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// 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.
// Defines HAS_UINT128 and uint128_t if applicable.
#include <stdbool.h>
#include "ryu/common.h"
#include "ryu/d2s_intrinsics.h"
static const uint64_t DOUBLE_POW5_INV_SPLIT2[15][2] = {
{ 1u, 2305843009213693952u },
{ 5955668970331000884u, 1784059615882449851u },
{ 8982663654677661702u, 1380349269358112757u },
{ 7286864317269821294u, 2135987035920910082u },
{ 7005857020398200553u, 1652639921975621497u },
{ 17965325103354776697u, 1278668206209430417u },
{ 8928596168509315048u, 1978643211784836272u },
{ 10075671573058298858u, 1530901034580419511u },
{ 597001226353042382u, 1184477304306571148u },
{ 1527430471115325346u, 1832889850782397517u },
{ 12533209867169019542u, 1418129833677084982u },
{ 5577825024675947042u, 2194449627517475473u },
{ 11006974540203867551u, 1697873161311732311u },
{ 10313493231639821582u, 1313665730009899186u },
{ 12701016819766672773u, 2032799256770390445u }
};
static const uint32_t POW5_INV_OFFSETS[22] = {
0x54544554, 0x04055545, 0x10041000, 0x00400414, 0x40010000, 0x41155555, 0x00000454, 0x00010044,
0x40000000, 0x44000041, 0x50454450, 0x55550054, 0x51655554, 0x40004000, 0x01000001, 0x00010500,
0x51515411, 0x05555554, 0x50411500, 0x40040000, 0x05040110, 0x00000000,
};
static const uint64_t DOUBLE_POW5_SPLIT2[13][2] = {
{ 0u, 1152921504606846976u },
{ 0u, 1490116119384765625u },
{ 1032610780636961552u, 1925929944387235853u },
{ 7910200175544436838u, 1244603055572228341u },
{ 16941905809032713930u, 1608611746708759036u },
{ 13024893955298202172u, 2079081953128979843u },
{ 6607496772837067824u, 1343575221513417750u },
{ 17332926989895652603u, 1736530273035216783u },
{ 13037379183483547984u, 2244412773384604712u },
{ 1605989338741628675u, 1450417759929778918u },
{ 9630225068416591280u, 1874621017369538693u },
{ 665883850346957067u, 1211445438634777304u },
{ 14931890668723713708u, 1565756531257009982u }
};
static const uint32_t POW5_OFFSETS[21]
= { 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x40000000, 0x59695995, 0x55545555,
0x56555515, 0x41150504, 0x40555410, 0x44555145, 0x44504540, 0x45555550, 0x40004000,
0x96440440, 0x55565565, 0x54454045, 0x40154151, 0x55559155, 0x51405555, 0x00000105 };
#define POW5_TABLE_SIZE 26
static const uint64_t DOUBLE_POW5_TABLE[POW5_TABLE_SIZE] = {
1ull,
5ull,
25ull,
125ull,
625ull,
3125ull,
15625ull,
78125ull,
390625ull,
1953125ull,
9765625ull,
48828125ull,
244140625ull,
1220703125ull,
6103515625ull,
30517578125ull,
152587890625ull,
762939453125ull,
3814697265625ull,
19073486328125ull,
95367431640625ull,
476837158203125ull,
2384185791015625ull,
11920928955078125ull,
59604644775390625ull,
298023223876953125ull //, 1490116119384765625ull
};
uint32_t
__pow5Factor(uint64_t value)
{
const uint64_t m_inv_5 = 14757395258967641293u; // 5 * m_inv_5 = 1 (mod 2^64)
const uint64_t n_div_5 = 3689348814741910323u; // #{ n | n = 0 (mod 2^64) } = 2^64 / 5
uint32_t count = 0;
for (;;) {
assert(value != 0);
value *= m_inv_5;
if (value > n_div_5)
break;
++count;
}
return count;
}
#if defined(HAS_UINT128)
// Computes 5^i in the form required by Ryu, and stores it in the given pointer.
void
__double_computePow5(const uint32_t i, uint64_t * const result)
{
const uint32_t base = i / POW5_TABLE_SIZE;
const uint32_t base2 = base * POW5_TABLE_SIZE;
const uint32_t offset = i - base2;
const uint64_t * const mul = DOUBLE_POW5_SPLIT2[base];
if (offset == 0) {
result[0] = mul[0];
result[1] = mul[1];
return;
}
const uint64_t m = DOUBLE_POW5_TABLE[offset];
const uint128_t b0 = ((uint128_t)m) * mul[0];
const uint128_t b2 = ((uint128_t)m) * mul[1];
const uint32_t delta = pow5bits(i) - pow5bits(base2);
const uint128_t shiftedSum
= (b0 >> delta) + (b2 << (64 - delta)) + ((POW5_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
result[0] = (uint64_t)shiftedSum;
result[1] = (uint64_t)(shiftedSum >> 64);
}
// Computes 5^-i in the form required by Ryu, and stores it in the given pointer.
void
__double_computeInvPow5(const uint32_t i, uint64_t * const result)
{
const uint32_t base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
const uint32_t base2 = base * POW5_TABLE_SIZE;
const uint32_t offset = base2 - i;
const uint64_t * const mul = DOUBLE_POW5_INV_SPLIT2[base]; // 1/5^base2
if (offset == 0) {
result[0] = mul[0];
result[1] = mul[1];
return;
}
const uint64_t m = DOUBLE_POW5_TABLE[offset]; // 5^offset
const uint128_t b0 = ((uint128_t)m) * (mul[0] - 1);
const uint128_t b2
= ((uint128_t)m) * mul[1]; // 1/5^base2 * 5^offset = 1/5^(base2-offset) = 1/5^i
const uint32_t delta = pow5bits(base2) - pow5bits(i);
const uint128_t shiftedSum = ((b0 >> delta) + (b2 << (64 - delta))) + 1
+ ((POW5_INV_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
result[0] = (uint64_t)shiftedSum;
result[1] = (uint64_t)(shiftedSum >> 64);
}
#else // defined(HAS_UINT128)
// Computes 5^i in the form required by Ryu, and stores it in the given pointer.
void
__double_computePow5(const uint32_t i, uint64_t * const result)
{
const uint32_t base = i / POW5_TABLE_SIZE;
const uint32_t base2 = base * POW5_TABLE_SIZE;
const uint32_t offset = i - base2;
const uint64_t * const mul = DOUBLE_POW5_SPLIT2[base];
if (offset == 0) {
result[0] = mul[0];
result[1] = mul[1];
return;
}
const uint64_t m = DOUBLE_POW5_TABLE[offset];
uint64_t high1;
const uint64_t low1 = umul128(m, mul[1], &high1);
uint64_t high0;
const uint64_t low0 = umul128(m, mul[0], &high0);
const uint64_t sum = high0 + low1;
if (sum < high0) {
++high1; // overflow into high1
}
// high1 | sum | low0
const uint32_t delta = pow5bits(i) - pow5bits(base2);
result[0] = shiftright128(low0, sum, delta) + ((POW5_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
result[1] = shiftright128(sum, high1, delta);
}
// Computes 5^-i in the form required by Ryu, and stores it in the given pointer.
void
__double_computeInvPow5(const uint32_t i, uint64_t * const result)
{
const uint32_t base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
const uint32_t base2 = base * POW5_TABLE_SIZE;
const uint32_t offset = base2 - i;
const uint64_t * const mul = DOUBLE_POW5_INV_SPLIT2[base]; // 1/5^base2
if (offset == 0) {
result[0] = mul[0];
result[1] = mul[1];
return;
}
const uint64_t m = DOUBLE_POW5_TABLE[offset];
uint64_t high1;
const uint64_t low1 = umul128(m, mul[1], &high1);
uint64_t high0;
const uint64_t low0 = umul128(m, mul[0] - 1, &high0);
const uint64_t sum = high0 + low1;
if (sum < high0) {
++high1; // overflow into high1
}
// high1 | sum | low0
const uint32_t delta = pow5bits(base2) - pow5bits(i);
result[0]
= shiftright128(low0, sum, delta) + 1 + ((POW5_INV_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
result[1] = shiftright128(sum, high1, delta);
}
#endif // defined(HAS_UINT128)
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