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ICU-11318 Integrating double-conversion into icu4c. Changing both old and new number formatting implementations to call it.

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X-SVN-Rev: 40929
This commit is contained in:
Shane Carr 2018-02-16 01:25:43 +00:00
parent 25950362de
commit 23872cb601
29 changed files with 5428 additions and 27 deletions
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4
icu4c/source/i18n/Makefile.in
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@ -107,7 +107,9 @@ number_affixutils.o number_compact.o number_decimalquantity.o \
number_decimfmtprops.o number_fluent.o number_formatimpl.o number_grouping.o \ number_decimfmtprops.o number_fluent.o number_formatimpl.o number_grouping.o \
number_integerwidth.o number_longnames.o number_modifiers.o number_notation.o \ number_integerwidth.o number_longnames.o number_modifiers.o number_notation.o \
number_padding.o number_patternmodifier.o number_patternstring.o \ number_padding.o number_patternmodifier.o number_patternstring.o \
number_rounding.o number_scientific.o number_stringbuilder.o number_rounding.o number_scientific.o number_stringbuilder.o \
double-conversion.o double-conversion-bignum-dtoa.o double-conversion-bignum.o \
double-conversion-cached-powers.o double-conversion-diy-fp.o double-conversion-fast-dtoa.o
## Header files to install ## Header files to install

50
icu4c/source/i18n/digitlst.cpp
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@ -44,12 +44,15 @@
#include "digitinterval.h" #include "digitinterval.h"
#include "ucln_in.h" #include "ucln_in.h"
#include "umutex.h" #include "umutex.h"
#include "double-conversion.h"
#include <stdlib.h> #include <stdlib.h>
#include <limits.h> #include <limits.h>
#include <string.h> #include <string.h>
#include <stdio.h> #include <stdio.h>
#include <limits> #include <limits>
using double_conversion::DoubleToStringConverter;
#if !defined(U_USE_STRTOD_L) #if !defined(U_USE_STRTOD_L)
# if U_PLATFORM_USES_ONLY_WIN32_API # if U_PLATFORM_USES_ONLY_WIN32_API
# define U_USE_STRTOD_L 1 # define U_USE_STRTOD_L 1
@ -850,8 +853,53 @@ DigitList::set(double source)
} else { } else {
uprv_strcpy(rep,"inf"); uprv_strcpy(rep,"inf");
} }
} else if (uprv_isNaN(source)) {
uprv_strcpy(rep, "NaN");
} else { } else {
sprintf(rep, "%+1.*e", MAX_DBL_DIGITS - 1, source); bool sign;
int32_t length;
int32_t point;
DoubleToStringConverter::DoubleToAscii(
source,
DoubleToStringConverter::DtoaMode::SHORTEST,
0,
rep + 1,
sizeof(rep),
&sign,
&length,
&point
);
// Convert the raw buffer into a string for decNumber
int32_t power = point - length;
if (sign) {
rep[0] = '-';
} else {
rep[0] = '0';
}
length++;
rep[length++] = 'E';
if (power < 0) {
rep[length++] = '-';
power = -power;
} else {
rep[length++] = '+';
}
if (power < 10) {
rep[length++] = power + '0';
} else if (power < 100) {
rep[length++] = (power / 10) + '0';
rep[length++] = (power % 10) + '0';
} else {
U_ASSERT(power < 1000);
rep[length + 2] = (power % 10) + '0';
power /= 10;
rep[length + 1] = (power % 10) + '0';
power /= 10;
rep[length] = power + '0';
length += 3;
}
rep[length++] = 0;
} }
U_ASSERT(uprv_strlen(rep) < sizeof(rep)); U_ASSERT(uprv_strlen(rep) < sizeof(rep));

648
icu4c/source/i18n/double-conversion-bignum-dtoa.cpp Normal file
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@ -0,0 +1,648 @@
// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// 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.
#include <math.h>
// ICU PATCH: Customize header file paths for ICU.
#include "double-conversion-bignum-dtoa.h"
#include "double-conversion-bignum.h"
#include "double-conversion-ieee.h"
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(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,
Vector<char> buffer, int* length);
// Generates 'requested_digits' after the decimal point.
static void BignumToFixed(int requested_digits, int* decimal_point,
Bignum* numerator, Bignum* denominator,
Vector<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,
Vector<char>(buffer), int* length);
void BignumDtoa(double v, BignumDtoaMode mode, int requested_digits,
Vector<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,
Vector<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);
}
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;
}
}
}
// 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,
Vector<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,
Vector<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;
} 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

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// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// 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_BIGNUM_DTOA_H_
#define DOUBLE_CONVERSION_BIGNUM_DTOA_H_
// ICU PATCH: Customize header file paths for ICU.
#include "double-conversion-utils.h"
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,
// 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,
Vector<char> buffer, int* length, int* point);
} // namespace double_conversion
#endif // DOUBLE_CONVERSION_BIGNUM_DTOA_H_

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// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// 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.
// ICU PATCH: Customize header file paths for ICU.
#include "double-conversion-bignum.h"
#include "double-conversion-utils.h"
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) {
(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(Vector<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(Vector<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();
}
static int HexCharValue(char c) {
if ('0' <= c && c <= '9') return c - '0';
if ('a' <= c && c <= 'f') return 10 + c - 'a';
ASSERT('A' <= c && c <= 'F');
return 10 + c - 'A';
}
void Bignum::AssignHexString(Vector<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 += HexCharValue(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 += HexCharValue(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++;
}
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 `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';
}
}
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;
}
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;
}
}
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];
}
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);
}
}
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);
}
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 double_conversion

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// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// 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_BIGNUM_H_
#define DOUBLE_CONVERSION_BIGNUM_H_
// ICU PATCH: Customize header file paths for ICU.
#include "double-conversion-utils.h"
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(Vector<const char> value);
void AssignHexString(Vector<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 vector backed by bigits_buffer_. This way accesses to the array are
// checked for out-of-bounds errors.
Vector<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
#endif // DOUBLE_CONVERSION_BIGNUM_H_

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// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// Copyright 2006-2008 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.
#include <stdarg.h>
#include <limits.h>
#include <math.h>
// ICU PATCH: Customize header file paths for ICU.
#include "double-conversion-utils.h"
#include "double-conversion-cached-powers.h"
namespace double_conversion {
struct CachedPower {
uint64_t significand;
int16_t binary_exponent;
int16_t decimal_exponent;
};
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},
};
static const int kCachedPowersOffset = 348; // -1 * the first decimal_exponent.
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

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// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// 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_CACHED_POWERS_H_
#define DOUBLE_CONVERSION_CACHED_POWERS_H_
// ICU PATCH: Customize header file paths for ICU.
#include "double-conversion-diy-fp.h"
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
#endif // DOUBLE_CONVERSION_CACHED_POWERS_H_

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// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// 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.
// ICU PATCH: Customize header file paths for ICU.
#include "double-conversion-diy-fp.h"
#include "double-conversion-utils.h"
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

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// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// 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_DIY_FP_H_
#define DOUBLE_CONVERSION_DIY_FP_H_
// ICU PATCH: Customize header file paths for ICU.
#include "double-conversion-utils.h"
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 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
#endif // DOUBLE_CONVERSION_DIY_FP_H_

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// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// 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:
//
// * 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.
// ICU PATCH: Customize header file paths for ICU.
#include "double-conversion-fast-dtoa.h"
#include "double-conversion-cached-powers.h"
#include "double-conversion-diy-fp.h"
#include "double-conversion-ieee.h"
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(Vector<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(Vector<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;
}
// 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,
Vector<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);
}
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);
}
}
}
// 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,
Vector<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);
}
// 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,
Vector<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,
Vector<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,
Vector<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

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// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// 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_FAST_DTOA_H_
#define DOUBLE_CONVERSION_FAST_DTOA_H_
// ICU PATCH: Customize header file paths for ICU.
#include "double-conversion-utils.h"
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.
FAST_DTOA_SHORTEST,
// Same as FAST_DTOA_SHORTEST but for single-precision floats.
FAST_DTOA_SHORTEST_SINGLE,
// Computes a representation where the precision (number of digits) is
// given as input. The precision is independent of the decimal point.
FAST_DTOA_PRECISION
};
// FastDtoa will produce at most kFastDtoaMaximalLength digits. This does not
// include the terminating '\0' character.
static const int kFastDtoaMaximalLength = 17;
// Same for single-precision numbers.
static const int kFastDtoaMaximalSingleLength = 9;
// Provides a decimal representation of v.
// The result should be interpreted as buffer * 10^(point - length).
//
// Precondition:
// * v must be a strictly positive finite double.
//
// Returns true if it succeeds, otherwise the result can not be trusted.
// There will be *length digits inside the buffer followed by a null terminator.
// If the function returns true and mode equals
// - FAST_DTOA_SHORTEST, then
// the parameter requested_digits is ignored.
// The result satisfies
// v == (double) (buffer * 10^(point - length)).
// The digits in the buffer are the shortest representation possible. E.g.
// if 0.099999999999 and 0.1 represent the same double then "1" is returned
// with point = 0.
// The last digit will be closest to the actual v. That is, even if several
// digits might correctly yield 'v' when read again, the buffer will contain
// the one closest to v.
// - FAST_DTOA_PRECISION, then
// the buffer contains requested_digits digits.
// the difference v - (buffer * 10^(point-length)) is closest to zero for
// all possible representations of requested_digits digits.
// If there are two values that are equally close, then FastDtoa returns
// false.
// For both modes the buffer must be large enough to hold the result.
bool FastDtoa(double d,
FastDtoaMode mode,
int requested_digits,
Vector<char> buffer,
int* length,
int* decimal_point);
} // namespace double_conversion
#endif // DOUBLE_CONVERSION_FAST_DTOA_H_

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// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// 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:
//
// * 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_
// ICU PATCH: Customize header file paths for ICU.
#include "double-conversion-diy-fp.h"
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); }
static uint32_t float_to_uint32(float f) { return BitCast<uint32_t>(f); }
static float uint32_to_float(uint32_t d32) { return BitCast<float>(d32); }
// 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();
}
}
double PreviousDouble() const {
if (d64_ == (kInfinity | kSignMask)) return -Infinity();
if (Sign() < 0) {
return Double(d64_ + 1).value();
} else {
if (Significand() == 0) return -0.0;
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();
DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
DiyFp m_minus;
if (LowerBoundaryIsCloser()) {
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;
}
bool LowerBoundaryIsCloser() const {
// The boundary is closer if the significand is of the form f == 2^p-1 then
// the lower 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.
bool physical_significand_is_zero = ((AsUint64() & kSignificandMask) == 0);
return physical_significand_is_zero && (Exponent() != kDenormalExponent);
}
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);
}
DISALLOW_COPY_AND_ASSIGN(Double);
};
class Single {
public:
static const uint32_t kSignMask = 0x80000000;
static const uint32_t kExponentMask = 0x7F800000;
static const uint32_t kSignificandMask = 0x007FFFFF;
static const uint32_t kHiddenBit = 0x00800000;
static const int kPhysicalSignificandSize = 23; // Excludes the hidden bit.
static const int kSignificandSize = 24;
Single() : d32_(0) {}
explicit Single(float f) : d32_(float_to_uint32(f)) {}
explicit Single(uint32_t d32) : d32_(d32) {}
// The value encoded by this Single 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());
}
// Returns the single's bit as uint64.
uint32_t AsUint32() const {
return d32_;
}
int Exponent() const {
if (IsDenormal()) return kDenormalExponent;
uint32_t d32 = AsUint32();
int biased_e =
static_cast<int>((d32 & kExponentMask) >> kPhysicalSignificandSize);
return biased_e - kExponentBias;
}
uint32_t Significand() const {
uint32_t d32 = AsUint32();
uint32_t significand = d32 & kSignificandMask;
if (!IsDenormal()) {
return significand + kHiddenBit;
} else {
return significand;
}
}
// Returns true if the single is a denormal.
bool IsDenormal() const {
uint32_t d32 = AsUint32();
return (d32 & kExponentMask) == 0;
}
// We consider denormals not to be special.
// Hence only Infinity and NaN are special.
bool IsSpecial() const {
uint32_t d32 = AsUint32();
return (d32 & kExponentMask) == kExponentMask;
}
bool IsNan() const {
uint32_t d32 = AsUint32();
return ((d32 & kExponentMask) == kExponentMask) &&
((d32 & kSignificandMask) != 0);
}
bool IsInfinite() const {
uint32_t d32 = AsUint32();
return ((d32 & kExponentMask) == kExponentMask) &&
((d32 & kSignificandMask) == 0);
}
int Sign() const {
uint32_t d32 = AsUint32();
return (d32 & kSignMask) == 0? 1: -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 Single must be greater than 0.
void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
ASSERT(value() > 0.0);
DiyFp v = this->AsDiyFp();
DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
DiyFp m_minus;
if (LowerBoundaryIsCloser()) {
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;
}
// Precondition: the value encoded by this Single must be greater or equal
// than +0.0.
DiyFp UpperBoundary() const {
ASSERT(Sign() > 0);
return DiyFp(Significand() * 2 + 1, Exponent() - 1);
}
bool LowerBoundaryIsCloser() const {
// The boundary is closer if the significand is of the form f == 2^p-1 then
// the lower 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.
bool physical_significand_is_zero = ((AsUint32() & kSignificandMask) == 0);
return physical_significand_is_zero && (Exponent() != kDenormalExponent);
}
float value() const { return uint32_to_float(d32_); }
static float Infinity() {
return Single(kInfinity).value();
}
static float NaN() {
return Single(kNaN).value();
}
private:
static const int kExponentBias = 0x7F + kPhysicalSignificandSize;
static const int kDenormalExponent = -kExponentBias + 1;
static const int kMaxExponent = 0xFF - kExponentBias;
static const uint32_t kInfinity = 0x7F800000;
static const uint32_t kNaN = 0x7FC00000;
const uint32_t d32_;
DISALLOW_COPY_AND_ASSIGN(Single);
};
} // namespace double_conversion
#endif // DOUBLE_CONVERSION_DOUBLE_H_

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// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// 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_UTILS_H_
#define DOUBLE_CONVERSION_UTILS_H_
#include <stdlib.h>
#include <string.h>
// ICU PATCH: Use U_ASSERT instead of <assert.h>
#include "uassert.h"
#define ASSERT U_ASSERT
#ifndef UNIMPLEMENTED
#define UNIMPLEMENTED() (abort())
#endif
#ifndef DOUBLE_CONVERSION_NO_RETURN
#ifdef _MSC_VER
#define DOUBLE_CONVERSION_NO_RETURN __declspec(noreturn)
#else
#define DOUBLE_CONVERSION_NO_RETURN __attribute__((noreturn))
#endif
#endif
#ifndef UNREACHABLE
#ifdef _MSC_VER
void DOUBLE_CONVERSION_NO_RETURN abort_noreturn();
inline void abort_noreturn() { abort(); }
#define UNREACHABLE() (abort_noreturn())
#else
#define UNREACHABLE() (abort())
#endif
#endif
// Double operations detection based on target architecture.
// Linux uses a 80bit wide floating point stack on x86. This induces double
// rounding, which in turn leads to wrong results.
// An easy way to test if the floating-point operations are correct is to
// evaluate: 89255.0/1e22. If the floating-point stack is 64 bits wide then
// the result is equal to 89255e-22.
// The best way to test this, is to create a division-function and to compare
// the output of the division with the expected result. (Inlining must be
// disabled.)
// On Linux,x86 89255e-22 != Div_double(89255.0/1e22)
#if defined(_M_X64) || defined(__x86_64__) || \
defined(__ARMEL__) || defined(__avr32__) || \
defined(__hppa__) || defined(__ia64__) || \
defined(__mips__) || \
defined(__powerpc__) || defined(__ppc__) || defined(__ppc64__) || \
defined(_POWER) || defined(_ARCH_PPC) || defined(_ARCH_PPC64) || \
defined(__sparc__) || defined(__sparc) || defined(__s390__) || \
defined(__SH4__) || defined(__alpha__) || \
defined(_MIPS_ARCH_MIPS32R2) || \
defined(__AARCH64EL__) || defined(__aarch64__) || \
defined(__riscv)
#define DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS 1
#elif defined(__mc68000__)
#undef DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS
#elif defined(_M_IX86) || defined(__i386__) || defined(__i386)
#if defined(_WIN32)
// Windows uses a 64bit wide floating point stack.
#define DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS 1
#else
#undef DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS
#endif // _WIN32
#else
#error Target architecture was not detected as supported by Double-Conversion.
#endif
#if defined(__GNUC__)
#define DOUBLE_CONVERSION_UNUSED __attribute__((unused))
#else
#define DOUBLE_CONVERSION_UNUSED
#endif
#if defined(_WIN32) && !defined(__MINGW32__)
typedef signed char int8_t;
typedef unsigned char uint8_t;
typedef short int16_t; // NOLINT
typedef unsigned short uint16_t; // NOLINT
typedef int int32_t;
typedef unsigned int uint32_t;
typedef __int64 int64_t;
typedef unsigned __int64 uint64_t;
// intptr_t and friends are defined in crtdefs.h through stdio.h.
#else
#include <stdint.h>
#endif
typedef uint16_t uc16;
// The following macro works on both 32 and 64-bit platforms.
// Usage: instead of writing 0x1234567890123456
// write UINT64_2PART_C(0x12345678,90123456);
#define UINT64_2PART_C(a, b) (((static_cast<uint64_t>(a) << 32) + 0x##b##u))
// The expression ARRAY_SIZE(a) is a compile-time constant of type
// size_t which represents the number of elements of the given
// array. You should only use ARRAY_SIZE on statically allocated
// arrays.
#ifndef ARRAY_SIZE
#define ARRAY_SIZE(a) \
((sizeof(a) / sizeof(*(a))) / \
static_cast<size_t>(!(sizeof(a) % sizeof(*(a)))))
#endif
// A macro to disallow the evil copy constructor and operator= functions
// This should be used in the private: declarations for a class
#ifndef DISALLOW_COPY_AND_ASSIGN
#define DISALLOW_COPY_AND_ASSIGN(TypeName) \
TypeName(const TypeName&); \
void operator=(const TypeName&)
#endif
// A macro to disallow all the implicit constructors, namely the
// default constructor, copy constructor and operator= functions.
//
// This should be used in the private: declarations for a class
// that wants to prevent anyone from instantiating it. This is
// especially useful for classes containing only static methods.
#ifndef DISALLOW_IMPLICIT_CONSTRUCTORS
#define DISALLOW_IMPLICIT_CONSTRUCTORS(TypeName) \
TypeName(); \
DISALLOW_COPY_AND_ASSIGN(TypeName)
#endif
namespace double_conversion {
static const int kCharSize = sizeof(char);
// Returns the maximum of the two parameters.
template <typename T>
static T Max(T a, T b) {
return a < b ? b : a;
}
// Returns the minimum of the two parameters.
template <typename T>
static T Min(T a, T b) {
return a < b ? a : b;
}
inline int StrLength(const char* string) {
size_t length = strlen(string);
ASSERT(length == static_cast<size_t>(static_cast<int>(length)));
return static_cast<int>(length);
}
// This is a simplified version of V8's Vector class.
template <typename T>
class Vector {
public:
Vector() : start_(NULL), length_(0) {}
Vector(T* data, int len) : start_(data), length_(len) {
ASSERT(len == 0 || (len > 0 && data != NULL));
}
// Returns a vector using the same backing storage as this one,
// spanning from and including 'from', to but not including 'to'.
Vector<T> SubVector(int from, int to) {
ASSERT(to <= length_);
ASSERT(from < to);
ASSERT(0 <= from);
return Vector<T>(start() + from, to - from);
}
// Returns the length of the vector.
int length() const { return length_; }
// Returns whether or not the vector is empty.
bool is_empty() const { return length_ == 0; }
// Returns the pointer to the start of the data in the vector.
T* start() const { return start_; }
// Access individual vector elements - checks bounds in debug mode.
T& operator[](int index) const {
ASSERT(0 <= index && index < length_);
return start_[index];
}
T& first() { return start_[0]; }
T& last() { return start_[length_ - 1]; }
private:
T* start_;
int length_;
};
// Helper class for building result strings in a character buffer. The
// purpose of the class is to use safe operations that checks the
// buffer bounds on all operations in debug mode.
class StringBuilder {
public:
StringBuilder(char* buffer, int buffer_size)
: buffer_(buffer, buffer_size), position_(0) { }
~StringBuilder() { if (!is_finalized()) Finalize(); }
int size() const { return buffer_.length(); }
// Get the current position in the builder.
int position() const {
ASSERT(!is_finalized());
return position_;
}
// Reset the position.
void Reset() { position_ = 0; }
// Add a single character to the builder. It is not allowed to add
// 0-characters; use the Finalize() method to terminate the string
// instead.
void AddCharacter(char c) {
ASSERT(c != '\0');
ASSERT(!is_finalized() && position_ < buffer_.length());
buffer_[position_++] = c;
}
// Add an entire string to the builder. Uses strlen() internally to
// compute the length of the input string.
void AddString(const char* s) {
AddSubstring(s, StrLength(s));
}
// Add the first 'n' characters of the given string 's' to the
// builder. The input string must have enough characters.
void AddSubstring(const char* s, int n) {
ASSERT(!is_finalized() && position_ + n < buffer_.length());
ASSERT(static_cast<size_t>(n) <= strlen(s));
memmove(&buffer_[position_], s, n * kCharSize);
position_ += n;
}
// Add character padding to the builder. If count is non-positive,
// nothing is added to the builder.
void AddPadding(char c, int count) {
for (int i = 0; i < count; i++) {
AddCharacter(c);
}
}
// Finalize the string by 0-terminating it and returning the buffer.
char* Finalize() {
ASSERT(!is_finalized() && position_ < buffer_.length());
buffer_[position_] = '\0';
// Make sure nobody managed to add a 0-character to the
// buffer while building the string.
ASSERT(strlen(buffer_.start()) == static_cast<size_t>(position_));
position_ = -1;
ASSERT(is_finalized());
return buffer_.start();
}
private:
Vector<char> buffer_;
int position_;
bool is_finalized() const { return position_ < 0; }
DISALLOW_IMPLICIT_CONSTRUCTORS(StringBuilder);
};
// The type-based aliasing rule allows the compiler to assume that pointers of
// different types (for some definition of different) never alias each other.
// Thus the following code does not work:
//
// float f = foo();
// int fbits = *(int*)(&f);
//
// The compiler 'knows' that the int pointer can't refer to f since the types
// don't match, so the compiler may cache f in a register, leaving random data
// in fbits. Using C++ style casts makes no difference, however a pointer to
// char data is assumed to alias any other pointer. This is the 'memcpy
// exception'.
//
// Bit_cast uses the memcpy exception to move the bits from a variable of one
// type of a variable of another type. Of course the end result is likely to
// be implementation dependent. Most compilers (gcc-4.2 and MSVC 2005)
// will completely optimize BitCast away.
//
// There is an additional use for BitCast.
// Recent gccs will warn when they see casts that may result in breakage due to
// the type-based aliasing rule. If you have checked that there is no breakage
// you can use BitCast to cast one pointer type to another. This confuses gcc
// enough that it can no longer see that you have cast one pointer type to
// another thus avoiding the warning.
template <class Dest, class Source>
inline Dest BitCast(const Source& source) {
// Compile time assertion: sizeof(Dest) == sizeof(Source)
// A compile error here means your Dest and Source have different sizes.
DOUBLE_CONVERSION_UNUSED
typedef char VerifySizesAreEqual[sizeof(Dest) == sizeof(Source) ? 1 : -1];
Dest dest;
memmove(&dest, &source, sizeof(dest));
return dest;
}
template <class Dest, class Source>
inline Dest BitCast(Source* source) {
return BitCast<Dest>(reinterpret_cast<uintptr_t>(source));
}
} // namespace double_conversion
#endif // DOUBLE_CONVERSION_UTILS_H_

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// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// 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.
#include <limits.h>
#include <math.h>
// ICU PATCH: Customize header file paths for ICU.
// The files fixed-dtoa.h and strtod.h are not needed.
#include "double-conversion.h"
#include "double-conversion-bignum-dtoa.h"
#include "double-conversion-fast-dtoa.h"
#include "double-conversion-ieee.h"
#include "double-conversion-utils.h"
namespace double_conversion {
#if 0 // not needed for ICU
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('-');
}
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('+');
}
}
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);
}
} 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');
}
}
}
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';
}
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';
}
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;
}
#endif // not needed for ICU
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) {
Vector<char> vector(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) {
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;
#if 0 // not needed for ICU
case SHORTEST_SINGLE:
fast_worked = FastDtoa(v, FAST_DTOA_SHORTEST_SINGLE, 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;
#endif // not needed for ICU
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, vector, length, point);
vector[*length] = '\0';
}
#if 0 // not needed for ICU
// Consumes the given substring from the iterator.
// Returns false, if the substring does not match.
template <class Iterator>
static bool ConsumeSubString(Iterator* current,
Iterator end,
const char* substring) {
ASSERT(**current == *substring);
for (substring++; *substring != '\0'; substring++) {
++*current;
if (*current == end || **current != *substring) return false;
}
++*current;
return true;
}
// 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 const char kWhitespaceTable7[] = { 32, 13, 10, 9, 11, 12 };
static const int kWhitespaceTable7Length = ARRAY_SIZE(kWhitespaceTable7);
static const uc16 kWhitespaceTable16[] = {
160, 8232, 8233, 5760, 6158, 8192, 8193, 8194, 8195,
8196, 8197, 8198, 8199, 8200, 8201, 8202, 8239, 8287, 12288, 65279
};
static const int kWhitespaceTable16Length = ARRAY_SIZE(kWhitespaceTable16);
static bool isWhitespace(int x) {
if (x < 128) {
for (int i = 0; i < kWhitespaceTable7Length; i++) {
if (kWhitespaceTable7[i] == x) return true;
}
} else {
for (int i = 0; i < kWhitespaceTable16Length; i++) {
if (kWhitespaceTable16[i] == x) return true;
}
}
return false;
}
// Returns true if a nonspace found and false if the end has reached.
template <class Iterator>
static inline bool AdvanceToNonspace(Iterator* current, Iterator end) {
while (*current != end) {
if (!isWhitespace(**current)) return true;
++*current;
}
return false;
}
static bool isDigit(int x, int radix) {
return (x >= '0' && x <= '9' && x < '0' + radix)
|| (radix > 10 && x >= 'a' && x < 'a' + radix - 10)
|| (radix > 10 && x >= 'A' && x < 'A' + radix - 10);
}
static double SignedZero(bool sign) {
return sign ? -0.0 : 0.0;
}
// Returns true if 'c' is a decimal digit that is valid for the given radix.
//
// The function is small and could be inlined, but VS2012 emitted a warning
// because it constant-propagated the radix and concluded that the last
// condition was always true. By moving it into a separate function the
// compiler wouldn't warn anymore.
#if _MSC_VER
#pragma optimize("",off)
static bool IsDecimalDigitForRadix(int c, int radix) {
return '0' <= c && c <= '9' && (c - '0') < radix;
}
#pragma optimize("",on)
#else
static bool inline IsDecimalDigitForRadix(int c, int radix) {
return '0' <= c && c <= '9' && (c - '0') < radix;
}
#endif
// Returns true if 'c' is a character digit that is valid for the given radix.
// The 'a_character' should be 'a' or 'A'.
//
// The function is small and could be inlined, but VS2012 emitted a warning
// because it constant-propagated the radix and concluded that the first
// condition was always false. By moving it into a separate function the
// compiler wouldn't warn anymore.
static bool IsCharacterDigitForRadix(int c, int radix, char a_character) {
return radix > 10 && c >= a_character && c < a_character + radix - 10;
}
// Parsing integers with radix 2, 4, 8, 16, 32. Assumes current != end.
template <int radix_log_2, class Iterator>
static double RadixStringToIeee(Iterator* current,
Iterator end,
bool sign,
bool allow_trailing_junk,
double junk_string_value,
bool read_as_double,
bool* result_is_junk) {
ASSERT(*current != end);
const int kDoubleSize = Double::kSignificandSize;
const int kSingleSize = Single::kSignificandSize;
const int kSignificandSize = read_as_double? kDoubleSize: kSingleSize;
*result_is_junk = true;
// Skip leading 0s.
while (**current == '0') {
++(*current);
if (*current == end) {
*result_is_junk = false;
return SignedZero(sign);
}
}
int64_t number = 0;
int exponent = 0;
const int radix = (1 << radix_log_2);
do {
int digit;
if (IsDecimalDigitForRadix(**current, radix)) {
digit = static_cast<char>(**current) - '0';
} else if (IsCharacterDigitForRadix(**current, radix, 'a')) {
digit = static_cast<char>(**current) - 'a' + 10;
} else if (IsCharacterDigitForRadix(**current, radix, 'A')) {
digit = static_cast<char>(**current) - 'A' + 10;
} else {
if (allow_trailing_junk || !AdvanceToNonspace(current, end)) {
break;
} else {
return junk_string_value;
}
}
number = number * radix + digit;
int overflow = static_cast<int>(number >> kSignificandSize);
if (overflow != 0) {
// Overflow occurred. Need to determine which direction to round the
// result.
int overflow_bits_count = 1;
while (overflow > 1) {
overflow_bits_count++;
overflow >>= 1;
}
int dropped_bits_mask = ((1 << overflow_bits_count) - 1);
int dropped_bits = static_cast<int>(number) & dropped_bits_mask;
number >>= overflow_bits_count;
exponent = overflow_bits_count;
bool zero_tail = true;
for (;;) {
++(*current);
if (*current == end || !isDigit(**current, radix)) break;
zero_tail = zero_tail && **current == '0';
exponent += radix_log_2;
}
if (!allow_trailing_junk && AdvanceToNonspace(current, end)) {
return junk_string_value;
}
int middle_value = (1 << (overflow_bits_count - 1));
if (dropped_bits > middle_value) {
number++; // Rounding up.
} else if (dropped_bits == middle_value) {
// Rounding to even to consistency with decimals: half-way case rounds
// up if significant part is odd and down otherwise.
if ((number & 1) != 0 || !zero_tail) {
number++; // Rounding up.
}
}
// Rounding up may cause overflow.
if ((number & ((int64_t)1 << kSignificandSize)) != 0) {
exponent++;
number >>= 1;
}
break;
}
++(*current);
} while (*current != end);
ASSERT(number < ((int64_t)1 << kSignificandSize));
ASSERT(static_cast<int64_t>(static_cast<double>(number)) == number);
*result_is_junk = false;
if (exponent == 0) {
if (sign) {
if (number == 0) return -0.0;
number = -number;
}
return static_cast<double>(number);
}
ASSERT(number != 0);
return Double(DiyFp(number, exponent)).value();
}
template <class Iterator>
double StringToDoubleConverter::StringToIeee(
Iterator input,
int length,
bool read_as_double,
int* processed_characters_count) const {
Iterator current = input;
Iterator end = input + length;
*processed_characters_count = 0;
const bool allow_trailing_junk = (flags_ & ALLOW_TRAILING_JUNK) != 0;
const bool allow_leading_spaces = (flags_ & ALLOW_LEADING_SPACES) != 0;
const bool allow_trailing_spaces = (flags_ & ALLOW_TRAILING_SPACES) != 0;
const bool allow_spaces_after_sign = (flags_ & ALLOW_SPACES_AFTER_SIGN) != 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'.
// 2. If AdvanceToNonspace returned false then current == 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 empty_string_value_;
if (allow_leading_spaces || allow_trailing_spaces) {
if (!AdvanceToNonspace(&current, end)) {
*processed_characters_count = static_cast<int>(current - input);
return empty_string_value_;
}
if (!allow_leading_spaces && (input != current)) {
// No leading spaces allowed, but AdvanceToNonspace moved forward.
return junk_string_value_;
}
}
// 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;
Iterator next_non_space = current;
// Skip following spaces (if allowed).
if (!AdvanceToNonspace(&next_non_space, end)) return junk_string_value_;
if (!allow_spaces_after_sign && (current != next_non_space)) {
return junk_string_value_;
}
current = next_non_space;
}
if (infinity_symbol_ != NULL) {
if (*current == infinity_symbol_[0]) {
if (!ConsumeSubString(&current, end, infinity_symbol_)) {
return junk_string_value_;
}
if (!(allow_trailing_spaces || allow_trailing_junk) && (current != end)) {
return junk_string_value_;
}
if (!allow_trailing_junk && AdvanceToNonspace(&current, end)) {
return junk_string_value_;
}
ASSERT(buffer_pos == 0);
*processed_characters_count = static_cast<int>(current - input);
return sign ? -Double::Infinity() : Double::Infinity();
}
}
if (nan_symbol_ != NULL) {
if (*current == nan_symbol_[0]) {
if (!ConsumeSubString(&current, end, nan_symbol_)) {
return junk_string_value_;
}
if (!(allow_trailing_spaces || allow_trailing_junk) && (current != end)) {
return junk_string_value_;
}
if (!allow_trailing_junk && AdvanceToNonspace(&current, end)) {
return junk_string_value_;
}
ASSERT(buffer_pos == 0);
*processed_characters_count = static_cast<int>(current - input);
return sign ? -Double::NaN() : Double::NaN();
}
}
bool leading_zero = false;
if (*current == '0') {
++current;
if (current == end) {
*processed_characters_count = static_cast<int>(current - input);
return SignedZero(sign);
}
leading_zero = true;
// It could be hexadecimal value.
if ((flags_ & ALLOW_HEX) && (*current == 'x' || *current == 'X')) {
++current;
if (current == end || !isDigit(*current, 16)) {
return junk_string_value_; // "0x".
}
bool result_is_junk;
double result = RadixStringToIeee<4>(&current,
end,
sign,
allow_trailing_junk,
junk_string_value_,
read_as_double,
&result_is_junk);
if (!result_is_junk) {
if (allow_trailing_spaces) AdvanceToNonspace(&current, end);
*processed_characters_count = static_cast<int>(current - input);
}
return result;
}
// Ignore leading zeros in the integer part.
while (*current == '0') {
++current;
if (current == end) {
*processed_characters_count = static_cast<int>(current - input);
return SignedZero(sign);
}
}
}
bool octal = leading_zero && (flags_ & ALLOW_OCTALS) != 0;
// Copy significant digits of the integer part (if any) to the buffer.
while (*current >= '0' && *current <= '9') {
if (significant_digits < kMaxSignificantDigits) {
ASSERT(buffer_pos < kBufferSize);
buffer[buffer_pos++] = static_cast<char>(*current);
significant_digits++;
// Will later check if it's an octal in the buffer.
} else {
insignificant_digits++; // Move the digit into the exponential part.
nonzero_digit_dropped = nonzero_digit_dropped || *current != '0';
}
octal = octal && *current < '8';
++current;
if (current == end) goto parsing_done;
}
if (significant_digits == 0) {
octal = false;
}
if (*current == '.') {
if (octal && !allow_trailing_junk) return junk_string_value_;
if (octal) goto parsing_done;
++current;
if (current == end) {
if (significant_digits == 0 && !leading_zero) {
return junk_string_value_;
} else {
goto parsing_done;
}
}
if (significant_digits == 0) {
// octal = false;
// 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 = static_cast<int>(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 (*current >= '0' && *current <= '9') {
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 junk_string_value_;
}
// Parse exponential part.
if (*current == 'e' || *current == 'E') {
if (octal && !allow_trailing_junk) return junk_string_value_;
if (octal) goto parsing_done;
++current;
if (current == end) {
if (allow_trailing_junk) {
goto parsing_done;
} else {
return junk_string_value_;
}
}
char exponen_sign = '+';
if (*current == '+' || *current == '-') {
exponen_sign = static_cast<char>(*current);
++current;
if (current == end) {
if (allow_trailing_junk) {
goto parsing_done;
} else {
return junk_string_value_;
}
}
}
if (current == end || *current < '0' || *current > '9') {
if (allow_trailing_junk) {
goto parsing_done;
} else {
return junk_string_value_;
}
}
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 && *current >= '0' && *current <= '9');
exponent += (exponen_sign == '-' ? -num : num);
}
if (!(allow_trailing_spaces || allow_trailing_junk) && (current != end)) {
return junk_string_value_;
}
if (!allow_trailing_junk && AdvanceToNonspace(&current, end)) {
return junk_string_value_;
}
if (allow_trailing_spaces) {
AdvanceToNonspace(&current, end);
}
parsing_done:
exponent += insignificant_digits;
if (octal) {
double result;
bool result_is_junk;
char* start = buffer;
result = RadixStringToIeee<3>(&start,
buffer + buffer_pos,
sign,
allow_trailing_junk,
junk_string_value_,
read_as_double,
&result_is_junk);
ASSERT(!result_is_junk);
*processed_characters_count = static_cast<int>(current - input);
return result;
}
if (nonzero_digit_dropped) {
buffer[buffer_pos++] = '1';
exponent--;
}
ASSERT(buffer_pos < kBufferSize);
buffer[buffer_pos] = '\0';
double converted;
if (read_as_double) {
converted = Strtod(Vector<const char>(buffer, buffer_pos), exponent);
} else {
converted = Strtof(Vector<const char>(buffer, buffer_pos), exponent);
}
*processed_characters_count = static_cast<int>(current - input);
return sign? -converted: converted;
}
double StringToDoubleConverter::StringToDouble(
const char* buffer,
int length,
int* processed_characters_count) const {
return StringToIeee(buffer, length, true, processed_characters_count);
}
double StringToDoubleConverter::StringToDouble(
const uc16* buffer,
int length,
int* processed_characters_count) const {
return StringToIeee(buffer, length, true, processed_characters_count);
}
float StringToDoubleConverter::StringToFloat(
const char* buffer,
int length,
int* processed_characters_count) const {
return static_cast<float>(StringToIeee(buffer, length, false,
processed_characters_count));
}
float StringToDoubleConverter::StringToFloat(
const uc16* buffer,
int length,
int* processed_characters_count) const {
return static_cast<float>(StringToIeee(buffer, length, false,
processed_characters_count));
}
#endif // not needed for ICU
} // namespace double_conversion

554
icu4c/source/i18n/double-conversion.h Normal file
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@ -0,0 +1,554 @@
// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// 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:
//
// * 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_CONVERSION_H_
#define DOUBLE_CONVERSION_DOUBLE_CONVERSION_H_
// ICU PATCH: Customize header file paths for ICU.
#include "double-conversion-utils.h"
namespace double_conversion {
class DoubleToStringConverter {
public:
#if 0 // not needed for ICU
// 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_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.
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).
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;
#endif // not needed for ICU
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 ascii. '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 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);
#if 0 // not needed for ICU
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_;
DISALLOW_IMPLICIT_CONSTRUCTORS(DoubleToStringConverter);
};
class StringToDoubleConverter {
public:
// Enumeration for allowing octals and ignoring junk when converting
// strings to numbers.
enum Flags {
NO_FLAGS = 0,
ALLOW_HEX = 1,
ALLOW_OCTALS = 2,
ALLOW_TRAILING_JUNK = 4,
ALLOW_LEADING_SPACES = 8,
ALLOW_TRAILING_SPACES = 16,
ALLOW_SPACES_AFTER_SIGN = 32
};
// Flags should be a bit-or combination of the possible Flags-enum.
// - NO_FLAGS: no special flags.
// - ALLOW_HEX: recognizes the prefix "0x". Hex numbers may only be integers.
// Ex: StringToDouble("0x1234") -> 4660.0
// In StringToDouble("0x1234.56") the characters ".56" are trailing
// junk. The result of the call is hence dependent on
// the ALLOW_TRAILING_JUNK flag and/or the junk value.
// With this flag "0x" is a junk-string. Even with ALLOW_TRAILING_JUNK,
// the string will not be parsed as "0" followed by junk.
//
// - ALLOW_OCTALS: recognizes the prefix "0" for octals:
// If a sequence of octal digits starts with '0', then the number is
// read as octal integer. Octal numbers may only be integers.
// Ex: StringToDouble("01234") -> 668.0
// StringToDouble("012349") -> 12349.0 // Not a sequence of octal
// // digits.
// In StringToDouble("01234.56") the characters ".56" are trailing
// junk. The result of the call is hence dependent on
// the ALLOW_TRAILING_JUNK flag and/or the junk value.
// In StringToDouble("01234e56") the characters "e56" are trailing
// junk, too.
// - ALLOW_TRAILING_JUNK: ignore trailing characters that are not part of
// a double literal.
// - ALLOW_LEADING_SPACES: skip over leading whitespace, including spaces,
// new-lines, and tabs.
// - ALLOW_TRAILING_SPACES: ignore trailing whitespace.
// - ALLOW_SPACES_AFTER_SIGN: ignore whitespace after the sign.
// Ex: StringToDouble("- 123.2") -> -123.2.
// StringToDouble("+ 123.2") -> 123.2
//
// empty_string_value is returned when an empty string is given as input.
// If ALLOW_LEADING_SPACES or ALLOW_TRAILING_SPACES are set, then a string
// containing only spaces is converted to the 'empty_string_value', too.
//
// junk_string_value is returned when
// a) ALLOW_TRAILING_JUNK is not set, and a junk character (a character not
// part of a double-literal) is found.
// b) ALLOW_TRAILING_JUNK is set, but the string does not start with a
// double literal.
//
// infinity_symbol and nan_symbol are strings that are used to detect
// inputs that represent infinity and NaN. They can be null, in which case
// they are ignored.
// The conversion routine first reads any possible signs. Then it compares the
// following character of the input-string with the first character of
// the infinity, and nan-symbol. If either matches, the function assumes, that
// a match has been found, and expects the following input characters to match
// the remaining characters of the special-value symbol.
// This means that the following restrictions apply to special-value symbols:
// - they must not start with signs ('+', or '-'),
// - they must not have the same first character.
// - they must not start with digits.
//
// Examples:
// flags = ALLOW_HEX | ALLOW_TRAILING_JUNK,
// empty_string_value = 0.0,
// junk_string_value = NaN,
// infinity_symbol = "infinity",
// nan_symbol = "nan":
// StringToDouble("0x1234") -> 4660.0.
// StringToDouble("0x1234K") -> 4660.0.
// StringToDouble("") -> 0.0 // empty_string_value.
// StringToDouble(" ") -> NaN // junk_string_value.
// StringToDouble(" 1") -> NaN // junk_string_value.
// StringToDouble("0x") -> NaN // junk_string_value.
// StringToDouble("-123.45") -> -123.45.
// StringToDouble("--123.45") -> NaN // junk_string_value.
// StringToDouble("123e45") -> 123e45.
// StringToDouble("123E45") -> 123e45.
// StringToDouble("123e+45") -> 123e45.
// StringToDouble("123E-45") -> 123e-45.
// StringToDouble("123e") -> 123.0 // trailing junk ignored.
// StringToDouble("123e-") -> 123.0 // trailing junk ignored.
// StringToDouble("+NaN") -> NaN // NaN string literal.
// StringToDouble("-infinity") -> -inf. // infinity literal.
// StringToDouble("Infinity") -> NaN // junk_string_value.
//
// flags = ALLOW_OCTAL | ALLOW_LEADING_SPACES,
// empty_string_value = 0.0,
// junk_string_value = NaN,
// infinity_symbol = NULL,
// nan_symbol = NULL:
// StringToDouble("0x1234") -> NaN // junk_string_value.
// StringToDouble("01234") -> 668.0.
// StringToDouble("") -> 0.0 // empty_string_value.
// StringToDouble(" ") -> 0.0 // empty_string_value.
// StringToDouble(" 1") -> 1.0
// StringToDouble("0x") -> NaN // junk_string_value.
// StringToDouble("0123e45") -> NaN // junk_string_value.
// StringToDouble("01239E45") -> 1239e45.
// StringToDouble("-infinity") -> NaN // junk_string_value.
// StringToDouble("NaN") -> NaN // junk_string_value.
StringToDoubleConverter(int flags,
double empty_string_value,
double junk_string_value,
const char* infinity_symbol,
const char* nan_symbol)
: flags_(flags),
empty_string_value_(empty_string_value),
junk_string_value_(junk_string_value),
infinity_symbol_(infinity_symbol),
nan_symbol_(nan_symbol) {
}
// Performs the conversion.
// The output parameter 'processed_characters_count' is set to the number
// of characters that have been processed to read the number.
// Spaces than are processed with ALLOW_{LEADING|TRAILING}_SPACES are included
// in the 'processed_characters_count'. Trailing junk is never included.
double StringToDouble(const char* buffer,
int length,
int* processed_characters_count) const;
// Same as StringToDouble above but for 16 bit characters.
double StringToDouble(const uc16* buffer,
int length,
int* processed_characters_count) const;
// Same as StringToDouble but reads a float.
// Note that this is not equivalent to static_cast<float>(StringToDouble(...))
// due to potential double-rounding.
float StringToFloat(const char* buffer,
int length,
int* processed_characters_count) const;
// Same as StringToFloat above but for 16 bit characters.
float StringToFloat(const uc16* buffer,
int length,
int* processed_characters_count) const;
private:
const int flags_;
const double empty_string_value_;
const double junk_string_value_;
const char* const infinity_symbol_;
const char* const nan_symbol_;
template <class Iterator>
double StringToIeee(Iterator start_pointer,
int length,
bool read_as_double,
int* processed_characters_count) const;
DISALLOW_IMPLICIT_CONSTRUCTORS(StringToDoubleConverter);
#endif // not needed for ICU
};
} // namespace double_conversion
#endif // DOUBLE_CONVERSION_DOUBLE_CONVERSION_H_

6
icu4c/source/i18n/i18n.vcxproj
View File

@ -327,6 +327,12 @@
<ClCompile Include="decimfmt.cpp" /> <ClCompile Include="decimfmt.cpp" />
<ClCompile Include="decNumber.cpp" /> <ClCompile Include="decNumber.cpp" />
<ClCompile Include="digitlst.cpp" /> <ClCompile Include="digitlst.cpp" />
<ClCompile Include="double-conversion-bignum-dtoa.cpp" />
<ClCompile Include="double-conversion-bignum.cpp" />
<ClCompile Include="double-conversion-cached-powers.cpp" />
<ClCompile Include="double-conversion-diy-fp.cpp" />
<ClCompile Include="double-conversion-fast-dtoa.cpp" />
<ClCompile Include="double-conversion.cpp" />
<ClCompile Include="dtfmtsym.cpp" /> <ClCompile Include="dtfmtsym.cpp" />
<ClCompile Include="dtitvfmt.cpp" /> <ClCompile Include="dtitvfmt.cpp" />
<ClCompile Include="dtitvinf.cpp" /> <ClCompile Include="dtitvinf.cpp" />

18
icu4c/source/i18n/i18n.vcxproj.filters
View File

@ -156,6 +156,24 @@
<ClCompile Include="digitlst.cpp"> <ClCompile Include="digitlst.cpp">
<Filter>formatting</Filter> <Filter>formatting</Filter>
</ClCompile> </ClCompile>
<ClCompile Include="double-conversion-bignum-dtoa.cpp">
<Filter>formatting</Filter>
</ClCompile>
<ClCompile Include="double-conversion-bignum.cpp">
<Filter>formatting</Filter>
</ClCompile>
<ClCompile Include="double-conversion-cached-powers.cpp">
<Filter>formatting</Filter>
</ClCompile>
<ClCompile Include="double-conversion-diy-fp.cpp">
<Filter>formatting</Filter>
</ClCompile>
<ClCompile Include="double-conversion-fast-dtoa.cpp">
<Filter>formatting</Filter>
</ClCompile>
<ClCompile Include="double-conversion.cpp">
<Filter>formatting</Filter>
</ClCompile>
<ClCompile Include="dtfmtsym.cpp"> <ClCompile Include="dtfmtsym.cpp">
<Filter>formatting</Filter> <Filter>formatting</Filter>
</ClCompile> </ClCompile>

65
icu4c/source/i18n/number_decimalquantity.cpp
View File

@ -14,12 +14,15 @@
#include "decContext.h" #include "decContext.h"
#include "decNumber.h" #include "decNumber.h"
#include "number_roundingutils.h" #include "number_roundingutils.h"
#include "double-conversion.h"
#include "unicode/plurrule.h" #include "unicode/plurrule.h"
using namespace icu; using namespace icu;
using namespace icu::number; using namespace icu::number;
using namespace icu::number::impl; using namespace icu::number::impl;
using double_conversion::DoubleToStringConverter;
namespace { namespace {
int8_t NEGATIVE_FLAG = 1; int8_t NEGATIVE_FLAG = 1;
@ -396,31 +399,27 @@ void DecimalQuantity::_setToDoubleFast(double n) {
} }
void DecimalQuantity::convertToAccurateDouble() { void DecimalQuantity::convertToAccurateDouble() {
double n = origDouble; U_ASSERT(origDouble != 0);
U_ASSERT(n != 0);
int32_t delta = origDelta; int32_t delta = origDelta;
// Call the slow oracle function (Double.toString in Java, DoubleToAscii in C++).
char buffer[DoubleToStringConverter::kBase10MaximalLength + 1];
bool sign; // unused; always positive
int32_t length;
int32_t point;
DoubleToStringConverter::DoubleToAscii(
origDouble,
DoubleToStringConverter::DtoaMode::SHORTEST,
0,
buffer,
sizeof(buffer),
&sign,
&length,
&point
);
setBcdToZero(); setBcdToZero();
readDoubleConversionToBcd(buffer, length, point);
// Call the slow oracle function (Double.toString in Java, sprintf in C++).
// The <float.h> constant DBL_DIG defines a platform-specific number of digits in a double.
// However, this tends to be too low (see #11318). Instead, we always use 14 decimal places.
static constexpr size_t CAP = 1 + 14 + 8; // Extra space for '+', '.', e+NNN, and '\0'
char dstr[CAP];
snprintf(dstr, CAP, "%+1.14e", n);
// uprv_decNumberFromString() will parse the string expecting '.' as a
// decimal separator, however sprintf() can use ',' in certain locales.
// Overwrite a ',' with '.' here before proceeding.
char *decimalSeparator = strchr(dstr, ',');
if (decimalSeparator != nullptr) {
*decimalSeparator = '.';
}
StringPiece sp(dstr);
DecNumberWithStorage dn;
stringToDecNumber(dstr, dn);
_setToDecNumber(dn.getAlias());
scale += delta; scale += delta;
explicitExactDouble = true; explicitExactDouble = true;
} }
@ -837,6 +836,26 @@ void DecimalQuantity::readDecNumberToBcd(decNumber *dn) {
precision = dn->digits; precision = dn->digits;
} }
void DecimalQuantity::readDoubleConversionToBcd(
const char* buffer, int32_t length, int32_t point) {
// NOTE: Despite the fact that double-conversion's API is called
// "DoubleToAscii", they actually use '0' (as opposed to u8'0').
if (length > 16) {
ensureCapacity(length);
for (int32_t i = 0; i < length; i++) {
fBCD.bcdBytes.ptr[i] = buffer[length-i-1] - '0';
}
} else {
uint64_t result = 0L;
for (int32_t i = 0; i < length; i++) {
result |= static_cast<uint64_t>(buffer[length-i-1] - '0') << (4 * i);
}
fBCD.bcdLong = result;
}
scale = point - length;
precision = length;
}
void DecimalQuantity::compact() { void DecimalQuantity::compact() {
if (usingBytes) { if (usingBytes) {
int32_t delta = 0; int32_t delta = 0;

2
icu4c/source/i18n/number_decimalquantity.h
View File

@ -398,6 +398,8 @@ class U_I18N_API DecimalQuantity : public IFixedDecimal, public UMemory {
void readDecNumberToBcd(decNumber *dn); void readDecNumberToBcd(decNumber *dn);
void readDoubleConversionToBcd(const char* buffer, int32_t length, int32_t point);
void copyBcdFrom(const DecimalQuantity &other); void copyBcdFrom(const DecimalQuantity &other);
/** /**

2
icu4c/source/test/intltest/Makefile.in
View File

@ -64,7 +64,7 @@ scientificnumberformattertest.o datadrivennumberformattestsuite.o \
numberformattesttuple.o numberformat2test.o pluralmaptest.o \ numberformattesttuple.o numberformat2test.o pluralmaptest.o \
numbertest_affixutils.o numbertest_api.o numbertest_decimalquantity.o \ numbertest_affixutils.o numbertest_api.o numbertest_decimalquantity.o \
numbertest_modifiers.o numbertest_patternmodifier.o numbertest_patternstring.o \ numbertest_modifiers.o numbertest_patternmodifier.o numbertest_patternstring.o \
numbertest_stringbuilder.o numbertest_stringbuilder.o numbertest_doubleconversion.o
DEPS = $(OBJECTS:.o=.d) DEPS = $(OBJECTS:.o=.d)

1
icu4c/source/test/intltest/intltest.vcxproj
View File

@ -327,6 +327,7 @@
<ClCompile Include="numbertest_affixutils.cpp" /> <ClCompile Include="numbertest_affixutils.cpp" />
<ClCompile Include="numbertest_api.cpp" /> <ClCompile Include="numbertest_api.cpp" />
<ClCompile Include="numbertest_decimalquantity.cpp" /> <ClCompile Include="numbertest_decimalquantity.cpp" />
<ClCompile Include="numbertest_doubleconversion.cpp" />
<ClCompile Include="numbertest_modifiers.cpp" /> <ClCompile Include="numbertest_modifiers.cpp" />
<ClCompile Include="numbertest_patternmodifier.cpp" /> <ClCompile Include="numbertest_patternmodifier.cpp" />
<ClCompile Include="numbertest_patternstring.cpp" /> <ClCompile Include="numbertest_patternstring.cpp" />

3
icu4c/source/test/intltest/intltest.vcxproj.filters
View File

@ -268,6 +268,9 @@
<ClCompile Include="numbertest_decimalquantity.cpp"> <ClCompile Include="numbertest_decimalquantity.cpp">
<Filter>formatting</Filter> <Filter>formatting</Filter>
</ClCompile> </ClCompile>
<ClCompile Include="numbertest_doubleconversion.cpp">
<Filter>formatting</Filter>
</ClCompile>
<ClCompile Include="numbertest_modifiers.cpp"> <ClCompile Include="numbertest_modifiers.cpp">
<Filter>formatting</Filter> <Filter>formatting</Filter>
</ClCompile> </ClCompile>

9
icu4c/source/test/intltest/numbertest.h
View File

@ -110,6 +110,7 @@ class DecimalQuantityTest : public IntlTest {
void testAppend(); void testAppend();
void testConvertToAccurateDouble(); void testConvertToAccurateDouble();
void testUseApproximateDoubleWhenAble(); void testUseApproximateDoubleWhenAble();
void testHardDoubleConversion();
void runIndexedTest(int32_t index, UBool exec, const char *&name, char *par = 0); void runIndexedTest(int32_t index, UBool exec, const char *&name, char *par = 0);
@ -120,6 +121,13 @@ class DecimalQuantityTest : public IntlTest {
void checkDoubleBehavior(double d, bool explicitRequired); void checkDoubleBehavior(double d, bool explicitRequired);
}; };
class DoubleConversionTest : public IntlTest {
public:
void testDoubleConversionApi();
void runIndexedTest(int32_t index, UBool exec, const char *&name, char *par = 0);
};
class ModifiersTest : public IntlTest { class ModifiersTest : public IntlTest {
public: public:
void testConstantAffixModifier(); void testConstantAffixModifier();
@ -207,6 +215,7 @@ class NumberTest : public IntlTest {
TESTCLASS(4, PatternModifierTest); TESTCLASS(4, PatternModifierTest);
TESTCLASS(5, PatternStringTest); TESTCLASS(5, PatternStringTest);
TESTCLASS(6, NumberStringBuilderTest); TESTCLASS(6, NumberStringBuilderTest);
TESTCLASS(7, DoubleConversionTest);
default: name = ""; break; // needed to end loop default: name = ""; break; // needed to end loop
} }
} }

32
icu4c/source/test/intltest/numbertest_decimalquantity.cpp
View File

@ -20,6 +20,7 @@ void DecimalQuantityTest::runIndexedTest(int32_t index, UBool exec, const char *
TESTCASE_AUTO(testAppend); TESTCASE_AUTO(testAppend);
TESTCASE_AUTO(testConvertToAccurateDouble); TESTCASE_AUTO(testConvertToAccurateDouble);
TESTCASE_AUTO(testUseApproximateDoubleWhenAble); TESTCASE_AUTO(testUseApproximateDoubleWhenAble);
TESTCASE_AUTO(testHardDoubleConversion);
TESTCASE_AUTO_END; TESTCASE_AUTO_END;
} }
@ -233,7 +234,7 @@ void DecimalQuantityTest::testConvertToAccurateDouble() {
} }
void DecimalQuantityTest::testUseApproximateDoubleWhenAble() { void DecimalQuantityTest::testUseApproximateDoubleWhenAble() {
struct TestCase { static const struct TestCase {
double d; double d;
int32_t maxFrac; int32_t maxFrac;
RoundingMode roundingMode; RoundingMode roundingMode;
@ -264,4 +265,33 @@ void DecimalQuantityTest::testUseApproximateDoubleWhenAble() {
} }
} }
void DecimalQuantityTest::testHardDoubleConversion() {
static const struct TestCase {
double input;
const char16_t* expectedOutput;
} cases[] = {
{ 512.0000000000017, u"512.0000000000017" },
{ 4095.9999999999977, u"4095.9999999999977" },
{ 4095.999999999998, u"4095.999999999998" },
{ 4095.9999999999986, u"4095.9999999999986" },
{ 4095.999999999999, u"4095.999999999999" },
{ 4095.9999999999995, u"4095.9999999999995" },
{ 4096.000000000001, u"4096.000000000001" },
{ 4096.000000000002, u"4096.000000000002" },
{ 4096.000000000003, u"4096.000000000003" },
{ 4096.000000000004, u"4096.000000000004" },
{ 4096.000000000005, u"4096.000000000005" },
{ 4096.0000000000055, u"4096.0000000000055" },
{ 4096.000000000006, u"4096.000000000006" },
{ 4096.000000000007, u"4096.000000000007" } };
for (auto& cas : cases) {
DecimalQuantity q;
q.setToDouble(cas.input);
q.roundToInfinity();
UnicodeString actualOutput = q.toPlainString();
assertEquals("", cas.expectedOutput, actualOutput);
}
}
#endif /* #if !UCONFIG_NO_FORMATTING */ #endif /* #if !UCONFIG_NO_FORMATTING */

45
icu4c/source/test/intltest/numbertest_doubleconversion.cpp Normal file
View File

@ -0,0 +1,45 @@
// © 2017 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
#include "unicode/utypes.h"
#if !UCONFIG_NO_FORMATTING && !UPRV_INCOMPLETE_CPP11_SUPPORT
#include "numbertest.h"
#include "double-conversion.h"
using namespace double_conversion;
void DoubleConversionTest::runIndexedTest(int32_t index, UBool exec, const char *&name, char *) {
if (exec) {
logln("TestSuite DoubleConversionTest: ");
}
TESTCASE_AUTO_BEGIN;
TESTCASE_AUTO(testDoubleConversionApi);
TESTCASE_AUTO_END;
}
void DoubleConversionTest::testDoubleConversionApi() {
double v = 87.65;
char buffer[DoubleToStringConverter::kBase10MaximalLength + 1];
bool sign;
int32_t length;
int32_t point;
DoubleToStringConverter::DoubleToAscii(
v,
DoubleToStringConverter::DtoaMode::SHORTEST,
0,
buffer,
sizeof(buffer),
&sign,
&length,
&point
);
UnicodeString result(buffer, length);
assertEquals("Digits", u"8765", result);
assertEquals("Scale", 2, point);
}
#endif /* #if !UCONFIG_NO_FORMATTING */

11
icu4c/source/test/intltest/numfmtst.cpp
View File

@ -627,6 +627,7 @@ void NumberFormatTest::runIndexedTest( int32_t index, UBool exec, const char* &n
TESTCASE_AUTO(Test13327_numberingSystemBufferOverflow); TESTCASE_AUTO(Test13327_numberingSystemBufferOverflow);
TESTCASE_AUTO(Test13391_chakmaParsing); TESTCASE_AUTO(Test13391_chakmaParsing);
TESTCASE_AUTO(Test11035_FormatCurrencyAmount); TESTCASE_AUTO(Test11035_FormatCurrencyAmount);
TESTCASE_AUTO(Test11318_DoubleConversion);
TESTCASE_AUTO_END; TESTCASE_AUTO_END;
} }
@ -8952,4 +8953,14 @@ void NumberFormatTest::Test11035_FormatCurrencyAmount() {
} }
} }
void NumberFormatTest::Test11318_DoubleConversion() {
IcuTestErrorCode status(*this, "Test11318_DoubleConversion");
LocalPointer<NumberFormat> nf(NumberFormat::createInstance("en", status));
nf->setMaximumFractionDigits(40);
nf->setMaximumIntegerDigits(40);
UnicodeString appendTo;
nf->format(999999999999999.9, appendTo);
assertEquals("Should render all digits", u"999,999,999,999,999.9", appendTo);
}
#endif /* #if !UCONFIG_NO_FORMATTING */ #endif /* #if !UCONFIG_NO_FORMATTING */

1
icu4c/source/test/intltest/numfmtst.h
View File

@ -220,6 +220,7 @@ class NumberFormatTest: public CalendarTimeZoneTest {
void checkExceptionIssue11735(); void checkExceptionIssue11735();
void Test11035_FormatCurrencyAmount(); void Test11035_FormatCurrencyAmount();
void Test11318_DoubleConversion();
private: private:
UBool testFormattableAsUFormattable(const char *file, int line, Formattable &f); UBool testFormattableAsUFormattable(const char *file, int line, Formattable &f);

31
icu4j/main/tests/core/src/com/ibm/icu/dev/test/number/DecimalQuantityTest.java
View File

@ -532,6 +532,37 @@ public class DecimalQuantityTest extends TestFmwk {
assertFalse("10^20 should not fit", quantity.fitsInLong()); assertFalse("10^20 should not fit", quantity.fitsInLong());
} }
@Test
public void testHardDoubleConversion() {
// This test is somewhat duplicated from previous tests, but it is needed
// for ICU4C compatibility.
Object[][] cases = {
{ 512.0000000000017, "512.0000000000017" },
{ 4095.9999999999977, "4095.9999999999977" },
{ 4095.999999999998, "4095.999999999998" },
{ 4095.9999999999986, "4095.9999999999986" },
{ 4095.999999999999, "4095.999999999999" },
{ 4095.9999999999995, "4095.9999999999995" },
{ 4096.000000000001, "4096.000000000001" },
{ 4096.000000000002, "4096.000000000002" },
{ 4096.000000000003, "4096.000000000003" },
{ 4096.000000000004, "4096.000000000004" },
{ 4096.000000000005, "4096.000000000005" },
{ 4096.0000000000055, "4096.0000000000055" },
{ 4096.000000000006, "4096.000000000006" },
{ 4096.000000000007, "4096.000000000007" } };
for (Object[] cas : cases) {
double input = (Double) cas[0];
String expectedOutput = (String) cas[1];
DecimalQuantity q = new DecimalQuantity_DualStorageBCD(input);
q.roundToInfinity();
String actualOutput = q.toPlainString();
assertEquals("", expectedOutput, actualOutput);
}
}
static void assertDoubleEquals(String message, double d1, double d2) { static void assertDoubleEquals(String message, double d1, double d2) {
boolean equal = (Math.abs(d1 - d2) < 1e-6) || (Math.abs((d1 - d2) / d1) < 1e-6); boolean equal = (Math.abs(d1 - d2) < 1e-6) || (Math.abs((d1 - d2) / d1) < 1e-6);
handleAssert(equal, message, d1, d2, null, false); handleAssert(equal, message, d1, d2, null, false);