991, 4078536d), -874, -244},
- {UINT64_2PART_C(0x823c1279, 5db6ce57), -847, -236},
- {UINT64_2PART_C(0xc2109436, 4dfb5637), -821, -228},
- {UINT64_2PART_C(0x9096ea6f, 3848984f), -794, -220},
- {UINT64_2PART_C(0xd77485cb, 25823ac7), -768, -212},
- {UINT64_2PART_C(0xa086cfcd, 97bf97f4), -741, -204},
- {UINT64_2PART_C(0xef340a98, 172aace5), -715, -196},
- {UINT64_2PART_C(0xb23867fb, 2a35b28e), -688, -188},
- {UINT64_2PART_C(0x84c8d4df, d2c63f3b), -661, -180},
- {UINT64_2PART_C(0xc5dd4427, 1ad3cdba), -635, -172},
- {UINT64_2PART_C(0x936b9fce, bb25c996), -608, -164},
- {UINT64_2PART_C(0xdbac6c24, 7d62a584), -582, -156},
- {UINT64_2PART_C(0xa3ab6658, 0d5fdaf6), -555, -148},
- {UINT64_2PART_C(0xf3e2f893, dec3f126), -529, -140},
- {UINT64_2PART_C(0xb5b5ada8, aaff80b8), -502, -132},
- {UINT64_2PART_C(0x87625f05, 6c7c4a8b), -475, -124},
- {UINT64_2PART_C(0xc9bcff60, 34c13053), -449, -116},
- {UINT64_2PART_C(0x964e858c, 91ba2655), -422, -108},
- {UINT64_2PART_C(0xdff97724, 70297ebd), -396, -100},
- {UINT64_2PART_C(0xa6dfbd9f, b8e5b88f), -369, -92},
- {UINT64_2PART_C(0xf8a95fcf, 88747d94), -343, -84},
- {UINT64_2PART_C(0xb9447093, 8fa89bcf), -316, -76},
- {UINT64_2PART_C(0x8a08f0f8, bf0f156b), -289, -68},
- {UINT64_2PART_C(0xcdb02555, 653131b6), -263, -60},
- {UINT64_2PART_C(0x993fe2c6, d07b7fac), -236, -52},
- {UINT64_2PART_C(0xe45c10c4, 2a2b3b06), -210, -44},
- {UINT64_2PART_C(0xaa242499, 697392d3), -183, -36},
- {UINT64_2PART_C(0xfd87b5f2, 8300ca0e), -157, -28},
- {UINT64_2PART_C(0xbce50864, 92111aeb), -130, -20},
- {UINT64_2PART_C(0x8cbccc09, 6f5088cc), -103, -12},
- {UINT64_2PART_C(0xd1b71758, e219652c), -77, -4},
- {UINT64_2PART_C(0x9c400000, 00000000), -50, 4},
- {UINT64_2PART_C(0xe8d4a510, 00000000), -24, 12},
- {UINT64_2PART_C(0xad78ebc5, ac620000), 3, 20},
- {UINT64_2PART_C(0x813f3978, f8940984), 30, 28},
- {UINT64_2PART_C(0xc097ce7b, c90715b3), 56, 36},
- {UINT64_2PART_C(0x8f7e32ce, 7bea5c70), 83, 44},
- {UINT64_2PART_C(0xd5d238a4, abe98068), 109, 52},
- {UINT64_2PART_C(0x9f4f2726, 179a2245), 136, 60},
- {UINT64_2PART_C(0xed63a231, d4c4fb27), 162, 68},
- {UINT64_2PART_C(0xb0de6538, 8cc8ada8), 189, 76},
- {UINT64_2PART_C(0x83c7088e, 1aab65db), 216, 84},
- {UINT64_2PART_C(0xc45d1df9, 42711d9a), 242, 92},
- {UINT64_2PART_C(0x924d692c, a61be758), 269, 100},
- {UINT64_2PART_C(0xda01ee64, 1a708dea), 295, 108},
- {UINT64_2PART_C(0xa26da399, 9aef774a), 322, 116},
- {UINT64_2PART_C(0xf209787b, b47d6b85), 348, 124},
- {UINT64_2PART_C(0xb454e4a1, 79dd1877), 375, 132},
- {UINT64_2PART_C(0x865b8692, 5b9bc5c2), 402, 140},
- {UINT64_2PART_C(0xc83553c5, c8965d3d), 428, 148},
- {UINT64_2PART_C(0x952ab45c, fa97a0b3), 455, 156},
- {UINT64_2PART_C(0xde469fbd, 99a05fe3), 481, 164},
- {UINT64_2PART_C(0xa59bc234, db398c25), 508, 172},
- {UINT64_2PART_C(0xf6c69a72, a3989f5c), 534, 180},
- {UINT64_2PART_C(0xb7dcbf53, 54e9bece), 561, 188},
- {UINT64_2PART_C(0x88fcf317, f22241e2), 588, 196},
- {UINT64_2PART_C(0xcc20ce9b, d35c78a5), 614, 204},
- {UINT64_2PART_C(0x98165af3, 7b2153df), 641, 212},
- {UINT64_2PART_C(0xe2a0b5dc, 971f303a), 667, 220},
- {UINT64_2PART_C(0xa8d9d153, 5ce3b396), 694, 228},
- {UINT64_2PART_C(0xfb9b7cd9, a4a7443c), 720, 236},
- {UINT64_2PART_C(0xbb764c4c, a7a44410), 747, 244},
- {UINT64_2PART_C(0x8bab8eef, b6409c1a), 774, 252},
- {UINT64_2PART_C(0xd01fef10, a657842c), 800, 260},
- {UINT64_2PART_C(0x9b10a4e5, e9913129), 827, 268},
- {UINT64_2PART_C(0xe7109bfb, a19c0c9d), 853, 276},
- {UINT64_2PART_C(0xac2820d9, 623bf429), 880, 284},
- {UINT64_2PART_C(0x80444b5e, 7aa7cf85), 907, 292},
- {UINT64_2PART_C(0xbf21e440, 03acdd2d), 933, 300},
- {UINT64_2PART_C(0x8e679c2f, 5e44ff8f), 960, 308},
- {UINT64_2PART_C(0xd433179d, 9c8cb841), 986, 316},
- {UINT64_2PART_C(0x9e19db92, b4e31ba9), 1013, 324},
- {UINT64_2PART_C(0xeb96bf6e, badf77d9), 1039, 332},
- {UINT64_2PART_C(0xaf87023b, 9bf0ee6b), 1066, 340},
- };
- constexpr static const int kCachedPowersLength { ARRAY_SIZE(kCachedPowers) };
- constexpr static const int kCachedPowersOffset { -kCachedPowers[0].decimal_exponent };
-
- const int PowersOfTenCache::kDecimalExponentDistance { kCachedPowers[1].decimal_exponent - kCachedPowers[0].decimal_exponent };
- const int PowersOfTenCache::kMinDecimalExponent { kCachedPowers[0].decimal_exponent };
- const int PowersOfTenCache::kMaxDecimalExponent { kCachedPowers[kCachedPowersLength - 1].decimal_exponent };
-
- void PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
- int min_exponent,
- int max_exponent,
- DiyFp* power,
- int* decimal_exponent) {
- UNUSED_PARAM(max_exponent);
- int kQ = DiyFp::kSignificandSize;
- double k = ceil((min_exponent + kQ - 1) * kD_1_LOG2_10);
- int foo = kCachedPowersOffset;
- int index =
- (foo + static_cast<int>(k) - 1) / kDecimalExponentDistance + 1;
- ASSERT(0 <= index && index < kCachedPowersLength);
- CachedPower cached_power = kCachedPowers[index];
- ASSERT(min_exponent <= cached_power.binary_exponent);
- ASSERT(cached_power.binary_exponent <= max_exponent);
- *decimal_exponent = cached_power.decimal_exponent;
- *power = DiyFp(cached_power.significand, cached_power.binary_exponent);
- }
-
-
- void PowersOfTenCache::GetCachedPowerForDecimalExponent(int requested_exponent,
- DiyFp* power,
- int* found_exponent) {
- ASSERT(kMinDecimalExponent <= requested_exponent);
- ASSERT(requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance);
- int index =
- (requested_exponent + kCachedPowersOffset) / kDecimalExponentDistance;
- CachedPower cached_power = kCachedPowers[index];
- *power = DiyFp(cached_power.significand, cached_power.binary_exponent);
- *found_exponent = cached_power.decimal_exponent;
- ASSERT(*found_exponent <= requested_exponent);
- ASSERT(requested_exponent < *found_exponent + kDecimalExponentDistance);
- }
-
-} // namespace double_conversion
-} // namespace WTF
+struct CachedPower {
+ uint64_t significand;
+ int16_t binary_exponent;
+ int16_t decimal_exponent;
+};
+
+constexpr static const CachedPower kCachedPowers[] = {
+ {UINT64_2PART_C(0xfa8fd5a0, 081c0288), -1220, -348},
+ {UINT64_2PART_C(0xbaaee17f, a23ebf76), -1193, -340},
+ {UINT64_2PART_C(0x8b16fb20, 3055ac76), -1166, -332},
+ {UINT64_2PART_C(0xcf42894a, 5dce35ea), -1140, -324},
+ {UINT64_2PART_C(0x9a6bb0aa, 55653b2d), -1113, -316},
+ {UINT64_2PART_C(0xe61acf03, 3d1a45df), -1087, -308},
+ {UINT64_2PART_C(0xab70fe17, c79ac6ca), -1060, -300},
+ {UINT64_2PART_C(0xff77b1fc, bebcdc4f), -1034, -292},
+ {UINT64_2PART_C(0xbe5691ef, 416bd60c), -1007, -284},
+ {UINT64_2PART_C(0x8dd01fad, 907ffc3c), -980, -276},
+ {UINT64_2PART_C(0xd3515c28, 31559a83), -954, -268},
+ {UINT64_2PART_C(0x9d71ac8f, ada6c9b5), -927, -260},
+ {UINT64_2PART_C(0xea9c2277, 23ee8bcb), -901, -252},
+ {UINT64_2PART_C(0xaecc4991, 4078536d), -874, -244},
+ {UINT64_2PART_C(0x823c1279, 5db6ce57), -847, -236},
+ {UINT64_2PART_C(0xc2109436, 4dfb5637), -821, -228},
+ {UINT64_2PART_C(0x9096ea6f, 3848984f), -794, -220},
+ {UINT64_2PART_C(0xd77485cb, 25823ac7), -768, -212},
+ {UINT64_2PART_C(0xa086cfcd, 97bf97f4), -741, -204},
+ {UINT64_2PART_C(0xef340a98, 172aace5), -715, -196},
+ {UINT64_2PART_C(0xb23867fb, 2a35b28e), -688, -188},
+ {UINT64_2PART_C(0x84c8d4df, d2c63f3b), -661, -180},
+ {UINT64_2PART_C(0xc5dd4427, 1ad3cdba), -635, -172},
+ {UINT64_2PART_C(0x936b9fce, bb25c996), -608, -164},
+ {UINT64_2PART_C(0xdbac6c24, 7d62a584), -582, -156},
+ {UINT64_2PART_C(0xa3ab6658, 0d5fdaf6), -555, -148},
+ {UINT64_2PART_C(0xf3e2f893, dec3f126), -529, -140},
+ {UINT64_2PART_C(0xb5b5ada8, aaff80b8), -502, -132},
+ {UINT64_2PART_C(0x87625f05, 6c7c4a8b), -475, -124},
+ {UINT64_2PART_C(0xc9bcff60, 34c13053), -449, -116},
+ {UINT64_2PART_C(0x964e858c, 91ba2655), -422, -108},
+ {UINT64_2PART_C(0xdff97724, 70297ebd), -396, -100},
+ {UINT64_2PART_C(0xa6dfbd9f, b8e5b88f), -369, -92},
+ {UINT64_2PART_C(0xf8a95fcf, 88747d94), -343, -84},
+ {UINT64_2PART_C(0xb9447093, 8fa89bcf), -316, -76},
+ {UINT64_2PART_C(0x8a08f0f8, bf0f156b), -289, -68},
+ {UINT64_2PART_C(0xcdb02555, 653131b6), -263, -60},
+ {UINT64_2PART_C(0x993fe2c6, d07b7fac), -236, -52},
+ {UINT64_2PART_C(0xe45c10c4, 2a2b3b06), -210, -44},
+ {UINT64_2PART_C(0xaa242499, 697392d3), -183, -36},
+ {UINT64_2PART_C(0xfd87b5f2, 8300ca0e), -157, -28},
+ {UINT64_2PART_C(0xbce50864, 92111aeb), -130, -20},
+ {UINT64_2PART_C(0x8cbccc09, 6f5088cc), -103, -12},
+ {UINT64_2PART_C(0xd1b71758, e219652c), -77, -4},
+ {UINT64_2PART_C(0x9c400000, 00000000), -50, 4},
+ {UINT64_2PART_C(0xe8d4a510, 00000000), -24, 12},
+ {UINT64_2PART_C(0xad78ebc5, ac620000), 3, 20},
+ {UINT64_2PART_C(0x813f3978, f8940984), 30, 28},
+ {UINT64_2PART_C(0xc097ce7b, c90715b3), 56, 36},
+ {UINT64_2PART_C(0x8f7e32ce, 7bea5c70), 83, 44},
+ {UINT64_2PART_C(0xd5d238a4, abe98068), 109, 52},
+ {UINT64_2PART_C(0x9f4f2726, 179a2245), 136, 60},
+ {UINT64_2PART_C(0xed63a231, d4c4fb27), 162, 68},
+ {UINT64_2PART_C(0xb0de6538, 8cc8ada8), 189, 76},
+ {UINT64_2PART_C(0x83c7088e, 1aab65db), 216, 84},
+ {UINT64_2PART_C(0xc45d1df9, 42711d9a), 242, 92},
+ {UINT64_2PART_C(0x924d692c, a61be758), 269, 100},
+ {UINT64_2PART_C(0xda01ee64, 1a708dea), 295, 108},
+ {UINT64_2PART_C(0xa26da399, 9aef774a), 322, 116},
+ {UINT64_2PART_C(0xf209787b, b47d6b85), 348, 124},
+ {UINT64_2PART_C(0xb454e4a1, 79dd1877), 375, 132},
+ {UINT64_2PART_C(0x865b8692, 5b9bc5c2), 402, 140},
+ {UINT64_2PART_C(0xc83553c5, c8965d3d), 428, 148},
+ {UINT64_2PART_C(0x952ab45c, fa97a0b3), 455, 156},
+ {UINT64_2PART_C(0xde469fbd, 99a05fe3), 481, 164},
+ {UINT64_2PART_C(0xa59bc234, db398c25), 508, 172},
+ {UINT64_2PART_C(0xf6c69a72, a3989f5c), 534, 180},
+ {UINT64_2PART_C(0xb7dcbf53, 54e9bece), 561, 188},
+ {UINT64_2PART_C(0x88fcf317, f22241e2), 588, 196},
+ {UINT64_2PART_C(0xcc20ce9b, d35c78a5), 614, 204},
+ {UINT64_2PART_C(0x98165af3, 7b2153df), 641, 212},
+ {UINT64_2PART_C(0xe2a0b5dc, 971f303a), 667, 220},
+ {UINT64_2PART_C(0xa8d9d153, 5ce3b396), 694, 228},
+ {UINT64_2PART_C(0xfb9b7cd9, a4a7443c), 720, 236},
+ {UINT64_2PART_C(0xbb764c4c, a7a44410), 747, 244},
+ {UINT64_2PART_C(0x8bab8eef, b6409c1a), 774, 252},
+ {UINT64_2PART_C(0xd01fef10, a657842c), 800, 260},
+ {UINT64_2PART_C(0x9b10a4e5, e9913129), 827, 268},
+ {UINT64_2PART_C(0xe7109bfb, a19c0c9d), 853, 276},
+ {UINT64_2PART_C(0xac2820d9, 623bf429), 880, 284},
+ {UINT64_2PART_C(0x80444b5e, 7aa7cf85), 907, 292},
+ {UINT64_2PART_C(0xbf21e440, 03acdd2d), 933, 300},
+ {UINT64_2PART_C(0x8e679c2f, 5e44ff8f), 960, 308},
+ {UINT64_2PART_C(0xd433179d, 9c8cb841), 986, 316},
+ {UINT64_2PART_C(0x9e19db92, b4e31ba9), 1013, 324},
+ {UINT64_2PART_C(0xeb96bf6e, badf77d9), 1039, 332},
+ {UINT64_2PART_C(0xaf87023b, 9bf0ee6b), 1066, 340},
+};
+
+constexpr static const int kCachedPowersOffset = 348; // -1 * the first decimal_exponent.
+constexpr static const double kD_1_LOG2_10 = 0.30102999566398114; // 1 / lg(10)
+// Difference between the decimal exponents in the table above.
+const int PowersOfTenCache::kDecimalExponentDistance = 8;
+const int PowersOfTenCache::kMinDecimalExponent = -348;
+const int PowersOfTenCache::kMaxDecimalExponent = 340;
+
+void PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
+ int min_exponent,
+ int max_exponent,
+ DiyFp* power,
+ int* decimal_exponent) {
+ int kQ = DiyFp::kSignificandSize;
+ double k = ceil((min_exponent + kQ - 1) * kD_1_LOG2_10);
+ int foo = kCachedPowersOffset;
+ int index =
+ (foo + static_cast<int>(k) - 1) / kDecimalExponentDistance + 1;
+ ASSERT(0 <= index && index < static_cast<int>(ARRAY_SIZE(kCachedPowers)));
+ CachedPower cached_power = kCachedPowers[index];
+ ASSERT(min_exponent <= cached_power.binary_exponent);
+ (void) max_exponent; // Mark variable as used.
+ ASSERT(cached_power.binary_exponent <= max_exponent);
+ *decimal_exponent = cached_power.decimal_exponent;
+ *power = DiyFp(cached_power.significand, cached_power.binary_exponent);
+}
+
+
+void PowersOfTenCache::GetCachedPowerForDecimalExponent(int requested_exponent,
+ DiyFp* power,
+ int* found_exponent) {
+ ASSERT(kMinDecimalExponent <= requested_exponent);
+ ASSERT(requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance);
+ int index =
+ (requested_exponent + kCachedPowersOffset) / kDecimalExponentDistance;
+ CachedPower cached_power = kCachedPowers[index];
+ *power = DiyFp(cached_power.significand, cached_power.binary_exponent);
+ *found_exponent = cached_power.decimal_exponent;
+ ASSERT(*found_exponent <= requested_exponent);
+ ASSERT(requested_exponent < *found_exponent + kDecimalExponentDistance);
+}
+
+} // namespace double_conversion
+} // namespace WTF
#ifndef DOUBLE_CONVERSION_CACHED_POWERS_H_
#define DOUBLE_CONVERSION_CACHED_POWERS_H_
-#include "diy-fp.h"
+#include <wtf/dtoa/diy-fp.h>
namespace WTF {
-
namespace double_conversion {
-
- class PowersOfTenCache {
- public:
-
- // Not all powers of ten are cached. The decimal exponent of two neighboring
- // cached numbers will differ by kDecimalExponentDistance.
- static const int kDecimalExponentDistance;
-
- static const int kMinDecimalExponent;
- static const int kMaxDecimalExponent;
-
- // Returns a cached power-of-ten with a binary exponent in the range
- // [min_exponent; max_exponent] (boundaries included).
- static void GetCachedPowerForBinaryExponentRange(int min_exponent,
- int max_exponent,
- DiyFp* power,
- int* decimal_exponent);
-
- // Returns a cached power of ten x ~= 10^k such that
- // k <= decimal_exponent < k + kCachedPowersDecimalDistance.
- // The given decimal_exponent must satisfy
- // kMinDecimalExponent <= requested_exponent, and
- // requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance.
- static void GetCachedPowerForDecimalExponent(int requested_exponent,
- DiyFp* power,
- int* found_exponent);
- };
-
-} // namespace double_conversion
-} // namespace WTF
+class PowersOfTenCache {
+ public:
+
+ // Not all powers of ten are cached. The decimal exponent of two neighboring
+ // cached numbers will differ by kDecimalExponentDistance.
+ static const int kDecimalExponentDistance;
+
+ static const int kMinDecimalExponent;
+ static const int kMaxDecimalExponent;
+
+ // Returns a cached power-of-ten with a binary exponent in the range
+ // [min_exponent; max_exponent] (boundaries included).
+ static void GetCachedPowerForBinaryExponentRange(int min_exponent,
+ int max_exponent,
+ DiyFp* power,
+ int* decimal_exponent);
+
+ // Returns a cached power of ten x ~= 10^k such that
+ // k <= decimal_exponent < k + kCachedPowersDecimalDistance.
+ // The given decimal_exponent must satisfy
+ // kMinDecimalExponent <= requested_exponent, and
+ // requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance.
+ static void GetCachedPowerForDecimalExponent(int requested_exponent,
+ DiyFp* power,
+ int* found_exponent);
+};
+
+} // namespace double_conversion
+} // namespace WTF
#endif // DOUBLE_CONVERSION_CACHED_POWERS_H_
#include "config.h"
-#include "diy-fp.h"
-#include "utils.h"
+#include <wtf/dtoa/diy-fp.h>
+#include <wtf/dtoa/utils.h>
namespace WTF {
-
namespace double_conversion {
-
- void DiyFp::Multiply(const DiyFp& other) {
- // Simply "emulates" a 128 bit multiplication.
- // However: the resulting number only contains 64 bits. The least
- // significant 64 bits are only used for rounding the most significant 64
- // bits.
- const uint64_t kM32 = 0xFFFFFFFFU;
- uint64_t a = f_ >> 32;
- uint64_t b = f_ & kM32;
- uint64_t c = other.f_ >> 32;
- uint64_t d = other.f_ & kM32;
- uint64_t ac = a * c;
- uint64_t bc = b * c;
- uint64_t ad = a * d;
- uint64_t bd = b * d;
- uint64_t tmp = (bd >> 32) + (ad & kM32) + (bc & kM32);
- // By adding 1U << 31 to tmp we round the final result.
- // Halfway cases will be round up.
- tmp += 1U << 31;
- uint64_t result_f = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32);
- e_ += other.e_ + 64;
- f_ = result_f;
- }
-
-} // namespace double_conversion
-} // namespace WTF
+void DiyFp::Multiply(const DiyFp& other) {
+ // Simply "emulates" a 128 bit multiplication.
+ // However: the resulting number only contains 64 bits. The least
+ // significant 64 bits are only used for rounding the most significant 64
+ // bits.
+ const uint64_t kM32 = 0xFFFFFFFFU;
+ uint64_t a = f_ >> 32;
+ uint64_t b = f_ & kM32;
+ uint64_t c = other.f_ >> 32;
+ uint64_t d = other.f_ & kM32;
+ uint64_t ac = a * c;
+ uint64_t bc = b * c;
+ uint64_t ad = a * d;
+ uint64_t bd = b * d;
+ uint64_t tmp = (bd >> 32) + (ad & kM32) + (bc & kM32);
+ // By adding 1U << 31 to tmp we round the final result.
+ // Halfway cases will be round up.
+ tmp += 1U << 31;
+ uint64_t result_f = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32);
+ e_ += other.e_ + 64;
+ f_ = result_f;
+}
+
+} // namespace double_conversion
+} // namespace WTF
#ifndef DOUBLE_CONVERSION_DIY_FP_H_
#define DOUBLE_CONVERSION_DIY_FP_H_
-#include "utils.h"
+#include <wtf/dtoa/utils.h>
namespace WTF {
-
namespace double_conversion {
-
- // This "Do It Yourself Floating Point" class implements a floating-point number
- // with a uint64 significand and an int exponent. Normalized DiyFp numbers will
- // have the most significant bit of the significand set.
- // Multiplication and Subtraction do not normalize their results.
- // DiyFp are not designed to contain special doubles (NaN and Infinity).
- class DiyFp {
- public:
- static const int kSignificandSize = 64;
-
- DiyFp() : f_(0), e_(0) {}
- DiyFp(uint64_t f, int e) : f_(f), e_(e) {}
-
- // this = this - other.
- // The exponents of both numbers must be the same and the significand of this
- // must be bigger than the significand of other.
- // The result will not be normalized.
- void Subtract(const DiyFp& other) {
- ASSERT(e_ == other.e_);
- ASSERT(f_ >= other.f_);
- f_ -= other.f_;
- }
-
- // Returns a - b.
- // The exponents of both numbers must be the same and this must be bigger
- // than other. The result will not be normalized.
- static DiyFp Minus(const DiyFp& a, const DiyFp& b) {
- DiyFp result = a;
- result.Subtract(b);
- return result;
- }
-
-
- // this = this * other.
- void Multiply(const DiyFp& other);
-
- // returns a * b;
- static DiyFp Times(const DiyFp& a, const DiyFp& b) {
- DiyFp result = a;
- result.Multiply(b);
- return result;
- }
-
- void Normalize() {
- ASSERT(f_ != 0);
- uint64_t f = f_;
- int e = e_;
-
- // This method is mainly called for normalizing boundaries. In general
- // boundaries need to be shifted by 10 bits. We thus optimize for this case.
- const uint64_t k10MSBits = UINT64_2PART_C(0xFFC00000, 00000000);
- while ((f & k10MSBits) == 0) {
- f <<= 10;
- e -= 10;
- }
- while ((f & kUint64MSB) == 0) {
- f <<= 1;
- e--;
- }
- f_ = f;
- e_ = e;
- }
-
- static DiyFp Normalize(const DiyFp& a) {
- DiyFp result = a;
- result.Normalize();
- return result;
- }
-
- uint64_t f() const { return f_; }
- int e() const { return e_; }
-
- void set_f(uint64_t new_value) { f_ = new_value; }
- void set_e(int new_value) { e_ = new_value; }
-
- private:
- static const uint64_t kUint64MSB = UINT64_2PART_C(0x80000000, 00000000);
-
- uint64_t f_;
- int e_;
- };
-
-} // namespace double_conversion
-} // namespace WTF
+// This "Do It Yourself Floating Point" class implements a floating-point number
+// with a uint64 significand and an int exponent. Normalized DiyFp numbers will
+// have the most significant bit of the significand set.
+// Multiplication and Subtraction do not normalize their results.
+// DiyFp are not designed to contain special doubles (NaN and Infinity).
+class DiyFp {
+ public:
+ static const int kSignificandSize = 64;
+
+ DiyFp() : f_(0), e_(0) {}
+ DiyFp(uint64_t significand, int exponent) : f_(significand), e_(exponent) {}
+
+ // this = this - other.
+ // The exponents of both numbers must be the same and the significand of this
+ // must be bigger than the significand of other.
+ // The result will not be normalized.
+ void Subtract(const DiyFp& other) {
+ ASSERT(e_ == other.e_);
+ ASSERT(f_ >= other.f_);
+ f_ -= other.f_;
+ }
+
+ // Returns a - b.
+ // The exponents of both numbers must be the same and this must be bigger
+ // than other. The result will not be normalized.
+ static DiyFp Minus(const DiyFp& a, const DiyFp& b) {
+ DiyFp result = a;
+ result.Subtract(b);
+ return result;
+ }
+
+
+ // this = this * other.
+ void Multiply(const DiyFp& other);
+
+ // returns a * b;
+ static DiyFp Times(const DiyFp& a, const DiyFp& b) {
+ DiyFp result = a;
+ result.Multiply(b);
+ return result;
+ }
+
+ void Normalize() {
+ ASSERT(f_ != 0);
+ uint64_t significand = f_;
+ int exponent = e_;
+
+ // This method is mainly called for normalizing boundaries. In general
+ // boundaries need to be shifted by 10 bits. We thus optimize for this case.
+ const uint64_t k10MSBits = UINT64_2PART_C(0xFFC00000, 00000000);
+ while ((significand & k10MSBits) == 0) {
+ significand <<= 10;
+ exponent -= 10;
+ }
+ while ((significand & kUint64MSB) == 0) {
+ significand <<= 1;
+ exponent--;
+ }
+ f_ = significand;
+ e_ = exponent;
+ }
+
+ static DiyFp Normalize(const DiyFp& a) {
+ DiyFp result = a;
+ result.Normalize();
+ return result;
+ }
+
+ uint64_t f() const { return f_; }
+ int e() const { return e_; }
+
+ void set_f(uint64_t new_value) { f_ = new_value; }
+ void set_e(int new_value) { e_ = new_value; }
+
+ private:
+ static const uint64_t kUint64MSB = UINT64_2PART_C(0x80000000, 00000000);
+
+ uint64_t f_;
+ int e_;
+};
+
+} // namespace double_conversion
+} // namespace WTF
#endif // DOUBLE_CONVERSION_DIY_FP_H_
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#include "config.h"
-#include "double-conversion.h"
-
-#include "bignum-dtoa.h"
-#include "double.h"
-#include "fast-dtoa.h"
-#include "fixed-dtoa.h"
-#include "strtod.h"
-#include "utils.h"
-#include <limits.h>
-#include <math.h>
+
+#include <climits>
+#include <locale>
+#include <cmath>
+
+#include <wtf/dtoa/double-conversion.h>
+
+#include <wtf/dtoa/bignum-dtoa.h>
+#include <wtf/dtoa/fast-dtoa.h>
+#include <wtf/dtoa/fixed-dtoa.h>
+#include <wtf/dtoa/ieee.h>
+#include <wtf/dtoa/strtod.h>
+#include <wtf/dtoa/utils.h>
+
#include <wtf/ASCIICType.h>
namespace WTF {
-
namespace double_conversion {
-
- const DoubleToStringConverter& DoubleToStringConverter::EcmaScriptConverter() {
- int flags = UNIQUE_ZERO | EMIT_POSITIVE_EXPONENT_SIGN;
- static DoubleToStringConverter converter(flags,
- "Infinity",
- "NaN",
- 'e',
- -6, 21,
- 6, 0);
- return converter;
+
+const DoubleToStringConverter& DoubleToStringConverter::EcmaScriptConverter() {
+ int flags = UNIQUE_ZERO | EMIT_POSITIVE_EXPONENT_SIGN;
+ static DoubleToStringConverter converter(flags,
+ "Infinity",
+ "NaN",
+ 'e',
+ -6, 21,
+ 6, 0);
+ return converter;
+}
+
+
+bool DoubleToStringConverter::HandleSpecialValues(
+ double value,
+ StringBuilder* result_builder) const {
+ Double double_inspect(value);
+ if (double_inspect.IsInfinite()) {
+ if (infinity_symbol_ == NULL) return false;
+ if (value < 0) {
+ result_builder->AddCharacter('-');
}
-
-
- bool DoubleToStringConverter::HandleSpecialValues(
- double value,
- StringBuilder* result_builder) const {
- Double double_inspect(value);
- if (double_inspect.IsInfinite()) {
- if (infinity_symbol_ == NULL) return false;
- if (value < 0) {
- result_builder->AddCharacter('-');
- }
- result_builder->AddString(infinity_symbol_);
- return true;
- }
- if (double_inspect.IsNan()) {
- if (nan_symbol_ == NULL) return false;
- result_builder->AddString(nan_symbol_);
- return true;
- }
- return false;
+ result_builder->AddString(infinity_symbol_);
+ return true;
+ }
+ if (double_inspect.IsNan()) {
+ if (nan_symbol_ == NULL) return false;
+ result_builder->AddString(nan_symbol_);
+ return true;
+ }
+ return false;
+}
+
+
+void DoubleToStringConverter::CreateExponentialRepresentation(
+ const char* decimal_digits,
+ int length,
+ int exponent,
+ StringBuilder* result_builder) const {
+ ASSERT(length != 0);
+ result_builder->AddCharacter(decimal_digits[0]);
+ if (length != 1) {
+ result_builder->AddCharacter('.');
+ result_builder->AddSubstring(&decimal_digits[1], length-1);
+ }
+ result_builder->AddCharacter(exponent_character_);
+ if (exponent < 0) {
+ result_builder->AddCharacter('-');
+ exponent = -exponent;
+ } else {
+ if ((flags_ & EMIT_POSITIVE_EXPONENT_SIGN) != 0) {
+ result_builder->AddCharacter('+');
}
-
-
- void DoubleToStringConverter::CreateExponentialRepresentation(
- const char* decimal_digits,
- int length,
- int exponent,
- StringBuilder* result_builder) const {
- ASSERT(length != 0);
- result_builder->AddCharacter(decimal_digits[0]);
- if (length != 1) {
- result_builder->AddCharacter('.');
- result_builder->AddSubstring(&decimal_digits[1], length-1);
- }
- result_builder->AddCharacter(exponent_character_);
- if (exponent < 0) {
- result_builder->AddCharacter('-');
- exponent = -exponent;
- } else {
- if ((flags_ & EMIT_POSITIVE_EXPONENT_SIGN) != 0) {
- result_builder->AddCharacter('+');
- }
- }
- if (exponent == 0) {
- result_builder->AddCharacter('0');
- return;
- }
- ASSERT(exponent < 1e4);
- const int kMaxExponentLength = 5;
- char buffer[kMaxExponentLength + 1];
- int first_char_pos = kMaxExponentLength;
- buffer[first_char_pos] = '\0';
- while (exponent > 0) {
- buffer[--first_char_pos] = '0' + (exponent % 10);
- exponent /= 10;
- }
- result_builder->AddSubstring(&buffer[first_char_pos],
- kMaxExponentLength - first_char_pos);
+ }
+ if (exponent == 0) {
+ result_builder->AddCharacter('0');
+ return;
+ }
+ ASSERT(exponent < 1e4);
+ const int kMaxExponentLength = 5;
+ char buffer[kMaxExponentLength + 1];
+ buffer[kMaxExponentLength] = '\0';
+ int first_char_pos = kMaxExponentLength;
+ while (exponent > 0) {
+ buffer[--first_char_pos] = '0' + (exponent % 10);
+ exponent /= 10;
+ }
+ result_builder->AddSubstring(&buffer[first_char_pos],
+ kMaxExponentLength - first_char_pos);
+}
+
+
+void DoubleToStringConverter::CreateDecimalRepresentation(
+ const char* decimal_digits,
+ int length,
+ int decimal_point,
+ int digits_after_point,
+ StringBuilder* result_builder) const {
+ // Create a representation that is padded with zeros if needed.
+ if (decimal_point <= 0) {
+ // "0.00000decimal_rep" or "0.000decimal_rep00".
+ result_builder->AddCharacter('0');
+ if (digits_after_point > 0) {
+ result_builder->AddCharacter('.');
+ result_builder->AddPadding('0', -decimal_point);
+ ASSERT(length <= digits_after_point - (-decimal_point));
+ result_builder->AddSubstring(decimal_digits, length);
+ int remaining_digits = digits_after_point - (-decimal_point) - length;
+ result_builder->AddPadding('0', remaining_digits);
}
-
-
- void DoubleToStringConverter::CreateDecimalRepresentation(
- const char* decimal_digits,
- int length,
- int decimal_point,
- int digits_after_point,
- StringBuilder* result_builder) const {
- // Create a representation that is padded with zeros if needed.
- if (decimal_point <= 0) {
- // "0.00000decimal_rep".
- result_builder->AddCharacter('0');
- if (digits_after_point > 0) {
- result_builder->AddCharacter('.');
- result_builder->AddPadding('0', -decimal_point);
- ASSERT(length <= digits_after_point - (-decimal_point));
- result_builder->AddSubstring(decimal_digits, length);
- int remaining_digits = digits_after_point - (-decimal_point) - length;
- result_builder->AddPadding('0', remaining_digits);
- }
- } else if (decimal_point >= length) {
- // "decimal_rep0000.00000" or "decimal_rep.0000"
- result_builder->AddSubstring(decimal_digits, length);
- result_builder->AddPadding('0', decimal_point - length);
- if (digits_after_point > 0) {
- result_builder->AddCharacter('.');
- result_builder->AddPadding('0', digits_after_point);
- }
- } else {
- // "decima.l_rep000"
- ASSERT(digits_after_point > 0);
- result_builder->AddSubstring(decimal_digits, decimal_point);
- result_builder->AddCharacter('.');
- ASSERT(length - decimal_point <= digits_after_point);
- result_builder->AddSubstring(&decimal_digits[decimal_point],
- length - decimal_point);
- int remaining_digits = digits_after_point - (length - decimal_point);
- result_builder->AddPadding('0', remaining_digits);
- }
- if (digits_after_point == 0) {
- if ((flags_ & EMIT_TRAILING_DECIMAL_POINT) != 0) {
- result_builder->AddCharacter('.');
- }
- if ((flags_ & EMIT_TRAILING_ZERO_AFTER_POINT) != 0) {
- result_builder->AddCharacter('0');
- }
- }
+ } else if (decimal_point >= length) {
+ // "decimal_rep0000.00000" or "decimal_rep.0000".
+ result_builder->AddSubstring(decimal_digits, length);
+ result_builder->AddPadding('0', decimal_point - length);
+ if (digits_after_point > 0) {
+ result_builder->AddCharacter('.');
+ result_builder->AddPadding('0', digits_after_point);
}
-
-
- bool DoubleToStringConverter::ToShortest(double value,
- StringBuilder* result_builder) const {
- if (Double(value).IsSpecial()) {
- return HandleSpecialValues(value, result_builder);
- }
-
- int decimal_point;
- bool sign;
- const int kDecimalRepCapacity = kBase10MaximalLength + 1;
- char decimal_rep[kDecimalRepCapacity];
- int decimal_rep_length;
-
- DoubleToAscii(value, SHORTEST, 0, decimal_rep, kDecimalRepCapacity,
- &sign, &decimal_rep_length, &decimal_point);
-
- bool unique_zero = (flags_ & UNIQUE_ZERO) != 0;
- if (sign && (value != 0.0 || !unique_zero)) {
- result_builder->AddCharacter('-');
- }
-
- int exponent = decimal_point - 1;
- if ((decimal_in_shortest_low_ <= exponent) &&
- (exponent < decimal_in_shortest_high_)) {
- CreateDecimalRepresentation(decimal_rep, decimal_rep_length,
- decimal_point,
- Max(0, decimal_rep_length - decimal_point),
- result_builder);
- } else {
- CreateExponentialRepresentation(decimal_rep, decimal_rep_length, exponent,
- result_builder);
- }
- return true;
+ } else {
+ // "decima.l_rep000".
+ ASSERT(digits_after_point > 0);
+ result_builder->AddSubstring(decimal_digits, decimal_point);
+ result_builder->AddCharacter('.');
+ ASSERT(length - decimal_point <= digits_after_point);
+ result_builder->AddSubstring(&decimal_digits[decimal_point],
+ length - decimal_point);
+ int remaining_digits = digits_after_point - (length - decimal_point);
+ result_builder->AddPadding('0', remaining_digits);
+ }
+ if (digits_after_point == 0) {
+ if ((flags_ & EMIT_TRAILING_DECIMAL_POINT) != 0) {
+ result_builder->AddCharacter('.');
}
-
-
- bool DoubleToStringConverter::ToFixed(double value,
- int requested_digits,
- StringBuilder* result_builder) const {
- ASSERT(kMaxFixedDigitsBeforePoint == 60);
- const double kFirstNonFixed = 1e60;
-
- if (Double(value).IsSpecial()) {
- return HandleSpecialValues(value, result_builder);
- }
-
- if (requested_digits > kMaxFixedDigitsAfterPoint) return false;
- if (value >= kFirstNonFixed || value <= -kFirstNonFixed) return false;
-
- // Find a sufficiently precise decimal representation of n.
- int decimal_point;
- bool sign;
- // Add space for the '\0' byte.
- const int kDecimalRepCapacity =
- kMaxFixedDigitsBeforePoint + kMaxFixedDigitsAfterPoint + 1;
- char decimal_rep[kDecimalRepCapacity];
- int decimal_rep_length;
- DoubleToAscii(value, FIXED, requested_digits,
- decimal_rep, kDecimalRepCapacity,
- &sign, &decimal_rep_length, &decimal_point);
-
- bool unique_zero = ((flags_ & UNIQUE_ZERO) != 0);
- if (sign && (value != 0.0 || !unique_zero)) {
- result_builder->AddCharacter('-');
- }
-
- CreateDecimalRepresentation(decimal_rep, decimal_rep_length, decimal_point,
- requested_digits, result_builder);
- return true;
+ if ((flags_ & EMIT_TRAILING_ZERO_AFTER_POINT) != 0) {
+ result_builder->AddCharacter('0');
}
-
-
- bool DoubleToStringConverter::ToExponential(
- double value,
- int requested_digits,
- StringBuilder* result_builder) const {
- if (Double(value).IsSpecial()) {
- return HandleSpecialValues(value, result_builder);
- }
-
- if (requested_digits < -1) return false;
- if (requested_digits > kMaxExponentialDigits) return false;
-
- int decimal_point;
- bool sign;
- // Add space for digit before the decimal point and the '\0' character.
- const int kDecimalRepCapacity = kMaxExponentialDigits + 2;
- ASSERT(kDecimalRepCapacity > kBase10MaximalLength);
- char decimal_rep[kDecimalRepCapacity];
- int decimal_rep_length;
-
- if (requested_digits == -1) {
- DoubleToAscii(value, SHORTEST, 0,
- decimal_rep, kDecimalRepCapacity,
- &sign, &decimal_rep_length, &decimal_point);
- } else {
- DoubleToAscii(value, PRECISION, requested_digits + 1,
- decimal_rep, kDecimalRepCapacity,
- &sign, &decimal_rep_length, &decimal_point);
- ASSERT(decimal_rep_length <= requested_digits + 1);
-
- for (int i = decimal_rep_length; i < requested_digits + 1; ++i) {
- decimal_rep[i] = '0';
- }
- decimal_rep_length = requested_digits + 1;
- }
-
- bool unique_zero = ((flags_ & UNIQUE_ZERO) != 0);
- if (sign && (value != 0.0 || !unique_zero)) {
- result_builder->AddCharacter('-');
- }
-
- int exponent = decimal_point - 1;
- CreateExponentialRepresentation(decimal_rep,
- decimal_rep_length,
- exponent,
- result_builder);
- return true;
+ }
+}
+
+
+bool DoubleToStringConverter::ToShortestIeeeNumber(
+ double value,
+ StringBuilder* result_builder,
+ DoubleToStringConverter::DtoaMode mode) const {
+ ASSERT(mode == SHORTEST || mode == SHORTEST_SINGLE);
+ if (Double(value).IsSpecial()) {
+ return HandleSpecialValues(value, result_builder);
+ }
+
+ int decimal_point;
+ bool sign;
+ const int kDecimalRepCapacity = kBase10MaximalLength + 1;
+ char decimal_rep[kDecimalRepCapacity];
+ int decimal_rep_length;
+
+ DoubleToAscii(value, mode, 0, decimal_rep, kDecimalRepCapacity,
+ &sign, &decimal_rep_length, &decimal_point);
+
+ bool unique_zero = (flags_ & UNIQUE_ZERO) != 0;
+ if (sign && (value != 0.0 || !unique_zero)) {
+ result_builder->AddCharacter('-');
+ }
+
+ int exponent = decimal_point - 1;
+ if ((decimal_in_shortest_low_ <= exponent) &&
+ (exponent < decimal_in_shortest_high_)) {
+ CreateDecimalRepresentation(decimal_rep, decimal_rep_length,
+ decimal_point,
+ Max(0, decimal_rep_length - decimal_point),
+ result_builder);
+ } else {
+ CreateExponentialRepresentation(decimal_rep, decimal_rep_length, exponent,
+ result_builder);
+ }
+ return true;
+}
+
+
+bool DoubleToStringConverter::ToFixed(double value,
+ int requested_digits,
+ StringBuilder* result_builder) const {
+ ASSERT(kMaxFixedDigitsBeforePoint == 60);
+ const double kFirstNonFixed = 1e60;
+
+ if (Double(value).IsSpecial()) {
+ return HandleSpecialValues(value, result_builder);
+ }
+
+ if (requested_digits > kMaxFixedDigitsAfterPoint) return false;
+ if (value >= kFirstNonFixed || value <= -kFirstNonFixed) return false;
+
+ // Find a sufficiently precise decimal representation of n.
+ int decimal_point;
+ bool sign;
+ // Add space for the '\0' byte.
+ const int kDecimalRepCapacity =
+ kMaxFixedDigitsBeforePoint + kMaxFixedDigitsAfterPoint + 1;
+ char decimal_rep[kDecimalRepCapacity];
+ int decimal_rep_length;
+ DoubleToAscii(value, FIXED, requested_digits,
+ decimal_rep, kDecimalRepCapacity,
+ &sign, &decimal_rep_length, &decimal_point);
+
+ bool unique_zero = ((flags_ & UNIQUE_ZERO) != 0);
+ if (sign && (value != 0.0 || !unique_zero)) {
+ result_builder->AddCharacter('-');
+ }
+
+ CreateDecimalRepresentation(decimal_rep, decimal_rep_length, decimal_point,
+ requested_digits, result_builder);
+ return true;
+}
+
+
+bool DoubleToStringConverter::ToExponential(
+ double value,
+ int requested_digits,
+ StringBuilder* result_builder) const {
+ if (Double(value).IsSpecial()) {
+ return HandleSpecialValues(value, result_builder);
+ }
+
+ if (requested_digits < -1) return false;
+ if (requested_digits > kMaxExponentialDigits) return false;
+
+ int decimal_point;
+ bool sign;
+ // Add space for digit before the decimal point and the '\0' character.
+ const int kDecimalRepCapacity = kMaxExponentialDigits + 2;
+ ASSERT(kDecimalRepCapacity > kBase10MaximalLength);
+ char decimal_rep[kDecimalRepCapacity];
+ int decimal_rep_length;
+
+ if (requested_digits == -1) {
+ DoubleToAscii(value, SHORTEST, 0,
+ decimal_rep, kDecimalRepCapacity,
+ &sign, &decimal_rep_length, &decimal_point);
+ } else {
+ DoubleToAscii(value, PRECISION, requested_digits + 1,
+ decimal_rep, kDecimalRepCapacity,
+ &sign, &decimal_rep_length, &decimal_point);
+ ASSERT(decimal_rep_length <= requested_digits + 1);
+
+ for (int i = decimal_rep_length; i < requested_digits + 1; ++i) {
+ decimal_rep[i] = '0';
}
-
-
- bool DoubleToStringConverter::ToPrecision(double value,
- int precision,
- StringBuilder* result_builder) const {
- if (Double(value).IsSpecial()) {
- return HandleSpecialValues(value, result_builder);
- }
-
- if (precision < kMinPrecisionDigits || precision > kMaxPrecisionDigits) {
- return false;
- }
-
- // Find a sufficiently precise decimal representation of n.
- int decimal_point;
- bool sign;
- // Add one for the terminating null character.
- const int kDecimalRepCapacity = kMaxPrecisionDigits + 1;
- char decimal_rep[kDecimalRepCapacity];
- int decimal_rep_length;
-
- DoubleToAscii(value, PRECISION, precision,
- decimal_rep, kDecimalRepCapacity,
- &sign, &decimal_rep_length, &decimal_point);
- ASSERT(decimal_rep_length <= precision);
-
- bool unique_zero = ((flags_ & UNIQUE_ZERO) != 0);
- if (sign && (value != 0.0 || !unique_zero)) {
- result_builder->AddCharacter('-');
- }
-
- // The exponent if we print the number as x.xxeyyy. That is with the
- // decimal point after the first digit.
- int exponent = decimal_point - 1;
-
- int extra_zero = ((flags_ & EMIT_TRAILING_ZERO_AFTER_POINT) != 0) ? 1 : 0;
- if ((-decimal_point + 1 > max_leading_padding_zeroes_in_precision_mode_) ||
- (decimal_point - precision + extra_zero >
- max_trailing_padding_zeroes_in_precision_mode_)) {
- // Fill buffer to contain 'precision' digits.
- // Usually the buffer is already at the correct length, but 'DoubleToAscii'
- // is allowed to return less characters.
- for (int i = decimal_rep_length; i < precision; ++i) {
- decimal_rep[i] = '0';
- }
-
- CreateExponentialRepresentation(decimal_rep,
- precision,
- exponent,
- result_builder);
- } else {
- CreateDecimalRepresentation(decimal_rep, decimal_rep_length, decimal_point,
- Max(0, precision - decimal_point),
- result_builder);
- }
- return true;
+ decimal_rep_length = requested_digits + 1;
+ }
+
+ bool unique_zero = ((flags_ & UNIQUE_ZERO) != 0);
+ if (sign && (value != 0.0 || !unique_zero)) {
+ result_builder->AddCharacter('-');
+ }
+
+ int exponent = decimal_point - 1;
+ CreateExponentialRepresentation(decimal_rep,
+ decimal_rep_length,
+ exponent,
+ result_builder);
+ return true;
+}
+
+
+bool DoubleToStringConverter::ToPrecision(double value,
+ int precision,
+ StringBuilder* result_builder) const {
+ if (Double(value).IsSpecial()) {
+ return HandleSpecialValues(value, result_builder);
+ }
+
+ if (precision < kMinPrecisionDigits || precision > kMaxPrecisionDigits) {
+ return false;
+ }
+
+ // Find a sufficiently precise decimal representation of n.
+ int decimal_point;
+ bool sign;
+ // Add one for the terminating null character.
+ const int kDecimalRepCapacity = kMaxPrecisionDigits + 1;
+ char decimal_rep[kDecimalRepCapacity];
+ int decimal_rep_length;
+
+ DoubleToAscii(value, PRECISION, precision,
+ decimal_rep, kDecimalRepCapacity,
+ &sign, &decimal_rep_length, &decimal_point);
+ ASSERT(decimal_rep_length <= precision);
+
+ bool unique_zero = ((flags_ & UNIQUE_ZERO) != 0);
+ if (sign && (value != 0.0 || !unique_zero)) {
+ result_builder->AddCharacter('-');
+ }
+
+ // The exponent if we print the number as x.xxeyyy. That is with the
+ // decimal point after the first digit.
+ int exponent = decimal_point - 1;
+
+ int extra_zero = ((flags_ & EMIT_TRAILING_ZERO_AFTER_POINT) != 0) ? 1 : 0;
+ if ((-decimal_point + 1 > max_leading_padding_zeroes_in_precision_mode_) ||
+ (decimal_point - precision + extra_zero >
+ max_trailing_padding_zeroes_in_precision_mode_)) {
+ // Fill buffer to contain 'precision' digits.
+ // Usually the buffer is already at the correct length, but 'DoubleToAscii'
+ // is allowed to return less characters.
+ for (int i = decimal_rep_length; i < precision; ++i) {
+ decimal_rep[i] = '0';
}
-
-
- static BignumDtoaMode DtoaToBignumDtoaMode(
- DoubleToStringConverter::DtoaMode dtoa_mode) {
- switch (dtoa_mode) {
- case DoubleToStringConverter::SHORTEST: return BIGNUM_DTOA_SHORTEST;
- case DoubleToStringConverter::FIXED: return BIGNUM_DTOA_FIXED;
- case DoubleToStringConverter::PRECISION: return BIGNUM_DTOA_PRECISION;
- default:
- UNREACHABLE();
- return BIGNUM_DTOA_SHORTEST; // To silence compiler.
- }
+
+ CreateExponentialRepresentation(decimal_rep,
+ precision,
+ exponent,
+ result_builder);
+ } else {
+ CreateDecimalRepresentation(decimal_rep, decimal_rep_length, decimal_point,
+ Max(0, precision - decimal_point),
+ result_builder);
+ }
+ return true;
+}
+
+
+static BignumDtoaMode DtoaToBignumDtoaMode(
+ DoubleToStringConverter::DtoaMode dtoa_mode) {
+ switch (dtoa_mode) {
+ case DoubleToStringConverter::SHORTEST: return BIGNUM_DTOA_SHORTEST;
+ case DoubleToStringConverter::SHORTEST_SINGLE:
+ return BIGNUM_DTOA_SHORTEST_SINGLE;
+ case DoubleToStringConverter::FIXED: return BIGNUM_DTOA_FIXED;
+ case DoubleToStringConverter::PRECISION: return BIGNUM_DTOA_PRECISION;
+ default:
+ UNREACHABLE();
+ }
+}
+
+
+void DoubleToStringConverter::DoubleToAscii(double v,
+ DtoaMode mode,
+ int requested_digits,
+ char* buffer,
+ int buffer_length,
+ bool* sign,
+ int* length,
+ int* point) {
+ BufferReference<char> bufferReference(buffer, buffer_length);
+ ASSERT(!Double(v).IsSpecial());
+ ASSERT(mode == SHORTEST || mode == SHORTEST_SINGLE || requested_digits >= 0);
+
+ if (Double(v).Sign() < 0) {
+ *sign = true;
+ v = -v;
+ } else {
+ *sign = false;
+ }
+
+ if (mode == PRECISION && requested_digits == 0) {
+ bufferReference[0] = '\0';
+ *length = 0;
+ return;
+ }
+
+ if (v == 0) {
+ bufferReference[0] = '0';
+ bufferReference[1] = '\0';
+ *length = 1;
+ *point = 1;
+ return;
+ }
+
+ bool fast_worked;
+ switch (mode) {
+ case SHORTEST:
+ fast_worked = FastDtoa(v, FAST_DTOA_SHORTEST, 0, bufferReference, length, point);
+ break;
+ case SHORTEST_SINGLE:
+ fast_worked = FastDtoa(v, FAST_DTOA_SHORTEST_SINGLE, 0,
+ bufferReference, length, point);
+ break;
+ case FIXED:
+ fast_worked = FastFixedDtoa(v, requested_digits, bufferReference, length, point);
+ break;
+ case PRECISION:
+ fast_worked = FastDtoa(v, FAST_DTOA_PRECISION, requested_digits,
+ bufferReference, length, point);
+ break;
+ default:
+ fast_worked = false;
+ UNREACHABLE();
+ }
+ if (fast_worked) return;
+
+ // If the fast dtoa didn't succeed use the slower bignum version.
+ BignumDtoaMode bignum_mode = DtoaToBignumDtoaMode(mode);
+ BignumDtoa(v, bignum_mode, requested_digits, bufferReference, length, point);
+ bufferReference[*length] = '\0';
+}
+
+// Maximum number of significant digits in decimal representation.
+// The longest possible double in decimal representation is
+// (2^53 - 1) * 2 ^ -1074 that is (2 ^ 53 - 1) * 5 ^ 1074 / 10 ^ 1074
+// (768 digits). If we parse a number whose first digits are equal to a
+// mean of 2 adjacent doubles (that could have up to 769 digits) the result
+// must be rounded to the bigger one unless the tail consists of zeros, so
+// we don't need to preserve all the digits.
+const int kMaxSignificantDigits = 772;
+
+
+static double SignedZero(bool sign) {
+ return sign ? -0.0 : 0.0;
+}
+
+
+// Returns true, when the iterator is equal to end.
+template<class Iterator>
+static inline bool Advance(Iterator* it, Iterator& end) {
+ ++(*it);
+ return *it == end;
+}
+
+template <typename FloatingPointType>
+inline FloatingPointType StringToFloatingPointType(BufferReference<const char> buffer, int exponent);
+
+template <>
+inline double StringToFloatingPointType<double>(BufferReference<const char> buffer, int exponent) {
+ return Strtod(buffer, exponent);
+}
+
+template <>
+inline float StringToFloatingPointType<float>(BufferReference<const char> buffer, int exponent) {
+ return Strtof(buffer, exponent);
+}
+
+template <typename FloatingPointType, class Iterator>
+static FloatingPointType StringToIeee(
+ Iterator input,
+ size_t length,
+ size_t* processed_characters_count) {
+ static_assert(std::is_floating_point<FloatingPointType>::value, "Only floating point types are allowed.");
+
+ Iterator current = input;
+ Iterator end = input + length;
+
+ *processed_characters_count = 0;
+
+ // To make sure that iterator dereferencing is valid the following
+ // convention is used:
+ // 1. Each '++current' statement is followed by check for equality to 'end'.
+ // 3. If 'current' becomes equal to 'end' the function returns or goes to
+ // 'parsing_done'.
+ // 4. 'current' is not dereferenced after the 'parsing_done' label.
+ // 5. Code before 'parsing_done' may rely on 'current != end'.
+
+ if (current == end) return 0.0;
+
+ // The longest form of simplified number is: "-<significant digits>.1eXXX\0".
+ const int kBufferSize = kMaxSignificantDigits + 10;
+ char buffer[kBufferSize]; // NOLINT: size is known at compile time.
+ int buffer_pos = 0;
+
+ // Exponent will be adjusted if insignificant digits of the integer part
+ // or insignificant leading zeros of the fractional part are dropped.
+ int exponent = 0;
+ int significant_digits = 0;
+ int insignificant_digits = 0;
+ bool nonzero_digit_dropped = false;
+
+ bool sign = false;
+
+ if (*current == '+' || *current == '-') {
+ sign = (*current == '-');
+ ++current;
+ if (current == end) return 0.0;
+ }
+
+ bool leading_zero = false;
+ if (*current == '0') {
+ if (Advance(¤t, end)) {
+ *processed_characters_count = static_cast<size_t>(current - input);
+ return SignedZero(sign);
}
-
-
- void DoubleToStringConverter::DoubleToAscii(double v,
- DtoaMode mode,
- int requested_digits,
- char* buffer,
- int buffer_length,
- bool* sign,
- int* length,
- int* point) {
- BufferReference<char> vector(buffer, buffer_length);
- ASSERT(!Double(v).IsSpecial());
- ASSERT(mode == SHORTEST || requested_digits >= 0);
-
- if (Double(v).Sign() < 0) {
- *sign = true;
- v = -v;
- } else {
- *sign = false;
- }
-
- if (mode == PRECISION && requested_digits == 0) {
- vector[0] = '\0';
- *length = 0;
- return;
- }
-
- if (v == 0) {
- vector[0] = '0';
- vector[1] = '\0';
- *length = 1;
- *point = 1;
- return;
- }
-
- bool fast_worked;
- switch (mode) {
- case SHORTEST:
- fast_worked = FastDtoa(v, FAST_DTOA_SHORTEST, 0, vector, length, point);
- break;
- case FIXED:
- fast_worked = FastFixedDtoa(v, requested_digits, vector, length, point);
- break;
- case PRECISION:
- fast_worked = FastDtoa(v, FAST_DTOA_PRECISION, requested_digits,
- vector, length, point);
- break;
- default:
- UNREACHABLE();
- fast_worked = false;
- }
- if (fast_worked) return;
-
- // If the fast dtoa didn't succeed use the slower bignum version.
- BignumDtoaMode bignum_mode = DtoaToBignumDtoaMode(mode);
- BignumDtoa(v, bignum_mode, requested_digits, vector, length, point);
- vector[*length] = '\0';
+
+ leading_zero = true;
+
+ // Ignore leading zeros in the integer part.
+ while (*current == '0') {
+ if (Advance(¤t, end)) {
+ *processed_characters_count = static_cast<size_t>(current - input);
+ return SignedZero(sign);
+ }
}
-
-
- // Maximum number of significant digits in decimal representation.
- // The longest possible double in decimal representation is
- // (2^53 - 1) * 2 ^ -1074 that is (2 ^ 53 - 1) * 5 ^ 1074 / 10 ^ 1074
- // (768 digits). If we parse a number whose first digits are equal to a
- // mean of 2 adjacent doubles (that could have up to 769 digits) the result
- // must be rounded to the bigger one unless the tail consists of zeros, so
- // we don't need to preserve all the digits.
- const int kMaxSignificantDigits = 772;
-
-
- static double SignedZero(bool sign) {
- return sign ? -0.0 : 0.0;
+ }
+
+ // Copy significant digits of the integer part (if any) to the buffer.
+ while (isASCIIDigit(*current)) {
+ if (significant_digits < kMaxSignificantDigits) {
+ ASSERT(buffer_pos < kBufferSize);
+ buffer[buffer_pos++] = static_cast<char>(*current);
+ significant_digits++;
+ } else {
+ insignificant_digits++; // Move the digit into the exponential part.
+ nonzero_digit_dropped = nonzero_digit_dropped || *current != '0';
}
-
-
- double StringToDoubleConverter::StringToDouble(
- const char* input,
- size_t length,
- size_t* processed_characters_count) {
- const char* current = input;
- const char* end = input + length;
-
- *processed_characters_count = 0;
-
- // To make sure that iterator dereferencing is valid the following
- // convention is used:
- // 1. Each '++current' statement is followed by check for equality to 'end'.
- // 3. If 'current' becomes equal to 'end' the function returns or goes to
- // 'parsing_done'.
- // 4. 'current' is not dereferenced after the 'parsing_done' label.
- // 5. Code before 'parsing_done' may rely on 'current != end'.
- if (current == end) return 0.0;
-
- // The longest form of simplified number is: "-<significant digits>.1eXXX\0".
- const unsigned kBufferSize = kMaxSignificantDigits + 10;
- char buffer[kBufferSize]; // NOLINT: size is known at compile time.
- unsigned buffer_pos = 0;
-
- // Exponent will be adjusted if insignificant digits of the integer part
- // or insignificant leading zeros of the fractional part are dropped.
- int exponent = 0;
- int significant_digits = 0;
- int insignificant_digits = 0;
- bool nonzero_digit_dropped = false;
- bool sign = false;
-
- if (*current == '+' || *current == '-') {
- sign = (*current == '-');
- ++current;
- if (current == end) return 0.0;
- }
-
- bool leading_zero = false;
- if (*current == '0') {
- ++current;
- if (current == end) {
- *processed_characters_count = current - input;
- return SignedZero(sign);
- }
-
- leading_zero = true;
-
- // Ignore leading zeros in the integer part.
- while (*current == '0') {
- ++current;
- if (current == end) {
- *processed_characters_count = current - input;
- return SignedZero(sign);
- }
- }
- }
-
- // Copy significant digits of the integer part (if any) to the buffer.
- while (isASCIIDigit(*current)) {
- if (significant_digits < kMaxSignificantDigits) {
- ASSERT(buffer_pos < kBufferSize);
- buffer[buffer_pos++] = static_cast<char>(*current);
- significant_digits++;
- } else {
- insignificant_digits++; // Move the digit into the exponential part.
- nonzero_digit_dropped = nonzero_digit_dropped || *current != '0';
- }
- ++current;
- if (current == end) goto parsing_done;
- }
-
- if (*current == '.') {
- ++current;
- if (current == end) {
- if (significant_digits == 0 && !leading_zero) {
- return 0.0;
- } else {
- goto parsing_done;
- }
- }
-
- if (significant_digits == 0) {
- // Integer part consists of 0 or is absent. Significant digits start after
- // leading zeros (if any).
- while (*current == '0') {
- ++current;
- if (current == end) {
- *processed_characters_count = current - input;
- return SignedZero(sign);
- }
- exponent--; // Move this 0 into the exponent.
- }
- }
-
- // There is a fractional part.
- while (isASCIIDigit(*current)) {
- if (significant_digits < kMaxSignificantDigits) {
- ASSERT(buffer_pos < kBufferSize);
- buffer[buffer_pos++] = static_cast<char>(*current);
- significant_digits++;
- exponent--;
- } else {
- // Ignore insignificant digits in the fractional part.
- nonzero_digit_dropped = nonzero_digit_dropped || *current != '0';
- }
- ++current;
- if (current == end) goto parsing_done;
- }
- }
-
- if (!leading_zero && exponent == 0 && significant_digits == 0) {
- // If leading_zeros is true then the string contains zeros.
- // If exponent < 0 then string was [+-]\.0*...
- // If significant_digits != 0 the string is not equal to 0.
- // Otherwise there are no digits in the string.
- return 0.0;
- }
-
- // Parse exponential part.
- if (*current == 'e' || *current == 'E') {
- ++current;
- if (current == end) {
- --current;
- goto parsing_done;
- }
- char sign = 0;
- if (*current == '+' || *current == '-') {
- sign = static_cast<char>(*current);
- ++current;
- if (current == end) {
- current -= 2;
- goto parsing_done;
- }
- }
-
- if (*current < '0' || *current > '9') {
- if (sign)
- --current;
- --current;
- goto parsing_done;
- }
-
- const int max_exponent = INT_MAX / 2;
- ASSERT(-max_exponent / 2 <= exponent && exponent <= max_exponent / 2);
- int num = 0;
- do {
- // Check overflow.
- int digit = *current - '0';
- if (num >= max_exponent / 10
- && !(num == max_exponent / 10 && digit <= max_exponent % 10)) {
- num = max_exponent;
- } else {
- num = num * 10 + digit;
- }
- ++current;
- } while (current != end && isASCIIDigit(*current));
-
- exponent += (sign == '-' ? -num : num);
- }
-
- parsing_done:
- exponent += insignificant_digits;
-
- if (nonzero_digit_dropped) {
- buffer[buffer_pos++] = '1';
- exponent--;
+ if (Advance(¤t, end)) goto parsing_done;
+ }
+
+ if (*current == '.') {
+ if (Advance(¤t, end)) {
+ if (significant_digits == 0 && !leading_zero) {
+ return 0.0;
+ } else {
+ goto parsing_done;
+ }
+ }
+
+ if (significant_digits == 0) {
+ // Integer part consists of 0 or is absent. Significant digits start after
+ // leading zeros (if any).
+ while (*current == '0') {
+ if (Advance(¤t, end)) {
+ *processed_characters_count = static_cast<size_t>(current - input);
+ return SignedZero(sign);
}
-
+ exponent--; // Move this 0 into the exponent.
+ }
+ }
+
+ // There is a fractional part.
+ // We don't emit a '.', but adjust the exponent instead.
+ while (isASCIIDigit(*current)) {
+ if (significant_digits < kMaxSignificantDigits) {
ASSERT(buffer_pos < kBufferSize);
- buffer[buffer_pos] = '\0';
-
- double converted = Strtod(BufferReference<const char>(buffer, buffer_pos), exponent);
- *processed_characters_count = current - input;
- return sign? -converted: converted;
+ buffer[buffer_pos++] = static_cast<char>(*current);
+ significant_digits++;
+ exponent--;
+ } else {
+ // Ignore insignificant digits in the fractional part.
+ nonzero_digit_dropped = nonzero_digit_dropped || *current != '0';
+ }
+ if (Advance(¤t, end)) goto parsing_done;
+ }
+ }
+
+ if (!leading_zero && exponent == 0 && significant_digits == 0) {
+ // If leading_zeros is true then the string contains zeros.
+ // If exponent < 0 then string was [+-]\.0*...
+ // If significant_digits != 0 the string is not equal to 0.
+ // Otherwise there are no digits in the string.
+ return 0.0;
+ }
+
+ // Parse exponential part.
+ if (*current == 'e' || *current == 'E') {
+ ++current;
+ if (current == end) {
+ --current;
+ goto parsing_done;
+ }
+ char exponen_sign = 0;
+ if (*current == '+' || *current == '-') {
+ exponen_sign = static_cast<char>(*current);
+ ++current;
+ if (current == end) {
+ current -= 2;
+ goto parsing_done;
+ }
}
-
-} // namespace double_conversion
-} // namespace WTF
+ if (*current < '0' || *current > '9') {
+ if (exponen_sign)
+ --current;
+ --current;
+ goto parsing_done;
+ }
+
+ const int max_exponent = INT_MAX / 2;
+ ASSERT(-max_exponent / 2 <= exponent && exponent <= max_exponent / 2);
+ int num = 0;
+ do {
+ // Check overflow.
+ int digit = *current - '0';
+ if (num >= max_exponent / 10
+ && !(num == max_exponent / 10 && digit <= max_exponent % 10)) {
+ num = max_exponent;
+ } else {
+ num = num * 10 + digit;
+ }
+ ++current;
+ } while (current != end && isASCIIDigit(*current));
+
+ exponent += (exponen_sign == '-' ? -num : num);
+ }
+
+ parsing_done:
+ exponent += insignificant_digits;
+
+ if (nonzero_digit_dropped) {
+ buffer[buffer_pos++] = '1';
+ exponent--;
+ }
+
+ ASSERT(buffer_pos < kBufferSize);
+ buffer[buffer_pos] = '\0';
+
+ auto converted = StringToFloatingPointType<FloatingPointType>(BufferReference<const char>(buffer, buffer_pos), exponent);
+ *processed_characters_count = static_cast<size_t>(current - input);
+ return sign? -converted: converted;
+}
+
+double StringToDoubleConverter::StringToDouble(
+ const char* buffer,
+ size_t length,
+ size_t* processed_characters_count) {
+ return StringToIeee<double>(buffer, length, processed_characters_count);
+}
+
+
+double StringToDoubleConverter::StringToDouble(
+ const uc16* buffer,
+ size_t length,
+ size_t* processed_characters_count) {
+ return StringToIeee<double>(buffer, length, processed_characters_count);
+}
+
+
+float StringToDoubleConverter::StringToFloat(
+ const char* buffer,
+ size_t length,
+ size_t* processed_characters_count) {
+ return StringToIeee<float>(buffer, length, processed_characters_count);
+}
+
+
+float StringToDoubleConverter::StringToFloat(
+ const uc16* buffer,
+ size_t length,
+ size_t* processed_characters_count) {
+ return StringToIeee<float>(buffer, length, processed_characters_count);
+}
+
+} // namespace double_conversion
+} // namespace WTF
-// Copyright 2010 the V8 project authors. All rights reserved.
+// Copyright 2012 the V8 project authors. All rights reserved.
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
#include <wtf/dtoa/utils.h>
namespace WTF {
-
namespace double_conversion {
-
- class DoubleToStringConverter {
- public:
- // When calling ToFixed with a double > 10^kMaxFixedDigitsBeforePoint
- // or a requested_digits parameter > kMaxFixedDigitsAfterPoint then the
- // function returns false.
- static const int kMaxFixedDigitsBeforePoint = 60;
- static const int kMaxFixedDigitsAfterPoint = 60;
-
- // When calling ToExponential with a requested_digits
- // parameter > kMaxExponentialDigits then the function returns false.
- static const int kMaxExponentialDigits = 120;
-
- // When calling ToPrecision with a requested_digits
- // parameter < kMinPrecisionDigits or requested_digits > kMaxPrecisionDigits
- // then the function returns false.
- static const int kMinPrecisionDigits = 1;
- static const int kMaxPrecisionDigits = 120;
-
- enum Flags {
- NO_FLAGS = 0,
- EMIT_POSITIVE_EXPONENT_SIGN = 1,
- EMIT_TRAILING_DECIMAL_POINT = 2,
- EMIT_TRAILING_ZERO_AFTER_POINT = 4,
- UNIQUE_ZERO = 8
- };
-
- // Flags should be a bit-or combination of the possible Flags-enum.
- // - NO_FLAGS: no special flags.
- // - EMIT_POSITIVE_EXPONENT_SIGN: when the number is converted into exponent
- // form, emits a '+' for positive exponents. Example: 1.2e+2.
- // - EMIT_TRAILING_DECIMAL_POINT: when the input number is an integer and is
- // converted into decimal format then a trailing decimal point is appended.
- // Example: 2345.0 is converted to "2345.".
- // - EMIT_TRAILING_ZERO_AFTER_POINT: in addition to a trailing decimal point
- // emits a trailing '0'-character. This flag requires the
- // EXMIT_TRAILING_DECIMAL_POINT flag.
- // Example: 2345.0 is converted to "2345.0".
- // - UNIQUE_ZERO: "-0.0" is converted to "0.0".
- //
- // Infinity symbol and nan_symbol provide the string representation for these
- // special values. If the string is NULL and the special value is encountered
- // then the conversion functions return false.
- //
- // The exponent_character is used in exponential representations. It is
- // usually 'e' or 'E'.
- //
- // When converting to the shortest representation the converter will
- // represent input numbers in decimal format if they are in the interval
- // [10^decimal_in_shortest_low; 10^decimal_in_shortest_high[
- // (lower boundary included, greater boundary excluded).
- // Example: with decimal_in_shortest_low = -6 and
- // decimal_in_shortest_high = 21:
- // ToShortest(0.000001) -> "0.000001"
- // ToShortest(0.0000001) -> "1e-7"
- // ToShortest(111111111111111111111.0) -> "111111111111111110000"
- // ToShortest(100000000000000000000.0) -> "100000000000000000000"
- // ToShortest(1111111111111111111111.0) -> "1.1111111111111111e+21"
- //
- // When converting to precision mode the converter may add
- // max_leading_padding_zeroes before returning the number in exponential
- // format.
- // Example with max_leading_padding_zeroes_in_precision_mode = 6.
- // ToPrecision(0.0000012345, 2) -> "0.0000012"
- // ToPrecision(0.00000012345, 2) -> "1.2e-7"
- // Similarily the converter may add up to
- // max_trailing_padding_zeroes_in_precision_mode in precision mode to avoid
- // returning an exponential representation. A zero added by the
- // EMIT_TRAILING_ZERO_AFTER_POINT flag is counted for this limit.
- // Examples for max_trailing_padding_zeroes_in_precision_mode = 1:
- // ToPrecision(230.0, 2) -> "230"
- // ToPrecision(230.0, 2) -> "230." with EMIT_TRAILING_DECIMAL_POINT.
- // ToPrecision(230.0, 2) -> "2.3e2" with EMIT_TRAILING_ZERO_AFTER_POINT.
- DoubleToStringConverter(int flags,
- const char* infinity_symbol,
- const char* nan_symbol,
- char exponent_character,
- int decimal_in_shortest_low,
- int decimal_in_shortest_high,
- int max_leading_padding_zeroes_in_precision_mode,
- int max_trailing_padding_zeroes_in_precision_mode)
- : flags_(flags),
+
+class DoubleToStringConverter {
+ public:
+ // When calling ToFixed with a double > 10^kMaxFixedDigitsBeforePoint
+ // or a requested_digits parameter > kMaxFixedDigitsAfterPoint then the
+ // function returns false.
+ static const int kMaxFixedDigitsBeforePoint = 60;
+ static const int kMaxFixedDigitsAfterPoint = 60;
+
+ // When calling ToExponential with a requested_digits
+ // parameter > kMaxExponentialDigits then the function returns false.
+ static const int kMaxExponentialDigits = 120;
+
+ // When calling ToPrecision with a requested_digits
+ // parameter < kMinPrecisionDigits or requested_digits > kMaxPrecisionDigits
+ // then the function returns false.
+ static const int kMinPrecisionDigits = 1;
+ static const int kMaxPrecisionDigits = 120;
+
+ enum Flags {
+ NO_FLAGS = 0,
+ EMIT_POSITIVE_EXPONENT_SIGN = 1,
+ EMIT_TRAILING_DECIMAL_POINT = 2,
+ EMIT_TRAILING_ZERO_AFTER_POINT = 4,
+ UNIQUE_ZERO = 8
+ };
+
+ // Flags should be a bit-or combination of the possible Flags-enum.
+ // - NO_FLAGS: no special flags.
+ // - EMIT_POSITIVE_EXPONENT_SIGN: when the number is converted into exponent
+ // form, emits a '+' for positive exponents. Example: 1.2e+2.
+ // - EMIT_TRAILING_DECIMAL_POINT: when the input number is an integer and is
+ // converted into decimal format then a trailing decimal point is appended.
+ // Example: 2345.0 is converted to "2345.".
+ // - EMIT_TRAILING_ZERO_AFTER_POINT: in addition to a trailing decimal point
+ // emits a trailing '0'-character. This flag requires the
+ // EXMIT_TRAILING_DECIMAL_POINT flag.
+ // Example: 2345.0 is converted to "2345.0".
+ // - UNIQUE_ZERO: "-0.0" is converted to "0.0".
+ //
+ // Infinity symbol and nan_symbol provide the string representation for these
+ // special values. If the string is NULL and the special value is encountered
+ // then the conversion functions return false.
+ //
+ // The exponent_character is used in exponential representations. It is
+ // usually 'e' or 'E'.
+ //
+ // When converting to the shortest representation the converter will
+ // represent input numbers in decimal format if they are in the interval
+ // [10^decimal_in_shortest_low; 10^decimal_in_shortest_high[
+ // (lower boundary included, greater boundary excluded).
+ // Example: with decimal_in_shortest_low = -6 and
+ // decimal_in_shortest_high = 21:
+ // ToShortest(0.000001) -> "0.000001"
+ // ToShortest(0.0000001) -> "1e-7"
+ // ToShortest(111111111111111111111.0) -> "111111111111111110000"
+ // ToShortest(100000000000000000000.0) -> "100000000000000000000"
+ // ToShortest(1111111111111111111111.0) -> "1.1111111111111111e+21"
+ //
+ // When converting to precision mode the converter may add
+ // max_leading_padding_zeroes before returning the number in exponential
+ // format.
+ // Example with max_leading_padding_zeroes_in_precision_mode = 6.
+ // ToPrecision(0.0000012345, 2) -> "0.0000012"
+ // ToPrecision(0.00000012345, 2) -> "1.2e-7"
+ // Similarily the converter may add up to
+ // max_trailing_padding_zeroes_in_precision_mode in precision mode to avoid
+ // returning an exponential representation. A zero added by the
+ // EMIT_TRAILING_ZERO_AFTER_POINT flag is counted for this limit.
+ // Examples for max_trailing_padding_zeroes_in_precision_mode = 1:
+ // ToPrecision(230.0, 2) -> "230"
+ // ToPrecision(230.0, 2) -> "230." with EMIT_TRAILING_DECIMAL_POINT.
+ // ToPrecision(230.0, 2) -> "2.3e2" with EMIT_TRAILING_ZERO_AFTER_POINT.
+ DoubleToStringConverter(int flags,
+ const char* infinity_symbol,
+ const char* nan_symbol,
+ char exponent_character,
+ int decimal_in_shortest_low,
+ int decimal_in_shortest_high,
+ int max_leading_padding_zeroes_in_precision_mode,
+ int max_trailing_padding_zeroes_in_precision_mode)
+ : flags_(flags),
infinity_symbol_(infinity_symbol),
nan_symbol_(nan_symbol),
exponent_character_(exponent_character),
decimal_in_shortest_low_(decimal_in_shortest_low),
decimal_in_shortest_high_(decimal_in_shortest_high),
max_leading_padding_zeroes_in_precision_mode_(
- max_leading_padding_zeroes_in_precision_mode),
+ max_leading_padding_zeroes_in_precision_mode),
max_trailing_padding_zeroes_in_precision_mode_(
- max_trailing_padding_zeroes_in_precision_mode) {
- // When 'trailing zero after the point' is set, then 'trailing point'
- // must be set too.
- ASSERT(((flags & EMIT_TRAILING_DECIMAL_POINT) != 0) ||
- !((flags & EMIT_TRAILING_ZERO_AFTER_POINT) != 0));
- }
-
- // Returns a converter following the EcmaScript specification.
- WTF_EXPORT_PRIVATE static const DoubleToStringConverter& EcmaScriptConverter();
-
- // Computes the shortest string of digits that correctly represent the input
- // number. Depending on decimal_in_shortest_low and decimal_in_shortest_high
- // (see constructor) it then either returns a decimal representation, or an
- // exponential representation.
- // Example with decimal_in_shortest_low = -6,
- // decimal_in_shortest_high = 21,
- // EMIT_POSITIVE_EXPONENT_SIGN activated, and
- // EMIT_TRAILING_DECIMAL_POINT deactived:
- // ToShortest(0.000001) -> "0.000001"
- // ToShortest(0.0000001) -> "1e-7"
- // ToShortest(111111111111111111111.0) -> "111111111111111110000"
- // ToShortest(100000000000000000000.0) -> "100000000000000000000"
- // ToShortest(1111111111111111111111.0) -> "1.1111111111111111e+21"
- //
- // Note: the conversion may round the output if the returned string
- // is accurate enough to uniquely identify the input-number.
- // For example the most precise representation of the double 9e59 equals
- // "899999999999999918767229449717619953810131273674690656206848", but
- // the converter will return the shorter (but still correct) "9e59".
- //
- // Returns true if the conversion succeeds. The conversion always succeeds
- // except when the input value is special and no infinity_symbol or
- // nan_symbol has been given to the constructor.
- bool ToShortest(double value, StringBuilder* result_builder) const;
-
-
- // Computes a decimal representation with a fixed number of digits after the
- // decimal point. The last emitted digit is rounded.
- //
- // Examples:
- // ToFixed(3.12, 1) -> "3.1"
- // ToFixed(3.1415, 3) -> "3.142"
- // ToFixed(1234.56789, 4) -> "1234.5679"
- // ToFixed(1.23, 5) -> "1.23000"
- // ToFixed(0.1, 4) -> "0.1000"
- // ToFixed(1e30, 2) -> "1000000000000000019884624838656.00"
- // ToFixed(0.1, 30) -> "0.100000000000000005551115123126"
- // ToFixed(0.1, 17) -> "0.10000000000000001"
- //
- // If requested_digits equals 0, then the tail of the result depends on
- // the EMIT_TRAILING_DECIMAL_POINT and EMIT_TRAILING_ZERO_AFTER_POINT.
- // Examples, for requested_digits == 0,
- // let EMIT_TRAILING_DECIMAL_POINT and EMIT_TRAILING_ZERO_AFTER_POINT be
- // - false and false: then 123.45 -> 123
- // 0.678 -> 1
- // - true and false: then 123.45 -> 123.
- // 0.678 -> 1.
- // - true and true: then 123.45 -> 123.0
- // 0.678 -> 1.0
- //
- // Returns true if the conversion succeeds. The conversion always succeeds
- // except for the following cases:
- // - the input value is special and no infinity_symbol or nan_symbol has
- // been provided to the constructor,
- // - 'value' > 10^kMaxFixedDigitsBeforePoint, or
- // - 'requested_digits' > kMaxFixedDigitsAfterPoint.
- // The last two conditions imply that the result will never contain more than
- // 1 + kMaxFixedDigitsBeforePoint + 1 + kMaxFixedDigitsAfterPoint characters
- // (one additional character for the sign, and one for the decimal point).
- bool ToFixed(double value,
- int requested_digits,
- StringBuilder* result_builder) const;
-
- // Computes a representation in exponential format with requested_digits
- // after the decimal point. The last emitted digit is rounded.
- // If requested_digits equals -1, then the shortest exponential representation
- // is computed.
- //
- // Examples with EMIT_POSITIVE_EXPONENT_SIGN deactivated, and
- // exponent_character set to 'e'.
- // ToExponential(3.12, 1) -> "3.1e0"
- // ToExponential(5.0, 3) -> "5.000e0"
- // ToExponential(0.001, 2) -> "1.00e-3"
- // ToExponential(3.1415, -1) -> "3.1415e0"
- // ToExponential(3.1415, 4) -> "3.1415e0"
- // ToExponential(3.1415, 3) -> "3.142e0"
- // ToExponential(123456789000000, 3) -> "1.235e14"
- // ToExponential(1000000000000000019884624838656.0, -1) -> "1e30"
- // ToExponential(1000000000000000019884624838656.0, 32) ->
- // "1.00000000000000001988462483865600e30"
- // ToExponential(1234, 0) -> "1e3"
- //
- // Returns true if the conversion succeeds. The conversion always succeeds
- // except for the following cases:
- // - the input value is special and no infinity_symbol or nan_symbol has
- // been provided to the constructor,
- // - 'requested_digits' > kMaxExponentialDigits.
- // The last condition implies that the result will never contain more than
- // kMaxExponentialDigits + 8 characters (the sign, the digit before the
- // decimal point, the decimal point, the exponent character, the
- // exponent's sign, and at most 3 exponent digits).
- WTF_EXPORT_PRIVATE bool ToExponential(double value,
- int requested_digits,
- StringBuilder* result_builder) const;
-
- // Computes 'precision' leading digits of the given 'value' and returns them
- // either in exponential or decimal format, depending on
- // max_{leading|trailing}_padding_zeroes_in_precision_mode (given to the
- // constructor).
- // The last computed digit is rounded.
- //
- // Example with max_leading_padding_zeroes_in_precision_mode = 6.
- // ToPrecision(0.0000012345, 2) -> "0.0000012"
- // ToPrecision(0.00000012345, 2) -> "1.2e-7"
- // Similarily the converter may add up to
- // max_trailing_padding_zeroes_in_precision_mode in precision mode to avoid
- // returning an exponential representation. A zero added by the
- // EMIT_TRAILING_ZERO_AFTER_POINT flag is counted for this limit.
- // Examples for max_trailing_padding_zeroes_in_precision_mode = 1:
- // ToPrecision(230.0, 2) -> "230"
- // ToPrecision(230.0, 2) -> "230." with EMIT_TRAILING_DECIMAL_POINT.
- // ToPrecision(230.0, 2) -> "2.3e2" with EMIT_TRAILING_ZERO_AFTER_POINT.
- // Examples for max_trailing_padding_zeroes_in_precision_mode = 3, and no
- // EMIT_TRAILING_ZERO_AFTER_POINT:
- // ToPrecision(123450.0, 6) -> "123450"
- // ToPrecision(123450.0, 5) -> "123450"
- // ToPrecision(123450.0, 4) -> "123500"
- // ToPrecision(123450.0, 3) -> "123000"
- // ToPrecision(123450.0, 2) -> "1.2e5"
- //
- // Returns true if the conversion succeeds. The conversion always succeeds
- // except for the following cases:
- // - the input value is special and no infinity_symbol or nan_symbol has
- // been provided to the constructor,
- // - precision < kMinPericisionDigits
- // - precision > kMaxPrecisionDigits
- // The last condition implies that the result will never contain more than
- // kMaxPrecisionDigits + 7 characters (the sign, the decimal point, the
- // exponent character, the exponent's sign, and at most 3 exponent digits).
- bool ToPrecision(double value,
- int precision,
- StringBuilder* result_builder) const;
-
- enum DtoaMode {
- // Produce the shortest correct representation.
- // For example the output of 0.299999999999999988897 is (the less accurate
- // but correct) 0.3.
- SHORTEST,
- // Produce a fixed number of digits after the decimal point.
- // For instance fixed(0.1, 4) becomes 0.1000
- // If the input number is big, the output will be big.
- FIXED,
- // Fixed number of digits (independent of the decimal point).
- PRECISION
- };
-
- // The maximal number of digits that are needed to emit a double in base 10.
- // A higher precision can be achieved by using more digits, but the shortest
- // accurate representation of any double will never use more digits than
- // kBase10MaximalLength.
- // Note that DoubleToAscii null-terminates its input. So the given buffer
- // should be at least kBase10MaximalLength + 1 characters long.
- static const int kBase10MaximalLength = 17;
-
- // Converts the given double 'v' to ascii.
- // The result should be interpreted as buffer * 10^(point-length).
- //
- // The output depends on the given mode:
- // - SHORTEST: produce the least amount of digits for which the internal
- // identity requirement is still satisfied. If the digits are printed
- // (together with the correct exponent) then reading this number will give
- // 'v' again. The buffer will choose the representation that is closest to
- // 'v'. If there are two at the same distance, than the one farther away
- // from 0 is chosen (halfway cases - ending with 5 - are rounded up).
- // In this mode the 'requested_digits' parameter is ignored.
- // - FIXED: produces digits necessary to print a given number with
- // 'requested_digits' digits after the decimal point. The produced digits
- // might be too short in which case the caller has to fill the remainder
- // with '0's.
- // Example: toFixed(0.001, 5) is allowed to return buffer="1", point=-2.
- // Halfway cases are rounded towards +/-Infinity (away from 0). The call
- // toFixed(0.15, 2) thus returns buffer="2", point=0.
- // The returned buffer may contain digits that would be truncated from the
- // shortest representation of the input.
- // - PRECISION: produces 'requested_digits' where the first digit is not '0'.
- // Even though the length of produced digits usually equals
- // 'requested_digits', the function is allowed to return fewer digits, in
- // which case the caller has to fill the missing digits with '0's.
- // Halfway cases are again rounded away from 0.
- // DoubleToAscii expects the given buffer to be big enough to hold all
- // digits and a terminating null-character. In SHORTEST-mode it expects a
- // buffer of at least kBase10MaximalLength + 1. In all other modes the
- // requested_digits parameter (+ 1 for the null-character) limits the size of
- // the output. The given length is only used in debug mode to ensure the
- // buffer is big enough.
- static void DoubleToAscii(double v,
- DtoaMode mode,
- int requested_digits,
- char* buffer,
- int buffer_length,
- bool* sign,
- int* length,
- int* point);
-
- private:
- // If the value is a special value (NaN or Infinity) constructs the
- // corresponding string using the configured infinity/nan-symbol.
- // If either of them is NULL or the value is not special then the
- // function returns false.
- bool HandleSpecialValues(double value, StringBuilder* result_builder) const;
- // Constructs an exponential representation (i.e. 1.234e56).
- // The given exponent assumes a decimal point after the first decimal digit.
- void CreateExponentialRepresentation(const char* decimal_digits,
- int length,
- int exponent,
- StringBuilder* result_builder) const;
- // Creates a decimal representation (i.e 1234.5678).
- void CreateDecimalRepresentation(const char* decimal_digits,
- int length,
- int decimal_point,
- int digits_after_point,
- StringBuilder* result_builder) const;
-
- const int flags_;
- const char* const infinity_symbol_;
- const char* const nan_symbol_;
- const char exponent_character_;
- const int decimal_in_shortest_low_;
- const int decimal_in_shortest_high_;
- const int max_leading_padding_zeroes_in_precision_mode_;
- const int max_trailing_padding_zeroes_in_precision_mode_;
-
- DISALLOW_IMPLICIT_CONSTRUCTORS(DoubleToStringConverter);
- };
-
-
- class StringToDoubleConverter {
- public:
- // Performs the conversion.
- // The output parameter 'processed_characters_count' is set to the number
- // of characters that have been processed to read the number.
- WTF_EXPORT_PRIVATE static double StringToDouble(const char* buffer, size_t length, size_t* processed_characters_count);
-
- private:
- DISALLOW_IMPLICIT_CONSTRUCTORS(StringToDoubleConverter);
- };
-
-} // namespace double_conversion
+ max_trailing_padding_zeroes_in_precision_mode) {
+ // When 'trailing zero after the point' is set, then 'trailing point'
+ // must be set too.
+ ASSERT(((flags & EMIT_TRAILING_DECIMAL_POINT) != 0) ||
+ !((flags & EMIT_TRAILING_ZERO_AFTER_POINT) != 0));
+ }
+
+ // Returns a converter following the EcmaScript specification.
+ WTF_EXPORT_PRIVATE static const DoubleToStringConverter& EcmaScriptConverter();
+
+ // Computes the shortest string of digits that correctly represent the input
+ // number. Depending on decimal_in_shortest_low and decimal_in_shortest_high
+ // (see constructor) it then either returns a decimal representation, or an
+ // exponential representation.
+ // Example with decimal_in_shortest_low = -6,
+ // decimal_in_shortest_high = 21,
+ // EMIT_POSITIVE_EXPONENT_SIGN activated, and
+ // EMIT_TRAILING_DECIMAL_POINT deactived:
+ // ToShortest(0.000001) -> "0.000001"
+ // ToShortest(0.0000001) -> "1e-7"
+ // ToShortest(111111111111111111111.0) -> "111111111111111110000"
+ // ToShortest(100000000000000000000.0) -> "100000000000000000000"
+ // ToShortest(1111111111111111111111.0) -> "1.1111111111111111e+21"
+ //
+ // Note: the conversion may round the output if the returned string
+ // is accurate enough to uniquely identify the input-number.
+ // For example the most precise representation of the double 9e59 equals
+ // "899999999999999918767229449717619953810131273674690656206848", but
+ // the converter will return the shorter (but still correct) "9e59".
+ //
+ // Returns true if the conversion succeeds. The conversion always succeeds
+ // except when the input value is special and no infinity_symbol or
+ // nan_symbol has been given to the constructor.
+ bool ToShortest(double value, StringBuilder* result_builder) const {
+ return ToShortestIeeeNumber(value, result_builder, SHORTEST);
+ }
+
+ // Same as ToShortest, but for single-precision floats.
+ bool ToShortestSingle(float value, StringBuilder* result_builder) const {
+ return ToShortestIeeeNumber(value, result_builder, SHORTEST_SINGLE);
+ }
+
+
+ // Computes a decimal representation with a fixed number of digits after the
+ // decimal point. The last emitted digit is rounded.
+ //
+ // Examples:
+ // ToFixed(3.12, 1) -> "3.1"
+ // ToFixed(3.1415, 3) -> "3.142"
+ // ToFixed(1234.56789, 4) -> "1234.5679"
+ // ToFixed(1.23, 5) -> "1.23000"
+ // ToFixed(0.1, 4) -> "0.1000"
+ // ToFixed(1e30, 2) -> "1000000000000000019884624838656.00"
+ // ToFixed(0.1, 30) -> "0.100000000000000005551115123126"
+ // ToFixed(0.1, 17) -> "0.10000000000000001"
+ //
+ // If requested_digits equals 0, then the tail of the result depends on
+ // the EMIT_TRAILING_DECIMAL_POINT and EMIT_TRAILING_ZERO_AFTER_POINT.
+ // Examples, for requested_digits == 0,
+ // let EMIT_TRAILING_DECIMAL_POINT and EMIT_TRAILING_ZERO_AFTER_POINT be
+ // - false and false: then 123.45 -> 123
+ // 0.678 -> 1
+ // - true and false: then 123.45 -> 123.
+ // 0.678 -> 1.
+ // - true and true: then 123.45 -> 123.0
+ // 0.678 -> 1.0
+ //
+ // Returns true if the conversion succeeds. The conversion always succeeds
+ // except for the following cases:
+ // - the input value is special and no infinity_symbol or nan_symbol has
+ // been provided to the constructor,
+ // - 'value' > 10^kMaxFixedDigitsBeforePoint, or
+ // - 'requested_digits' > kMaxFixedDigitsAfterPoint.
+ // The last two conditions imply that the result will never contain more than
+ // 1 + kMaxFixedDigitsBeforePoint + 1 + kMaxFixedDigitsAfterPoint characters
+ // (one additional character for the sign, and one for the decimal point).
+ bool ToFixed(double value,
+ int requested_digits,
+ StringBuilder* result_builder) const;
+
+ // Computes a representation in exponential format with requested_digits
+ // after the decimal point. The last emitted digit is rounded.
+ // If requested_digits equals -1, then the shortest exponential representation
+ // is computed.
+ //
+ // Examples with EMIT_POSITIVE_EXPONENT_SIGN deactivated, and
+ // exponent_character set to 'e'.
+ // ToExponential(3.12, 1) -> "3.1e0"
+ // ToExponential(5.0, 3) -> "5.000e0"
+ // ToExponential(0.001, 2) -> "1.00e-3"
+ // ToExponential(3.1415, -1) -> "3.1415e0"
+ // ToExponential(3.1415, 4) -> "3.1415e0"
+ // ToExponential(3.1415, 3) -> "3.142e0"
+ // ToExponential(123456789000000, 3) -> "1.235e14"
+ // ToExponential(1000000000000000019884624838656.0, -1) -> "1e30"
+ // ToExponential(1000000000000000019884624838656.0, 32) ->
+ // "1.00000000000000001988462483865600e30"
+ // ToExponential(1234, 0) -> "1e3"
+ //
+ // Returns true if the conversion succeeds. The conversion always succeeds
+ // except for the following cases:
+ // - the input value is special and no infinity_symbol or nan_symbol has
+ // been provided to the constructor,
+ // - 'requested_digits' > kMaxExponentialDigits.
+ // The last condition implies that the result will never contain more than
+ // kMaxExponentialDigits + 8 characters (the sign, the digit before the
+ // decimal point, the decimal point, the exponent character, the
+ // exponent's sign, and at most 3 exponent digits).
+ WTF_EXPORT_PRIVATE bool ToExponential(double value,
+ int requested_digits,
+ StringBuilder* result_builder) const;
+
+ // Computes 'precision' leading digits of the given 'value' and returns them
+ // either in exponential or decimal format, depending on
+ // max_{leading|trailing}_padding_zeroes_in_precision_mode (given to the
+ // constructor).
+ // The last computed digit is rounded.
+ //
+ // Example with max_leading_padding_zeroes_in_precision_mode = 6.
+ // ToPrecision(0.0000012345, 2) -> "0.0000012"
+ // ToPrecision(0.00000012345, 2) -> "1.2e-7"
+ // Similarily the converter may add up to
+ // max_trailing_padding_zeroes_in_precision_mode in precision mode to avoid
+ // returning an exponential representation. A zero added by the
+ // EMIT_TRAILING_ZERO_AFTER_POINT flag is counted for this limit.
+ // Examples for max_trailing_padding_zeroes_in_precision_mode = 1:
+ // ToPrecision(230.0, 2) -> "230"
+ // ToPrecision(230.0, 2) -> "230." with EMIT_TRAILING_DECIMAL_POINT.
+ // ToPrecision(230.0, 2) -> "2.3e2" with EMIT_TRAILING_ZERO_AFTER_POINT.
+ // Examples for max_trailing_padding_zeroes_in_precision_mode = 3, and no
+ // EMIT_TRAILING_ZERO_AFTER_POINT:
+ // ToPrecision(123450.0, 6) -> "123450"
+ // ToPrecision(123450.0, 5) -> "123450"
+ // ToPrecision(123450.0, 4) -> "123500"
+ // ToPrecision(123450.0, 3) -> "123000"
+ // ToPrecision(123450.0, 2) -> "1.2e5"
+ //
+ // Returns true if the conversion succeeds. The conversion always succeeds
+ // except for the following cases:
+ // - the input value is special and no infinity_symbol or nan_symbol has
+ // been provided to the constructor,
+ // - precision < kMinPericisionDigits
+ // - precision > kMaxPrecisionDigits
+ // The last condition implies that the result will never contain more than
+ // kMaxPrecisionDigits + 7 characters (the sign, the decimal point, the
+ // exponent character, the exponent's sign, and at most 3 exponent digits).
+ bool ToPrecision(double value,
+ int precision,
+ StringBuilder* result_builder) const;
-} // namespace WTF
+ enum DtoaMode {
+ // Produce the shortest correct representation.
+ // For example the output of 0.299999999999999988897 is (the less accurate
+ // but correct) 0.3.
+ SHORTEST,
+ // Same as SHORTEST, but for single-precision floats.
+ SHORTEST_SINGLE,
+ // Produce a fixed number of digits after the decimal point.
+ // For instance fixed(0.1, 4) becomes 0.1000
+ // If the input number is big, the output will be big.
+ FIXED,
+ // Fixed number of digits (independent of the decimal point).
+ PRECISION
+ };
+
+ // The maximal number of digits that are needed to emit a double in base 10.
+ // A higher precision can be achieved by using more digits, but the shortest
+ // accurate representation of any double will never use more digits than
+ // kBase10MaximalLength.
+ // Note that DoubleToAscii null-terminates its input. So the given buffer
+ // should be at least kBase10MaximalLength + 1 characters long.
+ static const int kBase10MaximalLength = 17;
+
+ // Converts the given double 'v' to digit characters. 'v' must not be NaN,
+ // +Infinity, or -Infinity. In SHORTEST_SINGLE-mode this restriction also
+ // applies to 'v' after it has been casted to a single-precision float. That
+ // is, in this mode static_cast<float>(v) must not be NaN, +Infinity or
+ // -Infinity.
+ //
+ // The result should be interpreted as buffer * 10^(point-length).
+ //
+ // The digits are written to the buffer in the platform's charset, which is
+ // often UTF-8 (with ASCII-range digits) but may be another charset, such
+ // as EBCDIC.
+ //
+ // The output depends on the given mode:
+ // - SHORTEST: produce the least amount of digits for which the internal
+ // identity requirement is still satisfied. If the digits are printed
+ // (together with the correct exponent) then reading this number will give
+ // 'v' again. The buffer will choose the representation that is closest to
+ // 'v'. If there are two at the same distance, than the one farther away
+ // from 0 is chosen (halfway cases - ending with 5 - are rounded up).
+ // In this mode the 'requested_digits' parameter is ignored.
+ // - SHORTEST_SINGLE: same as SHORTEST but with single-precision.
+ // - FIXED: produces digits necessary to print a given number with
+ // 'requested_digits' digits after the decimal point. The produced digits
+ // might be too short in which case the caller has to fill the remainder
+ // with '0's.
+ // Example: toFixed(0.001, 5) is allowed to return buffer="1", point=-2.
+ // Halfway cases are rounded towards +/-Infinity (away from 0). The call
+ // toFixed(0.15, 2) thus returns buffer="2", point=0.
+ // The returned buffer may contain digits that would be truncated from the
+ // shortest representation of the input.
+ // - PRECISION: produces 'requested_digits' where the first digit is not '0'.
+ // Even though the length of produced digits usually equals
+ // 'requested_digits', the function is allowed to return fewer digits, in
+ // which case the caller has to fill the missing digits with '0's.
+ // Halfway cases are again rounded away from 0.
+ // DoubleToAscii expects the given buffer to be big enough to hold all
+ // digits and a terminating null-character. In SHORTEST-mode it expects a
+ // buffer of at least kBase10MaximalLength + 1. In all other modes the
+ // requested_digits parameter and the padding-zeroes limit the size of the
+ // output. Don't forget the decimal point, the exponent character and the
+ // terminating null-character when computing the maximal output size.
+ // The given length is only used in debug mode to ensure the buffer is big
+ // enough.
+ static void DoubleToAscii(double v,
+ DtoaMode mode,
+ int requested_digits,
+ char* buffer,
+ int buffer_length,
+ bool* sign,
+ int* length,
+ int* point);
+
+ private:
+ // Implementation for ToShortest and ToShortestSingle.
+ bool ToShortestIeeeNumber(double value,
+ StringBuilder* result_builder,
+ DtoaMode mode) const;
+
+ // If the value is a special value (NaN or Infinity) constructs the
+ // corresponding string using the configured infinity/nan-symbol.
+ // If either of them is NULL or the value is not special then the
+ // function returns false.
+ bool HandleSpecialValues(double value, StringBuilder* result_builder) const;
+ // Constructs an exponential representation (i.e. 1.234e56).
+ // The given exponent assumes a decimal point after the first decimal digit.
+ void CreateExponentialRepresentation(const char* decimal_digits,
+ int length,
+ int exponent,
+ StringBuilder* result_builder) const;
+ // Creates a decimal representation (i.e 1234.5678).
+ void CreateDecimalRepresentation(const char* decimal_digits,
+ int length,
+ int decimal_point,
+ int digits_after_point,
+ StringBuilder* result_builder) const;
+
+ const int flags_;
+ const char* const infinity_symbol_;
+ const char* const nan_symbol_;
+ const char exponent_character_;
+ const int decimal_in_shortest_low_;
+ const int decimal_in_shortest_high_;
+ const int max_leading_padding_zeroes_in_precision_mode_;
+ const int max_trailing_padding_zeroes_in_precision_mode_;
+
+ DC_DISALLOW_IMPLICIT_CONSTRUCTORS(DoubleToStringConverter);
+};
+
+
+class StringToDoubleConverter {
+ public:
+ // Performs the conversion.
+ // The output parameter 'processed_characters_count' is set to the number
+ // of characters that have been processed to read the number.
+ WTF_EXPORT_PRIVATE static double StringToDouble(const char* buffer,
+ size_t length,
+ size_t* processed_characters_count);
+
+ // Same as StringToDouble above but for 16 bit characters.
+ WTF_EXPORT_PRIVATE static double StringToDouble(const uc16* buffer,
+ size_t length,
+ size_t* processed_characters_count);
+
+ // Same as StringToDouble but reads a float.
+ // Note that this is not equivalent to static_cast<float>(StringToDouble(...))
+ // due to potential double-rounding.
+ WTF_EXPORT_PRIVATE static float StringToFloat(const char* buffer,
+ size_t length,
+ size_t* processed_characters_count);
+
+ // Same as StringToFloat above but for 16 bit characters.
+ WTF_EXPORT_PRIVATE static float StringToFloat(const uc16* buffer,
+ size_t length,
+ size_t* processed_characters_count);
+
+ private:
+ DC_DISALLOW_IMPLICIT_CONSTRUCTORS(StringToDoubleConverter);
+};
+
+} // namespace double_conversion
+} // namespace WTF
#endif // DOUBLE_CONVERSION_DOUBLE_CONVERSION_H_
+++ /dev/null
-// Copyright 2010 the V8 project authors. All rights reserved.
-// Redistribution and use in source and binary forms, with or without
-// modification, are permitted provided that the following conditions are
-// met:
-//
-// * Redistributions of source code must retain the above copyright
-// notice, this list of conditions and the following disclaimer.
-// * Redistributions in binary form must reproduce the above
-// copyright notice, this list of conditions and the following
-// disclaimer in the documentation and/or other materials provided
-// with the distribution.
-// * Neither the name of Google Inc. nor the names of its
-// contributors may be used to endorse or promote products derived
-// from this software without specific prior written permission.
-//
-// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
-// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
-// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
-// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
-// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
-// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
-// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
-// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-
-#ifndef DOUBLE_CONVERSION_DOUBLE_H_
-#define DOUBLE_CONVERSION_DOUBLE_H_
-
-#include "diy-fp.h"
-
-namespace WTF {
-
-namespace double_conversion {
-
- // We assume that doubles and uint64_t have the same endianness.
- static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); }
- static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); }
-
- // Helper functions for doubles.
- class Double {
- public:
- static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000);
- static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 00000000);
- static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFFFFFF);
- static const uint64_t kHiddenBit = UINT64_2PART_C(0x00100000, 00000000);
- static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit.
- static const int kSignificandSize = 53;
-
- Double() : d64_(0) {}
- explicit Double(double d) : d64_(double_to_uint64(d)) {}
- explicit Double(uint64_t d64) : d64_(d64) {}
- explicit Double(DiyFp diy_fp)
- : d64_(DiyFpToUint64(diy_fp)) {}
-
- // The value encoded by this Double must be greater or equal to +0.0.
- // It must not be special (infinity, or NaN).
- DiyFp AsDiyFp() const {
- ASSERT(Sign() > 0);
- ASSERT(!IsSpecial());
- return DiyFp(Significand(), Exponent());
- }
-
- // The value encoded by this Double must be strictly greater than 0.
- DiyFp AsNormalizedDiyFp() const {
- ASSERT(value() > 0.0);
- uint64_t f = Significand();
- int e = Exponent();
-
- // The current double could be a denormal.
- while ((f & kHiddenBit) == 0) {
- f <<= 1;
- e--;
- }
- // Do the final shifts in one go.
- f <<= DiyFp::kSignificandSize - kSignificandSize;
- e -= DiyFp::kSignificandSize - kSignificandSize;
- return DiyFp(f, e);
- }
-
- // Returns the double's bit as uint64.
- uint64_t AsUint64() const {
- return d64_;
- }
-
- // Returns the next greater double. Returns +infinity on input +infinity.
- double NextDouble() const {
- if (d64_ == kInfinity) return Double(kInfinity).value();
- if (Sign() < 0 && Significand() == 0) {
- // -0.0
- return 0.0;
- }
- if (Sign() < 0) {
- return Double(d64_ - 1).value();
- } else {
- return Double(d64_ + 1).value();
- }
- }
-
- int Exponent() const {
- if (IsDenormal()) return kDenormalExponent;
-
- uint64_t d64 = AsUint64();
- int biased_e =
- static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
- return biased_e - kExponentBias;
- }
-
- uint64_t Significand() const {
- uint64_t d64 = AsUint64();
- uint64_t significand = d64 & kSignificandMask;
- if (!IsDenormal()) {
- return significand + kHiddenBit;
- } else {
- return significand;
- }
- }
-
- // Returns true if the double is a denormal.
- bool IsDenormal() const {
- uint64_t d64 = AsUint64();
- return (d64 & kExponentMask) == 0;
- }
-
- // We consider denormals not to be special.
- // Hence only Infinity and NaN are special.
- bool IsSpecial() const {
- uint64_t d64 = AsUint64();
- return (d64 & kExponentMask) == kExponentMask;
- }
-
- bool IsNan() const {
- uint64_t d64 = AsUint64();
- return ((d64 & kExponentMask) == kExponentMask) &&
- ((d64 & kSignificandMask) != 0);
- }
-
- bool IsInfinite() const {
- uint64_t d64 = AsUint64();
- return ((d64 & kExponentMask) == kExponentMask) &&
- ((d64 & kSignificandMask) == 0);
- }
-
- int Sign() const {
- uint64_t d64 = AsUint64();
- return (d64 & kSignMask) == 0? 1: -1;
- }
-
- // Precondition: the value encoded by this Double must be greater or equal
- // than +0.0.
- DiyFp UpperBoundary() const {
- ASSERT(Sign() > 0);
- return DiyFp(Significand() * 2 + 1, Exponent() - 1);
- }
-
- // Computes the two boundaries of this.
- // The bigger boundary (m_plus) is normalized. The lower boundary has the same
- // exponent as m_plus.
- // Precondition: the value encoded by this Double must be greater than 0.
- void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
- ASSERT(value() > 0.0);
- DiyFp v = this->AsDiyFp();
- bool significand_is_zero = (v.f() == kHiddenBit);
- DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
- DiyFp m_minus;
- if (significand_is_zero && v.e() != kDenormalExponent) {
- // The boundary is closer. Think of v = 1000e10 and v- = 9999e9.
- // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
- // at a distance of 1e8.
- // The only exception is for the smallest normal: the largest denormal is
- // at the same distance as its successor.
- // Note: denormals have the same exponent as the smallest normals.
- m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
- } else {
- m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
- }
- m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
- m_minus.set_e(m_plus.e());
- *out_m_plus = m_plus;
- *out_m_minus = m_minus;
- }
-
- double value() const { return uint64_to_double(d64_); }
-
- // Returns the significand size for a given order of magnitude.
- // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude.
- // This function returns the number of significant binary digits v will have
- // once it's encoded into a double. In almost all cases this is equal to
- // kSignificandSize. The only exceptions are denormals. They start with
- // leading zeroes and their effective significand-size is hence smaller.
- static int SignificandSizeForOrderOfMagnitude(int order) {
- if (order >= (kDenormalExponent + kSignificandSize)) {
- return kSignificandSize;
- }
- if (order <= kDenormalExponent) return 0;
- return order - kDenormalExponent;
- }
-
- static double Infinity() {
- return Double(kInfinity).value();
- }
-
- static double NaN() {
- return Double(kNaN).value();
- }
-
- private:
- static const int kExponentBias = 0x3FF + kPhysicalSignificandSize;
- static const int kDenormalExponent = -kExponentBias + 1;
- static const int kMaxExponent = 0x7FF - kExponentBias;
- static const uint64_t kInfinity = UINT64_2PART_C(0x7FF00000, 00000000);
- static const uint64_t kNaN = UINT64_2PART_C(0x7FF80000, 00000000);
-
- const uint64_t d64_;
-
- static uint64_t DiyFpToUint64(DiyFp diy_fp) {
- uint64_t significand = diy_fp.f();
- int exponent = diy_fp.e();
- while (significand > kHiddenBit + kSignificandMask) {
- significand >>= 1;
- exponent++;
- }
- if (exponent >= kMaxExponent) {
- return kInfinity;
- }
- if (exponent < kDenormalExponent) {
- return 0;
- }
- while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) {
- significand <<= 1;
- exponent--;
- }
- uint64_t biased_exponent;
- if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) {
- biased_exponent = 0;
- } else {
- biased_exponent = static_cast<uint64_t>(exponent + kExponentBias);
- }
- return (significand & kSignificandMask) |
- (biased_exponent << kPhysicalSignificandSize);
- }
- };
-
-} // namespace double_conversion
-
-} // namespace WTF
-
-#endif // DOUBLE_CONVERSION_DOUBLE_H_
-// Copyright 2010 the V8 project authors. All rights reserved.
+// Copyright 2012 the V8 project authors. All rights reserved.
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
#include "config.h"
-#include "fast-dtoa.h"
+#include <wtf/dtoa/fast-dtoa.h>
-#include "cached-powers.h"
-#include "diy-fp.h"
-#include "double.h"
+#include <wtf/dtoa/cached-powers.h>
+#include <wtf/dtoa/diy-fp.h>
+#include <wtf/dtoa/ieee.h>
namespace WTF {
-
namespace double_conversion {
-
- // The minimal and maximal target exponent define the range of w's binary
- // exponent, where 'w' is the result of multiplying the input by a cached power
- // of ten.
- //
- // A different range might be chosen on a different platform, to optimize digit
- // generation, but a smaller range requires more powers of ten to be cached.
- static const int kMinimalTargetExponent = -60;
- static const int kMaximalTargetExponent = -32;
-
-
- // Adjusts the last digit of the generated number, and screens out generated
- // solutions that may be inaccurate. A solution may be inaccurate if it is
- // outside the safe interval, or if we cannot prove that it is closer to the
- // input than a neighboring representation of the same length.
- //
- // Input: * buffer containing the digits of too_high / 10^kappa
- // * the buffer's length
- // * distance_too_high_w == (too_high - w).f() * unit
- // * unsafe_interval == (too_high - too_low).f() * unit
- // * rest = (too_high - buffer * 10^kappa).f() * unit
- // * ten_kappa = 10^kappa * unit
- // * unit = the common multiplier
- // Output: returns true if the buffer is guaranteed to contain the closest
- // representable number to the input.
- // Modifies the generated digits in the buffer to approach (round towards) w.
- static bool RoundWeed(BufferReference<char> buffer,
- int length,
- uint64_t distance_too_high_w,
- uint64_t unsafe_interval,
- uint64_t rest,
- uint64_t ten_kappa,
- uint64_t unit) {
- uint64_t small_distance = distance_too_high_w - unit;
- uint64_t big_distance = distance_too_high_w + unit;
- // Let w_low = too_high - big_distance, and
- // w_high = too_high - small_distance.
- // Note: w_low < w < w_high
- //
- // The real w (* unit) must lie somewhere inside the interval
- // ]w_low; w_high[ (often written as "(w_low; w_high)")
-
- // Basically the buffer currently contains a number in the unsafe interval
- // ]too_low; too_high[ with too_low < w < too_high
- //
- // too_high - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- // ^v 1 unit ^ ^ ^ ^
- // boundary_high --------------------- . . . .
- // ^v 1 unit . . . .
- // - - - - - - - - - - - - - - - - - - - + - - + - - - - - - . .
- // . . ^ . .
- // . big_distance . . .
- // . . . . rest
- // small_distance . . . .
- // v . . . .
- // w_high - - - - - - - - - - - - - - - - - - . . . .
- // ^v 1 unit . . . .
- // w ---------------------------------------- . . . .
- // ^v 1 unit v . . .
- // w_low - - - - - - - - - - - - - - - - - - - - - . . .
- // . . v
- // buffer --------------------------------------------------+-------+--------
- // . .
- // safe_interval .
- // v .
- // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - .
- // ^v 1 unit .
- // boundary_low ------------------------- unsafe_interval
- // ^v 1 unit v
- // too_low - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- //
- //
- // Note that the value of buffer could lie anywhere inside the range too_low
- // to too_high.
- //
- // boundary_low, boundary_high and w are approximations of the real boundaries
- // and v (the input number). They are guaranteed to be precise up to one unit.
- // In fact the error is guaranteed to be strictly less than one unit.
- //
- // Anything that lies outside the unsafe interval is guaranteed not to round
- // to v when read again.
- // Anything that lies inside the safe interval is guaranteed to round to v
- // when read again.
- // If the number inside the buffer lies inside the unsafe interval but not
- // inside the safe interval then we simply do not know and bail out (returning
- // false).
- //
- // Similarly we have to take into account the imprecision of 'w' when finding
- // the closest representation of 'w'. If we have two potential
- // representations, and one is closer to both w_low and w_high, then we know
- // it is closer to the actual value v.
- //
- // By generating the digits of too_high we got the largest (closest to
- // too_high) buffer that is still in the unsafe interval. In the case where
- // w_high < buffer < too_high we try to decrement the buffer.
- // This way the buffer approaches (rounds towards) w.
- // There are 3 conditions that stop the decrementation process:
- // 1) the buffer is already below w_high
- // 2) decrementing the buffer would make it leave the unsafe interval
- // 3) decrementing the buffer would yield a number below w_high and farther
- // away than the current number. In other words:
- // (buffer{-1} < w_high) && w_high - buffer{-1} > buffer - w_high
- // Instead of using the buffer directly we use its distance to too_high.
- // Conceptually rest ~= too_high - buffer
- // We need to do the following tests in this order to avoid over- and
- // underflows.
- ASSERT(rest <= unsafe_interval);
- while (rest < small_distance && // Negated condition 1
- unsafe_interval - rest >= ten_kappa && // Negated condition 2
- (rest + ten_kappa < small_distance || // buffer{-1} > w_high
- small_distance - rest >= rest + ten_kappa - small_distance)) {
- buffer[length - 1]--;
- rest += ten_kappa;
- }
-
- // We have approached w+ as much as possible. We now test if approaching w-
- // would require changing the buffer. If yes, then we have two possible
- // representations close to w, but we cannot decide which one is closer.
- if (rest < big_distance &&
- unsafe_interval - rest >= ten_kappa &&
- (rest + ten_kappa < big_distance ||
- big_distance - rest > rest + ten_kappa - big_distance)) {
- return false;
- }
-
- // Weeding test.
- // The safe interval is [too_low + 2 ulp; too_high - 2 ulp]
- // Since too_low = too_high - unsafe_interval this is equivalent to
- // [too_high - unsafe_interval + 4 ulp; too_high - 2 ulp]
- // Conceptually we have: rest ~= too_high - buffer
- return (2 * unit <= rest) && (rest <= unsafe_interval - 4 * unit);
- }
-
-
- // Rounds the buffer upwards if the result is closer to v by possibly adding
- // 1 to the buffer. If the precision of the calculation is not sufficient to
- // round correctly, return false.
- // The rounding might shift the whole buffer in which case the kappa is
- // adjusted. For example "99", kappa = 3 might become "10", kappa = 4.
- //
- // If 2*rest > ten_kappa then the buffer needs to be round up.
- // rest can have an error of +/- 1 unit. This function accounts for the
- // imprecision and returns false, if the rounding direction cannot be
- // unambiguously determined.
- //
- // Precondition: rest < ten_kappa.
- static bool RoundWeedCounted(BufferReference<char> buffer,
- int length,
- uint64_t rest,
- uint64_t ten_kappa,
- uint64_t unit,
- int* kappa) {
- ASSERT(rest < ten_kappa);
- // The following tests are done in a specific order to avoid overflows. They
- // will work correctly with any uint64 values of rest < ten_kappa and unit.
- //
- // If the unit is too big, then we don't know which way to round. For example
- // a unit of 50 means that the real number lies within rest +/- 50. If
- // 10^kappa == 40 then there is no way to tell which way to round.
- if (unit >= ten_kappa) return false;
- // Even if unit is just half the size of 10^kappa we are already completely
- // lost. (And after the previous test we know that the expression will not
- // over/underflow.)
- if (ten_kappa - unit <= unit) return false;
- // If 2 * (rest + unit) <= 10^kappa we can safely round down.
- if ((ten_kappa - rest > rest) && (ten_kappa - 2 * rest >= 2 * unit)) {
- return true;
- }
- // If 2 * (rest - unit) >= 10^kappa, then we can safely round up.
- if ((rest > unit) && (ten_kappa - (rest - unit) <= (rest - unit))) {
- // Increment the last digit recursively until we find a non '9' digit.
- buffer[length - 1]++;
- for (int i = length - 1; i > 0; --i) {
- if (buffer[i] != '0' + 10) break;
- buffer[i] = '0';
- buffer[i - 1]++;
- }
- // If the first digit is now '0'+ 10 we had a buffer with all '9's. With the
- // exception of the first digit all digits are now '0'. Simply switch the
- // first digit to '1' and adjust the kappa. Example: "99" becomes "10" and
- // the power (the kappa) is increased.
- if (buffer[0] == '0' + 10) {
- buffer[0] = '1';
- (*kappa) += 1;
- }
- return true;
- }
- return false;
- }
-
-
- static const uint32_t kTen4 = 10000;
- static const uint32_t kTen5 = 100000;
- static const uint32_t kTen6 = 1000000;
- static const uint32_t kTen7 = 10000000;
- static const uint32_t kTen8 = 100000000;
- static const uint32_t kTen9 = 1000000000;
-
- // Returns the biggest power of ten that is less than or equal to the given
- // number. We furthermore receive the maximum number of bits 'number' has.
- // If number_bits == 0 then 0^-1 is returned
- // The number of bits must be <= 32.
- // Precondition: number < (1 << (number_bits + 1)).
- static void BiggestPowerTen(uint32_t number,
- int number_bits,
- uint32_t* power,
- int* exponent) {
- ASSERT(number < (uint32_t)(1 << (number_bits + 1)));
-
- switch (number_bits) {
- case 32:
- case 31:
- case 30:
- if (kTen9 <= number) {
- *power = kTen9;
- *exponent = 9;
- break;
- }
- FALLTHROUGH;
- case 29:
- case 28:
- case 27:
- if (kTen8 <= number) {
- *power = kTen8;
- *exponent = 8;
- break;
- }
- FALLTHROUGH;
- case 26:
- case 25:
- case 24:
- if (kTen7 <= number) {
- *power = kTen7;
- *exponent = 7;
- break;
- }
- FALLTHROUGH;
- case 23:
- case 22:
- case 21:
- case 20:
- if (kTen6 <= number) {
- *power = kTen6;
- *exponent = 6;
- break;
- }
- FALLTHROUGH;
- case 19:
- case 18:
- case 17:
- if (kTen5 <= number) {
- *power = kTen5;
- *exponent = 5;
- break;
- }
- FALLTHROUGH;
- case 16:
- case 15:
- case 14:
- if (kTen4 <= number) {
- *power = kTen4;
- *exponent = 4;
- break;
- }
- FALLTHROUGH;
- case 13:
- case 12:
- case 11:
- case 10:
- if (1000 <= number) {
- *power = 1000;
- *exponent = 3;
- break;
- }
- FALLTHROUGH;
- case 9:
- case 8:
- case 7:
- if (100 <= number) {
- *power = 100;
- *exponent = 2;
- break;
- }
- FALLTHROUGH;
- case 6:
- case 5:
- case 4:
- if (10 <= number) {
- *power = 10;
- *exponent = 1;
- break;
- }
- FALLTHROUGH;
- case 3:
- case 2:
- case 1:
- if (1 <= number) {
- *power = 1;
- *exponent = 0;
- break;
- }
- FALLTHROUGH;
- case 0:
- *power = 0;
- *exponent = -1;
- break;
- default:
- // Following assignments are here to silence compiler warnings.
- *power = 0;
- *exponent = 0;
- UNREACHABLE();
- }
- }
-
-
- // Generates the digits of input number w.
- // w is a floating-point number (DiyFp), consisting of a significand and an
- // exponent. Its exponent is bounded by kMinimalTargetExponent and
- // kMaximalTargetExponent.
- // Hence -60 <= w.e() <= -32.
- //
- // Returns false if it fails, in which case the generated digits in the buffer
- // should not be used.
- // Preconditions:
- // * low, w and high are correct up to 1 ulp (unit in the last place). That
- // is, their error must be less than a unit of their last digits.
- // * low.e() == w.e() == high.e()
- // * low < w < high, and taking into account their error: low~ <= high~
- // * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
- // Postconditions: returns false if procedure fails.
- // otherwise:
- // * buffer is not null-terminated, but len contains the number of digits.
- // * buffer contains the shortest possible decimal digit-sequence
- // such that LOW < buffer * 10^kappa < HIGH, where LOW and HIGH are the
- // correct values of low and high (without their error).
- // * if more than one decimal representation gives the minimal number of
- // decimal digits then the one closest to W (where W is the correct value
- // of w) is chosen.
- // Remark: this procedure takes into account the imprecision of its input
- // numbers. If the precision is not enough to guarantee all the postconditions
- // then false is returned. This usually happens rarely (~0.5%).
- //
- // Say, for the sake of example, that
- // w.e() == -48, and w.f() == 0x1234567890abcdef
- // w's value can be computed by w.f() * 2^w.e()
- // We can obtain w's integral digits by simply shifting w.f() by -w.e().
- // -> w's integral part is 0x1234
- // w's fractional part is therefore 0x567890abcdef.
- // Printing w's integral part is easy (simply print 0x1234 in decimal).
- // In order to print its fraction we repeatedly multiply the fraction by 10 and
- // get each digit. Example the first digit after the point would be computed by
- // (0x567890abcdef * 10) >> 48. -> 3
- // The whole thing becomes slightly more complicated because we want to stop
- // once we have enough digits. That is, once the digits inside the buffer
- // represent 'w' we can stop. Everything inside the interval low - high
- // represents w. However we have to pay attention to low, high and w's
- // imprecision.
- static bool DigitGen(DiyFp low,
- DiyFp w,
- DiyFp high,
- BufferReference<char> buffer,
- int* length,
- int* kappa) {
- ASSERT(low.e() == w.e() && w.e() == high.e());
- ASSERT(low.f() + 1 <= high.f() - 1);
- ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent);
- // low, w and high are imprecise, but by less than one ulp (unit in the last
- // place).
- // If we remove (resp. add) 1 ulp from low (resp. high) we are certain that
- // the new numbers are outside of the interval we want the final
- // representation to lie in.
- // Inversely adding (resp. removing) 1 ulp from low (resp. high) would yield
- // numbers that are certain to lie in the interval. We will use this fact
- // later on.
- // We will now start by generating the digits within the uncertain
- // interval. Later we will weed out representations that lie outside the safe
- // interval and thus _might_ lie outside the correct interval.
- uint64_t unit = 1;
- DiyFp too_low = DiyFp(low.f() - unit, low.e());
- DiyFp too_high = DiyFp(high.f() + unit, high.e());
- // too_low and too_high are guaranteed to lie outside the interval we want the
- // generated number in.
- DiyFp unsafe_interval = DiyFp::Minus(too_high, too_low);
- // We now cut the input number into two parts: the integral digits and the
- // fractionals. We will not write any decimal separator though, but adapt
- // kappa instead.
- // Reminder: we are currently computing the digits (stored inside the buffer)
- // such that: too_low < buffer * 10^kappa < too_high
- // We use too_high for the digit_generation and stop as soon as possible.
- // If we stop early we effectively round down.
- DiyFp one = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
- // Division by one is a shift.
- uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e());
- // Modulo by one is an and.
- uint64_t fractionals = too_high.f() & (one.f() - 1);
- uint32_t divisor;
- int divisor_exponent;
- BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
- &divisor, &divisor_exponent);
- *kappa = divisor_exponent + 1;
- *length = 0;
- // Loop invariant: buffer = too_high / 10^kappa (integer division)
- // The invariant holds for the first iteration: kappa has been initialized
- // with the divisor exponent + 1. And the divisor is the biggest power of ten
- // that is smaller than integrals.
- while (*kappa > 0) {
- int digit = integrals / divisor;
- buffer[*length] = '0' + digit;
- (*length)++;
- integrals %= divisor;
- (*kappa)--;
- // Note that kappa now equals the exponent of the divisor and that the
- // invariant thus holds again.
- uint64_t rest =
- (static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
- // Invariant: too_high = buffer * 10^kappa + DiyFp(rest, one.e())
- // Reminder: unsafe_interval.e() == one.e()
- if (rest < unsafe_interval.f()) {
- // Rounding down (by not emitting the remaining digits) yields a number
- // that lies within the unsafe interval.
- return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f(),
- unsafe_interval.f(), rest,
- static_cast<uint64_t>(divisor) << -one.e(), unit);
- }
- divisor /= 10;
- }
-
- // The integrals have been generated. We are at the point of the decimal
- // separator. In the following loop we simply multiply the remaining digits by
- // 10 and divide by one. We just need to pay attention to multiply associated
- // data (like the interval or 'unit'), too.
- // Note that the multiplication by 10 does not overflow, because w.e >= -60
- // and thus one.e >= -60.
- ASSERT(one.e() >= -60);
- ASSERT(fractionals < one.f());
- ASSERT(UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
- while (true) {
- fractionals *= 10;
- unit *= 10;
- unsafe_interval.set_f(unsafe_interval.f() * 10);
- // Integer division by one.
- int digit = static_cast<int>(fractionals >> -one.e());
- buffer[*length] = '0' + digit;
- (*length)++;
- fractionals &= one.f() - 1; // Modulo by one.
- (*kappa)--;
- if (fractionals < unsafe_interval.f()) {
- return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f() * unit,
- unsafe_interval.f(), fractionals, one.f(), unit);
- }
- }
- }
-
-
-
- // Generates (at most) requested_digits digits of input number w.
- // w is a floating-point number (DiyFp), consisting of a significand and an
- // exponent. Its exponent is bounded by kMinimalTargetExponent and
- // kMaximalTargetExponent.
- // Hence -60 <= w.e() <= -32.
- //
- // Returns false if it fails, in which case the generated digits in the buffer
- // should not be used.
- // Preconditions:
- // * w is correct up to 1 ulp (unit in the last place). That
- // is, its error must be strictly less than a unit of its last digit.
- // * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
- //
- // Postconditions: returns false if procedure fails.
- // otherwise:
- // * buffer is not null-terminated, but length contains the number of
- // digits.
- // * the representation in buffer is the most precise representation of
- // requested_digits digits.
- // * buffer contains at most requested_digits digits of w. If there are less
- // than requested_digits digits then some trailing '0's have been removed.
- // * kappa is such that
- // w = buffer * 10^kappa + eps with |eps| < 10^kappa / 2.
- //
- // Remark: This procedure takes into account the imprecision of its input
- // numbers. If the precision is not enough to guarantee all the postconditions
- // then false is returned. This usually happens rarely, but the failure-rate
- // increases with higher requested_digits.
- static bool DigitGenCounted(DiyFp w,
- int requested_digits,
- BufferReference<char> buffer,
- int* length,
- int* kappa) {
- ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent);
- ASSERT(kMinimalTargetExponent >= -60);
- ASSERT(kMaximalTargetExponent <= -32);
- // w is assumed to have an error less than 1 unit. Whenever w is scaled we
- // also scale its error.
- uint64_t w_error = 1;
- // We cut the input number into two parts: the integral digits and the
- // fractional digits. We don't emit any decimal separator, but adapt kappa
- // instead. Example: instead of writing "1.2" we put "12" into the buffer and
- // increase kappa by 1.
- DiyFp one = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
- // Division by one is a shift.
- uint32_t integrals = static_cast<uint32_t>(w.f() >> -one.e());
- // Modulo by one is an and.
- uint64_t fractionals = w.f() & (one.f() - 1);
- uint32_t divisor;
- int divisor_exponent;
- BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
- &divisor, &divisor_exponent);
- *kappa = divisor_exponent + 1;
- *length = 0;
-
- // Loop invariant: buffer = w / 10^kappa (integer division)
- // The invariant holds for the first iteration: kappa has been initialized
- // with the divisor exponent + 1. And the divisor is the biggest power of ten
- // that is smaller than 'integrals'.
- while (*kappa > 0) {
- int digit = integrals / divisor;
- buffer[*length] = '0' + digit;
- (*length)++;
- requested_digits--;
- integrals %= divisor;
- (*kappa)--;
- // Note that kappa now equals the exponent of the divisor and that the
- // invariant thus holds again.
- if (requested_digits == 0) break;
- divisor /= 10;
- }
-
- if (requested_digits == 0) {
- uint64_t rest =
- (static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
- return RoundWeedCounted(buffer, *length, rest,
- static_cast<uint64_t>(divisor) << -one.e(), w_error,
- kappa);
- }
-
- // The integrals have been generated. We are at the point of the decimal
- // separator. In the following loop we simply multiply the remaining digits by
- // 10 and divide by one. We just need to pay attention to multiply associated
- // data (the 'unit'), too.
- // Note that the multiplication by 10 does not overflow, because w.e >= -60
- // and thus one.e >= -60.
- ASSERT(one.e() >= -60);
- ASSERT(fractionals < one.f());
- ASSERT(UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
- while (requested_digits > 0 && fractionals > w_error) {
- fractionals *= 10;
- w_error *= 10;
- // Integer division by one.
- int digit = static_cast<int>(fractionals >> -one.e());
- buffer[*length] = '0' + digit;
- (*length)++;
- requested_digits--;
- fractionals &= one.f() - 1; // Modulo by one.
- (*kappa)--;
- }
- if (requested_digits != 0) return false;
- return RoundWeedCounted(buffer, *length, fractionals, one.f(), w_error,
- kappa);
+
+// The minimal and maximal target exponent define the range of w's binary
+// exponent, where 'w' is the result of multiplying the input by a cached power
+// of ten.
+//
+// A different range might be chosen on a different platform, to optimize digit
+// generation, but a smaller range requires more powers of ten to be cached.
+static const int kMinimalTargetExponent = -60;
+static const int kMaximalTargetExponent = -32;
+
+
+// Adjusts the last digit of the generated number, and screens out generated
+// solutions that may be inaccurate. A solution may be inaccurate if it is
+// outside the safe interval, or if we cannot prove that it is closer to the
+// input than a neighboring representation of the same length.
+//
+// Input: * buffer containing the digits of too_high / 10^kappa
+// * the buffer's length
+// * distance_too_high_w == (too_high - w).f() * unit
+// * unsafe_interval == (too_high - too_low).f() * unit
+// * rest = (too_high - buffer * 10^kappa).f() * unit
+// * ten_kappa = 10^kappa * unit
+// * unit = the common multiplier
+// Output: returns true if the buffer is guaranteed to contain the closest
+// representable number to the input.
+// Modifies the generated digits in the buffer to approach (round towards) w.
+static bool RoundWeed(BufferReference<char> buffer,
+ int length,
+ uint64_t distance_too_high_w,
+ uint64_t unsafe_interval,
+ uint64_t rest,
+ uint64_t ten_kappa,
+ uint64_t unit) {
+ uint64_t small_distance = distance_too_high_w - unit;
+ uint64_t big_distance = distance_too_high_w + unit;
+ // Let w_low = too_high - big_distance, and
+ // w_high = too_high - small_distance.
+ // Note: w_low < w < w_high
+ //
+ // The real w (* unit) must lie somewhere inside the interval
+ // ]w_low; w_high[ (often written as "(w_low; w_high)")
+
+ // Basically the buffer currently contains a number in the unsafe interval
+ // ]too_low; too_high[ with too_low < w < too_high
+ //
+ // too_high - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+ // ^v 1 unit ^ ^ ^ ^
+ // boundary_high --------------------- . . . .
+ // ^v 1 unit . . . .
+ // - - - - - - - - - - - - - - - - - - - + - - + - - - - - - . .
+ // . . ^ . .
+ // . big_distance . . .
+ // . . . . rest
+ // small_distance . . . .
+ // v . . . .
+ // w_high - - - - - - - - - - - - - - - - - - . . . .
+ // ^v 1 unit . . . .
+ // w ---------------------------------------- . . . .
+ // ^v 1 unit v . . .
+ // w_low - - - - - - - - - - - - - - - - - - - - - . . .
+ // . . v
+ // buffer --------------------------------------------------+-------+--------
+ // . .
+ // safe_interval .
+ // v .
+ // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - .
+ // ^v 1 unit .
+ // boundary_low ------------------------- unsafe_interval
+ // ^v 1 unit v
+ // too_low - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+ //
+ //
+ // Note that the value of buffer could lie anywhere inside the range too_low
+ // to too_high.
+ //
+ // boundary_low, boundary_high and w are approximations of the real boundaries
+ // and v (the input number). They are guaranteed to be precise up to one unit.
+ // In fact the error is guaranteed to be strictly less than one unit.
+ //
+ // Anything that lies outside the unsafe interval is guaranteed not to round
+ // to v when read again.
+ // Anything that lies inside the safe interval is guaranteed to round to v
+ // when read again.
+ // If the number inside the buffer lies inside the unsafe interval but not
+ // inside the safe interval then we simply do not know and bail out (returning
+ // false).
+ //
+ // Similarly we have to take into account the imprecision of 'w' when finding
+ // the closest representation of 'w'. If we have two potential
+ // representations, and one is closer to both w_low and w_high, then we know
+ // it is closer to the actual value v.
+ //
+ // By generating the digits of too_high we got the largest (closest to
+ // too_high) buffer that is still in the unsafe interval. In the case where
+ // w_high < buffer < too_high we try to decrement the buffer.
+ // This way the buffer approaches (rounds towards) w.
+ // There are 3 conditions that stop the decrementation process:
+ // 1) the buffer is already below w_high
+ // 2) decrementing the buffer would make it leave the unsafe interval
+ // 3) decrementing the buffer would yield a number below w_high and farther
+ // away than the current number. In other words:
+ // (buffer{-1} < w_high) && w_high - buffer{-1} > buffer - w_high
+ // Instead of using the buffer directly we use its distance to too_high.
+ // Conceptually rest ~= too_high - buffer
+ // We need to do the following tests in this order to avoid over- and
+ // underflows.
+ ASSERT(rest <= unsafe_interval);
+ while (rest < small_distance && // Negated condition 1
+ unsafe_interval - rest >= ten_kappa && // Negated condition 2
+ (rest + ten_kappa < small_distance || // buffer{-1} > w_high
+ small_distance - rest >= rest + ten_kappa - small_distance)) {
+ buffer[length - 1]--;
+ rest += ten_kappa;
+ }
+
+ // We have approached w+ as much as possible. We now test if approaching w-
+ // would require changing the buffer. If yes, then we have two possible
+ // representations close to w, but we cannot decide which one is closer.
+ if (rest < big_distance &&
+ unsafe_interval - rest >= ten_kappa &&
+ (rest + ten_kappa < big_distance ||
+ big_distance - rest > rest + ten_kappa - big_distance)) {
+ return false;
+ }
+
+ // Weeding test.
+ // The safe interval is [too_low + 2 ulp; too_high - 2 ulp]
+ // Since too_low = too_high - unsafe_interval this is equivalent to
+ // [too_high - unsafe_interval + 4 ulp; too_high - 2 ulp]
+ // Conceptually we have: rest ~= too_high - buffer
+ return (2 * unit <= rest) && (rest <= unsafe_interval - 4 * unit);
+}
+
+
+// Rounds the buffer upwards if the result is closer to v by possibly adding
+// 1 to the buffer. If the precision of the calculation is not sufficient to
+// round correctly, return false.
+// The rounding might shift the whole buffer in which case the kappa is
+// adjusted. For example "99", kappa = 3 might become "10", kappa = 4.
+//
+// If 2*rest > ten_kappa then the buffer needs to be round up.
+// rest can have an error of +/- 1 unit. This function accounts for the
+// imprecision and returns false, if the rounding direction cannot be
+// unambiguously determined.
+//
+// Precondition: rest < ten_kappa.
+static bool RoundWeedCounted(BufferReference<char> buffer,
+ int length,
+ uint64_t rest,
+ uint64_t ten_kappa,
+ uint64_t unit,
+ int* kappa) {
+ ASSERT(rest < ten_kappa);
+ // The following tests are done in a specific order to avoid overflows. They
+ // will work correctly with any uint64 values of rest < ten_kappa and unit.
+ //
+ // If the unit is too big, then we don't know which way to round. For example
+ // a unit of 50 means that the real number lies within rest +/- 50. If
+ // 10^kappa == 40 then there is no way to tell which way to round.
+ if (unit >= ten_kappa) return false;
+ // Even if unit is just half the size of 10^kappa we are already completely
+ // lost. (And after the previous test we know that the expression will not
+ // over/underflow.)
+ if (ten_kappa - unit <= unit) return false;
+ // If 2 * (rest + unit) <= 10^kappa we can safely round down.
+ if ((ten_kappa - rest > rest) && (ten_kappa - 2 * rest >= 2 * unit)) {
+ return true;
+ }
+ // If 2 * (rest - unit) >= 10^kappa, then we can safely round up.
+ if ((rest > unit) && (ten_kappa - (rest - unit) <= (rest - unit))) {
+ // Increment the last digit recursively until we find a non '9' digit.
+ buffer[length - 1]++;
+ for (int i = length - 1; i > 0; --i) {
+ if (buffer[i] != '0' + 10) break;
+ buffer[i] = '0';
+ buffer[i - 1]++;
}
-
-
- // Provides a decimal representation of v.
- // Returns true if it succeeds, otherwise the result cannot be trusted.
- // There will be *length digits inside the buffer (not null-terminated).
- // If the function returns true then
- // v == (double) (buffer * 10^decimal_exponent).
- // The digits in the buffer are the shortest representation possible: no
- // 0.09999999999999999 instead of 0.1. The shorter representation will even be
- // chosen even if the longer one would be closer to v.
- // The last digit will be closest to the actual v. That is, even if several
- // digits might correctly yield 'v' when read again, the closest will be
- // computed.
- static bool Grisu3(double v,
- BufferReference<char> buffer,
- int* length,
- int* decimal_exponent) {
- DiyFp w = Double(v).AsNormalizedDiyFp();
- // boundary_minus and boundary_plus are the boundaries between v and its
- // closest floating-point neighbors. Any number strictly between
- // boundary_minus and boundary_plus will round to v when convert to a double.
- // Grisu3 will never output representations that lie exactly on a boundary.
- DiyFp boundary_minus, boundary_plus;
- Double(v).NormalizedBoundaries(&boundary_minus, &boundary_plus);
- ASSERT(boundary_plus.e() == w.e());
- DiyFp ten_mk; // Cached power of ten: 10^-k
- int mk; // -k
- int ten_mk_minimal_binary_exponent =
- kMinimalTargetExponent - (w.e() + DiyFp::kSignificandSize);
- int ten_mk_maximal_binary_exponent =
- kMaximalTargetExponent - (w.e() + DiyFp::kSignificandSize);
- PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
- ten_mk_minimal_binary_exponent,
- ten_mk_maximal_binary_exponent,
- &ten_mk, &mk);
- ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
- DiyFp::kSignificandSize) &&
- (kMaximalTargetExponent >= w.e() + ten_mk.e() +
- DiyFp::kSignificandSize));
- // Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
- // 64 bit significand and ten_mk is thus only precise up to 64 bits.
-
- // The DiyFp::Times procedure rounds its result, and ten_mk is approximated
- // too. The variable scaled_w (as well as scaled_boundary_minus/plus) are now
- // off by a small amount.
- // In fact: scaled_w - w*10^k < 1ulp (unit in the last place) of scaled_w.
- // In other words: let f = scaled_w.f() and e = scaled_w.e(), then
- // (f-1) * 2^e < w*10^k < (f+1) * 2^e
- DiyFp scaled_w = DiyFp::Times(w, ten_mk);
- ASSERT(scaled_w.e() ==
- boundary_plus.e() + ten_mk.e() + DiyFp::kSignificandSize);
- // In theory it would be possible to avoid some recomputations by computing
- // the difference between w and boundary_minus/plus (a power of 2) and to
- // compute scaled_boundary_minus/plus by subtracting/adding from
- // scaled_w. However the code becomes much less readable and the speed
- // enhancements are not terriffic.
- DiyFp scaled_boundary_minus = DiyFp::Times(boundary_minus, ten_mk);
- DiyFp scaled_boundary_plus = DiyFp::Times(boundary_plus, ten_mk);
-
- // DigitGen will generate the digits of scaled_w. Therefore we have
- // v == (double) (scaled_w * 10^-mk).
- // Set decimal_exponent == -mk and pass it to DigitGen. If scaled_w is not an
- // integer than it will be updated. For instance if scaled_w == 1.23 then
- // the buffer will be filled with "123" und the decimal_exponent will be
- // decreased by 2.
- int kappa;
- bool result = DigitGen(scaled_boundary_minus, scaled_w, scaled_boundary_plus,
- buffer, length, &kappa);
- *decimal_exponent = -mk + kappa;
- return result;
+ // If the first digit is now '0'+ 10 we had a buffer with all '9's. With the
+ // exception of the first digit all digits are now '0'. Simply switch the
+ // first digit to '1' and adjust the kappa. Example: "99" becomes "10" and
+ // the power (the kappa) is increased.
+ if (buffer[0] == '0' + 10) {
+ buffer[0] = '1';
+ (*kappa) += 1;
}
-
-
- // The "counted" version of grisu3 (see above) only generates requested_digits
- // number of digits. This version does not generate the shortest representation,
- // and with enough requested digits 0.1 will at some point print as 0.9999999...
- // Grisu3 is too imprecise for real halfway cases (1.5 will not work) and
- // therefore the rounding strategy for halfway cases is irrelevant.
- static bool Grisu3Counted(double v,
- int requested_digits,
- BufferReference<char> buffer,
- int* length,
- int* decimal_exponent) {
- DiyFp w = Double(v).AsNormalizedDiyFp();
- DiyFp ten_mk; // Cached power of ten: 10^-k
- int mk; // -k
- int ten_mk_minimal_binary_exponent =
- kMinimalTargetExponent - (w.e() + DiyFp::kSignificandSize);
- int ten_mk_maximal_binary_exponent =
- kMaximalTargetExponent - (w.e() + DiyFp::kSignificandSize);
- PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
- ten_mk_minimal_binary_exponent,
- ten_mk_maximal_binary_exponent,
- &ten_mk, &mk);
- ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
- DiyFp::kSignificandSize) &&
- (kMaximalTargetExponent >= w.e() + ten_mk.e() +
- DiyFp::kSignificandSize));
- // Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
- // 64 bit significand and ten_mk is thus only precise up to 64 bits.
-
- // The DiyFp::Times procedure rounds its result, and ten_mk is approximated
- // too. The variable scaled_w (as well as scaled_boundary_minus/plus) are now
- // off by a small amount.
- // In fact: scaled_w - w*10^k < 1ulp (unit in the last place) of scaled_w.
- // In other words: let f = scaled_w.f() and e = scaled_w.e(), then
- // (f-1) * 2^e < w*10^k < (f+1) * 2^e
- DiyFp scaled_w = DiyFp::Times(w, ten_mk);
-
- // We now have (double) (scaled_w * 10^-mk).
- // DigitGen will generate the first requested_digits digits of scaled_w and
- // return together with a kappa such that scaled_w ~= buffer * 10^kappa. (It
- // will not always be exactly the same since DigitGenCounted only produces a
- // limited number of digits.)
- int kappa;
- bool result = DigitGenCounted(scaled_w, requested_digits,
- buffer, length, &kappa);
- *decimal_exponent = -mk + kappa;
- return result;
+ return true;
+ }
+ return false;
+}
+
+// Returns the biggest power of ten that is less than or equal to the given
+// number. We furthermore receive the maximum number of bits 'number' has.
+//
+// Returns power == 10^(exponent_plus_one-1) such that
+// power <= number < power * 10.
+// If number_bits == 0 then 0^(0-1) is returned.
+// The number of bits must be <= 32.
+// Precondition: number < (1 << (number_bits + 1)).
+
+// Inspired by the method for finding an integer log base 10 from here:
+// http://graphics.stanford.edu/~seander/bithacks.html#IntegerLog10
+static unsigned int const kSmallPowersOfTen[] =
+ {0, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000,
+ 1000000000};
+
+static void BiggestPowerTen(uint32_t number,
+ int number_bits,
+ uint32_t* power,
+ int* exponent_plus_one) {
+ ASSERT(number < (1u << (number_bits + 1)));
+ // 1233/4096 is approximately 1/lg(10).
+ int exponent_plus_one_guess = ((number_bits + 1) * 1233 >> 12);
+ // We increment to skip over the first entry in the kPowersOf10 table.
+ // Note: kPowersOf10[i] == 10^(i-1).
+ exponent_plus_one_guess++;
+ // We don't have any guarantees that 2^number_bits <= number.
+ if (number < kSmallPowersOfTen[exponent_plus_one_guess]) {
+ exponent_plus_one_guess--;
+ }
+ *power = kSmallPowersOfTen[exponent_plus_one_guess];
+ *exponent_plus_one = exponent_plus_one_guess;
+}
+
+// Generates the digits of input number w.
+// w is a floating-point number (DiyFp), consisting of a significand and an
+// exponent. Its exponent is bounded by kMinimalTargetExponent and
+// kMaximalTargetExponent.
+// Hence -60 <= w.e() <= -32.
+//
+// Returns false if it fails, in which case the generated digits in the buffer
+// should not be used.
+// Preconditions:
+// * low, w and high are correct up to 1 ulp (unit in the last place). That
+// is, their error must be less than a unit of their last digits.
+// * low.e() == w.e() == high.e()
+// * low < w < high, and taking into account their error: low~ <= high~
+// * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
+// Postconditions: returns false if procedure fails.
+// otherwise:
+// * buffer is not null-terminated, but len contains the number of digits.
+// * buffer contains the shortest possible decimal digit-sequence
+// such that LOW < buffer * 10^kappa < HIGH, where LOW and HIGH are the
+// correct values of low and high (without their error).
+// * if more than one decimal representation gives the minimal number of
+// decimal digits then the one closest to W (where W is the correct value
+// of w) is chosen.
+// Remark: this procedure takes into account the imprecision of its input
+// numbers. If the precision is not enough to guarantee all the postconditions
+// then false is returned. This usually happens rarely (~0.5%).
+//
+// Say, for the sake of example, that
+// w.e() == -48, and w.f() == 0x1234567890abcdef
+// w's value can be computed by w.f() * 2^w.e()
+// We can obtain w's integral digits by simply shifting w.f() by -w.e().
+// -> w's integral part is 0x1234
+// w's fractional part is therefore 0x567890abcdef.
+// Printing w's integral part is easy (simply print 0x1234 in decimal).
+// In order to print its fraction we repeatedly multiply the fraction by 10 and
+// get each digit. Example the first digit after the point would be computed by
+// (0x567890abcdef * 10) >> 48. -> 3
+// The whole thing becomes slightly more complicated because we want to stop
+// once we have enough digits. That is, once the digits inside the buffer
+// represent 'w' we can stop. Everything inside the interval low - high
+// represents w. However we have to pay attention to low, high and w's
+// imprecision.
+static bool DigitGen(DiyFp low,
+ DiyFp w,
+ DiyFp high,
+ BufferReference<char> buffer,
+ int* length,
+ int* kappa) {
+ ASSERT(low.e() == w.e() && w.e() == high.e());
+ ASSERT(low.f() + 1 <= high.f() - 1);
+ ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent);
+ // low, w and high are imprecise, but by less than one ulp (unit in the last
+ // place).
+ // If we remove (resp. add) 1 ulp from low (resp. high) we are certain that
+ // the new numbers are outside of the interval we want the final
+ // representation to lie in.
+ // Inversely adding (resp. removing) 1 ulp from low (resp. high) would yield
+ // numbers that are certain to lie in the interval. We will use this fact
+ // later on.
+ // We will now start by generating the digits within the uncertain
+ // interval. Later we will weed out representations that lie outside the safe
+ // interval and thus _might_ lie outside the correct interval.
+ uint64_t unit = 1;
+ DiyFp too_low = DiyFp(low.f() - unit, low.e());
+ DiyFp too_high = DiyFp(high.f() + unit, high.e());
+ // too_low and too_high are guaranteed to lie outside the interval we want the
+ // generated number in.
+ DiyFp unsafe_interval = DiyFp::Minus(too_high, too_low);
+ // We now cut the input number into two parts: the integral digits and the
+ // fractionals. We will not write any decimal separator though, but adapt
+ // kappa instead.
+ // Reminder: we are currently computing the digits (stored inside the buffer)
+ // such that: too_low < buffer * 10^kappa < too_high
+ // We use too_high for the digit_generation and stop as soon as possible.
+ // If we stop early we effectively round down.
+ DiyFp one = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
+ // Division by one is a shift.
+ uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e());
+ // Modulo by one is an and.
+ uint64_t fractionals = too_high.f() & (one.f() - 1);
+ uint32_t divisor;
+ int divisor_exponent_plus_one;
+ BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
+ &divisor, &divisor_exponent_plus_one);
+ *kappa = divisor_exponent_plus_one;
+ *length = 0;
+ // Loop invariant: buffer = too_high / 10^kappa (integer division)
+ // The invariant holds for the first iteration: kappa has been initialized
+ // with the divisor exponent + 1. And the divisor is the biggest power of ten
+ // that is smaller than integrals.
+ while (*kappa > 0) {
+ int digit = integrals / divisor;
+ ASSERT(digit <= 9);
+ buffer[*length] = static_cast<char>('0' + digit);
+ (*length)++;
+ integrals %= divisor;
+ (*kappa)--;
+ // Note that kappa now equals the exponent of the divisor and that the
+ // invariant thus holds again.
+ uint64_t rest =
+ (static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
+ // Invariant: too_high = buffer * 10^kappa + DiyFp(rest, one.e())
+ // Reminder: unsafe_interval.e() == one.e()
+ if (rest < unsafe_interval.f()) {
+ // Rounding down (by not emitting the remaining digits) yields a number
+ // that lies within the unsafe interval.
+ return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f(),
+ unsafe_interval.f(), rest,
+ static_cast<uint64_t>(divisor) << -one.e(), unit);
}
-
-
- bool FastDtoa(double v,
- FastDtoaMode mode,
- int requested_digits,
- BufferReference<char> buffer,
- int* length,
- int* decimal_point) {
- ASSERT(v > 0);
- ASSERT(!Double(v).IsSpecial());
-
- bool result = false;
- int decimal_exponent = 0;
- switch (mode) {
- case FAST_DTOA_SHORTEST:
- result = Grisu3(v, buffer, length, &decimal_exponent);
- break;
- case FAST_DTOA_PRECISION:
- result = Grisu3Counted(v, requested_digits,
- buffer, length, &decimal_exponent);
- break;
- default:
- UNREACHABLE();
- }
- if (result) {
- *decimal_point = *length + decimal_exponent;
- buffer[*length] = '\0';
- }
- return result;
+ divisor /= 10;
+ }
+
+ // The integrals have been generated. We are at the point of the decimal
+ // separator. In the following loop we simply multiply the remaining digits by
+ // 10 and divide by one. We just need to pay attention to multiply associated
+ // data (like the interval or 'unit'), too.
+ // Note that the multiplication by 10 does not overflow, because w.e >= -60
+ // and thus one.e >= -60.
+ ASSERT(one.e() >= -60);
+ ASSERT(fractionals < one.f());
+ ASSERT(UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
+ for (;;) {
+ fractionals *= 10;
+ unit *= 10;
+ unsafe_interval.set_f(unsafe_interval.f() * 10);
+ // Integer division by one.
+ int digit = static_cast<int>(fractionals >> -one.e());
+ ASSERT(digit <= 9);
+ buffer[*length] = static_cast<char>('0' + digit);
+ (*length)++;
+ fractionals &= one.f() - 1; // Modulo by one.
+ (*kappa)--;
+ if (fractionals < unsafe_interval.f()) {
+ return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f() * unit,
+ unsafe_interval.f(), fractionals, one.f(), unit);
}
-
-} // namespace double_conversion
+ }
+}
+
+
+
+// Generates (at most) requested_digits digits of input number w.
+// w is a floating-point number (DiyFp), consisting of a significand and an
+// exponent. Its exponent is bounded by kMinimalTargetExponent and
+// kMaximalTargetExponent.
+// Hence -60 <= w.e() <= -32.
+//
+// Returns false if it fails, in which case the generated digits in the buffer
+// should not be used.
+// Preconditions:
+// * w is correct up to 1 ulp (unit in the last place). That
+// is, its error must be strictly less than a unit of its last digit.
+// * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
+//
+// Postconditions: returns false if procedure fails.
+// otherwise:
+// * buffer is not null-terminated, but length contains the number of
+// digits.
+// * the representation in buffer is the most precise representation of
+// requested_digits digits.
+// * buffer contains at most requested_digits digits of w. If there are less
+// than requested_digits digits then some trailing '0's have been removed.
+// * kappa is such that
+// w = buffer * 10^kappa + eps with |eps| < 10^kappa / 2.
+//
+// Remark: This procedure takes into account the imprecision of its input
+// numbers. If the precision is not enough to guarantee all the postconditions
+// then false is returned. This usually happens rarely, but the failure-rate
+// increases with higher requested_digits.
+static bool DigitGenCounted(DiyFp w,
+ int requested_digits,
+ BufferReference<char> buffer,
+ int* length,
+ int* kappa) {
+ ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent);
+ ASSERT(kMinimalTargetExponent >= -60);
+ ASSERT(kMaximalTargetExponent <= -32);
+ // w is assumed to have an error less than 1 unit. Whenever w is scaled we
+ // also scale its error.
+ uint64_t w_error = 1;
+ // We cut the input number into two parts: the integral digits and the
+ // fractional digits. We don't emit any decimal separator, but adapt kappa
+ // instead. Example: instead of writing "1.2" we put "12" into the buffer and
+ // increase kappa by 1.
+ DiyFp one = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
+ // Division by one is a shift.
+ uint32_t integrals = static_cast<uint32_t>(w.f() >> -one.e());
+ // Modulo by one is an and.
+ uint64_t fractionals = w.f() & (one.f() - 1);
+ uint32_t divisor;
+ int divisor_exponent_plus_one;
+ BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
+ &divisor, &divisor_exponent_plus_one);
+ *kappa = divisor_exponent_plus_one;
+ *length = 0;
+
+ // Loop invariant: buffer = w / 10^kappa (integer division)
+ // The invariant holds for the first iteration: kappa has been initialized
+ // with the divisor exponent + 1. And the divisor is the biggest power of ten
+ // that is smaller than 'integrals'.
+ while (*kappa > 0) {
+ int digit = integrals / divisor;
+ ASSERT(digit <= 9);
+ buffer[*length] = static_cast<char>('0' + digit);
+ (*length)++;
+ requested_digits--;
+ integrals %= divisor;
+ (*kappa)--;
+ // Note that kappa now equals the exponent of the divisor and that the
+ // invariant thus holds again.
+ if (requested_digits == 0) break;
+ divisor /= 10;
+ }
+
+ if (requested_digits == 0) {
+ uint64_t rest =
+ (static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
+ return RoundWeedCounted(buffer, *length, rest,
+ static_cast<uint64_t>(divisor) << -one.e(), w_error,
+ kappa);
+ }
+
+ // The integrals have been generated. We are at the point of the decimal
+ // separator. In the following loop we simply multiply the remaining digits by
+ // 10 and divide by one. We just need to pay attention to multiply associated
+ // data (the 'unit'), too.
+ // Note that the multiplication by 10 does not overflow, because w.e >= -60
+ // and thus one.e >= -60.
+ ASSERT(one.e() >= -60);
+ ASSERT(fractionals < one.f());
+ ASSERT(UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
+ while (requested_digits > 0 && fractionals > w_error) {
+ fractionals *= 10;
+ w_error *= 10;
+ // Integer division by one.
+ int digit = static_cast<int>(fractionals >> -one.e());
+ ASSERT(digit <= 9);
+ buffer[*length] = static_cast<char>('0' + digit);
+ (*length)++;
+ requested_digits--;
+ fractionals &= one.f() - 1; // Modulo by one.
+ (*kappa)--;
+ }
+ if (requested_digits != 0) return false;
+ return RoundWeedCounted(buffer, *length, fractionals, one.f(), w_error,
+ kappa);
+}
+
-} // namespace WTF
+// Provides a decimal representation of v.
+// Returns true if it succeeds, otherwise the result cannot be trusted.
+// There will be *length digits inside the buffer (not null-terminated).
+// If the function returns true then
+// v == (double) (buffer * 10^decimal_exponent).
+// The digits in the buffer are the shortest representation possible: no
+// 0.09999999999999999 instead of 0.1. The shorter representation will even be
+// chosen even if the longer one would be closer to v.
+// The last digit will be closest to the actual v. That is, even if several
+// digits might correctly yield 'v' when read again, the closest will be
+// computed.
+static bool Grisu3(double v,
+ FastDtoaMode mode,
+ BufferReference<char> buffer,
+ int* length,
+ int* decimal_exponent) {
+ DiyFp w = Double(v).AsNormalizedDiyFp();
+ // boundary_minus and boundary_plus are the boundaries between v and its
+ // closest floating-point neighbors. Any number strictly between
+ // boundary_minus and boundary_plus will round to v when convert to a double.
+ // Grisu3 will never output representations that lie exactly on a boundary.
+ DiyFp boundary_minus, boundary_plus;
+ if (mode == FAST_DTOA_SHORTEST) {
+ Double(v).NormalizedBoundaries(&boundary_minus, &boundary_plus);
+ } else {
+ ASSERT(mode == FAST_DTOA_SHORTEST_SINGLE);
+ float single_v = static_cast<float>(v);
+ Single(single_v).NormalizedBoundaries(&boundary_minus, &boundary_plus);
+ }
+ ASSERT(boundary_plus.e() == w.e());
+ DiyFp ten_mk; // Cached power of ten: 10^-k
+ int mk; // -k
+ int ten_mk_minimal_binary_exponent =
+ kMinimalTargetExponent - (w.e() + DiyFp::kSignificandSize);
+ int ten_mk_maximal_binary_exponent =
+ kMaximalTargetExponent - (w.e() + DiyFp::kSignificandSize);
+ PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
+ ten_mk_minimal_binary_exponent,
+ ten_mk_maximal_binary_exponent,
+ &ten_mk, &mk);
+ ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
+ DiyFp::kSignificandSize) &&
+ (kMaximalTargetExponent >= w.e() + ten_mk.e() +
+ DiyFp::kSignificandSize));
+ // Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
+ // 64 bit significand and ten_mk is thus only precise up to 64 bits.
+
+ // The DiyFp::Times procedure rounds its result, and ten_mk is approximated
+ // too. The variable scaled_w (as well as scaled_boundary_minus/plus) are now
+ // off by a small amount.
+ // In fact: scaled_w - w*10^k < 1ulp (unit in the last place) of scaled_w.
+ // In other words: let f = scaled_w.f() and e = scaled_w.e(), then
+ // (f-1) * 2^e < w*10^k < (f+1) * 2^e
+ DiyFp scaled_w = DiyFp::Times(w, ten_mk);
+ ASSERT(scaled_w.e() ==
+ boundary_plus.e() + ten_mk.e() + DiyFp::kSignificandSize);
+ // In theory it would be possible to avoid some recomputations by computing
+ // the difference between w and boundary_minus/plus (a power of 2) and to
+ // compute scaled_boundary_minus/plus by subtracting/adding from
+ // scaled_w. However the code becomes much less readable and the speed
+ // enhancements are not terriffic.
+ DiyFp scaled_boundary_minus = DiyFp::Times(boundary_minus, ten_mk);
+ DiyFp scaled_boundary_plus = DiyFp::Times(boundary_plus, ten_mk);
+
+ // DigitGen will generate the digits of scaled_w. Therefore we have
+ // v == (double) (scaled_w * 10^-mk).
+ // Set decimal_exponent == -mk and pass it to DigitGen. If scaled_w is not an
+ // integer than it will be updated. For instance if scaled_w == 1.23 then
+ // the buffer will be filled with "123" und the decimal_exponent will be
+ // decreased by 2.
+ int kappa;
+ bool result = DigitGen(scaled_boundary_minus, scaled_w, scaled_boundary_plus,
+ buffer, length, &kappa);
+ *decimal_exponent = -mk + kappa;
+ return result;
+}
+
+
+// The "counted" version of grisu3 (see above) only generates requested_digits
+// number of digits. This version does not generate the shortest representation,
+// and with enough requested digits 0.1 will at some point print as 0.9999999...
+// Grisu3 is too imprecise for real halfway cases (1.5 will not work) and
+// therefore the rounding strategy for halfway cases is irrelevant.
+static bool Grisu3Counted(double v,
+ int requested_digits,
+ BufferReference<char> buffer,
+ int* length,
+ int* decimal_exponent) {
+ DiyFp w = Double(v).AsNormalizedDiyFp();
+ DiyFp ten_mk; // Cached power of ten: 10^-k
+ int mk; // -k
+ int ten_mk_minimal_binary_exponent =
+ kMinimalTargetExponent - (w.e() + DiyFp::kSignificandSize);
+ int ten_mk_maximal_binary_exponent =
+ kMaximalTargetExponent - (w.e() + DiyFp::kSignificandSize);
+ PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
+ ten_mk_minimal_binary_exponent,
+ ten_mk_maximal_binary_exponent,
+ &ten_mk, &mk);
+ ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
+ DiyFp::kSignificandSize) &&
+ (kMaximalTargetExponent >= w.e() + ten_mk.e() +
+ DiyFp::kSignificandSize));
+ // Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
+ // 64 bit significand and ten_mk is thus only precise up to 64 bits.
+
+ // The DiyFp::Times procedure rounds its result, and ten_mk is approximated
+ // too. The variable scaled_w (as well as scaled_boundary_minus/plus) are now
+ // off by a small amount.
+ // In fact: scaled_w - w*10^k < 1ulp (unit in the last place) of scaled_w.
+ // In other words: let f = scaled_w.f() and e = scaled_w.e(), then
+ // (f-1) * 2^e < w*10^k < (f+1) * 2^e
+ DiyFp scaled_w = DiyFp::Times(w, ten_mk);
+
+ // We now have (double) (scaled_w * 10^-mk).
+ // DigitGen will generate the first requested_digits digits of scaled_w and
+ // return together with a kappa such that scaled_w ~= buffer * 10^kappa. (It
+ // will not always be exactly the same since DigitGenCounted only produces a
+ // limited number of digits.)
+ int kappa;
+ bool result = DigitGenCounted(scaled_w, requested_digits,
+ buffer, length, &kappa);
+ *decimal_exponent = -mk + kappa;
+ return result;
+}
+
+
+bool FastDtoa(double v,
+ FastDtoaMode mode,
+ int requested_digits,
+ BufferReference<char> buffer,
+ int* length,
+ int* decimal_point) {
+ ASSERT(v > 0);
+ ASSERT(!Double(v).IsSpecial());
+
+ bool result = false;
+ int decimal_exponent = 0;
+ switch (mode) {
+ case FAST_DTOA_SHORTEST:
+ case FAST_DTOA_SHORTEST_SINGLE:
+ result = Grisu3(v, mode, buffer, length, &decimal_exponent);
+ break;
+ case FAST_DTOA_PRECISION:
+ result = Grisu3Counted(v, requested_digits,
+ buffer, length, &decimal_exponent);
+ break;
+ default:
+ UNREACHABLE();
+ }
+ if (result) {
+ *decimal_point = *length + decimal_exponent;
+ buffer[*length] = '\0';
+ }
+ return result;
+}
+
+} // namespace double_conversion
+} // namespace WTF
#ifndef DOUBLE_CONVERSION_FAST_DTOA_H_
#define DOUBLE_CONVERSION_FAST_DTOA_H_
-#include "utils.h"
+#include <wtf/dtoa/utils.h>
namespace WTF {
-
namespace double_conversion {
-
- enum FastDtoaMode {
- // Computes the shortest representation of the given input. The returned
- // result will be the most accurate number of this length. Longer
- // representations might be more accurate.
git://git.webkit.org / WebKit-https.git / commitdiff