134 lines
5.9 KiB
C
134 lines
5.9 KiB
C
/* fpconv_powers.h -- floating point conversion utilities.
|
|
*
|
|
* Fast and accurate double to string conversion based on Florian Loitsch's
|
|
* Grisu-algorithm[1].
|
|
*
|
|
* [1] https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf
|
|
* ----------------------------------------------------------------------------
|
|
*
|
|
* Copyright (c) 2021, Redis Labs
|
|
* Copyright (c) 2013-2019, night-shift <as.smljk at gmail dot com>
|
|
* Copyright (c) 2009, Florian Loitsch < florian.loitsch at inria dot fr >
|
|
* All rights reserved.
|
|
*
|
|
* Boost Software License - Version 1.0 - August 17th, 2003
|
|
*
|
|
* Permission is hereby granted, free of charge, to any person or organization
|
|
* obtaining a copy of the software and accompanying documentation covered by
|
|
* this license (the "Software") to use, reproduce, display, distribute,
|
|
* execute, and transmit the Software, and to prepare derivative works of the
|
|
* Software, and to permit third-parties to whom the Software is furnished to
|
|
* do so, all subject to the following:
|
|
*
|
|
* The copyright notices in the Software and this entire statement, including
|
|
* the above license grant, this restriction and the following disclaimer,
|
|
* must be included in all copies of the Software, in whole or in part, and
|
|
* all derivative works of the Software, unless such copies or derivative
|
|
* works are solely in the form of machine-executable object code generated by
|
|
* a source language processor.
|
|
*
|
|
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
|
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
|
* FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
|
|
* SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
|
|
* FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
|
|
* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
|
|
* DEALINGS IN THE SOFTWARE.
|
|
*/
|
|
|
|
#include <stdint.h>
|
|
|
|
#define npowers 87
|
|
#define steppowers 8
|
|
#define firstpower -348 /* 10 ^ -348 */
|
|
|
|
#define expmax -32
|
|
#define expmin -60
|
|
|
|
|
|
typedef struct Fp {
|
|
uint64_t frac;
|
|
int exp;
|
|
} Fp;
|
|
|
|
static Fp powers_ten[] = {
|
|
{ 18054884314459144840U, -1220 }, { 13451937075301367670U, -1193 },
|
|
{ 10022474136428063862U, -1166 }, { 14934650266808366570U, -1140 },
|
|
{ 11127181549972568877U, -1113 }, { 16580792590934885855U, -1087 },
|
|
{ 12353653155963782858U, -1060 }, { 18408377700990114895U, -1034 },
|
|
{ 13715310171984221708U, -1007 }, { 10218702384817765436U, -980 },
|
|
{ 15227053142812498563U, -954 }, { 11345038669416679861U, -927 },
|
|
{ 16905424996341287883U, -901 }, { 12595523146049147757U, -874 },
|
|
{ 9384396036005875287U, -847 }, { 13983839803942852151U, -821 },
|
|
{ 10418772551374772303U, -794 }, { 15525180923007089351U, -768 },
|
|
{ 11567161174868858868U, -741 }, { 17236413322193710309U, -715 },
|
|
{ 12842128665889583758U, -688 }, { 9568131466127621947U, -661 },
|
|
{ 14257626930069360058U, -635 }, { 10622759856335341974U, -608 },
|
|
{ 15829145694278690180U, -582 }, { 11793632577567316726U, -555 },
|
|
{ 17573882009934360870U, -529 }, { 13093562431584567480U, -502 },
|
|
{ 9755464219737475723U, -475 }, { 14536774485912137811U, -449 },
|
|
{ 10830740992659433045U, -422 }, { 16139061738043178685U, -396 },
|
|
{ 12024538023802026127U, -369 }, { 17917957937422433684U, -343 },
|
|
{ 13349918974505688015U, -316 }, { 9946464728195732843U, -289 },
|
|
{ 14821387422376473014U, -263 }, { 11042794154864902060U, -236 },
|
|
{ 16455045573212060422U, -210 }, { 12259964326927110867U, -183 },
|
|
{ 18268770466636286478U, -157 }, { 13611294676837538539U, -130 },
|
|
{ 10141204801825835212U, -103 }, { 15111572745182864684U, -77 },
|
|
{ 11258999068426240000U, -50 }, { 16777216000000000000U, -24 },
|
|
{ 12500000000000000000U, 3 }, { 9313225746154785156U, 30 },
|
|
{ 13877787807814456755U, 56 }, { 10339757656912845936U, 83 },
|
|
{ 15407439555097886824U, 109 }, { 11479437019748901445U, 136 },
|
|
{ 17105694144590052135U, 162 }, { 12744735289059618216U, 189 },
|
|
{ 9495567745759798747U, 216 }, { 14149498560666738074U, 242 },
|
|
{ 10542197943230523224U, 269 }, { 15709099088952724970U, 295 },
|
|
{ 11704190886730495818U, 322 }, { 17440603504673385349U, 348 },
|
|
{ 12994262207056124023U, 375 }, { 9681479787123295682U, 402 },
|
|
{ 14426529090290212157U, 428 }, { 10748601772107342003U, 455 },
|
|
{ 16016664761464807395U, 481 }, { 11933345169920330789U, 508 },
|
|
{ 17782069995880619868U, 534 }, { 13248674568444952270U, 561 },
|
|
{ 9871031767461413346U, 588 }, { 14708983551653345445U, 614 },
|
|
{ 10959046745042015199U, 641 }, { 16330252207878254650U, 667 },
|
|
{ 12166986024289022870U, 694 }, { 18130221999122236476U, 720 },
|
|
{ 13508068024458167312U, 747 }, { 10064294952495520794U, 774 },
|
|
{ 14996968138956309548U, 800 }, { 11173611982879273257U, 827 },
|
|
{ 16649979327439178909U, 853 }, { 12405201291620119593U, 880 },
|
|
{ 9242595204427927429U, 907 }, { 13772540099066387757U, 933 },
|
|
{ 10261342003245940623U, 960 }, { 15290591125556738113U, 986 },
|
|
{ 11392378155556871081U, 1013 }, { 16975966327722178521U, 1039 },
|
|
{ 12648080533535911531U, 1066 }
|
|
};
|
|
|
|
/**
|
|
* Grisu needs a cache of precomputed powers-of-ten.
|
|
* This function, given an exponent and an integer k
|
|
* return the normalized floating-point approximation of the power of 10.
|
|
* @param exp
|
|
* @param k
|
|
* @return
|
|
*/
|
|
static Fp find_cachedpow10(int exp, int* k)
|
|
{
|
|
const double one_log_ten = 0.30102999566398114;
|
|
|
|
const int approx = -(exp + npowers) * one_log_ten;
|
|
int idx = (approx - firstpower) / steppowers;
|
|
|
|
while(1) {
|
|
int current = exp + powers_ten[idx].exp + 64;
|
|
|
|
if(current < expmin) {
|
|
idx++;
|
|
continue;
|
|
}
|
|
|
|
if(current > expmax) {
|
|
idx--;
|
|
continue;
|
|
}
|
|
|
|
*k = (firstpower + idx * steppowers);
|
|
|
|
return powers_ten[idx];
|
|
}
|
|
}
|