81e7f597b0
Duplicate identifier detection must be an early syntax error in strict code, so errors in otherwise lazily compiled functions must be caught in the preparser. Originally introduced in r8541 and reverted in r8542. Now really compiles on Windows. Review URL: http://codereview.chromium.org/7782023 git-svn-id: http://v8.googlecode.com/svn/branches/bleeding_edge@9172 ce2b1a6d-e550-0410-aec6-3dcde31c8c00
659 lines
28 KiB
C++
659 lines
28 KiB
C++
// Copyright 2011 the V8 project authors. All rights reserved.
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above
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// copyright notice, this list of conditions and the following
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// disclaimer in the documentation and/or other materials provided
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// with the distribution.
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// * Neither the name of Google Inc. nor the names of its
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// contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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#include <math.h>
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#include "../include/v8stdint.h"
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#include "checks.h"
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#include "utils.h"
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#include "bignum-dtoa.h"
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#include "bignum.h"
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#include "double.h"
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namespace v8 {
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namespace internal {
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static int NormalizedExponent(uint64_t significand, int exponent) {
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ASSERT(significand != 0);
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while ((significand & Double::kHiddenBit) == 0) {
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significand = significand << 1;
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exponent = exponent - 1;
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}
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return exponent;
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}
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// Forward declarations:
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// Returns an estimation of k such that 10^(k-1) <= v < 10^k.
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static int EstimatePower(int exponent);
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// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
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// and denominator.
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static void InitialScaledStartValues(double v,
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int estimated_power,
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bool need_boundary_deltas,
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Bignum* numerator,
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Bignum* denominator,
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Bignum* delta_minus,
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Bignum* delta_plus);
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// Multiplies numerator/denominator so that its values lies in the range 1-10.
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// Returns decimal_point s.t.
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// v = numerator'/denominator' * 10^(decimal_point-1)
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// where numerator' and denominator' are the values of numerator and
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// denominator after the call to this function.
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static void FixupMultiply10(int estimated_power, bool is_even,
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int* decimal_point,
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Bignum* numerator, Bignum* denominator,
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Bignum* delta_minus, Bignum* delta_plus);
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// Generates digits from the left to the right and stops when the generated
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// digits yield the shortest decimal representation of v.
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static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
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Bignum* delta_minus, Bignum* delta_plus,
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bool is_even,
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Vector<char> buffer, int* length);
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// Generates 'requested_digits' after the decimal point.
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static void BignumToFixed(int requested_digits, int* decimal_point,
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Bignum* numerator, Bignum* denominator,
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Vector<char>(buffer), int* length);
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// Generates 'count' digits of numerator/denominator.
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// Once 'count' digits have been produced rounds the result depending on the
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// remainder (remainders of exactly .5 round upwards). Might update the
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// decimal_point when rounding up (for example for 0.9999).
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static void GenerateCountedDigits(int count, int* decimal_point,
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Bignum* numerator, Bignum* denominator,
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Vector<char>(buffer), int* length);
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void BignumDtoa(double v, BignumDtoaMode mode, int requested_digits,
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Vector<char> buffer, int* length, int* decimal_point) {
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ASSERT(v > 0);
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ASSERT(!Double(v).IsSpecial());
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uint64_t significand = Double(v).Significand();
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bool is_even = (significand & 1) == 0;
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int exponent = Double(v).Exponent();
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int normalized_exponent = NormalizedExponent(significand, exponent);
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// estimated_power might be too low by 1.
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int estimated_power = EstimatePower(normalized_exponent);
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// Shortcut for Fixed.
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// The requested digits correspond to the digits after the point. If the
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// number is much too small, then there is no need in trying to get any
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// digits.
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if (mode == BIGNUM_DTOA_FIXED && -estimated_power - 1 > requested_digits) {
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buffer[0] = '\0';
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*length = 0;
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// Set decimal-point to -requested_digits. This is what Gay does.
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// Note that it should not have any effect anyways since the string is
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// empty.
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*decimal_point = -requested_digits;
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return;
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}
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Bignum numerator;
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Bignum denominator;
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Bignum delta_minus;
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Bignum delta_plus;
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// Make sure the bignum can grow large enough. The smallest double equals
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// 4e-324. In this case the denominator needs fewer than 324*4 binary digits.
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// The maximum double is 1.7976931348623157e308 which needs fewer than
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// 308*4 binary digits.
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ASSERT(Bignum::kMaxSignificantBits >= 324*4);
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bool need_boundary_deltas = (mode == BIGNUM_DTOA_SHORTEST);
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InitialScaledStartValues(v, estimated_power, need_boundary_deltas,
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&numerator, &denominator,
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&delta_minus, &delta_plus);
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// We now have v = (numerator / denominator) * 10^estimated_power.
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FixupMultiply10(estimated_power, is_even, decimal_point,
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&numerator, &denominator,
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&delta_minus, &delta_plus);
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// We now have v = (numerator / denominator) * 10^(decimal_point-1), and
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// 1 <= (numerator + delta_plus) / denominator < 10
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switch (mode) {
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case BIGNUM_DTOA_SHORTEST:
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GenerateShortestDigits(&numerator, &denominator,
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&delta_minus, &delta_plus,
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is_even, buffer, length);
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break;
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case BIGNUM_DTOA_FIXED:
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BignumToFixed(requested_digits, decimal_point,
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&numerator, &denominator,
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buffer, length);
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break;
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case BIGNUM_DTOA_PRECISION:
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GenerateCountedDigits(requested_digits, decimal_point,
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&numerator, &denominator,
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buffer, length);
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break;
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default:
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UNREACHABLE();
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}
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buffer[*length] = '\0';
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}
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// The procedure starts generating digits from the left to the right and stops
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// when the generated digits yield the shortest decimal representation of v. A
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// decimal representation of v is a number lying closer to v than to any other
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// double, so it converts to v when read.
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//
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// This is true if d, the decimal representation, is between m- and m+, the
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// upper and lower boundaries. d must be strictly between them if !is_even.
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// m- := (numerator - delta_minus) / denominator
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// m+ := (numerator + delta_plus) / denominator
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//
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// Precondition: 0 <= (numerator+delta_plus) / denominator < 10.
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// If 1 <= (numerator+delta_plus) / denominator < 10 then no leading 0 digit
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// will be produced. This should be the standard precondition.
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static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
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Bignum* delta_minus, Bignum* delta_plus,
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bool is_even,
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Vector<char> buffer, int* length) {
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// Small optimization: if delta_minus and delta_plus are the same just reuse
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// one of the two bignums.
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if (Bignum::Equal(*delta_minus, *delta_plus)) {
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delta_plus = delta_minus;
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}
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*length = 0;
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while (true) {
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uint16_t digit;
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digit = numerator->DivideModuloIntBignum(*denominator);
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ASSERT(digit <= 9); // digit is a uint16_t and therefore always positive.
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// digit = numerator / denominator (integer division).
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// numerator = numerator % denominator.
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buffer[(*length)++] = digit + '0';
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// Can we stop already?
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// If the remainder of the division is less than the distance to the lower
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// boundary we can stop. In this case we simply round down (discarding the
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// remainder).
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// Similarly we test if we can round up (using the upper boundary).
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bool in_delta_room_minus;
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bool in_delta_room_plus;
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if (is_even) {
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in_delta_room_minus = Bignum::LessEqual(*numerator, *delta_minus);
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} else {
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in_delta_room_minus = Bignum::Less(*numerator, *delta_minus);
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}
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if (is_even) {
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in_delta_room_plus =
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Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
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} else {
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in_delta_room_plus =
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Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
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}
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if (!in_delta_room_minus && !in_delta_room_plus) {
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// Prepare for next iteration.
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numerator->Times10();
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delta_minus->Times10();
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// We optimized delta_plus to be equal to delta_minus (if they share the
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// same value). So don't multiply delta_plus if they point to the same
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// object.
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if (delta_minus != delta_plus) {
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delta_plus->Times10();
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}
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} else if (in_delta_room_minus && in_delta_room_plus) {
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// Let's see if 2*numerator < denominator.
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// If yes, then the next digit would be < 5 and we can round down.
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int compare = Bignum::PlusCompare(*numerator, *numerator, *denominator);
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if (compare < 0) {
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// Remaining digits are less than .5. -> Round down (== do nothing).
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} else if (compare > 0) {
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// Remaining digits are more than .5 of denominator. -> Round up.
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// Note that the last digit could not be a '9' as otherwise the whole
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// loop would have stopped earlier.
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// We still have an assert here in case the preconditions were not
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// satisfied.
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ASSERT(buffer[(*length) - 1] != '9');
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buffer[(*length) - 1]++;
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} else {
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// Halfway case.
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// TODO(floitsch): need a way to solve half-way cases.
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// For now let's round towards even (since this is what Gay seems to
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// do).
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if ((buffer[(*length) - 1] - '0') % 2 == 0) {
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// Round down => Do nothing.
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} else {
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ASSERT(buffer[(*length) - 1] != '9');
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buffer[(*length) - 1]++;
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}
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}
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return;
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} else if (in_delta_room_minus) {
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// Round down (== do nothing).
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return;
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} else { // in_delta_room_plus
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// Round up.
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// Note again that the last digit could not be '9' since this would have
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// stopped the loop earlier.
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// We still have an ASSERT here, in case the preconditions were not
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// satisfied.
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ASSERT(buffer[(*length) -1] != '9');
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buffer[(*length) - 1]++;
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return;
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}
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}
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}
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// Let v = numerator / denominator < 10.
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// Then we generate 'count' digits of d = x.xxxxx... (without the decimal point)
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// from left to right. Once 'count' digits have been produced we decide wether
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// to round up or down. Remainders of exactly .5 round upwards. Numbers such
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// as 9.999999 propagate a carry all the way, and change the
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// exponent (decimal_point), when rounding upwards.
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static void GenerateCountedDigits(int count, int* decimal_point,
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Bignum* numerator, Bignum* denominator,
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Vector<char>(buffer), int* length) {
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ASSERT(count >= 0);
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for (int i = 0; i < count - 1; ++i) {
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uint16_t digit;
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digit = numerator->DivideModuloIntBignum(*denominator);
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ASSERT(digit <= 9); // digit is a uint16_t and therefore always positive.
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// digit = numerator / denominator (integer division).
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// numerator = numerator % denominator.
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buffer[i] = digit + '0';
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// Prepare for next iteration.
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numerator->Times10();
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}
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// Generate the last digit.
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uint16_t digit;
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digit = numerator->DivideModuloIntBignum(*denominator);
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if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
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digit++;
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}
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buffer[count - 1] = digit + '0';
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// Correct bad digits (in case we had a sequence of '9's). Propagate the
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// carry until we hat a non-'9' or til we reach the first digit.
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for (int i = count - 1; i > 0; --i) {
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if (buffer[i] != '0' + 10) break;
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buffer[i] = '0';
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buffer[i - 1]++;
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}
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if (buffer[0] == '0' + 10) {
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// Propagate a carry past the top place.
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buffer[0] = '1';
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(*decimal_point)++;
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}
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*length = count;
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}
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// Generates 'requested_digits' after the decimal point. It might omit
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// trailing '0's. If the input number is too small then no digits at all are
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// generated (ex.: 2 fixed digits for 0.00001).
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//
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// Input verifies: 1 <= (numerator + delta) / denominator < 10.
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static void BignumToFixed(int requested_digits, int* decimal_point,
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Bignum* numerator, Bignum* denominator,
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Vector<char>(buffer), int* length) {
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// Note that we have to look at more than just the requested_digits, since
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// a number could be rounded up. Example: v=0.5 with requested_digits=0.
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// Even though the power of v equals 0 we can't just stop here.
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if (-(*decimal_point) > requested_digits) {
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// The number is definitively too small.
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// Ex: 0.001 with requested_digits == 1.
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// Set decimal-point to -requested_digits. This is what Gay does.
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// Note that it should not have any effect anyways since the string is
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// empty.
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*decimal_point = -requested_digits;
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*length = 0;
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return;
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} else if (-(*decimal_point) == requested_digits) {
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// We only need to verify if the number rounds down or up.
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// Ex: 0.04 and 0.06 with requested_digits == 1.
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ASSERT(*decimal_point == -requested_digits);
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// Initially the fraction lies in range (1, 10]. Multiply the denominator
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// by 10 so that we can compare more easily.
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denominator->Times10();
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if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
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// If the fraction is >= 0.5 then we have to include the rounded
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// digit.
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buffer[0] = '1';
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*length = 1;
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(*decimal_point)++;
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} else {
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// Note that we caught most of similar cases earlier.
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*length = 0;
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}
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return;
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} else {
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// The requested digits correspond to the digits after the point.
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// The variable 'needed_digits' includes the digits before the point.
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int needed_digits = (*decimal_point) + requested_digits;
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GenerateCountedDigits(needed_digits, decimal_point,
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numerator, denominator,
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buffer, length);
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}
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}
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// Returns an estimation of k such that 10^(k-1) <= v < 10^k where
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// v = f * 2^exponent and 2^52 <= f < 2^53.
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// v is hence a normalized double with the given exponent. The output is an
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// approximation for the exponent of the decimal approimation .digits * 10^k.
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//
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// The result might undershoot by 1 in which case 10^k <= v < 10^k+1.
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// Note: this property holds for v's upper boundary m+ too.
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// 10^k <= m+ < 10^k+1.
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// (see explanation below).
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//
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// Examples:
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// EstimatePower(0) => 16
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// EstimatePower(-52) => 0
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//
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// Note: e >= 0 => EstimatedPower(e) > 0. No similar claim can be made for e<0.
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static int EstimatePower(int exponent) {
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// This function estimates log10 of v where v = f*2^e (with e == exponent).
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// Note that 10^floor(log10(v)) <= v, but v <= 10^ceil(log10(v)).
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// Note that f is bounded by its container size. Let p = 53 (the double's
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// significand size). Then 2^(p-1) <= f < 2^p.
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//
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// Given that log10(v) == log2(v)/log2(10) and e+(len(f)-1) is quite close
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// to log2(v) the function is simplified to (e+(len(f)-1)/log2(10)).
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// The computed number undershoots by less than 0.631 (when we compute log3
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// and not log10).
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//
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// Optimization: since we only need an approximated result this computation
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// can be performed on 64 bit integers. On x86/x64 architecture the speedup is
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// not really measurable, though.
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//
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// Since we want to avoid overshooting we decrement by 1e10 so that
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// floating-point imprecisions don't affect us.
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//
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// Explanation for v's boundary m+: the computation takes advantage of
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// the fact that 2^(p-1) <= f < 2^p. Boundaries still satisfy this requirement
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// (even for denormals where the delta can be much more important).
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const double k1Log10 = 0.30102999566398114; // 1/lg(10)
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// For doubles len(f) == 53 (don't forget the hidden bit).
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const int kSignificandSize = 53;
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double estimate = ceil((exponent + kSignificandSize - 1) * k1Log10 - 1e-10);
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return static_cast<int>(estimate);
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}
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// See comments for InitialScaledStartValues.
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static void InitialScaledStartValuesPositiveExponent(
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double v, int estimated_power, bool need_boundary_deltas,
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Bignum* numerator, Bignum* denominator,
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Bignum* delta_minus, Bignum* delta_plus) {
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// A positive exponent implies a positive power.
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ASSERT(estimated_power >= 0);
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// Since the estimated_power is positive we simply multiply the denominator
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// by 10^estimated_power.
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// numerator = v.
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numerator->AssignUInt64(Double(v).Significand());
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numerator->ShiftLeft(Double(v).Exponent());
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// denominator = 10^estimated_power.
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denominator->AssignPowerUInt16(10, estimated_power);
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if (need_boundary_deltas) {
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// Introduce a common denominator so that the deltas to the boundaries are
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// integers.
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denominator->ShiftLeft(1);
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numerator->ShiftLeft(1);
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// Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
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// denominator (of 2) delta_plus equals 2^e.
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delta_plus->AssignUInt16(1);
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delta_plus->ShiftLeft(Double(v).Exponent());
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// Same for delta_minus (with adjustments below if f == 2^p-1).
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delta_minus->AssignUInt16(1);
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delta_minus->ShiftLeft(Double(v).Exponent());
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// If the significand (without the hidden bit) is 0, then the lower
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// boundary is closer than just half a ulp (unit in the last place).
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// There is only one exception: if the next lower number is a denormal then
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// the distance is 1 ulp. This cannot be the case for exponent >= 0 (but we
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|
// have to test it in the other function where exponent < 0).
|
|
uint64_t v_bits = Double(v).AsUint64();
|
|
if ((v_bits & Double::kSignificandMask) == 0) {
|
|
// The lower boundary is closer at half the distance of "normal" numbers.
|
|
// Increase the common denominator and adapt all but the delta_minus.
|
|
denominator->ShiftLeft(1); // *2
|
|
numerator->ShiftLeft(1); // *2
|
|
delta_plus->ShiftLeft(1); // *2
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
// See comments for InitialScaledStartValues
|
|
static void InitialScaledStartValuesNegativeExponentPositivePower(
|
|
double v, int estimated_power, bool need_boundary_deltas,
|
|
Bignum* numerator, Bignum* denominator,
|
|
Bignum* delta_minus, Bignum* delta_plus) {
|
|
uint64_t significand = Double(v).Significand();
|
|
int exponent = Double(v).Exponent();
|
|
// v = f * 2^e with e < 0, and with estimated_power >= 0.
|
|
// This means that e is close to 0 (have a look at how estimated_power is
|
|
// computed).
|
|
|
|
// numerator = significand
|
|
// since v = significand * 2^exponent this is equivalent to
|
|
// numerator = v * / 2^-exponent
|
|
numerator->AssignUInt64(significand);
|
|
// denominator = 10^estimated_power * 2^-exponent (with exponent < 0)
|
|
denominator->AssignPowerUInt16(10, estimated_power);
|
|
denominator->ShiftLeft(-exponent);
|
|
|
|
if (need_boundary_deltas) {
|
|
// Introduce a common denominator so that the deltas to the boundaries are
|
|
// integers.
|
|
denominator->ShiftLeft(1);
|
|
numerator->ShiftLeft(1);
|
|
// Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
|
|
// denominator (of 2) delta_plus equals 2^e.
|
|
// Given that the denominator already includes v's exponent the distance
|
|
// to the boundaries is simply 1.
|
|
delta_plus->AssignUInt16(1);
|
|
// Same for delta_minus (with adjustments below if f == 2^p-1).
|
|
delta_minus->AssignUInt16(1);
|
|
|
|
// If the significand (without the hidden bit) is 0, then the lower
|
|
// boundary is closer than just one ulp (unit in the last place).
|
|
// There is only one exception: if the next lower number is a denormal
|
|
// then the distance is 1 ulp. Since the exponent is close to zero
|
|
// (otherwise estimated_power would have been negative) this cannot happen
|
|
// here either.
|
|
uint64_t v_bits = Double(v).AsUint64();
|
|
if ((v_bits & Double::kSignificandMask) == 0) {
|
|
// The lower boundary is closer at half the distance of "normal" numbers.
|
|
// Increase the denominator and adapt all but the delta_minus.
|
|
denominator->ShiftLeft(1); // *2
|
|
numerator->ShiftLeft(1); // *2
|
|
delta_plus->ShiftLeft(1); // *2
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
// See comments for InitialScaledStartValues
|
|
static void InitialScaledStartValuesNegativeExponentNegativePower(
|
|
double v, int estimated_power, bool need_boundary_deltas,
|
|
Bignum* numerator, Bignum* denominator,
|
|
Bignum* delta_minus, Bignum* delta_plus) {
|
|
const uint64_t kMinimalNormalizedExponent =
|
|
V8_2PART_UINT64_C(0x00100000, 00000000);
|
|
uint64_t significand = Double(v).Significand();
|
|
int exponent = Double(v).Exponent();
|
|
// Instead of multiplying the denominator with 10^estimated_power we
|
|
// multiply all values (numerator and deltas) by 10^-estimated_power.
|
|
|
|
// Use numerator as temporary container for power_ten.
|
|
Bignum* power_ten = numerator;
|
|
power_ten->AssignPowerUInt16(10, -estimated_power);
|
|
|
|
if (need_boundary_deltas) {
|
|
// Since power_ten == numerator we must make a copy of 10^estimated_power
|
|
// before we complete the computation of the numerator.
|
|
// delta_plus = delta_minus = 10^estimated_power
|
|
delta_plus->AssignBignum(*power_ten);
|
|
delta_minus->AssignBignum(*power_ten);
|
|
}
|
|
|
|
// numerator = significand * 2 * 10^-estimated_power
|
|
// since v = significand * 2^exponent this is equivalent to
|
|
// numerator = v * 10^-estimated_power * 2 * 2^-exponent.
|
|
// Remember: numerator has been abused as power_ten. So no need to assign it
|
|
// to itself.
|
|
ASSERT(numerator == power_ten);
|
|
numerator->MultiplyByUInt64(significand);
|
|
|
|
// denominator = 2 * 2^-exponent with exponent < 0.
|
|
denominator->AssignUInt16(1);
|
|
denominator->ShiftLeft(-exponent);
|
|
|
|
if (need_boundary_deltas) {
|
|
// Introduce a common denominator so that the deltas to the boundaries are
|
|
// integers.
|
|
numerator->ShiftLeft(1);
|
|
denominator->ShiftLeft(1);
|
|
// With this shift the boundaries have their correct value, since
|
|
// delta_plus = 10^-estimated_power, and
|
|
// delta_minus = 10^-estimated_power.
|
|
// These assignments have been done earlier.
|
|
|
|
// The special case where the lower boundary is twice as close.
|
|
// This time we have to look out for the exception too.
|
|
uint64_t v_bits = Double(v).AsUint64();
|
|
if ((v_bits & Double::kSignificandMask) == 0 &&
|
|
// The only exception where a significand == 0 has its boundaries at
|
|
// "normal" distances:
|
|
(v_bits & Double::kExponentMask) != kMinimalNormalizedExponent) {
|
|
numerator->ShiftLeft(1); // *2
|
|
denominator->ShiftLeft(1); // *2
|
|
delta_plus->ShiftLeft(1); // *2
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
// Let v = significand * 2^exponent.
|
|
// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
|
|
// and denominator. The functions GenerateShortestDigits and
|
|
// GenerateCountedDigits will then convert this ratio to its decimal
|
|
// representation d, with the required accuracy.
|
|
// Then d * 10^estimated_power is the representation of v.
|
|
// (Note: the fraction and the estimated_power might get adjusted before
|
|
// generating the decimal representation.)
|
|
//
|
|
// The initial start values consist of:
|
|
// - a scaled numerator: s.t. numerator/denominator == v / 10^estimated_power.
|
|
// - a scaled (common) denominator.
|
|
// optionally (used by GenerateShortestDigits to decide if it has the shortest
|
|
// decimal converting back to v):
|
|
// - v - m-: the distance to the lower boundary.
|
|
// - m+ - v: the distance to the upper boundary.
|
|
//
|
|
// v, m+, m-, and therefore v - m- and m+ - v all share the same denominator.
|
|
//
|
|
// Let ep == estimated_power, then the returned values will satisfy:
|
|
// v / 10^ep = numerator / denominator.
|
|
// v's boundarys m- and m+:
|
|
// m- / 10^ep == v / 10^ep - delta_minus / denominator
|
|
// m+ / 10^ep == v / 10^ep + delta_plus / denominator
|
|
// Or in other words:
|
|
// m- == v - delta_minus * 10^ep / denominator;
|
|
// m+ == v + delta_plus * 10^ep / denominator;
|
|
//
|
|
// Since 10^(k-1) <= v < 10^k (with k == estimated_power)
|
|
// or 10^k <= v < 10^(k+1)
|
|
// we then have 0.1 <= numerator/denominator < 1
|
|
// or 1 <= numerator/denominator < 10
|
|
//
|
|
// It is then easy to kickstart the digit-generation routine.
|
|
//
|
|
// The boundary-deltas are only filled if need_boundary_deltas is set.
|
|
static void InitialScaledStartValues(double v,
|
|
int estimated_power,
|
|
bool need_boundary_deltas,
|
|
Bignum* numerator,
|
|
Bignum* denominator,
|
|
Bignum* delta_minus,
|
|
Bignum* delta_plus) {
|
|
if (Double(v).Exponent() >= 0) {
|
|
InitialScaledStartValuesPositiveExponent(
|
|
v, estimated_power, need_boundary_deltas,
|
|
numerator, denominator, delta_minus, delta_plus);
|
|
} else if (estimated_power >= 0) {
|
|
InitialScaledStartValuesNegativeExponentPositivePower(
|
|
v, estimated_power, need_boundary_deltas,
|
|
numerator, denominator, delta_minus, delta_plus);
|
|
} else {
|
|
InitialScaledStartValuesNegativeExponentNegativePower(
|
|
v, estimated_power, need_boundary_deltas,
|
|
numerator, denominator, delta_minus, delta_plus);
|
|
}
|
|
}
|
|
|
|
|
|
// 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 v8::internal
|