chromium/v8/src/base/numbers/bignum-dtoa.cc

// Copyright 2011 the V8 project authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

#include "src/base/numbers/bignum-dtoa.h"

#include <cmath>

#include "src/base/logging.h"
#include "src/base/numbers/bignum.h"
#include "src/base/numbers/double.h"

namespace v8 {
namespace base {

static int NormalizedExponent(uint64_t significand, int exponent) {}

// Forward declarations:
// Returns an estimation of k such that 10^(k-1) <= v < 10^k.
static int EstimatePower(int exponent);
// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
// and denominator.
static void InitialScaledStartValues(double v, int estimated_power,
                                     bool need_boundary_deltas,
                                     Bignum* numerator, Bignum* denominator,
                                     Bignum* delta_minus, Bignum* delta_plus);
// Multiplies numerator/denominator so that its values lies in the range 1-10.
// Returns decimal_point s.t.
//  v = numerator'/denominator' * 10^(decimal_point-1)
//     where numerator' and denominator' are the values of numerator and
//     denominator after the call to this function.
static void FixupMultiply10(int estimated_power, bool is_even,
                            int* decimal_point, Bignum* numerator,
                            Bignum* denominator, Bignum* delta_minus,
                            Bignum* delta_plus);
// Generates digits from the left to the right and stops when the generated
// digits yield the shortest decimal representation of v.
static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
                                   Bignum* delta_minus, Bignum* delta_plus,
                                   bool is_even, 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) {}

// 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) {}

// 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) {}

// 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) {}

// 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) {}

// See comments for InitialScaledStartValues.
static void InitialScaledStartValuesPositiveExponent(
    double v, int estimated_power, bool need_boundary_deltas, Bignum* numerator,
    Bignum* denominator, Bignum* delta_minus, Bignum* delta_plus) {}

// 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) {}

// 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) {}

// 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) {}

// 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) {}

}  // namespace base
}  // namespace v8