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fix: support high precision for float parsing (#54)

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Co-authored-by: liuqiang <liuqiang.06@bytedance.com>
This commit is contained in:
liu 2021-07-18 11:37:59 +08:00 committed by GitHub
parent f519f80384
commit a5efd7e8b7
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GPG key ID: 4AEE18F83AFDEB23
10 changed files with 15883 additions and 3840 deletions
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8850
internal/native/avx/native_amd64.s
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16
internal/native/avx/native_subr_amd64.go
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@ -19,16 +19,16 @@ var (
_subr__lspace = **(**uintptr)(unsafe.Pointer(&_func__base)) + 238
_subr__lzero = **(**uintptr)(unsafe.Pointer(&_func__base)) + 0
_subr__quote = **(**uintptr)(unsafe.Pointer(&_func__base)) + 4951
_subr__skip_array = **(**uintptr)(unsafe.Pointer(&_func__base)) + 14035
_subr__skip_object = **(**uintptr)(unsafe.Pointer(&_func__base)) + 14070
_subr__skip_one = **(**uintptr)(unsafe.Pointer(&_func__base)) + 11713
_subr__skip_array = **(**uintptr)(unsafe.Pointer(&_func__base)) + 16916
_subr__skip_object = **(**uintptr)(unsafe.Pointer(&_func__base)) + 16951
_subr__skip_one = **(**uintptr)(unsafe.Pointer(&_func__base)) + 14594
_subr__u64toa = **(**uintptr)(unsafe.Pointer(&_func__base)) + 3731
_subr__unquote = **(**uintptr)(unsafe.Pointer(&_func__base)) + 5972
_subr__value = **(**uintptr)(unsafe.Pointer(&_func__base)) + 7664
_subr__vnumber = **(**uintptr)(unsafe.Pointer(&_func__base)) + 10191
_subr__vsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 11163
_subr__vstring = **(**uintptr)(unsafe.Pointer(&_func__base)) + 9270
_subr__vunsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 11440
_subr__value = **(**uintptr)(unsafe.Pointer(&_func__base)) + 10112
_subr__vnumber = **(**uintptr)(unsafe.Pointer(&_func__base)) + 12979
_subr__vsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 14044
_subr__vstring = **(**uintptr)(unsafe.Pointer(&_func__base)) + 11718
_subr__vunsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 14321
)
var (

9187
internal/native/avx2/native_amd64.s
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16
internal/native/avx2/native_subr_amd64.go
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@ -19,16 +19,16 @@ var (
_subr__lspace = **(**uintptr)(unsafe.Pointer(&_func__base)) + 366
_subr__lzero = **(**uintptr)(unsafe.Pointer(&_func__base)) + 0
_subr__quote = **(**uintptr)(unsafe.Pointer(&_func__base)) + 5299
_subr__skip_array = **(**uintptr)(unsafe.Pointer(&_func__base)) + 15920
_subr__skip_object = **(**uintptr)(unsafe.Pointer(&_func__base)) + 15955
_subr__skip_one = **(**uintptr)(unsafe.Pointer(&_func__base)) + 13120
_subr__skip_array = **(**uintptr)(unsafe.Pointer(&_func__base)) + 19341
_subr__skip_object = **(**uintptr)(unsafe.Pointer(&_func__base)) + 19376
_subr__skip_one = **(**uintptr)(unsafe.Pointer(&_func__base)) + 16541
_subr__u64toa = **(**uintptr)(unsafe.Pointer(&_func__base)) + 3979
_subr__unquote = **(**uintptr)(unsafe.Pointer(&_func__base)) + 7136
_subr__value = **(**uintptr)(unsafe.Pointer(&_func__base)) + 9082
_subr__vnumber = **(**uintptr)(unsafe.Pointer(&_func__base)) + 11598
_subr__vsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 12570
_subr__vstring = **(**uintptr)(unsafe.Pointer(&_func__base)) + 10793
_subr__vunsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 12847
_subr__value = **(**uintptr)(unsafe.Pointer(&_func__base)) + 12070
_subr__vnumber = **(**uintptr)(unsafe.Pointer(&_func__base)) + 14926
_subr__vsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 15991
_subr__vstring = **(**uintptr)(unsafe.Pointer(&_func__base)) + 13781
_subr__vunsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 16268
)
var (

38
issue8_test.go Normal file
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@ -0,0 +1,38 @@
/*
* Copyright 2021 ByteDance Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package sonic
import (
"encoding/json"
"reflect"
"testing"
)
func TestFloat(t *testing.T) {
data := `{"test":0.6666}`
var stdobj map[string]interface{}
if err := json.Unmarshal([]byte(data), &stdobj); err != nil {
t.Fatal(err)
}
var sonicobj map[string]interface{}
if err := Unmarshal([]byte(data), &sonicobj); err != nil {
t.Fatal(err)
}
if !reflect.DeepEqual(stdobj, sonicobj) {
t.Fatalf("exp: \n%#v, \ngot: \n%#v\n", stdobj, sonicobj)
}
}

861
native/atof_eisel_lemire.c Normal file
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@ -0,0 +1,861 @@
/*
* Copyright 2021 ByteDance Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include "native.h"
/* two uint64_t represent a 128-bit unsigned integer */
typedef struct u128_output {
uint64_t hi;
uint64_t lo;
} u128_output;
static const uint8_t U8_LEN_TAB[256];
static const uint64_t POW10_M128_TAB[697][2];
static inline int count_len_u64(uint64_t val) {
if (val >> 32) {
return count_len_u64(val >> 32) + 32;
}
if (val >> 16) {
return count_len_u64(val >> 16) + 16;
}
if (val >> 8) {
return count_len_u64(val >> 8) + 8;
}
return U8_LEN_TAB[val];
}
static inline int count_leading_zeros_u64(uint64_t val) {
return 64 - count_len_u64(val);
}
static inline u128_output mul_u64(uint64_t x, uint64_t y) {
u128_output ret;
__uint128_t z = ((__uint128_t)x) * ((__uint128_t)y);
ret.hi = (uint64_t)(z >> 64);
ret.lo = (uint64_t)z;
return ret;
}
/* This is Eisel Lemire ParseFloat algorithm implemented in C.
* reference: https://nigeltao.github.io/blog/2020/eisel-lemire.html
*/
int atof_eisel_lemire64(uint64_t mant, int exp10, int sgn, double *val) {
if (exp10 < -348 || exp10 > 347) {
return 0;
}
/* Calculate the 2-base exponent of float */
int clz = count_leading_zeros_u64(mant);
mant <<= clz;
/* lg10/lg2 ≈ 217706>>16 */
uint64_t ret_exp2 = ((uint64_t)((217706 * exp10) >> 16) + 64 + 1023) - ((uint64_t)clz);
/* Calculate the mantissa of float */
u128_output x = mul_u64(mant, POW10_M128_TAB[exp10 + 348][1]); // higher 64 bits of POW10 mantissa
uint64_t x_hi = x.hi;
uint64_t x_lo = x.lo;
/* Wider approximation for the float.
* mant * PWO10_M * exp2 <= ret float < mant * (PWO10_M + 1) * exp2.
* mant * PWO10_M <= ret_man < mant * (PWO10_M + 1)
* If the lower 9 bits of x_hi is 0x1FF and the mant + x_lo is overflow，
* x_hi needs to add 1 for the upper bound, and it is ambiguous for higher 54 bits of ret_man.
*/
if ((x_hi & 0x1FF) == 0x1FF && (x_lo + mant) < mant) {
/* lower 64 bits of POW10 mantissa */
u128_output y = mul_u64(mant, POW10_M128_TAB[exp10 + 347][0]);
uint64_t merged_hi = x_hi;
uint64_t merged_lo = x_lo + y.hi;
/* lower 64 bits of multiply output overflow */
if (merged_lo < x_lo) {
merged_hi ++;
}
/* Still ambigunous */
if ((merged_hi & 0x1FF) == 0x1FF && (merged_lo + 1) == 0 && (y.lo + mant) < mant) {
return 0;
}
x_hi = merged_hi;
x_lo = merged_lo;
}
/* Remain 54 bits */
int msb = x_hi >> 63;
uint64_t ret_man = x_hi >> (msb + 9);
ret_exp2 -= 1 ^ msb;
/* Half-way Ambiguity */
if ((x_lo == 0) && ((x_hi & 0x1FF) == 0) && ((ret_man & 3) == 1)) {
return 0;
}
/* If not half-way, then it's rounding to-nearest
* Remain 53 bits.
*/
ret_man += ret_man & 1;
ret_man >>= 1;
/* If rounding overflowed, shift again */
if ((ret_man >> 53) > 0) {
ret_man >>= 1;
ret_exp2 += 1;
}
/* ret_exp2 < 0 means subnormal double.
* ret_exp2 >= 0x7FF means INF/inf.
*/
if ((ret_exp2 - 1) >= (0x7FF - 1)) {
return 0;
}
/* Get the lower 52 bits as finnal mantissa */
uint64_t bits = (ret_exp2 << 52) | (ret_man & 0x000FFFFFFFFFFFFF);
if (sgn == -1) {
bits |= ((uint64_t)1) << 63;
}
*(int64_t*)val = bits;
return 1;
}
/* the len of significant digits for unit8 */
static const uint8_t U8_LEN_TAB[256] = {
0x00, 0x01, 0x02, 0x02, 0x03, 0x03, 0x03, 0x03, 0x04, 0x04, 0x04, 0x04, 0x04, 0x04, 0x04, 0x04,
0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05,
0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06,
0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06,
0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07,
0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07,
0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07,
0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
};
/* Including 128-bit mantissa approximations (rounded down) of the powers of 10.
* For example:
* 1e-348 ≈ 0xFA8FD5A0081C0288_1732C869CD60E453 * (2 ** (-348 * lg10 / lg2 - 127)).
* 1e-348 ≈ 0xFA8FD5A0081C0288 * (2 ** (-348 * lg10 / lg2 - 63)).
* lg10/lg2 ≈ 217706.0/65536.0.
*/
static const uint64_t POW10_M128_TAB[697][2] = {
{0x1732C869CD60E453, 0xFA8FD5A0081C0288}, // 1e-348
{0x0E7FBD42205C8EB4, 0x9C99E58405118195}, // 1e-347
{0x521FAC92A873B261, 0xC3C05EE50655E1FA}, // 1e-346
{0xE6A797B752909EF9, 0xF4B0769E47EB5A78}, // 1e-345
{0x9028BED2939A635C, 0x98EE4A22ECF3188B}, // 1e-344
{0x7432EE873880FC33, 0xBF29DCABA82FDEAE}, // 1e-343
{0x113FAA2906A13B3F, 0xEEF453D6923BD65A}, // 1e-342
{0x4AC7CA59A424C507, 0x9558B4661B6565F8}, // 1e-341
{0x5D79BCF00D2DF649, 0xBAAEE17FA23EBF76}, // 1e-340
{0xF4D82C2C107973DC, 0xE95A99DF8ACE6F53}, // 1e-339
{0x79071B9B8A4BE869, 0x91D8A02BB6C10594}, // 1e-338
{0x9748E2826CDEE284, 0xB64EC836A47146F9}, // 1e-337
{0xFD1B1B2308169B25, 0xE3E27A444D8D98B7}, // 1e-336
{0xFE30F0F5E50E20F7, 0x8E6D8C6AB0787F72}, // 1e-335
{0xBDBD2D335E51A935, 0xB208EF855C969F4F}, // 1e-334
{0xAD2C788035E61382, 0xDE8B2B66B3BC4723}, // 1e-333
{0x4C3BCB5021AFCC31, 0x8B16FB203055AC76}, // 1e-332
{0xDF4ABE242A1BBF3D, 0xADDCB9E83C6B1793}, // 1e-331
{0xD71D6DAD34A2AF0D, 0xD953E8624B85DD78}, // 1e-330
{0x8672648C40E5AD68, 0x87D4713D6F33AA6B}, // 1e-329
{0x680EFDAF511F18C2, 0xA9C98D8CCB009506}, // 1e-328
{0x0212BD1B2566DEF2, 0xD43BF0EFFDC0BA48}, // 1e-327
{0x014BB630F7604B57, 0x84A57695FE98746D}, // 1e-326
{0x419EA3BD35385E2D, 0xA5CED43B7E3E9188}, // 1e-325
{0x52064CAC828675B9, 0xCF42894A5DCE35EA}, // 1e-324
{0x7343EFEBD1940993, 0x818995CE7AA0E1B2}, // 1e-323
{0x1014EBE6C5F90BF8, 0xA1EBFB4219491A1F}, // 1e-322
{0xD41A26E077774EF6, 0xCA66FA129F9B60A6}, // 1e-321
{0x8920B098955522B4, 0xFD00B897478238D0}, // 1e-320
{0x55B46E5F5D5535B0, 0x9E20735E8CB16382}, // 1e-319
{0xEB2189F734AA831D, 0xC5A890362FDDBC62}, // 1e-318
{0xA5E9EC7501D523E4, 0xF712B443BBD52B7B}, // 1e-317
{0x47B233C92125366E, 0x9A6BB0AA55653B2D}, // 1e-316
{0x999EC0BB696E840A, 0xC1069CD4EABE89F8}, // 1e-315
{0xC00670EA43CA250D, 0xF148440A256E2C76}, // 1e-314
{0x380406926A5E5728, 0x96CD2A865764DBCA}, // 1e-313
{0xC605083704F5ECF2, 0xBC807527ED3E12BC}, // 1e-312
{0xF7864A44C633682E, 0xEBA09271E88D976B}, // 1e-311
{0x7AB3EE6AFBE0211D, 0x93445B8731587EA3}, // 1e-310
{0x5960EA05BAD82964, 0xB8157268FDAE9E4C}, // 1e-309
{0x6FB92487298E33BD, 0xE61ACF033D1A45DF}, // 1e-308
{0xA5D3B6D479F8E056, 0x8FD0C16206306BAB}, // 1e-307
{0x8F48A4899877186C, 0xB3C4F1BA87BC8696}, // 1e-306
{0x331ACDABFE94DE87, 0xE0B62E2929ABA83C}, // 1e-305
{0x9FF0C08B7F1D0B14, 0x8C71DCD9BA0B4925}, // 1e-304
{0x07ECF0AE5EE44DD9, 0xAF8E5410288E1B6F}, // 1e-303
{0xC9E82CD9F69D6150, 0xDB71E91432B1A24A}, // 1e-302
{0xBE311C083A225CD2, 0x892731AC9FAF056E}, // 1e-301
{0x6DBD630A48AAF406, 0xAB70FE17C79AC6CA}, // 1e-300
{0x092CBBCCDAD5B108, 0xD64D3D9DB981787D}, // 1e-299
{0x25BBF56008C58EA5, 0x85F0468293F0EB4E}, // 1e-298
{0xAF2AF2B80AF6F24E, 0xA76C582338ED2621}, // 1e-297
{0x1AF5AF660DB4AEE1, 0xD1476E2C07286FAA}, // 1e-296
{0x50D98D9FC890ED4D, 0x82CCA4DB847945CA}, // 1e-295
{0xE50FF107BAB528A0, 0xA37FCE126597973C}, // 1e-294
{0x1E53ED49A96272C8, 0xCC5FC196FEFD7D0C}, // 1e-293
{0x25E8E89C13BB0F7A, 0xFF77B1FCBEBCDC4F}, // 1e-292
{0x77B191618C54E9AC, 0x9FAACF3DF73609B1}, // 1e-291
{0xD59DF5B9EF6A2417, 0xC795830D75038C1D}, // 1e-290
{0x4B0573286B44AD1D, 0xF97AE3D0D2446F25}, // 1e-289
{0x4EE367F9430AEC32, 0x9BECCE62836AC577}, // 1e-288
{0x229C41F793CDA73F, 0xC2E801FB244576D5}, // 1e-287
{0x6B43527578C1110F, 0xF3A20279ED56D48A}, // 1e-286
{0x830A13896B78AAA9, 0x9845418C345644D6}, // 1e-285
{0x23CC986BC656D553, 0xBE5691EF416BD60C}, // 1e-284
{0x2CBFBE86B7EC8AA8, 0xEDEC366B11C6CB8F}, // 1e-283
{0x7BF7D71432F3D6A9, 0x94B3A202EB1C3F39}, // 1e-282
{0xDAF5CCD93FB0CC53, 0xB9E08A83A5E34F07}, // 1e-281
{0xD1B3400F8F9CFF68, 0xE858AD248F5C22C9}, // 1e-280
{0x23100809B9C21FA1, 0x91376C36D99995BE}, // 1e-279
{0xABD40A0C2832A78A, 0xB58547448FFFFB2D}, // 1e-278
{0x16C90C8F323F516C, 0xE2E69915B3FFF9F9}, // 1e-277
{0xAE3DA7D97F6792E3, 0x8DD01FAD907FFC3B}, // 1e-276
{0x99CD11CFDF41779C, 0xB1442798F49FFB4A}, // 1e-275
{0x40405643D711D583, 0xDD95317F31C7FA1D}, // 1e-274
{0x482835EA666B2572, 0x8A7D3EEF7F1CFC52}, // 1e-273
{0xDA3243650005EECF, 0xAD1C8EAB5EE43B66}, // 1e-272
{0x90BED43E40076A82, 0xD863B256369D4A40}, // 1e-271
{0x5A7744A6E804A291, 0x873E4F75E2224E68}, // 1e-270
{0x711515D0A205CB36, 0xA90DE3535AAAE202}, // 1e-269
{0x0D5A5B44CA873E03, 0xD3515C2831559A83}, // 1e-268
{0xE858790AFE9486C2, 0x8412D9991ED58091}, // 1e-267
{0x626E974DBE39A872, 0xA5178FFF668AE0B6}, // 1e-266
{0xFB0A3D212DC8128F, 0xCE5D73FF402D98E3}, // 1e-265
{0x7CE66634BC9D0B99, 0x80FA687F881C7F8E}, // 1e-264
{0x1C1FFFC1EBC44E80, 0xA139029F6A239F72}, // 1e-263
{0xA327FFB266B56220, 0xC987434744AC874E}, // 1e-262
{0x4BF1FF9F0062BAA8, 0xFBE9141915D7A922}, // 1e-261
{0x6F773FC3603DB4A9, 0x9D71AC8FADA6C9B5}, // 1e-260
{0xCB550FB4384D21D3, 0xC4CE17B399107C22}, // 1e-259
{0x7E2A53A146606A48, 0xF6019DA07F549B2B}, // 1e-258
{0x2EDA7444CBFC426D, 0x99C102844F94E0FB}, // 1e-257
{0xFA911155FEFB5308, 0xC0314325637A1939}, // 1e-256
{0x793555AB7EBA27CA, 0xF03D93EEBC589F88}, // 1e-255
{0x4BC1558B2F3458DE, 0x96267C7535B763B5}, // 1e-254
{0x9EB1AAEDFB016F16, 0xBBB01B9283253CA2}, // 1e-253
{0x465E15A979C1CADC, 0xEA9C227723EE8BCB}, // 1e-252
{0x0BFACD89EC191EC9, 0x92A1958A7675175F}, // 1e-251
{0xCEF980EC671F667B, 0xB749FAED14125D36}, // 1e-250
{0x82B7E12780E7401A, 0xE51C79A85916F484}, // 1e-249
{0xD1B2ECB8B0908810, 0x8F31CC0937AE58D2}, // 1e-248
{0x861FA7E6DCB4AA15, 0xB2FE3F0B8599EF07}, // 1e-247
{0x67A791E093E1D49A, 0xDFBDCECE67006AC9}, // 1e-246
{0xE0C8BB2C5C6D24E0, 0x8BD6A141006042BD}, // 1e-245
{0x58FAE9F773886E18, 0xAECC49914078536D}, // 1e-244
{0xAF39A475506A899E, 0xDA7F5BF590966848}, // 1e-243
{0x6D8406C952429603, 0x888F99797A5E012D}, // 1e-242
{0xC8E5087BA6D33B83, 0xAAB37FD7D8F58178}, // 1e-241
{0xFB1E4A9A90880A64, 0xD5605FCDCF32E1D6}, // 1e-240
{0x5CF2EEA09A55067F, 0x855C3BE0A17FCD26}, // 1e-239
{0xF42FAA48C0EA481E, 0xA6B34AD8C9DFC06F}, // 1e-238
{0xF13B94DAF124DA26, 0xD0601D8EFC57B08B}, // 1e-237
{0x76C53D08D6B70858, 0x823C12795DB6CE57}, // 1e-236
{0x54768C4B0C64CA6E, 0xA2CB1717B52481ED}, // 1e-235
{0xA9942F5DCF7DFD09, 0xCB7DDCDDA26DA268}, // 1e-234
{0xD3F93B35435D7C4C, 0xFE5D54150B090B02}, // 1e-233
{0xC47BC5014A1A6DAF, 0x9EFA548D26E5A6E1}, // 1e-232
{0x359AB6419CA1091B, 0xC6B8E9B0709F109A}, // 1e-231
{0xC30163D203C94B62, 0xF867241C8CC6D4C0}, // 1e-230
{0x79E0DE63425DCF1D, 0x9B407691D7FC44F8}, // 1e-229
{0x985915FC12F542E4, 0xC21094364DFB5636}, // 1e-228
{0x3E6F5B7B17B2939D, 0xF294B943E17A2BC4}, // 1e-227
{0xA705992CEECF9C42, 0x979CF3CA6CEC5B5A}, // 1e-226
{0x50C6FF782A838353, 0xBD8430BD08277231}, // 1e-225
{0xA4F8BF5635246428, 0xECE53CEC4A314EBD}, // 1e-224
{0x871B7795E136BE99, 0x940F4613AE5ED136}, // 1e-223
{0x28E2557B59846E3F, 0xB913179899F68584}, // 1e-222
{0x331AEADA2FE589CF, 0xE757DD7EC07426E5}, // 1e-221
{0x3FF0D2C85DEF7621, 0x9096EA6F3848984F}, // 1e-220
{0x0FED077A756B53A9, 0xB4BCA50B065ABE63}, // 1e-219
{0xD3E8495912C62894, 0xE1EBCE4DC7F16DFB}, // 1e-218
{0x64712DD7ABBBD95C, 0x8D3360F09CF6E4BD}, // 1e-217
{0xBD8D794D96AACFB3, 0xB080392CC4349DEC}, // 1e-216
{0xECF0D7A0FC5583A0, 0xDCA04777F541C567}, // 1e-215
{0xF41686C49DB57244, 0x89E42CAAF9491B60}, // 1e-214
{0x311C2875C522CED5, 0xAC5D37D5B79B6239}, // 1e-213
{0x7D633293366B828B, 0xD77485CB25823AC7}, // 1e-212
{0xAE5DFF9C02033197, 0x86A8D39EF77164BC}, // 1e-211
{0xD9F57F830283FDFC, 0xA8530886B54DBDEB}, // 1e-210
{0xD072DF63C324FD7B, 0xD267CAA862A12D66}, // 1e-209
{0x4247CB9E59F71E6D, 0x8380DEA93DA4BC60}, // 1e-208
{0x52D9BE85F074E608, 0xA46116538D0DEB78}, // 1e-207
{0x67902E276C921F8B, 0xCD795BE870516656}, // 1e-206
{0x00BA1CD8A3DB53B6, 0x806BD9714632DFF6}, // 1e-205
{0x80E8A40ECCD228A4, 0xA086CFCD97BF97F3}, // 1e-204
{0x6122CD128006B2CD, 0xC8A883C0FDAF7DF0}, // 1e-203
{0x796B805720085F81, 0xFAD2A4B13D1B5D6C}, // 1e-202
{0xCBE3303674053BB0, 0x9CC3A6EEC6311A63}, // 1e-201
{0xBEDBFC4411068A9C, 0xC3F490AA77BD60FC}, // 1e-200
{0xEE92FB5515482D44, 0xF4F1B4D515ACB93B}, // 1e-199
{0x751BDD152D4D1C4A, 0x991711052D8BF3C5}, // 1e-198
{0xD262D45A78A0635D, 0xBF5CD54678EEF0B6}, // 1e-197
{0x86FB897116C87C34, 0xEF340A98172AACE4}, // 1e-196
{0xD45D35E6AE3D4DA0, 0x9580869F0E7AAC0E}, // 1e-195
{0x8974836059CCA109, 0xBAE0A846D2195712}, // 1e-194
{0x2BD1A438703FC94B, 0xE998D258869FACD7}, // 1e-193
{0x7B6306A34627DDCF, 0x91FF83775423CC06}, // 1e-192
{0x1A3BC84C17B1D542, 0xB67F6455292CBF08}, // 1e-191
{0x20CABA5F1D9E4A93, 0xE41F3D6A7377EECA}, // 1e-190
{0x547EB47B7282EE9C, 0x8E938662882AF53E}, // 1e-189
{0xE99E619A4F23AA43, 0xB23867FB2A35B28D}, // 1e-188
{0x6405FA00E2EC94D4, 0xDEC681F9F4C31F31}, // 1e-187
{0xDE83BC408DD3DD04, 0x8B3C113C38F9F37E}, // 1e-186
{0x9624AB50B148D445, 0xAE0B158B4738705E}, // 1e-185
{0x3BADD624DD9B0957, 0xD98DDAEE19068C76}, // 1e-184
{0xE54CA5D70A80E5D6, 0x87F8A8D4CFA417C9}, // 1e-183
{0x5E9FCF4CCD211F4C, 0xA9F6D30A038D1DBC}, // 1e-182
{0x7647C3200069671F, 0xD47487CC8470652B}, // 1e-181
{0x29ECD9F40041E073, 0x84C8D4DFD2C63F3B}, // 1e-180
{0xF468107100525890, 0xA5FB0A17C777CF09}, // 1e-179
{0x7182148D4066EEB4, 0xCF79CC9DB955C2CC}, // 1e-178
{0xC6F14CD848405530, 0x81AC1FE293D599BF}, // 1e-177
{0xB8ADA00E5A506A7C, 0xA21727DB38CB002F}, // 1e-176
{0xA6D90811F0E4851C, 0xCA9CF1D206FDC03B}, // 1e-175
{0x908F4A166D1DA663, 0xFD442E4688BD304A}, // 1e-174
{0x9A598E4E043287FE, 0x9E4A9CEC15763E2E}, // 1e-173
{0x40EFF1E1853F29FD, 0xC5DD44271AD3CDBA}, // 1e-172
{0xD12BEE59E68EF47C, 0xF7549530E188C128}, // 1e-171
{0x82BB74F8301958CE, 0x9A94DD3E8CF578B9}, // 1e-170
{0xE36A52363C1FAF01, 0xC13A148E3032D6E7}, // 1e-169
{0xDC44E6C3CB279AC1, 0xF18899B1BC3F8CA1}, // 1e-168
{0x29AB103A5EF8C0B9, 0x96F5600F15A7B7E5}, // 1e-167
{0x7415D448F6B6F0E7, 0xBCB2B812DB11A5DE}, // 1e-166
{0x111B495B3464AD21, 0xEBDF661791D60F56}, // 1e-165
{0xCAB10DD900BEEC34, 0x936B9FCEBB25C995}, // 1e-164
{0x3D5D514F40EEA742, 0xB84687C269EF3BFB}, // 1e-163
{0x0CB4A5A3112A5112, 0xE65829B3046B0AFA}, // 1e-162
{0x47F0E785EABA72AB, 0x8FF71A0FE2C2E6DC}, // 1e-161
{0x59ED216765690F56, 0xB3F4E093DB73A093}, // 1e-160
{0x306869C13EC3532C, 0xE0F218B8D25088B8}, // 1e-159
{0x1E414218C73A13FB, 0x8C974F7383725573}, // 1e-158
{0xE5D1929EF90898FA, 0xAFBD2350644EEACF}, // 1e-157
{0xDF45F746B74ABF39, 0xDBAC6C247D62A583}, // 1e-156
{0x6B8BBA8C328EB783, 0x894BC396CE5DA772}, // 1e-155
{0x066EA92F3F326564, 0xAB9EB47C81F5114F}, // 1e-154
{0xC80A537B0EFEFEBD, 0xD686619BA27255A2}, // 1e-153
{0xBD06742CE95F5F36, 0x8613FD0145877585}, // 1e-152
{0x2C48113823B73704, 0xA798FC4196E952E7}, // 1e-151
{0xF75A15862CA504C5, 0xD17F3B51FCA3A7A0}, // 1e-150
{0x9A984D73DBE722FB, 0x82EF85133DE648C4}, // 1e-149
{0xC13E60D0D2E0EBBA, 0xA3AB66580D5FDAF5}, // 1e-148
{0x318DF905079926A8, 0xCC963FEE10B7D1B3}, // 1e-147
{0xFDF17746497F7052, 0xFFBBCFE994E5C61F}, // 1e-146
{0xFEB6EA8BEDEFA633, 0x9FD561F1FD0F9BD3}, // 1e-145
{0xFE64A52EE96B8FC0, 0xC7CABA6E7C5382C8}, // 1e-144
{0x3DFDCE7AA3C673B0, 0xF9BD690A1B68637B}, // 1e-143
{0x06BEA10CA65C084E, 0x9C1661A651213E2D}, // 1e-142
{0x486E494FCFF30A62, 0xC31BFA0FE5698DB8}, // 1e-141
{0x5A89DBA3C3EFCCFA, 0xF3E2F893DEC3F126}, // 1e-140
{0xF89629465A75E01C, 0x986DDB5C6B3A76B7}, // 1e-139
{0xF6BBB397F1135823, 0xBE89523386091465}, // 1e-138
{0x746AA07DED582E2C, 0xEE2BA6C0678B597F}, // 1e-137
{0xA8C2A44EB4571CDC, 0x94DB483840B717EF}, // 1e-136
{0x92F34D62616CE413, 0xBA121A4650E4DDEB}, // 1e-135
{0x77B020BAF9C81D17, 0xE896A0D7E51E1566}, // 1e-134
{0x0ACE1474DC1D122E, 0x915E2486EF32CD60}, // 1e-133
{0x0D819992132456BA, 0xB5B5ADA8AAFF80B8}, // 1e-132
{0x10E1FFF697ED6C69, 0xE3231912D5BF60E6}, // 1e-131
{0xCA8D3FFA1EF463C1, 0x8DF5EFABC5979C8F}, // 1e-130
{0xBD308FF8A6B17CB2, 0xB1736B96B6FD83B3}, // 1e-129
{0xAC7CB3F6D05DDBDE, 0xDDD0467C64BCE4A0}, // 1e-128
{0x6BCDF07A423AA96B, 0x8AA22C0DBEF60EE4}, // 1e-127
{0x86C16C98D2C953C6, 0xAD4AB7112EB3929D}, // 1e-126
{0xE871C7BF077BA8B7, 0xD89D64D57A607744}, // 1e-125
{0x11471CD764AD4972, 0x87625F056C7C4A8B}, // 1e-124
{0xD598E40D3DD89BCF, 0xA93AF6C6C79B5D2D}, // 1e-123
{0x4AFF1D108D4EC2C3, 0xD389B47879823479}, // 1e-122
{0xCEDF722A585139BA, 0x843610CB4BF160CB}, // 1e-121
{0xC2974EB4EE658828, 0xA54394FE1EEDB8FE}, // 1e-120
{0x733D226229FEEA32, 0xCE947A3DA6A9273E}, // 1e-119
{0x0806357D5A3F525F, 0x811CCC668829B887}, // 1e-118
{0xCA07C2DCB0CF26F7, 0xA163FF802A3426A8}, // 1e-117
{0xFC89B393DD02F0B5, 0xC9BCFF6034C13052}, // 1e-116
{0xBBAC2078D443ACE2, 0xFC2C3F3841F17C67}, // 1e-115
{0xD54B944B84AA4C0D, 0x9D9BA7832936EDC0}, // 1e-114
{0x0A9E795E65D4DF11, 0xC5029163F384A931}, // 1e-113
{0x4D4617B5FF4A16D5, 0xF64335BCF065D37D}, // 1e-112
{0x504BCED1BF8E4E45, 0x99EA0196163FA42E}, // 1e-111
{0xE45EC2862F71E1D6, 0xC06481FB9BCF8D39}, // 1e-110
{0x5D767327BB4E5A4C, 0xF07DA27A82C37088}, // 1e-109
{0x3A6A07F8D510F86F, 0x964E858C91BA2655}, // 1e-108
{0x890489F70A55368B, 0xBBE226EFB628AFEA}, // 1e-107
{0x2B45AC74CCEA842E, 0xEADAB0ABA3B2DBE5}, // 1e-106
{0x3B0B8BC90012929D, 0x92C8AE6B464FC96F}, // 1e-105
{0x09CE6EBB40173744, 0xB77ADA0617E3BBCB}, // 1e-104
{0xCC420A6A101D0515, 0xE55990879DDCAABD}, // 1e-103
{0x9FA946824A12232D, 0x8F57FA54C2A9EAB6}, // 1e-102
{0x47939822DC96ABF9, 0xB32DF8E9F3546564}, // 1e-101
{0x59787E2B93BC56F7, 0xDFF9772470297EBD}, // 1e-100
{0x57EB4EDB3C55B65A, 0x8BFBEA76C619EF36}, // 1e-99
{0xEDE622920B6B23F1, 0xAEFAE51477A06B03}, // 1e-98
{0xE95FAB368E45ECED, 0xDAB99E59958885C4}, // 1e-97
{0x11DBCB0218EBB414, 0x88B402F7FD75539B}, // 1e-96
{0xD652BDC29F26A119, 0xAAE103B5FCD2A881}, // 1e-95
{0x4BE76D3346F0495F, 0xD59944A37C0752A2}, // 1e-94
{0x6F70A4400C562DDB, 0x857FCAE62D8493A5}, // 1e-93
{0xCB4CCD500F6BB952, 0xA6DFBD9FB8E5B88E}, // 1e-92
{0x7E2000A41346A7A7, 0xD097AD07A71F26B2}, // 1e-91
{0x8ED400668C0C28C8, 0x825ECC24C873782F}, // 1e-90
{0x728900802F0F32FA, 0xA2F67F2DFA90563B}, // 1e-89
{0x4F2B40A03AD2FFB9, 0xCBB41EF979346BCA}, // 1e-88
{0xE2F610C84987BFA8, 0xFEA126B7D78186BC}, // 1e-87
{0x0DD9CA7D2DF4D7C9, 0x9F24B832E6B0F436}, // 1e-86
{0x91503D1C79720DBB, 0xC6EDE63FA05D3143}, // 1e-85
{0x75A44C6397CE912A, 0xF8A95FCF88747D94}, // 1e-84
{0xC986AFBE3EE11ABA, 0x9B69DBE1B548CE7C}, // 1e-83
{0xFBE85BADCE996168, 0xC24452DA229B021B}, // 1e-82
{0xFAE27299423FB9C3, 0xF2D56790AB41C2A2}, // 1e-81
{0xDCCD879FC967D41A, 0x97C560BA6B0919A5}, // 1e-80
{0x5400E987BBC1C920, 0xBDB6B8E905CB600F}, // 1e-79
{0x290123E9AAB23B68, 0xED246723473E3813}, // 1e-78
{0xF9A0B6720AAF6521, 0x9436C0760C86E30B}, // 1e-77
{0xF808E40E8D5B3E69, 0xB94470938FA89BCE}, // 1e-76
{0xB60B1D1230B20E04, 0xE7958CB87392C2C2}, // 1e-75
{0xB1C6F22B5E6F48C2, 0x90BD77F3483BB9B9}, // 1e-74
{0x1E38AEB6360B1AF3, 0xB4ECD5F01A4AA828}, // 1e-73
{0x25C6DA63C38DE1B0, 0xE2280B6C20DD5232}, // 1e-72
{0x579C487E5A38AD0E, 0x8D590723948A535F}, // 1e-71
{0x2D835A9DF0C6D851, 0xB0AF48EC79ACE837}, // 1e-70
{0xF8E431456CF88E65, 0xDCDB1B2798182244}, // 1e-69
{0x1B8E9ECB641B58FF, 0x8A08F0F8BF0F156B}, // 1e-68
{0xE272467E3D222F3F, 0xAC8B2D36EED2DAC5}, // 1e-67
{0x5B0ED81DCC6ABB0F, 0xD7ADF884AA879177}, // 1e-66
{0x98E947129FC2B4E9, 0x86CCBB52EA94BAEA}, // 1e-65
{0x3F2398D747B36224, 0xA87FEA27A539E9A5}, // 1e-64
{0x8EEC7F0D19A03AAD, 0xD29FE4B18E88640E}, // 1e-63
{0x1953CF68300424AC, 0x83A3EEEEF9153E89}, // 1e-62
{0x5FA8C3423C052DD7, 0xA48CEAAAB75A8E2B}, // 1e-61
{0x3792F412CB06794D, 0xCDB02555653131B6}, // 1e-60
{0xE2BBD88BBEE40BD0, 0x808E17555F3EBF11}, // 1e-59
{0x5B6ACEAEAE9D0EC4, 0xA0B19D2AB70E6ED6}, // 1e-58
{0xF245825A5A445275, 0xC8DE047564D20A8B}, // 1e-57
{0xEED6E2F0F0D56712, 0xFB158592BE068D2E}, // 1e-56
{0x55464DD69685606B, 0x9CED737BB6C4183D}, // 1e-55
{0xAA97E14C3C26B886, 0xC428D05AA4751E4C}, // 1e-54
{0xD53DD99F4B3066A8, 0xF53304714D9265DF}, // 1e-53
{0xE546A8038EFE4029, 0x993FE2C6D07B7FAB}, // 1e-52
{0xDE98520472BDD033, 0xBF8FDB78849A5F96}, // 1e-51
{0x963E66858F6D4440, 0xEF73D256A5C0F77C}, // 1e-50
{0xDDE7001379A44AA8, 0x95A8637627989AAD}, // 1e-49
{0x5560C018580D5D52, 0xBB127C53B17EC159}, // 1e-48
{0xAAB8F01E6E10B4A6, 0xE9D71B689DDE71AF}, // 1e-47
{0xCAB3961304CA70E8, 0x9226712162AB070D}, // 1e-46
{0x3D607B97C5FD0D22, 0xB6B00D69BB55C8D1}, // 1e-45
{0x8CB89A7DB77C506A, 0xE45C10C42A2B3B05}, // 1e-44
{0x77F3608E92ADB242, 0x8EB98A7A9A5B04E3}, // 1e-43
{0x55F038B237591ED3, 0xB267ED1940F1C61C}, // 1e-42
{0x6B6C46DEC52F6688, 0xDF01E85F912E37A3}, // 1e-41
{0x2323AC4B3B3DA015, 0x8B61313BBABCE2C6}, // 1e-40
{0xABEC975E0A0D081A, 0xAE397D8AA96C1B77}, // 1e-39
{0x96E7BD358C904A21, 0xD9C7DCED53C72255}, // 1e-38
{0x7E50D64177DA2E54, 0x881CEA14545C7575}, // 1e-37
{0xDDE50BD1D5D0B9E9, 0xAA242499697392D2}, // 1e-36
{0x955E4EC64B44E864, 0xD4AD2DBFC3D07787}, // 1e-35
{0xBD5AF13BEF0B113E, 0x84EC3C97DA624AB4}, // 1e-34
{0xECB1AD8AEACDD58E, 0xA6274BBDD0FADD61}, // 1e-33
{0x67DE18EDA5814AF2, 0xCFB11EAD453994BA}, // 1e-32
{0x80EACF948770CED7, 0x81CEB32C4B43FCF4}, // 1e-31
{0xA1258379A94D028D, 0xA2425FF75E14FC31}, // 1e-30
{0x096EE45813A04330, 0xCAD2F7F5359A3B3E}, // 1e-29
{0x8BCA9D6E188853FC, 0xFD87B5F28300CA0D}, // 1e-28
{0x775EA264CF55347D, 0x9E74D1B791E07E48}, // 1e-27
{0x95364AFE032A819D, 0xC612062576589DDA}, // 1e-26
{0x3A83DDBD83F52204, 0xF79687AED3EEC551}, // 1e-25
{0xC4926A9672793542, 0x9ABE14CD44753B52}, // 1e-24
{0x75B7053C0F178293, 0xC16D9A0095928A27}, // 1e-23
{0x5324C68B12DD6338, 0xF1C90080BAF72CB1}, // 1e-22
{0xD3F6FC16EBCA5E03, 0x971DA05074DA7BEE}, // 1e-21
{0x88F4BB1CA6BCF584, 0xBCE5086492111AEA}, // 1e-20
{0x2B31E9E3D06C32E5, 0xEC1E4A7DB69561A5}, // 1e-19
{0x3AFF322E62439FCF, 0x9392EE8E921D5D07}, // 1e-18
{0x09BEFEB9FAD487C2, 0xB877AA3236A4B449}, // 1e-17
{0x4C2EBE687989A9B3, 0xE69594BEC44DE15B}, // 1e-16
{0x0F9D37014BF60A10, 0x901D7CF73AB0ACD9}, // 1e-15
{0x538484C19EF38C94, 0xB424DC35095CD80F}, // 1e-14
{0x2865A5F206B06FB9, 0xE12E13424BB40E13}, // 1e-13
{0xF93F87B7442E45D3, 0x8CBCCC096F5088CB}, // 1e-12
{0xF78F69A51539D748, 0xAFEBFF0BCB24AAFE}, // 1e-11
{0xB573440E5A884D1B, 0xDBE6FECEBDEDD5BE}, // 1e-10
{0x31680A88F8953030, 0x89705F4136B4A597}, // 1e-9
{0xFDC20D2B36BA7C3D, 0xABCC77118461CEFC}, // 1e-8
{0x3D32907604691B4C, 0xD6BF94D5E57A42BC}, // 1e-7
{0xA63F9A49C2C1B10F, 0x8637BD05AF6C69B5}, // 1e-6
{0x0FCF80DC33721D53, 0xA7C5AC471B478423}, // 1e-5
{0xD3C36113404EA4A8, 0xD1B71758E219652B}, // 1e-4
{0x645A1CAC083126E9, 0x83126E978D4FDF3B}, // 1e-3
{0x3D70A3D70A3D70A3, 0xA3D70A3D70A3D70A}, // 1e-2
{0xCCCCCCCCCCCCCCCC, 0xCCCCCCCCCCCCCCCC}, // 1e-1
{0x0000000000000000, 0x8000000000000000}, // 1e0
{0x0000000000000000, 0xA000000000000000}, // 1e1
{0x0000000000000000, 0xC800000000000000}, // 1e2
{0x0000000000000000, 0xFA00000000000000}, // 1e3
{0x0000000000000000, 0x9C40000000000000}, // 1e4
{0x0000000000000000, 0xC350000000000000}, // 1e5
{0x0000000000000000, 0xF424000000000000}, // 1e6
{0x0000000000000000, 0x9896800000000000}, // 1e7
{0x0000000000000000, 0xBEBC200000000000}, // 1e8
{0x0000000000000000, 0xEE6B280000000000}, // 1e9
{0x0000000000000000, 0x9502F90000000000}, // 1e10
{0x0000000000000000, 0xBA43B74000000000}, // 1e11
{0x0000000000000000, 0xE8D4A51000000000}, // 1e12
{0x0000000000000000, 0x9184E72A00000000}, // 1e13
{0x0000000000000000, 0xB5E620F480000000}, // 1e14
{0x0000000000000000, 0xE35FA931A0000000}, // 1e15
{0x0000000000000000, 0x8E1BC9BF04000000}, // 1e16
{0x0000000000000000, 0xB1A2BC2EC5000000}, // 1e17
{0x0000000000000000, 0xDE0B6B3A76400000}, // 1e18
{0x0000000000000000, 0x8AC7230489E80000}, // 1e19
{0x0000000000000000, 0xAD78EBC5AC620000}, // 1e20
{0x0000000000000000, 0xD8D726B7177A8000}, // 1e21
{0x0000000000000000, 0x878678326EAC9000}, // 1e22
{0x0000000000000000, 0xA968163F0A57B400}, // 1e23
{0x0000000000000000, 0xD3C21BCECCEDA100}, // 1e24
{0x0000000000000000, 0x84595161401484A0}, // 1e25
{0x0000000000000000, 0xA56FA5B99019A5C8}, // 1e26
{0x0000000000000000, 0xCECB8F27F4200F3A}, // 1e27
{0x4000000000000000, 0x813F3978F8940984}, // 1e28
{0x5000000000000000, 0xA18F07D736B90BE5}, // 1e29
{0xA400000000000000, 0xC9F2C9CD04674EDE}, // 1e30
{0x4D00000000000000, 0xFC6F7C4045812296}, // 1e31
{0xF020000000000000, 0x9DC5ADA82B70B59D}, // 1e32
{0x6C28000000000000, 0xC5371912364CE305}, // 1e33
{0xC732000000000000, 0xF684DF56C3E01BC6}, // 1e34
{0x3C7F400000000000, 0x9A130B963A6C115C}, // 1e35
{0x4B9F100000000000, 0xC097CE7BC90715B3}, // 1e36
{0x1E86D40000000000, 0xF0BDC21ABB48DB20}, // 1e37
{0x1314448000000000, 0x96769950B50D88F4}, // 1e38
{0x17D955A000000000, 0xBC143FA4E250EB31}, // 1e39
{0x5DCFAB0800000000, 0xEB194F8E1AE525FD}, // 1e40
{0x5AA1CAE500000000, 0x92EFD1B8D0CF37BE}, // 1e41
{0xF14A3D9E40000000, 0xB7ABC627050305AD}, // 1e42
{0x6D9CCD05D0000000, 0xE596B7B0C643C719}, // 1e43
{0xE4820023A2000000, 0x8F7E32CE7BEA5C6F}, // 1e44
{0xDDA2802C8A800000, 0xB35DBF821AE4F38B}, // 1e45
{0xD50B2037AD200000, 0xE0352F62A19E306E}, // 1e46
{0x4526F422CC340000, 0x8C213D9DA502DE45}, // 1e47
{0x9670B12B7F410000, 0xAF298D050E4395D6}, // 1e48
{0x3C0CDD765F114000, 0xDAF3F04651D47B4C}, // 1e49
{0xA5880A69FB6AC800, 0x88D8762BF324CD0F}, // 1e50
{0x8EEA0D047A457A00, 0xAB0E93B6EFEE0053}, // 1e51
{0x72A4904598D6D880, 0xD5D238A4ABE98068}, // 1e52
{0x47A6DA2B7F864750, 0x85A36366EB71F041}, // 1e53
{0x999090B65F67D924, 0xA70C3C40A64E6C51}, // 1e54
{0xFFF4B4E3F741CF6D, 0xD0CF4B50CFE20765}, // 1e55
{0xBFF8F10E7A8921A4, 0x82818F1281ED449F}, // 1e56
{0xAFF72D52192B6A0D, 0xA321F2D7226895C7}, // 1e57
{0x9BF4F8A69F764490, 0xCBEA6F8CEB02BB39}, // 1e58
{0x02F236D04753D5B4, 0xFEE50B7025C36A08}, // 1e59
{0x01D762422C946590, 0x9F4F2726179A2245}, // 1e60
{0x424D3AD2B7B97EF5, 0xC722F0EF9D80AAD6}, // 1e61
{0xD2E0898765A7DEB2, 0xF8EBAD2B84E0D58B}, // 1e62
{0x63CC55F49F88EB2F, 0x9B934C3B330C8577}, // 1e63
{0x3CBF6B71C76B25FB, 0xC2781F49FFCFA6D5}, // 1e64
{0x8BEF464E3945EF7A, 0xF316271C7FC3908A}, // 1e65
{0x97758BF0E3CBB5AC, 0x97EDD871CFDA3A56}, // 1e66
{0x3D52EEED1CBEA317, 0xBDE94E8E43D0C8EC}, // 1e67
{0x4CA7AAA863EE4BDD, 0xED63A231D4C4FB27}, // 1e68
{0x8FE8CAA93E74EF6A, 0x945E455F24FB1CF8}, // 1e69
{0xB3E2FD538E122B44, 0xB975D6B6EE39E436}, // 1e70
{0x60DBBCA87196B616, 0xE7D34C64A9C85D44}, // 1e71
{0xBC8955E946FE31CD, 0x90E40FBEEA1D3A4A}, // 1e72
{0x6BABAB6398BDBE41, 0xB51D13AEA4A488DD}, // 1e73
{0xC696963C7EED2DD1, 0xE264589A4DCDAB14}, // 1e74
{0xFC1E1DE5CF543CA2, 0x8D7EB76070A08AEC}, // 1e75
{0x3B25A55F43294BCB, 0xB0DE65388CC8ADA8}, // 1e76
{0x49EF0EB713F39EBE, 0xDD15FE86AFFAD912}, // 1e77
{0x6E3569326C784337, 0x8A2DBF142DFCC7AB}, // 1e78
{0x49C2C37F07965404, 0xACB92ED9397BF996}, // 1e79
{0xDC33745EC97BE906, 0xD7E77A8F87DAF7FB}, // 1e80
{0x69A028BB3DED71A3, 0x86F0AC99B4E8DAFD}, // 1e81
{0xC40832EA0D68CE0C, 0xA8ACD7C0222311BC}, // 1e82
{0xF50A3FA490C30190, 0xD2D80DB02AABD62B}, // 1e83
{0x792667C6DA79E0FA, 0x83C7088E1AAB65DB}, // 1e84
{0x577001B891185938, 0xA4B8CAB1A1563F52}, // 1e85
{0xED4C0226B55E6F86, 0xCDE6FD5E09ABCF26}, // 1e86
{0x544F8158315B05B4, 0x80B05E5AC60B6178}, // 1e87
{0x696361AE3DB1C721, 0xA0DC75F1778E39D6}, // 1e88
{0x03BC3A19CD1E38E9, 0xC913936DD571C84C}, // 1e89
{0x04AB48A04065C723, 0xFB5878494ACE3A5F}, // 1e90
{0x62EB0D64283F9C76, 0x9D174B2DCEC0E47B}, // 1e91
{0x3BA5D0BD324F8394, 0xC45D1DF942711D9A}, // 1e92
{0xCA8F44EC7EE36479, 0xF5746577930D6500}, // 1e93
{0x7E998B13CF4E1ECB, 0x9968BF6ABBE85F20}, // 1e94
{0x9E3FEDD8C321A67E, 0xBFC2EF456AE276E8}, // 1e95
{0xC5CFE94EF3EA101E, 0xEFB3AB16C59B14A2}, // 1e96
{0xBBA1F1D158724A12, 0x95D04AEE3B80ECE5}, // 1e97
{0x2A8A6E45AE8EDC97, 0xBB445DA9CA61281F}, // 1e98
{0xF52D09D71A3293BD, 0xEA1575143CF97226}, // 1e99
{0x593C2626705F9C56, 0x924D692CA61BE758}, // 1e100
{0x6F8B2FB00C77836C, 0xB6E0C377CFA2E12E}, // 1e101
{0x0B6DFB9C0F956447, 0xE498F455C38B997A}, // 1e102
{0x4724BD4189BD5EAC, 0x8EDF98B59A373FEC}, // 1e103
{0x58EDEC91EC2CB657, 0xB2977EE300C50FE7}, // 1e104
{0x2F2967B66737E3ED, 0xDF3D5E9BC0F653E1}, // 1e105
{0xBD79E0D20082EE74, 0x8B865B215899F46C}, // 1e106
{0xECD8590680A3AA11, 0xAE67F1E9AEC07187}, // 1e107
{0xE80E6F4820CC9495, 0xDA01EE641A708DE9}, // 1e108
{0x3109058D147FDCDD, 0x884134FE908658B2}, // 1e109
{0xBD4B46F0599FD415, 0xAA51823E34A7EEDE}, // 1e110
{0x6C9E18AC7007C91A, 0xD4E5E2CDC1D1EA96}, // 1e111
{0x03E2CF6BC604DDB0, 0x850FADC09923329E}, // 1e112
{0x84DB8346B786151C, 0xA6539930BF6BFF45}, // 1e113
{0xE612641865679A63, 0xCFE87F7CEF46FF16}, // 1e114
{0x4FCB7E8F3F60C07E, 0x81F14FAE158C5F6E}, // 1e115
{0xE3BE5E330F38F09D, 0xA26DA3999AEF7749}, // 1e116
{0x5CADF5BFD3072CC5, 0xCB090C8001AB551C}, // 1e117
{0x73D9732FC7C8F7F6, 0xFDCB4FA002162A63}, // 1e118
{0x2867E7FDDCDD9AFA, 0x9E9F11C4014DDA7E}, // 1e119
{0xB281E1FD541501B8, 0xC646D63501A1511D}, // 1e120
{0x1F225A7CA91A4226, 0xF7D88BC24209A565}, // 1e121
{0x3375788DE9B06958, 0x9AE757596946075F}, // 1e122
{0x0052D6B1641C83AE, 0xC1A12D2FC3978937}, // 1e123
{0xC0678C5DBD23A49A, 0xF209787BB47D6B84}, // 1e124
{0xF840B7BA963646E0, 0x9745EB4D50CE6332}, // 1e125
{0xB650E5A93BC3D898, 0xBD176620A501FBFF}, // 1e126
{0xA3E51F138AB4CEBE, 0xEC5D3FA8CE427AFF}, // 1e127
{0xC66F336C36B10137, 0x93BA47C980E98CDF}, // 1e128
{0xB80B0047445D4184, 0xB8A8D9BBE123F017}, // 1e129
{0xA60DC059157491E5, 0xE6D3102AD96CEC1D}, // 1e130
{0x87C89837AD68DB2F, 0x9043EA1AC7E41392}, // 1e131
{0x29BABE4598C311FB, 0xB454E4A179DD1877}, // 1e132
{0xF4296DD6FEF3D67A, 0xE16A1DC9D8545E94}, // 1e133
{0x1899E4A65F58660C, 0x8CE2529E2734BB1D}, // 1e134
{0x5EC05DCFF72E7F8F, 0xB01AE745B101E9E4}, // 1e135
{0x76707543F4FA1F73, 0xDC21A1171D42645D}, // 1e136
{0x6A06494A791C53A8, 0x899504AE72497EBA}, // 1e137
{0x0487DB9D17636892, 0xABFA45DA0EDBDE69}, // 1e138
{0x45A9D2845D3C42B6, 0xD6F8D7509292D603}, // 1e139
{0x0B8A2392BA45A9B2, 0x865B86925B9BC5C2}, // 1e140
{0x8E6CAC7768D7141E, 0xA7F26836F282B732}, // 1e141
{0x3207D795430CD926, 0xD1EF0244AF2364FF}, // 1e142
{0x7F44E6BD49E807B8, 0x8335616AED761F1F}, // 1e143
{0x5F16206C9C6209A6, 0xA402B9C5A8D3A6E7}, // 1e144
{0x36DBA887C37A8C0F, 0xCD036837130890A1}, // 1e145
{0xC2494954DA2C9789, 0x802221226BE55A64}, // 1e146
{0xF2DB9BAA10B7BD6C, 0xA02AA96B06DEB0FD}, // 1e147
{0x6F92829494E5ACC7, 0xC83553C5C8965D3D}, // 1e148
{0xCB772339BA1F17F9, 0xFA42A8B73ABBF48C}, // 1e149
{0xFF2A760414536EFB, 0x9C69A97284B578D7}, // 1e150
{0xFEF5138519684ABA, 0xC38413CF25E2D70D}, // 1e151
{0x7EB258665FC25D69, 0xF46518C2EF5B8CD1}, // 1e152
{0xEF2F773FFBD97A61, 0x98BF2F79D5993802}, // 1e153
{0xAAFB550FFACFD8FA, 0xBEEEFB584AFF8603}, // 1e154
{0x95BA2A53F983CF38, 0xEEAABA2E5DBF6784}, // 1e155
{0xDD945A747BF26183, 0x952AB45CFA97A0B2}, // 1e156
{0x94F971119AEEF9E4, 0xBA756174393D88DF}, // 1e157
{0x7A37CD5601AAB85D, 0xE912B9D1478CEB17}, // 1e158
{0xAC62E055C10AB33A, 0x91ABB422CCB812EE}, // 1e159
{0x577B986B314D6009, 0xB616A12B7FE617AA}, // 1e160
{0xED5A7E85FDA0B80B, 0xE39C49765FDF9D94}, // 1e161
{0x14588F13BE847307, 0x8E41ADE9FBEBC27D}, // 1e162
{0x596EB2D8AE258FC8, 0xB1D219647AE6B31C}, // 1e163
{0x6FCA5F8ED9AEF3BB, 0xDE469FBD99A05FE3}, // 1e164
{0x25DE7BB9480D5854, 0x8AEC23D680043BEE}, // 1e165
{0xAF561AA79A10AE6A, 0xADA72CCC20054AE9}, // 1e166
{0x1B2BA1518094DA04, 0xD910F7FF28069DA4}, // 1e167
{0x90FB44D2F05D0842, 0x87AA9AFF79042286}, // 1e168
{0x353A1607AC744A53, 0xA99541BF57452B28}, // 1e169
{0x42889B8997915CE8, 0xD3FA922F2D1675F2}, // 1e170
{0x69956135FEBADA11, 0x847C9B5D7C2E09B7}, // 1e171
{0x43FAB9837E699095, 0xA59BC234DB398C25}, // 1e172
{0x94F967E45E03F4BB, 0xCF02B2C21207EF2E}, // 1e173
{0x1D1BE0EEBAC278F5, 0x8161AFB94B44F57D}, // 1e174
{0x6462D92A69731732, 0xA1BA1BA79E1632DC}, // 1e175
{0x7D7B8F7503CFDCFE, 0xCA28A291859BBF93}, // 1e176
{0x5CDA735244C3D43E, 0xFCB2CB35E702AF78}, // 1e177
{0x3A0888136AFA64A7, 0x9DEFBF01B061ADAB}, // 1e178
{0x088AAA1845B8FDD0, 0xC56BAEC21C7A1916}, // 1e179
{0x8AAD549E57273D45, 0xF6C69A72A3989F5B}, // 1e180
{0x36AC54E2F678864B, 0x9A3C2087A63F6399}, // 1e181
{0x84576A1BB416A7DD, 0xC0CB28A98FCF3C7F}, // 1e182
{0x656D44A2A11C51D5, 0xF0FDF2D3F3C30B9F}, // 1e183
{0x9F644AE5A4B1B325, 0x969EB7C47859E743}, // 1e184
{0x873D5D9F0DDE1FEE, 0xBC4665B596706114}, // 1e185
{0xA90CB506D155A7EA, 0xEB57FF22FC0C7959}, // 1e186
{0x09A7F12442D588F2, 0x9316FF75DD87CBD8}, // 1e187
{0x0C11ED6D538AEB2F, 0xB7DCBF5354E9BECE}, // 1e188
{0x8F1668C8A86DA5FA, 0xE5D3EF282A242E81}, // 1e189
{0xF96E017D694487BC, 0x8FA475791A569D10}, // 1e190
{0x37C981DCC395A9AC, 0xB38D92D760EC4455}, // 1e191
{0x85BBE253F47B1417, 0xE070F78D3927556A}, // 1e192
{0x93956D7478CCEC8E, 0x8C469AB843B89562}, // 1e193
{0x387AC8D1970027B2, 0xAF58416654A6BABB}, // 1e194
{0x06997B05FCC0319E, 0xDB2E51BFE9D0696A}, // 1e195
{0x441FECE3BDF81F03, 0x88FCF317F22241E2}, // 1e196
{0xD527E81CAD7626C3, 0xAB3C2FDDEEAAD25A}, // 1e197
{0x8A71E223D8D3B074, 0xD60B3BD56A5586F1}, // 1e198
{0xF6872D5667844E49, 0x85C7056562757456}, // 1e199
{0xB428F8AC016561DB, 0xA738C6BEBB12D16C}, // 1e200
{0xE13336D701BEBA52, 0xD106F86E69D785C7}, // 1e201
{0xECC0024661173473, 0x82A45B450226B39C}, // 1e202
{0x27F002D7F95D0190, 0xA34D721642B06084}, // 1e203
{0x31EC038DF7B441F4, 0xCC20CE9BD35C78A5}, // 1e204
{0x7E67047175A15271, 0xFF290242C83396CE}, // 1e205
{0x0F0062C6E984D386, 0x9F79A169BD203E41}, // 1e206
{0x52C07B78A3E60868, 0xC75809C42C684DD1}, // 1e207
{0xA7709A56CCDF8A82, 0xF92E0C3537826145}, // 1e208
{0x88A66076400BB691, 0x9BBCC7A142B17CCB}, // 1e209
{0x6ACFF893D00EA435, 0xC2ABF989935DDBFE}, // 1e210
{0x0583F6B8C4124D43, 0xF356F7EBF83552FE}, // 1e211
{0xC3727A337A8B704A, 0x98165AF37B2153DE}, // 1e212
{0x744F18C0592E4C5C, 0xBE1BF1B059E9A8D6}, // 1e213
{0x1162DEF06F79DF73, 0xEDA2EE1C7064130C}, // 1e214
{0x8ADDCB5645AC2BA8, 0x9485D4D1C63E8BE7}, // 1e215
{0x6D953E2BD7173692, 0xB9A74A0637CE2EE1}, // 1e216
{0xC8FA8DB6CCDD0437, 0xE8111C87C5C1BA99}, // 1e217
{0x1D9C9892400A22A2, 0x910AB1D4DB9914A0}, // 1e218
{0x2503BEB6D00CAB4B, 0xB54D5E4A127F59C8}, // 1e219
{0x2E44AE64840FD61D, 0xE2A0B5DC971F303A}, // 1e220
{0x5CEAECFED289E5D2, 0x8DA471A9DE737E24}, // 1e221
{0x7425A83E872C5F47, 0xB10D8E1456105DAD}, // 1e222
{0xD12F124E28F77719, 0xDD50F1996B947518}, // 1e223
{0x82BD6B70D99AAA6F, 0x8A5296FFE33CC92F}, // 1e224
{0x636CC64D1001550B, 0xACE73CBFDC0BFB7B}, // 1e225
{0x3C47F7E05401AA4E, 0xD8210BEFD30EFA5A}, // 1e226
{0x65ACFAEC34810A71, 0x8714A775E3E95C78}, // 1e227
{0x7F1839A741A14D0D, 0xA8D9D1535CE3B396}, // 1e228
{0x1EDE48111209A050, 0xD31045A8341CA07C}, // 1e229
{0x934AED0AAB460432, 0x83EA2B892091E44D}, // 1e230
{0xF81DA84D5617853F, 0xA4E4B66B68B65D60}, // 1e231
{0x36251260AB9D668E, 0xCE1DE40642E3F4B9}, // 1e232
{0xC1D72B7C6B426019, 0x80D2AE83E9CE78F3}, // 1e233
{0xB24CF65B8612F81F, 0xA1075A24E4421730}, // 1e234
{0xDEE033F26797B627, 0xC94930AE1D529CFC}, // 1e235
{0x169840EF017DA3B1, 0xFB9B7CD9A4A7443C}, // 1e236
{0x8E1F289560EE864E, 0x9D412E0806E88AA5}, // 1e237
{0xF1A6F2BAB92A27E2, 0xC491798A08A2AD4E}, // 1e238
{0xAE10AF696774B1DB, 0xF5B5D7EC8ACB58A2}, // 1e239
{0xACCA6DA1E0A8EF29, 0x9991A6F3D6BF1765}, // 1e240
{0x17FD090A58D32AF3, 0xBFF610B0CC6EDD3F}, // 1e241
{0xDDFC4B4CEF07F5B0, 0xEFF394DCFF8A948E}, // 1e242
{0x4ABDAF101564F98E, 0x95F83D0A1FB69CD9}, // 1e243
{0x9D6D1AD41ABE37F1, 0xBB764C4CA7A4440F}, // 1e244
{0x84C86189216DC5ED, 0xEA53DF5FD18D5513}, // 1e245
{0x32FD3CF5B4E49BB4, 0x92746B9BE2F8552C}, // 1e246
{0x3FBC8C33221DC2A1, 0xB7118682DBB66A77}, // 1e247
{0x0FABAF3FEAA5334A, 0xE4D5E82392A40515}, // 1e248
{0x29CB4D87F2A7400E, 0x8F05B1163BA6832D}, // 1e249
{0x743E20E9EF511012, 0xB2C71D5BCA9023F8}, // 1e250
{0x914DA9246B255416, 0xDF78E4B2BD342CF6}, // 1e251
{0x1AD089B6C2F7548E, 0x8BAB8EEFB6409C1A}, // 1e252
{0xA184AC2473B529B1, 0xAE9672ABA3D0C320}, // 1e253
{0xC9E5D72D90A2741E, 0xDA3C0F568CC4F3E8}, // 1e254
{0x7E2FA67C7A658892, 0x8865899617FB1871}, // 1e255
{0xDDBB901B98FEEAB7, 0xAA7EEBFB9DF9DE8D}, // 1e256
{0x552A74227F3EA565, 0xD51EA6FA85785631}, // 1e257
{0xD53A88958F87275F, 0x8533285C936B35DE}, // 1e258
{0x8A892ABAF368F137, 0xA67FF273B8460356}, // 1e259
{0x2D2B7569B0432D85, 0xD01FEF10A657842C}, // 1e260
{0x9C3B29620E29FC73, 0x8213F56A67F6B29B}, // 1e261
{0x8349F3BA91B47B8F, 0xA298F2C501F45F42}, // 1e262
{0x241C70A936219A73, 0xCB3F2F7642717713}, // 1e263
{0xED238CD383AA0110, 0xFE0EFB53D30DD4D7}, // 1e264
{0xF4363804324A40AA, 0x9EC95D1463E8A506}, // 1e265
{0xB143C6053EDCD0D5, 0xC67BB4597CE2CE48}, // 1e266
{0xDD94B7868E94050A, 0xF81AA16FDC1B81DA}, // 1e267
{0xCA7CF2B4191C8326, 0x9B10A4E5E9913128}, // 1e268
{0xFD1C2F611F63A3F0, 0xC1D4CE1F63F57D72}, // 1e269
{0xBC633B39673C8CEC, 0xF24A01A73CF2DCCF}, // 1e270
{0xD5BE0503E085D813, 0x976E41088617CA01}, // 1e271
{0x4B2D8644D8A74E18, 0xBD49D14AA79DBC82}, // 1e272
{0xDDF8E7D60ED1219E, 0xEC9C459D51852BA2}, // 1e273
{0xCABB90E5C942B503, 0x93E1AB8252F33B45}, // 1e274
{0x3D6A751F3B936243, 0xB8DA1662E7B00A17}, // 1e275
{0x0CC512670A783AD4, 0xE7109BFBA19C0C9D}, // 1e276
{0x27FB2B80668B24C5, 0x906A617D450187E2}, // 1e277
{0xB1F9F660802DEDF6, 0xB484F9DC9641E9DA}, // 1e278
{0x5E7873F8A0396973, 0xE1A63853BBD26451}, // 1e279
{0xDB0B487B6423E1E8, 0x8D07E33455637EB2}, // 1e280
{0x91CE1A9A3D2CDA62, 0xB049DC016ABC5E5F}, // 1e281
{0x7641A140CC7810FB, 0xDC5C5301C56B75F7}, // 1e282
{0xA9E904C87FCB0A9D, 0x89B9B3E11B6329BA}, // 1e283
{0x546345FA9FBDCD44, 0xAC2820D9623BF429}, // 1e284
{0xA97C177947AD4095, 0xD732290FBACAF133}, // 1e285
{0x49ED8EABCCCC485D, 0x867F59A9D4BED6C0}, // 1e286
{0x5C68F256BFFF5A74, 0xA81F301449EE8C70}, // 1e287
{0x73832EEC6FFF3111, 0xD226FC195C6A2F8C}, // 1e288
{0xC831FD53C5FF7EAB, 0x83585D8FD9C25DB7}, // 1e289
{0xBA3E7CA8B77F5E55, 0xA42E74F3D032F525}, // 1e290
{0x28CE1BD2E55F35EB, 0xCD3A1230C43FB26F}, // 1e291
{0x7980D163CF5B81B3, 0x80444B5E7AA7CF85}, // 1e292
{0xD7E105BCC332621F, 0xA0555E361951C366}, // 1e293
{0x8DD9472BF3FEFAA7, 0xC86AB5C39FA63440}, // 1e294
{0xB14F98F6F0FEB951, 0xFA856334878FC150}, // 1e295
{0x6ED1BF9A569F33D3, 0x9C935E00D4B9D8D2}, // 1e296
{0x0A862F80EC4700C8, 0xC3B8358109E84F07}, // 1e297
{0xCD27BB612758C0FA, 0xF4A642E14C6262C8}, // 1e298
{0x8038D51CB897789C, 0x98E7E9CCCFBD7DBD}, // 1e299
{0xE0470A63E6BD56C3, 0xBF21E44003ACDD2C}, // 1e300
{0x1858CCFCE06CAC74, 0xEEEA5D5004981478}, // 1e301
{0x0F37801E0C43EBC8, 0x95527A5202DF0CCB}, // 1e302
{0xD30560258F54E6BA, 0xBAA718E68396CFFD}, // 1e303
{0x47C6B82EF32A2069, 0xE950DF20247C83FD}, // 1e304
{0x4CDC331D57FA5441, 0x91D28B7416CDD27E}, // 1e305
{0xE0133FE4ADF8E952, 0xB6472E511C81471D}, // 1e306
{0x58180FDDD97723A6, 0xE3D8F9E563A198E5}, // 1e307
{0x570F09EAA7EA7648, 0x8E679C2F5E44FF8F}, // 1e308
{0x2CD2CC6551E513DA, 0xB201833B35D63F73}, // 1e309
{0xF8077F7EA65E58D1, 0xDE81E40A034BCF4F}, // 1e310
{0xFB04AFAF27FAF782, 0x8B112E86420F6191}, // 1e311
{0x79C5DB9AF1F9B563, 0xADD57A27D29339F6}, // 1e312
{0x18375281AE7822BC, 0xD94AD8B1C7380874}, // 1e313
{0x8F2293910D0B15B5, 0x87CEC76F1C830548}, // 1e314
{0xB2EB3875504DDB22, 0xA9C2794AE3A3C69A}, // 1e315
{0x5FA60692A46151EB, 0xD433179D9C8CB841}, // 1e316
{0xDBC7C41BA6BCD333, 0x849FEEC281D7F328}, // 1e317
{0x12B9B522906C0800, 0xA5C7EA73224DEFF3}, // 1e318
{0xD768226B34870A00, 0xCF39E50FEAE16BEF}, // 1e319
{0xE6A1158300D46640, 0x81842F29F2CCE375}, // 1e320
{0x60495AE3C1097FD0, 0xA1E53AF46F801C53}, // 1e321
{0x385BB19CB14BDFC4, 0xCA5E89B18B602368}, // 1e322
{0x46729E03DD9ED7B5, 0xFCF62C1DEE382C42}, // 1e323
{0x6C07A2C26A8346D1, 0x9E19DB92B4E31BA9}, // 1e324
{0xC7098B7305241885, 0xC5A05277621BE293}, // 1e325
{0xB8CBEE4FC66D1EA7, 0xF70867153AA2DB38}, // 1e326
{0x737F74F1DC043328, 0x9A65406D44A5C903}, // 1e327
{0x505F522E53053FF2, 0xC0FE908895CF3B44}, // 1e328
{0x647726B9E7C68FEF, 0xF13E34AABB430A15}, // 1e329
{0x5ECA783430DC19F5, 0x96C6E0EAB509E64D}, // 1e330
{0xB67D16413D132072, 0xBC789925624C5FE0}, // 1e331
{0xE41C5BD18C57E88F, 0xEB96BF6EBADF77D8}, // 1e332
{0x8E91B962F7B6F159, 0x933E37A534CBAAE7}, // 1e333
{0x723627BBB5A4ADB0, 0xB80DC58E81FE95A1}, // 1e334
{0xCEC3B1AAA30DD91C, 0xE61136F2227E3B09}, // 1e335
{0x213A4F0AA5E8A7B1, 0x8FCAC257558EE4E6}, // 1e336
{0xA988E2CD4F62D19D, 0xB3BD72ED2AF29E1F}, // 1e337
{0x93EB1B80A33B8605, 0xE0ACCFA875AF45A7}, // 1e338
{0xBC72F130660533C3, 0x8C6C01C9498D8B88}, // 1e339
{0xEB8FAD7C7F8680B4, 0xAF87023B9BF0EE6A}, // 1e340
{0xA67398DB9F6820E1, 0xDB68C2CA82ED2A05}, // 1e341
{0x88083F8943A1148C, 0x892179BE91D43A43}, // 1e342
{0x6A0A4F6B948959B0, 0xAB69D82E364948D4}, // 1e343
{0x848CE34679ABB01C, 0xD6444E39C3DB9B09}, // 1e344
{0xF2D80E0C0C0B4E11, 0x85EAB0E41A6940E5}, // 1e345
{0x6F8E118F0F0E2195, 0xA7655D1D2103911F}, // 1e346
{0x4B7195F2D2D1A9FB, 0xD13EB46469447567}, // 1e347
};

499
native/atof_native.c Normal file
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@ -0,0 +1,499 @@
/*
* Copyright 2021 ByteDance Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include "native.h"
#define DECIMAL_MAX_DNUM 800
/* decimical shift witout overflow, e.g. 9 << 61 overflow */
#define MAX_SHIFT 60
/* Decimal represent the integer or float
* example 1: 1.1 {"11", 2, 1, 0}
* example 2: -0.1 {"1", 1, 0, 1}
* example 3: 999 {"999", 3, 3, 0}
*/
typedef struct Decimal {
char d[DECIMAL_MAX_DNUM];
int nd;
int dp;
int neg;
} Decimal;
/* decimal power of ten to binary power of two.
* For example: POW_TAB[1]: 10 ** 1 ~ 2 ** 3
*/
static const int POW_TAB[9] = {1, 3, 6, 9, 13, 16, 19, 23, 26};
/* Left shift information for decimal.
* For example, {2, "625"}. That means that it will add 2 digits to the new decimal
* when the prefix of decimal is from "625" to "999", and 1 digit from "0" to "624".
*/
typedef struct lshift_cheat {
int delta; // number of added digits when left shift
const char cutoff[DECIMAL_MAX_DNUM]; // minus one digit if under the half(cutoff).
} lshift_cheat;
/* Look up for the decimal shift information by binary shift bits.
* idx is shift bits for binary.
* value is the shift information for decimal.
* For example, idx is 4, the value is {2, "625"}.
* That means the binary shift 4 bits left, will cause add 2 digits to the decimal
* if the prefix of decimal is under "625".
*/
const static lshift_cheat LSHIFT_TAB[61];
static inline void decimal_init(Decimal *d) {
for (int i = 0; i < DECIMAL_MAX_DNUM; ++i) {
d->d[i] = 0;
}
d->dp = 0;
d->nd = 0;
d->neg = 0;
}
static inline void decimal_set(Decimal *d, const char *s, int len) {
int i = 0;
decimal_init(d);
if (s[i] == '+') {
i++;
}
else if (s[i] == '-') {
i++;
d->neg = 1;
}
int saw_dot = 0;
for (; i < len; i++) {
if ('0' <= s[i] && s[i] <= '9') {
if (s[i] == '0' && d->nd == 0) { // ignore leading zeros
d->dp--;
continue;
}
if (d->nd < DECIMAL_MAX_DNUM) {
d->d[d->nd] = s[i];
d->nd++;
} else if (s[i] != '0') {
/* truncat the remaining digits */
}
} else if (s[i] == '.') {
saw_dot = 1;
d->dp = d->nd;
} else {
break;
}
}
/* integer */
if (saw_dot == 0) {
d->dp = d->nd;
}
/* exponent */
if (i < len && (s[i] == 'e' || s[i] == 'E')) {
int exp = 0;
int esgn = 1;
i++;
if (s[i] == '+') {
i++;
} else if (s[i] == '-') {
i++;
esgn = -1;
}
for (; i < len && ('0' <= s[i] && s[i] <= '9'); i++) {
exp = exp * 10 + (s[i] - '0');
}
d->dp += exp * esgn;
}
return;
}
/* trim trailing zeros from number */
static inline void trim(Decimal *d) {
while (d->nd > 0 && d->d[d->nd - 1] == '0') {
d->nd--;
}
if (d->nd == 0) {
d->dp = 0;
}
}
/* Binary shift right (/ 2) by k bits. k <= maxShift to avoid overflow */
static inline void right_shift(Decimal *d, uint32_t k) {
int r = 0; // read pointer
int w = 0; // write pointer
uint64_t n = 0;
/* Pick up enough leading digits to cover first shift */
for (; n>>k == 0; r++) {
if (r >= d->nd) {
if (n == 0) {
d->nd = 0; // no digits for this num
return;
}
/* until n has enough bits for right shift */
while (n>>k == 0) {
n *= 10;
r++;
}
break;
}
n = n * 10 + d->d[r] - '0'; // read the value from d.d
}
d->dp -= r - 1; // point shift left
uint64_t mask = (((uint64_t)1) << k) - 1;
uint64_t dig = 0;
/* Pick up a digit, put down a digit */
for (; r < d->nd; r++) {
dig = n >> k;
n &= mask;
d->d[w++] = (char)(dig + '0');
n = n * 10 + d->d[r] - '0';
}
/* Put down extra digits */
while (n > 0) {
dig = n >> k;
n &= mask;
if (w < DECIMAL_MAX_DNUM) {
d->d[w] = (char)(dig + '0');
w++;
} else if (dig > 0) {
/* truncated */
}
n *= 10;
}
d->nd = w;
trim(d);
}
/* Compare the leading prefix, if b is lexicographically less, return 0 */
static inline int prefix_cmp(const char *b, const char *s, uint64_t len) {
int i = 0;
for (; i < len; i++) {
if (b[i] != s[i]) {
return b[i] > s[i];
}
}
/* when b is substr of s */
if (i < DECIMAL_MAX_DNUM && s[i] >= '0' && s[i] <= '9') {
return 0;
}
return 1;
}
/* Binary shift left (* 2) by k bits. k <= maxShift to avoid overflow */
static inline void left_shift(Decimal *d, uint32_t k) {
int delta = LSHIFT_TAB[k].delta;
if (prefix_cmp(d->d, LSHIFT_TAB[k].cutoff, d->nd) == 0){
delta--;
}
int r = d->nd - 1; // read index
int w = d->nd + delta - 1; // write index
uint64_t n = 0;
uint64_t quo = 0;
uint64_t rem = 0;
/* Pick up a digit, put down a digit */
for (; r >= 0; r--) {
n += (uint64_t)(d->d[r] - '0') << k;
quo = n / 10;
rem = n - 10 * quo;
if (w < DECIMAL_MAX_DNUM) {
d->d[w] = (char)(rem + '0');
w--;
} else if (rem != 0) {
/* truncated */
}
n = quo;
}
/* Put down extra digits */
while (n > 0) {
quo = n / 10;
rem = n - 10 * quo;
if (w < DECIMAL_MAX_DNUM) {
d->d[w] = (char)(rem + '0');
w--;
} else if (rem != 0) {
/* truncated */
}
n = quo;
}
d->nd += delta;
if (d->nd >= DECIMAL_MAX_DNUM) {
d->nd = DECIMAL_MAX_DNUM;
}
d->dp += delta;
trim(d);
}
static inline void decimal_shift(Decimal *d, int k) {
if (d->nd == 0 || k == 0) {
return;
}
if (k > 0) {
while (k > MAX_SHIFT) {
left_shift(d, MAX_SHIFT);
k -= MAX_SHIFT;
}
if (k) {
left_shift(d, k);
}
}
if (k < 0) {
while (k < -MAX_SHIFT) {
right_shift(d, MAX_SHIFT);
k += MAX_SHIFT;
}
if (k) {
right_shift(d, -k);
}
}
}
static inline int should_roundup(Decimal *d, int nd) {
if (nd < 0 || nd >= d->nd) {
return 0;
}
/* Exactly halfway - round to even */
if (d->d[nd] == '5' && nd+1 == d->nd) {
return nd > 0 && (d->d[nd-1]-'0')%2 != 0;
}
/* not halfway - round to the nearest */
return d->d[nd] >= '5';
}
/* Extract integer part, rounded appropriately */
static inline uint64_t rounded_integer(Decimal *d) {
if (d->dp > 20) { // overflow
return 0xFFFFFFFFFFFFFFFF; //64 bits
}
int i = 0;
uint64_t n = 0;
for (i = 0; i < d->dp && i < d->nd; i++) {
n = n * 10 + (d->d[i] - '0');
}
for (; i < d->dp; i++) {
n *= 10;
}
if (should_roundup(d, d->dp)) {
n++;
}
return n;
}
int decimal_to_f64(Decimal *d, double *val) {
int exp2 = 0;
uint64_t mant = 0;
uint64_t bits = 0;
/* d is zero */
if (d->nd == 0) {
mant = 0;
exp2 = -1023;
goto out;
}
/* Overflow, return inf/INF */
if (d->dp > 310) {
goto overflow;
}
/* Underflow, return zero */
if (d->dp < -330) {
mant = 0;
exp2 = -1023;
goto out;
}
/* Scale by powers of two until in range [0.5, 1.0) */
int n = 0;
while (d->dp > 0) { // d >= 1
if (d->dp >= 9) {
n = 27;
} else {
n = POW_TAB[d->dp];
}
decimal_shift(d, -n); // shift right
exp2 += n;
}
while ((d->dp < 0) || (d->dp == 0) && (d->d[0] < '5')) { // d < 0.5
if (-d->dp >= 9) {
n = 27;
} else {
n = POW_TAB[-d->dp];
}
decimal_shift(d, n); // shift left
exp2 -= n;
}
/* Our range is [0.5,1) but floating point range is [1,2) */
exp2 --;
/* Minimum exp2 for doulbe is -1022.
* If the exponent is smaller, move it up and
* adjust d accordingly.
*/
if (exp2 < -1022) {
n = -1022 - exp2;
decimal_shift(d, -n); // shift right
exp2 += n;
}
/* Exp2 too large */
if ((exp2 + 1023) >= 0x7FF) {
goto overflow;
}
/* Extract 53 bits. */
decimal_shift(d, 53); // shift left
mant = rounded_integer(d);
/* Rounding might have added a bit; shift down. */
if (mant == (((uint64_t)2) << 52)) { // mant has 54 bits
mant >>= 1;
exp2 ++;
if ((exp2 + 1023) >= 0x7FF) {
goto overflow;
}
}
/* Denormalized? */
if ((mant & (((uint64_t)1) << 52)) == 0) {
exp2 = -1023;
}
goto out;
overflow:
/* ±INF/inf */
mant = 0;
exp2 = 0x7FF - 1023;
out:
/* Assemble bits. */
bits = mant & 0x000FFFFFFFFFFFFF;
bits |= (uint64_t)((exp2 + 1023) & 0x7FF) << 52;
if (d->neg) {
bits |= ((uint64_t)1) << 63;
}
*(uint64_t*)val = bits;
return 0;
}
double atof_native_decimal(const char *buf, int len) {
Decimal d;
double val = 0;
decimal_set(&d, buf, len);
decimal_to_f64(&d, &val);
return val;
}
#undef DECIMAL_MAX_DNUM
#undef MAX_SHIFT
const static lshift_cheat LSHIFT_TAB[61] = {
// Leading digits of 1/2^i = 5^i.
// 5^23 is not an exact 64-bit floating point number,
// so have to use bc for the math.
// Go up to 60 to be large enough for 32bit and 64bit platforms.
/*
seq 60 | sed 's/^/5^/' | bc |
awk 'BEGIN{ print "\t{ 0, \"\" }," }
{
log2 = log(2)/log(10)
printf("\t{ %d, \"%s\" },\t// * %d\n",
int(log2*NR+1), $0, 2**NR)
}'
*/
{0, ""},
{1, "5"}, // * 2
{1, "25"}, // * 4
{1, "125"}, // * 8
{2, "625"}, // * 16
{2, "3125"}, // * 32
{2, "15625"}, // * 64
{3, "78125"}, // * 128
{3, "390625"}, // * 256
{3, "1953125"}, // * 512
{4, "9765625"}, // * 1024
{4, "48828125"}, // * 2048
{4, "244140625"}, // * 4096
{4, "1220703125"}, // * 8192
{5, "6103515625"}, // * 16384
{5, "30517578125"}, // * 32768
{5, "152587890625"}, // * 65536
{6, "762939453125"}, // * 131072
{6, "3814697265625"}, // * 262144
{6, "19073486328125"}, // * 524288
{7, "95367431640625"}, // * 1048576
{7, "476837158203125"}, // * 2097152
{7, "2384185791015625"}, // * 4194304
{7, "11920928955078125"}, // * 8388608
{8, "59604644775390625"}, // * 16777216
{8, "298023223876953125"}, // * 33554432
{8, "1490116119384765625"}, // * 67108864
{9, "7450580596923828125"}, // * 134217728
{9, "37252902984619140625"}, // * 268435456
{9, "186264514923095703125"}, // * 536870912
{10, "931322574615478515625"}, // * 1073741824
{10, "4656612873077392578125"}, // * 2147483648
{10, "23283064365386962890625"}, // * 4294967296
{10, "116415321826934814453125"}, // * 8589934592
{11, "582076609134674072265625"}, // * 17179869184
{11, "2910383045673370361328125"}, // * 34359738368
{11, "14551915228366851806640625"}, // * 68719476736
{12, "72759576141834259033203125"}, // * 137438953472
{12, "363797880709171295166015625"}, // * 274877906944
{12, "1818989403545856475830078125"}, // * 549755813888
{13, "9094947017729282379150390625"}, // * 1099511627776
{13, "45474735088646411895751953125"}, // * 2199023255552
{13, "227373675443232059478759765625"}, // * 4398046511104
{13, "1136868377216160297393798828125"}, // * 8796093022208
{14, "5684341886080801486968994140625"}, // * 17592186044416
{14, "28421709430404007434844970703125"}, // * 35184372088832
{14, "142108547152020037174224853515625"}, // * 70368744177664
{15, "710542735760100185871124267578125"}, // * 140737488355328
{15, "3552713678800500929355621337890625"}, // * 281474976710656
{15, "17763568394002504646778106689453125"}, // * 562949953421312
{16, "88817841970012523233890533447265625"}, // * 1125899906842624
{16, "444089209850062616169452667236328125"}, // * 2251799813685248
{16, "2220446049250313080847263336181640625"}, // * 4503599627370496
{16, "11102230246251565404236316680908203125"}, // * 9007199254740992
{17, "55511151231257827021181583404541015625"}, // * 18014398509481984
{17, "277555756156289135105907917022705078125"}, // * 36028797018963968
{17, "1387778780781445675529539585113525390625"}, // * 72057594037927936
{18, "6938893903907228377647697925567626953125"}, // * 144115188075855872
{18, "34694469519536141888238489627838134765625"}, // * 288230376151711744
{18, "173472347597680709441192448139190673828125"}, // * 576460752303423488
{19, "867361737988403547205962240695953369140625"}, // * 1152921504606846976
};

2
native/native.c
View file

@ -19,4 +19,6 @@
#include "fastfloat.c"
#include "fastint.c"
#include "parsing.c"
#include "atof_eisel_lemire.c"
#include "atof_native.c"
#include "scanning.c"

3
native/native.h
View file

@ -113,4 +113,7 @@ long skip_string(const GoString *src, long *p);
long skip_negative(const GoString *src, long *p);
long skip_positive(const GoString *src, long *p);
int atof_eisel_lemire64(uint64_t mant, int exp10, int sgn, double *val);
double atof_native_decimal(const char *buf, int len);
#endif

251
native/scanning.c
View file

@ -22,83 +22,13 @@ static const char *CS_OBJECT = "[]{},:\"[]{}:,\"[]";
static const uint64_t ODD_MASK = 0xaaaaaaaaaaaaaaaa;
static const uint64_t EVEN_MASK = 0x5555555555555555;
static const double P10_TAB[632] = {
/* <================= -Inf ================= */ 1e-323, 1e-322, 1e-321, 1e-320,
1e-319, 1e-318, 1e-317, 1e-316, 1e-315, 1e-314, 1e-313, 1e-312, 1e-311, 1e-310,
1e-309, 1e-308, 1e-307, 1e-306, 1e-305, 1e-304, 1e-303, 1e-302, 1e-301, 1e-300,
1e-299, 1e-298, 1e-297, 1e-296, 1e-295, 1e-294, 1e-293, 1e-292, 1e-291, 1e-290,
1e-289, 1e-288, 1e-287, 1e-286, 1e-285, 1e-284, 1e-283, 1e-282, 1e-281, 1e-280,
1e-279, 1e-278, 1e-277, 1e-276, 1e-275, 1e-274, 1e-273, 1e-272, 1e-271, 1e-270,
1e-269, 1e-268, 1e-267, 1e-266, 1e-265, 1e-264, 1e-263, 1e-262, 1e-261, 1e-260,
1e-259, 1e-258, 1e-257, 1e-256, 1e-255, 1e-254, 1e-253, 1e-252, 1e-251, 1e-250,
1e-249, 1e-248, 1e-247, 1e-246, 1e-245, 1e-244, 1e-243, 1e-242, 1e-241, 1e-240,
1e-239, 1e-238, 1e-237, 1e-236, 1e-235, 1e-234, 1e-233, 1e-232, 1e-231, 1e-230,
1e-229, 1e-228, 1e-227, 1e-226, 1e-225, 1e-224, 1e-223, 1e-222, 1e-221, 1e-220,
1e-219, 1e-218, 1e-217, 1e-216, 1e-215, 1e-214, 1e-213, 1e-212, 1e-211, 1e-210,
1e-209, 1e-208, 1e-207, 1e-206, 1e-205, 1e-204, 1e-203, 1e-202, 1e-201, 1e-200,
1e-199, 1e-198, 1e-197, 1e-196, 1e-195, 1e-194, 1e-193, 1e-192, 1e-191, 1e-190,
1e-189, 1e-188, 1e-187, 1e-186, 1e-185, 1e-184, 1e-183, 1e-182, 1e-181, 1e-180,
1e-179, 1e-178, 1e-177, 1e-176, 1e-175, 1e-174, 1e-173, 1e-172, 1e-171, 1e-170,
1e-169, 1e-168, 1e-167, 1e-166, 1e-165, 1e-164, 1e-163, 1e-162, 1e-161, 1e-160,
1e-159, 1e-158, 1e-157, 1e-156, 1e-155, 1e-154, 1e-153, 1e-152, 1e-151, 1e-150,
1e-149, 1e-148, 1e-147, 1e-146, 1e-145, 1e-144, 1e-143, 1e-142, 1e-141, 1e-140,
1e-139, 1e-138, 1e-137, 1e-136, 1e-135, 1e-134, 1e-133, 1e-132, 1e-131, 1e-130,
1e-129, 1e-128, 1e-127, 1e-126, 1e-125, 1e-124, 1e-123, 1e-122, 1e-121, 1e-120,
1e-119, 1e-118, 1e-117, 1e-116, 1e-115, 1e-114, 1e-113, 1e-112, 1e-111, 1e-110,
1e-109, 1e-108, 1e-107, 1e-106, 1e-105, 1e-104, 1e-103, 1e-102, 1e-101, 1e-100,
1e-099, 1e-098, 1e-097, 1e-096, 1e-095, 1e-094, 1e-093, 1e-092, 1e-091, 1e-090,
1e-089, 1e-088, 1e-087, 1e-086, 1e-085, 1e-084, 1e-083, 1e-082, 1e-081, 1e-080,
1e-079, 1e-078, 1e-077, 1e-076, 1e-075, 1e-074, 1e-073, 1e-072, 1e-071, 1e-070,
1e-069, 1e-068, 1e-067, 1e-066, 1e-065, 1e-064, 1e-063, 1e-062, 1e-061, 1e-060,
1e-059, 1e-058, 1e-057, 1e-056, 1e-055, 1e-054, 1e-053, 1e-052, 1e-051, 1e-050,
1e-049, 1e-048, 1e-047, 1e-046, 1e-045, 1e-044, 1e-043, 1e-042, 1e-041, 1e-040,
1e-039, 1e-038, 1e-037, 1e-036, 1e-035, 1e-034, 1e-033, 1e-032, 1e-031, 1e-030,
1e-029, 1e-028, 1e-027, 1e-026, 1e-025, 1e-024, 1e-023, 1e-022, 1e-021, 1e-020,
1e-019, 1e-018, 1e-017, 1e-016, 1e-015, 1e-014, 1e-013, 1e-012, 1e-011, 1e-010,
1e-009, 1e-008, 1e-007, 1e-006, 1e-005, 1e-004, 1e-003, 1e-002, 1e-001, 1e-000,
static const double P10_TAB[23] = {
/* <= the connvertion to double is not exact when less than 1 => */ 1e-000,
1e+001, 1e+002, 1e+003, 1e+004, 1e+005, 1e+006, 1e+007, 1e+008, 1e+009, 1e+010,
1e+011, 1e+012, 1e+013, 1e+014, 1e+015, 1e+016, 1e+017, 1e+018, 1e+019, 1e+020,
1e+021, 1e+022, 1e+023, 1e+024, 1e+025, 1e+026, 1e+027, 1e+028, 1e+029, 1e+030,
1e+031, 1e+032, 1e+033, 1e+034, 1e+035, 1e+036, 1e+037, 1e+038, 1e+039, 1e+040,
1e+041, 1e+042, 1e+043, 1e+044, 1e+045, 1e+046, 1e+047, 1e+048, 1e+049, 1e+050,
1e+051, 1e+052, 1e+053, 1e+054, 1e+055, 1e+056, 1e+057, 1e+058, 1e+059, 1e+060,
1e+061, 1e+062, 1e+063, 1e+064, 1e+065, 1e+066, 1e+067, 1e+068, 1e+069, 1e+070,
1e+071, 1e+072, 1e+073, 1e+074, 1e+075, 1e+076, 1e+077, 1e+078, 1e+079, 1e+080,
1e+081, 1e+082, 1e+083, 1e+084, 1e+085, 1e+086, 1e+087, 1e+088, 1e+089, 1e+090,
1e+091, 1e+092, 1e+093, 1e+094, 1e+095, 1e+096, 1e+097, 1e+098, 1e+099, 1e+100,
1e+101, 1e+102, 1e+103, 1e+104, 1e+105, 1e+106, 1e+107, 1e+108, 1e+109, 1e+110,
1e+111, 1e+112, 1e+113, 1e+114, 1e+115, 1e+116, 1e+117, 1e+118, 1e+119, 1e+120,
1e+121, 1e+122, 1e+123, 1e+124, 1e+125, 1e+126, 1e+127, 1e+128, 1e+129, 1e+130,
1e+131, 1e+132, 1e+133, 1e+134, 1e+135, 1e+136, 1e+137, 1e+138, 1e+139, 1e+140,
1e+141, 1e+142, 1e+143, 1e+144, 1e+145, 1e+146, 1e+147, 1e+148, 1e+149, 1e+150,
1e+151, 1e+152, 1e+153, 1e+154, 1e+155, 1e+156, 1e+157, 1e+158, 1e+159, 1e+160,
1e+161, 1e+162, 1e+163, 1e+164, 1e+165, 1e+166, 1e+167, 1e+168, 1e+169, 1e+170,
1e+171, 1e+172, 1e+173, 1e+174, 1e+175, 1e+176, 1e+177, 1e+178, 1e+179, 1e+180,
1e+181, 1e+182, 1e+183, 1e+184, 1e+185, 1e+186, 1e+187, 1e+188, 1e+189, 1e+190,
1e+191, 1e+192, 1e+193, 1e+194, 1e+195, 1e+196, 1e+197, 1e+198, 1e+199, 1e+200,
1e+201, 1e+202, 1e+203, 1e+204, 1e+205, 1e+206, 1e+207, 1e+208, 1e+209, 1e+210,
1e+211, 1e+212, 1e+213, 1e+214, 1e+215, 1e+216, 1e+217, 1e+218, 1e+219, 1e+220,
1e+221, 1e+222, 1e+223, 1e+224, 1e+225, 1e+226, 1e+227, 1e+228, 1e+229, 1e+230,
1e+231, 1e+232, 1e+233, 1e+234, 1e+235, 1e+236, 1e+237, 1e+238, 1e+239, 1e+240,
1e+241, 1e+242, 1e+243, 1e+244, 1e+245, 1e+246, 1e+247, 1e+248, 1e+249, 1e+250,
1e+251, 1e+252, 1e+253, 1e+254, 1e+255, 1e+256, 1e+257, 1e+258, 1e+259, 1e+260,
1e+261, 1e+262, 1e+263, 1e+264, 1e+265, 1e+266, 1e+267, 1e+268, 1e+269, 1e+270,
1e+271, 1e+272, 1e+273, 1e+274, 1e+275, 1e+276, 1e+277, 1e+278, 1e+279, 1e+280,
1e+281, 1e+282, 1e+283, 1e+284, 1e+285, 1e+286, 1e+287, 1e+288, 1e+289, 1e+290,
1e+291, 1e+292, 1e+293, 1e+294, 1e+295, 1e+296, 1e+297, 1e+298, 1e+299, 1e+300,
1e+301, 1e+302, 1e+303, 1e+304, 1e+305, 1e+306, 1e+307, 1e+308, /* = +Inf => */
1e+021, 1e+022 /* <= the connvertion to double is not exact when larger, => */
};
static inline double pow10(double v, int p) {
if (p < -323) {
return 0.0;
} else if (p > 308) {
return __builtin_inf();
} else {
return v * P10_TAB[p + 323];
}
}
static inline uint64_t add32(uint64_t v1, uint64_t v2, uint64_t *vo) {
uint32_t v;
uint32_t c = __builtin_uadd_overflow((uint32_t)v1, (uint32_t)v2, &v);
@ -473,6 +403,22 @@ void vstring(const GoString *src, long *p, JsonState *ret) {
check_eof() \
}
#define is_digit(val) \
'0' <= val && val <= '9'
#define add_integer_to_mantissa(man, man_nd, exp10, dig) \
if (man_nd < 19) { \
man = man * 10 + dig; \
man_nd++; \
} else { \
exp10++; \
} \
#define add_float_to_mantissa(man, man_nd, exp10, dig) \
man = man * 10 + dig; \
man_nd++; \
exp10--; \
#define parse_float_digits(val, sgn, ...) \
while (i < n && s[i] >= '0' && s[i] <= '9' __VA_ARGS__) { \
val *= 10; \
@ -536,71 +482,126 @@ void vstring(const GoString *src, long *p, JsonState *ret) {
*p = i; \
ret->iv = val;
/** check whether float can represent the val exactly **/
static inline int is_atof_exact(uint64_t man, int exp, int sgn, double *val) {
double f = (double)man;
if (man >> 52 != 0) {
return 0;
}
f *= sgn;
*val = 0;
if (exp == 0) {
*val = f;
return 1;
} else if (exp > 0 && exp <= 15+22) {
/* uint64 integers: accurate range <= 10^15 *
* Powers of 10: accurate range <= 10^22, as P10_TAB *
* Example: man 1, exp 36, is ok */
if (exp > 22) {
f *= P10_TAB[exp-22];
exp = 22;
}
/* f is not accurate when too larger */
if (f > 1e15 || f < -1e15) {
return 0;
}
*val = f * P10_TAB[exp];
return 1;
} else if (exp < 0 && exp >= -22) {
*val = f / P10_TAB[-exp];
return 1;
}
return 0;
}
double parse_float64(uint64_t man, int exp, int sgn, const GoString *src, long idx) {
double val = 0.0;
/* look-up for fast atof if the conversion can be exactly */
if (is_atof_exact(man, exp, sgn, &val)) {
return val;
}
/* A fast atof algorithm for high percison */
if (atof_eisel_lemire64(man, exp, sgn, &val)) {
return val;
}
/* when above algorithms failed, fallback. It is slow. */
return atof_native_decimal(src->buf + idx, src->len - idx);
}
void vnumber(const GoString *src, long *p, JsonState *ret) {
int dig;
int ovf = 0;
int sgn = 1;
double val = 0;
int64_t dec = 0;
int dig;
int ovf = 0;
int sgn = 1;
double val = 0;
uint64_t man = 0; // mantissa for double (float64)
int man_nd = 0; // # digits of mantissa, 10^19 fits uint64_t
int exp10 = 0; // man * exp10 represents the true value
/* initial buffer pointers */
long i = *p;
size_t n = src->len;
const char * s = src->buf;
long si = *p; // record the idx for fall-back when parsing float.
/* initialize the result, and check for EOF */
init_ret(V_INTEGER)
check_eof()
check_sign(sgn = -1)
/* zero */
if (i + 1 == n && s[i] == '0') {
i++;
goto out;
}
/* check for leading zero */
check_digit()
check_leading_zero()
/* parse the integer part */
while (i < n && s[i] >= '0' && s[i] <= '9') {
val = dec;
dig = sgn * (s[i++] - '0');
/* add the digit to the integer part if not overflowed */
if (add_digit_overflow(dec, dig)) {
ovf = 1;
val = (val * 10.0) + dig;
set_vt(V_DOUBLE)
break;
}
}
/* after overflow, we can only continue with floating point values */
if (!ovf) {
val = dec;
}
/* after overflow, we can only continue with floating point values */
while (ovf && i < n && s[i] >= '0' && s[i] <= '9') {
val *= 10.0;
val += sgn * (s[i++] - '0');
while (i < n && is_digit(s[i])) {
add_integer_to_mantissa(man, man_nd, exp10, (s[i] - '0'))
i++;
}
/* check for decimal points */
if (i < n && s[i] == '.') {
int idx = ++i;
int64_t rem = 0;
/* convert the fractional part (float64 can represent at most 16 digits) */
i++;
set_vt(V_DOUBLE)
check_eof()
check_digit()
parse_float_digits(rem, sgn, && i <= idx + 17)
}
/* combine with the decimal part */
idx -= i;
val += pow10(rem, idx);
/* skip the remaining digits */
while (i < n && s[i] >= '0' && s[i] <= '9') {
/* skip the leading zeros of 0.000xxxx */
if (man == 0 && exp10 == 0) {
int idx = i;
while (i < n && s[i] == '0') {
i++;
}
exp10 = idx - i;
man = 0;
man_nd = 0;
}
/* the fractional part (uint64_t mantissa can represent at most 19 digits) */
while (i < n && man_nd < 19 && is_digit(s[i])) {
add_float_to_mantissa(man, man_nd, exp10, (s[i] - '0'))
i++;
}
/* skip the remaining digits */
while (i < n && is_digit(s[i])) {
i++;
}
/* check for exponent */
@ -614,22 +615,29 @@ void vnumber(const GoString *src, long *p, JsonState *ret) {
check_eof()
parse_sign(esm)
check_digit()
parse_float_digits(exp, esm)
/* scale with */
if (exp != 1) {
val = pow10(val, exp);
while (i < n && is_digit(s[i])) {
exp = exp * 10 + (s[i++] - '0');
}
exp10 += exp * esm;
}
out:
if (ret->vt == V_INTEGER) {
/* if INT64_MIN <= man * sgn <= INT64_MAX */
if ( exp10 == 0 && (((man & ((uint64_t)1 << 63)) == 0) || ((man & sgn) == man))) {
ret->iv = (int64_t)man * sgn;
ret->dv = (double)(ret->iv);
} else { // integer overflow
set_vt(V_DOUBLE)
}
}
/* check for integer overflow */
if (!ovf) {
ret->iv = dec;
if (ret->vt == V_DOUBLE) {
ret->dv = parse_float64(man, exp10, sgn, src, si);
}
/* update the result */
*p = i;
ret->dv = val;
}
void vsigned(const GoString *src, long *p, JsonState *ret) {
@ -650,6 +658,9 @@ void vunsigned(const GoString *src, long *p, JsonState *ret) {
#undef check_digit
#undef check_leading_zero
#undef parse_sign
#undef is_digit
#undef add_integer_to_mantissa
#undef add_float_to_mantissa
#undef parse_float_digits
#undef parse_integer_digits
#undef add_digit_overflow