// Copyright 2018 Ulf Adams
//
// The contents of this file may be used under the terms of the Apache License,
// Version 2.0.
//
// (See accompanying file LICENSE-Apache or copy at
// http://www.apache.org/licenses/LICENSE-2.0)
//
// Alternatively, the contents of this file may be used under the terms of
// the Boost Software License, Version 1.0.
// (See accompanying file LICENSE-Boost or copy at
// https://www.boost.org/LICENSE_1_0.txt)
//
// Unless required by applicable law or agreed to in writing, this software
// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied.
// Runtime compiler options:
// -DRYU_DEBUG Generate verbose debugging output to stdout.
//
// -DRYU_ONLY_64_BIT_OPS Avoid using uint128_t or 64-bit intrinsics. Slower,
// depending on your compiler.
//
// -DRYU_OPTIMIZE_SIZE Use smaller lookup tables. Instead of storing every
// required power of 5, only store every 26th entry, and compute
// intermediate values with a multiplication. This reduces the lookup table
// size by about 10x (only one case, and only double) at the cost of some
// performance. Currently requires MSVC intrinsics.
/*
This is a derivative work
*/
#ifndef BOOST_JSON_DETAIL_RYU_IMPL_D2S_IPP
#define BOOST_JSON_DETAIL_RYU_IMPL_D2S_IPP
#include <boost/json/detail/ryu/ryu.hpp>
#include <cstdlib>
#include <cstring>
#ifdef RYU_DEBUG
#include <stdio.h>
#endif
// ABSL avoids uint128_t on Win32 even if __SIZEOF_INT128__ is defined.
// Let's do the same for now.
#if defined(__SIZEOF_INT128__) && !defined(_MSC_VER) && !defined(RYU_ONLY_64_BIT_OPS)
#define BOOST_JSON_RYU_HAS_UINT128
#elif defined(_MSC_VER) && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
#define BOOST_JSON_RYU_HAS_64_BIT_INTRINSICS
#endif
#include <boost/json/detail/ryu/detail/common.hpp>
#include <boost/json/detail/ryu/detail/digit_table.hpp>
#include <boost/json/detail/ryu/detail/d2s.hpp>
#include <boost/json/detail/ryu/detail/d2s_intrinsics.hpp>
BOOST_JSON_NS_BEGIN
namespace detail {
namespace ryu {
namespace detail {
// We need a 64x128-bit multiplication and a subsequent 128-bit shift.
// Multiplication:
// The 64-bit factor is variable and passed in, the 128-bit factor comes
// from a lookup table. We know that the 64-bit factor only has 55
// significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
// factor only has 124 significant bits (i.e., the 4 topmost bits are
// zeros).
// Shift:
// In principle, the multiplication result requires 55 + 124 = 179 bits to
// represent. However, we then shift this value to the right by j, which is
// at least j >= 115, so the result is guaranteed to fit into 179 - 115 = 64
// bits. This means that we only need the topmost 64 significant bits of
// the 64x128-bit multiplication.
//
// There are several ways to do this:
// 1. Best case: the compiler exposes a 128-bit type.
// We perform two 64x64-bit multiplications, add the higher 64 bits of the
// lower result to the higher result, and shift by j - 64 bits.
//
// We explicitly cast from 64-bit to 128-bit, so the compiler can tell
// that these are only 64-bit inputs, and can map these to the best
// possible sequence of assembly instructions.
// x64 machines happen to have matching assembly instructions for
// 64x64-bit multiplications and 128-bit shifts.
//
// 2. Second best case: the compiler exposes intrinsics for the x64 assembly
// instructions mentioned in 1.
//
// 3. We only have 64x64 bit instructions that return the lower 64 bits of
// the result, i.e., we have to use plain C.
// Our inputs are less than the full width, so we have three options:
// a. Ignore this fact and just implement the intrinsics manually.
// b. Split both into 31-bit pieces, which guarantees no internal overflow,
// but requires extra work upfront (unless we change the lookup table).
// c. Split only the first factor into 31-bit pieces, which also guarantees
// no internal overflow, but requires extra work since the intermediate
// results are not perfectly aligned.
#if defined(BOOST_JSON_RYU_HAS_UINT128)
// Best case: use 128-bit type.
inline
std::uint64_t
mulShift(
const std::uint64_t m,
const std::uint64_t* const mul,
const std::int32_t j) noexcept
{
const uint128_t b0 = ((uint128_t) m) * mul[0];
const uint128_t b2 = ((uint128_t) m) * mul[1];
return (std::uint64_t) (((b0 >> 64) + b2) >> (j - 64));
}
inline
uint64_t
mulShiftAll(
const std::uint64_t m,
const std::uint64_t* const mul,
std::int32_t const j,
std::uint64_t* const vp,
std::uint64_t* const vm,
const std::uint32_t mmShift) noexcept
{
// m <<= 2;
// uint128_t b0 = ((uint128_t) m) * mul[0]; // 0
// uint128_t b2 = ((uint128_t) m) * mul[1]; // 64
//
// uint128_t hi = (b0 >> 64) + b2;
// uint128_t lo = b0 & 0xffffffffffffffffull;
// uint128_t factor = (((uint128_t) mul[1]) << 64) + mul[0];
// uint128_t vpLo = lo + (factor << 1);
// *vp = (std::uint64_t) ((hi + (vpLo >> 64)) >> (j - 64));
// uint128_t vmLo = lo - (factor << mmShift);
// *vm = (std::uint64_t) ((hi + (vmLo >> 64) - (((uint128_t) 1ull) << 64)) >> (j - 64));
// return (std::uint64_t) (hi >> (j - 64));
*vp = mulShift(4 * m + 2, mul, j);
*vm = mulShift(4 * m - 1 - mmShift, mul, j);
return mulShift(4 * m, mul, j);
}
#elif defined(BOOST_JSON_RYU_HAS_64_BIT_INTRINSICS)
inline
std::uint64_t
mulShift(
const std::uint64_t m,
const std::uint64_t* const mul,
const std::int32_t j) noexcept
{
// m is maximum 55 bits
std::uint64_t high1; // 128
std::uint64_t const low1 = umul128(m, mul[1], &high1); // 64
std::uint64_t high0; // 64
umul128(m, mul[0], &high0); // 0
std::uint64_t const sum = high0 + low1;
if (sum < high0)
++high1; // overflow into high1
return shiftright128(sum, high1, j - 64);
}
inline
std::uint64_t
mulShiftAll(
const std::uint64_t m,
const std::uint64_t* const mul,
const std::int32_t j,
std::uint64_t* const vp,
std::uint64_t* const vm,
const std::uint32_t mmShift) noexcept
{
*vp = mulShift(4 * m + 2, mul, j);
*vm = mulShift(4 * m - 1 - mmShift, mul, j);
return mulShift(4 * m, mul, j);
}
#else // !defined(BOOST_JSON_RYU_HAS_UINT128) && !defined(BOOST_JSON_RYU_HAS_64_BIT_INTRINSICS)
inline
std::uint64_t
mulShiftAll(
std::uint64_t m,
const std::uint64_t* const mul,
const std::int32_t j,
std::uint64_t* const vp,
std::uint64_t* const vm,
const std::uint32_t mmShift)
{
m <<= 1;
// m is maximum 55 bits
std::uint64_t tmp;
std::uint64_t const lo = umul128(m, mul[0], &tmp);
std::uint64_t hi;
std::uint64_t const mid = tmp + umul128(m, mul[1], &hi);
hi += mid < tmp; // overflow into hi
const std::uint64_t lo2 = lo + mul[0];
const std::uint64_t mid2 = mid + mul[1] + (lo2 < lo);
const std::uint64_t hi2 = hi + (mid2 < mid);
*vp = shiftright128(mid2, hi2, (std::uint32_t)(j - 64 - 1));
if (mmShift == 1)
{
const std::uint64_t lo3 = lo - mul[0];
const std::uint64_t mid3 = mid - mul[1] - (lo3 > lo);
const std::uint64_t hi3 = hi - (mid3 > mid);
*vm = shiftright128(mid3, hi3, (std::uint32_t)(j - 64 - 1));
}
else
{
const std::uint64_t lo3 = lo + lo;
const std::uint64_t mid3 = mid + mid + (lo3 < lo);
const std::uint64_t hi3 = hi + hi + (mid3 < mid);
const std::uint64_t lo4 = lo3 - mul[0];
const std::uint64_t mid4 = mid3 - mul[1] - (lo4 > lo3);
const std::uint64_t hi4 = hi3 - (mid4 > mid3);
*vm = shiftright128(mid4, hi4, (std::uint32_t)(j - 64));
}
return shiftright128(mid, hi, (std::uint32_t)(j - 64 - 1));
}
#endif // BOOST_JSON_RYU_HAS_64_BIT_INTRINSICS
inline
std::uint32_t
decimalLength17(
const std::uint64_t v)
{
// This is slightly faster than a loop.
// The average output length is 16.38 digits, so we check high-to-low.
// Function precondition: v is not an 18, 19, or 20-digit number.
// (17 digits are sufficient for round-tripping.)
BOOST_ASSERT(v < 100000000000000000L);
if (v >= 10000000000000000L) { return 17; }
if (v >= 1000000000000000L) { return 16; }
if (v >= 100000000000000L) { return 15; }
if (v >= 10000000000000L) { return 14; }
if (v >= 1000000000000L) { return 13; }
if (v >= 100000000000L) { return 12; }
if (v >= 10000000000L) { return 11; }
if (v >= 1000000000L) { return 10; }
if (v >= 100000000L) { return 9; }
if (v >= 10000000L) { return 8; }
if (v >= 1000000L) { return 7; }
if (v >= 100000L) { return 6; }
if (v >= 10000L) { return 5; }
if (v >= 1000L) { return 4; }
if (v >= 100L) { return 3; }
if (v >= 10L) { return 2; }
return 1;
}
// A floating decimal representing m * 10^e.
struct floating_decimal_64
{
std::uint64_t mantissa;
// Decimal exponent's range is -324 to 308
// inclusive, and can fit in a short if needed.
std::int32_t exponent;
};
inline
floating_decimal_64
d2d(
const std::uint64_t ieeeMantissa,
const std::uint32_t ieeeExponent)
{
std::int32_t e2;
std::uint64_t m2;
if (ieeeExponent == 0)
{
// We subtract 2 so that the bounds computation has 2 additional bits.
e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
m2 = ieeeMantissa;
}
else
{
e2 = (std::int32_t)ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
}
const bool even = (m2 & 1) == 0;
const bool acceptBounds = even;
#ifdef RYU_DEBUG
printf("-> %" PRIu64 " * 2^%d\n", m2, e2 + 2);
#endif
// Step 2: Determine the interval of valid decimal representations.
const std::uint64_t mv = 4 * m2;
// Implicit bool -> int conversion. True is 1, false is 0.
const std::uint32_t mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
// We would compute mp and mm like this:
// uint64_t mp = 4 * m2 + 2;
// uint64_t mm = mv - 1 - mmShift;
// Step 3: Convert to a decimal power base using 128-bit arithmetic.
std::uint64_t vr, vp, vm;
std::int32_t e10;
bool vmIsTrailingZeros = false;
bool vrIsTrailingZeros = false;
if (e2 >= 0) {
// I tried special-casing q == 0, but there was no effect on performance.
// This expression is slightly faster than max(0, log10Pow2(e2) - 1).
const std::uint32_t q = log10Pow2(e2) - (e2 > 3);
e10 = (std::int32_t)q;
const std::int32_t k = DOUBLE_POW5_INV_BITCOUNT + pow5bits((int32_t)q) - 1;
const std::int32_t i = -e2 + (std::int32_t)q + k;
#if defined(BOOST_JSON_RYU_OPTIMIZE_SIZE)
uint64_t pow5[2];
double_computeInvPow5(q, pow5);
vr = mulShiftAll(m2, pow5, i, &vp, &vm, mmShift);
#else
vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT()[q], i, &vp, &vm, mmShift);
#endif
#ifdef RYU_DEBUG
printf("%" PRIu64 " * 2^%d / 10^%u\n", mv, e2, q);
printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
#endif
if (q <= 21)
{
// This should use q <= 22, but I think 21 is also safe. Smaller values
// may still be safe, but it's more difficult to reason about them.
// Only one of mp, mv, and mm can be a multiple of 5, if any.
const std::uint32_t mvMod5 = ((std::uint32_t)mv) - 5 * ((std::uint32_t)div5(mv));
if (mvMod5 == 0)
{
vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
}
else if (acceptBounds)
{
// Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
// <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
// <=> true && pow5Factor(mm) >= q, since e2 >= q.
vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
}
else
{
// Same as min(e2 + 1, pow5Factor(mp)) >= q.
vp -= multipleOfPowerOf5(mv + 2, q);
}
}
}
else
{
// This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
const std::uint32_t q = log10Pow5(-e2) - (-e2 > 1);
e10 = (std::int32_t)q + e2;
const std::int32_t i = -e2 - (std::int32_t)q;
const std::int32_t k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
const std::int32_t j = (std::int32_t)q - k;
#if defined(BOOST_JSON_RYU_OPTIMIZE_SIZE)
std::uint64_t pow5[2];
double_computePow5(i, pow5);
vr = mulShiftAll(m2, pow5, j, &vp, &vm, mmShift);
#else
vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT()[i], j, &vp, &vm, mmShift);
#endif
#ifdef RYU_DEBUG
printf("%" PRIu64 " * 5^%d / 10^%u\n", mv, -e2, q);
printf("%u %d %d %d\n", q, i, k, j);
printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
#endif
if (q <= 1)
{
// {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
// mv = 4 * m2, so it always has at least two trailing 0 bits.
vrIsTrailingZeros = true;
if (acceptBounds)
{
// mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
vmIsTrailingZeros = mmShift == 1;
}
else
{
// mp = mv + 2, so it always has at least one trailing 0 bit.
--vp;
}
}
else if (q < 63)
{
// TODO(ulfjack): Use a tighter bound here.
// We want to know if the full product has at least q trailing zeros.
// We need to compute min(p2(mv), p5(mv) - e2) >= q
// <=> p2(mv) >= q && p5(mv) - e2 >= q
// <=> p2(mv) >= q (because -e2 >= q)
vrIsTrailingZeros = multipleOfPowerOf2(mv, q);
#ifdef RYU_DEBUG
printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
#endif
}
}
#ifdef RYU_DEBUG
printf("e10=%d\n", e10);
printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false");
printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
#endif
// Step 4: Find the shortest decimal representation in the interval of valid representations.
std::int32_t removed = 0;
std::uint8_t lastRemovedDigit = 0;
std::uint64_t output;
// On average, we remove ~2 digits.
if (vmIsTrailingZeros || vrIsTrailingZeros)
{
// General case, which happens rarely (~0.7%).
for (;;)
{
const std::uint64_t vpDiv10 = div10(vp);
const std::uint64_t vmDiv10 = div10(vm);
if (vpDiv10 <= vmDiv10)
break;
const std::uint32_t vmMod10 = ((std::uint32_t)vm) - 10 * ((std::uint32_t)vmDiv10);
const std::uint64_t vrDiv10 = div10(vr);
const std::uint32_t vrMod10 = ((std::uint32_t)vr) - 10 * ((std::uint32_t)vrDiv10);
vmIsTrailingZeros &= vmMod10 == 0;
vrIsTrailingZeros &= lastRemovedDigit == 0;
lastRemovedDigit = (uint8_t)vrMod10;
vr = vrDiv10;
vp = vpDiv10;
vm = vmDiv10;
++removed;
}
#ifdef RYU_DEBUG
printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false");
#endif
if (vmIsTrailingZeros)
{
for (;;)
{
const std::uint64_t vmDiv10 = div10(vm);
const std::uint32_t vmMod10 = ((std::uint32_t)vm) - 10 * ((std::uint32_t)vmDiv10);
if (vmMod10 != 0)
break;
const std::uint64_t vpDiv10 = div10(vp);
const std::uint64_t vrDiv10 = div10(vr);
const std::uint32_t vrMod10 = ((std::uint32_t)vr) - 10 * ((std::uint32_t)vrDiv10);
vrIsTrailingZeros &= lastRemovedDigit == 0;
lastRemovedDigit = (uint8_t)vrMod10;
vr = vrDiv10;
vp = vpDiv10;
vm = vmDiv10;
++removed;
}
}
#ifdef RYU_DEBUG
printf("%" PRIu64 " %d\n", vr, lastRemovedDigit);
printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
#endif
if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
{
// Round even if the exact number is .....50..0.
lastRemovedDigit = 4;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up.
output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
}
else
{
// Specialized for the common case (~99.3%). Percentages below are relative to this.
bool roundUp = false;
const std::uint64_t vpDiv100 = div100(vp);
const std::uint64_t vmDiv100 = div100(vm);
if (vpDiv100 > vmDiv100)
{
// Optimization: remove two digits at a time (~86.2%).
const std::uint64_t vrDiv100 = div100(vr);
const std::uint32_t vrMod100 = ((std::uint32_t)vr) - 100 * ((std::uint32_t)vrDiv100);
roundUp = vrMod100 >= 50;
vr = vrDiv100;
vp = vpDiv100;
vm = vmDiv100;
removed += 2;
}
// Loop iterations below (approximately), without optimization above:
// 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
// Loop iterations below (approximately), with optimization above:
// 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
for (;;)
{
const std::uint64_t vpDiv10 = div10(vp);
const std::uint64_t vmDiv10 = div10(vm);
if (vpDiv10 <= vmDiv10)
break;
const std::uint64_t vrDiv10 = div10(vr);
const std::uint32_t vrMod10 = ((std::uint32_t)vr) - 10 * ((std::uint32_t)vrDiv10);
roundUp = vrMod10 >= 5;
vr = vrDiv10;
vp = vpDiv10;
vm = vmDiv10;
++removed;
}
#ifdef RYU_DEBUG
printf("%" PRIu64 " roundUp=%s\n", vr, roundUp ? "true" : "false");
printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
#endif
// We need to take vr + 1 if vr is outside bounds or we need to round up.
output = vr + (vr == vm || roundUp);
}
const std::int32_t exp = e10 + removed;
#ifdef RYU_DEBUG
printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
printf("O=%" PRIu64 "\n", output);
printf("EXP=%d\n", exp);
#endif
floating_decimal_64 fd;
fd.exponent = exp;
fd.mantissa = output;
return fd;
}
inline
int
to_chars(
const floating_decimal_64 v,
const bool sign,
char* const result)
{
// Step 5: Print the decimal representation.
int index = 0;
if (sign)
result[index++] = '-';
std::uint64_t output = v.mantissa;
std::uint32_t const olength = decimalLength17(output);
#ifdef RYU_DEBUG
printf("DIGITS=%" PRIu64 "\n", v.mantissa);
printf("OLEN=%u\n", olength);
printf("EXP=%u\n", v.exponent + olength);
#endif
// Print the decimal digits.
// The following code is equivalent to:
// for (uint32_t i = 0; i < olength - 1; ++i) {
// const uint32_t c = output % 10; output /= 10;
// result[index + olength - i] = (char) ('0' + c);
// }
// result[index] = '0' + output % 10;
std::uint32_t i = 0;
// We prefer 32-bit operations, even on 64-bit platforms.
// We have at most 17 digits, and uint32_t can store 9 digits.
// If output doesn't fit into uint32_t, we cut off 8 digits,
// so the rest will fit into uint32_t.
if ((output >> 32) != 0)
{
// Expensive 64-bit division.
std::uint64_t const q = div1e8(output);
std::uint32_t output2 = ((std::uint32_t)output) - 100000000 * ((std::uint32_t)q);
output = q;
const std::uint32_t c = output2 % 10000;
output2 /= 10000;
const std::uint32_t d = output2 % 10000;
const std::uint32_t c0 = (c % 100) << 1;
const std::uint32_t c1 = (c / 100) << 1;
const std::uint32_t d0 = (d % 100) << 1;
const std::uint32_t d1 = (d / 100) << 1;
std::memcpy(result + index + olength - i - 1, DIGIT_TABLE() + c0, 2);
std::memcpy(result + index + olength - i - 3, DIGIT_TABLE() + c1, 2);
std::memcpy(result + index + olength - i - 5, DIGIT_TABLE() + d0, 2);
std::memcpy(result + index + olength - i - 7, DIGIT_TABLE() + d1, 2);
i += 8;
}
uint32_t output2 = (std::uint32_t)output;
while (output2 >= 10000)
{
#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
const uint32_t c = output2 - 10000 * (output2 / 10000);
#else
const uint32_t c = output2 % 10000;
#endif
output2 /= 10000;
const uint32_t c0 = (c % 100) << 1;
const uint32_t c1 = (c / 100) << 1;
memcpy(result + index + olength - i - 1, DIGIT_TABLE() + c0, 2);
memcpy(result + index + olength - i - 3, DIGIT_TABLE() + c1, 2);
i += 4;
}
if (output2 >= 100) {
const uint32_t c = (output2 % 100) << 1;
output2 /= 100;
memcpy(result + index + olength - i - 1, DIGIT_TABLE() + c, 2);
i += 2;
}
if (output2 >= 10) {
const uint32_t c = output2 << 1;
// We can't use memcpy here: the decimal dot goes between these two digits.
result[index + olength - i] = DIGIT_TABLE()[c + 1];
result[index] = DIGIT_TABLE()[c];
}
else {
result[index] = (char)('0' + output2);
}
// Print decimal point if needed.
if (olength > 1) {
result[index + 1] = '.';
index += olength + 1;
}
else {
++index;
}
// Print the exponent.
result[index++] = 'E';
int32_t exp = v.exponent + (int32_t)olength - 1;
if (exp < 0) {
result[index++] = '-';
exp = -exp;
}
if (exp >= 100) {
const int32_t c = exp % 10;
memcpy(result + index, DIGIT_TABLE() + 2 * (exp / 10), 2);
result[index + 2] = (char)('0' + c);
index += 3;
}
else if (exp >= 10) {
memcpy(result + index, DIGIT_TABLE() + 2 * exp, 2);
index += 2;
}
else {
result[index++] = (char)('0' + exp);
}
return index;
}
static inline bool d2d_small_int(const uint64_t ieeeMantissa, const uint32_t ieeeExponent,
floating_decimal_64* const v) {
const uint64_t m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
const int32_t e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
if (e2 > 0) {
// f = m2 * 2^e2 >= 2^53 is an integer.
// Ignore this case for now.
return false;
}
if (e2 < -52) {
// f < 1.
return false;
}
// Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52: 1 <= f = m2 / 2^-e2 < 2^53.
// Test if the lower -e2 bits of the significand are 0, i.e. whether the fraction is 0.
const uint64_t mask = (1ull << -e2) - 1;
const uint64_t fraction = m2 & mask;
if (fraction != 0) {
return false;
}
// f is an integer in the range [1, 2^53).
// Note: mantissa might contain trailing (decimal) 0's.
// Note: since 2^53 < 10^16, there is no need to adjust decimalLength17().
v->mantissa = m2 >> -e2;
v->exponent = 0;
return true;
}
} // detail
int
d2s_buffered_n(
double f,
char* result) noexcept
{
using namespace detail;
// Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
std::uint64_t const bits = double_to_bits(f);
#ifdef RYU_DEBUG
printf("IN=");
for (std::int32_t bit = 63; bit >= 0; --bit) {
printf("%d", (int)((bits >> bit) & 1));
}
printf("\n");
#endif
// Decode bits into sign, mantissa, and exponent.
const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
const std::uint64_t ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
const std::uint32_t ieeeExponent = (std::uint32_t)((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
// Case distinction; exit early for the easy cases.
if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) {
return copy_special_str(result, ieeeSign, ieeeExponent != 0, ieeeMantissa != 0);
}
floating_decimal_64 v;
const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
if (isSmallInt) {
// For small integers in the range [1, 2^53), v.mantissa might contain trailing (decimal) zeros.
// For scientific notation we need to move these zeros into the exponent.
// (This is not needed for fixed-point notation, so it might be beneficial to trim
// trailing zeros in to_chars only if needed - once fixed-point notation output is implemented.)
for (;;) {
std::uint64_t const q = div10(v.mantissa);
std::uint32_t const r = ((std::uint32_t) v.mantissa) - 10 * ((std::uint32_t) q);
if (r != 0)
break;
v.mantissa = q;
++v.exponent;
}
}
else {
v = d2d(ieeeMantissa, ieeeExponent);
}
return to_chars(v, ieeeSign, result);
}
} // ryu
} // detail
BOOST_JSON_NS_END
#endif