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330 lines
11 KiB
C
330 lines
11 KiB
C
/*
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* Copyright (c) 2016 Mikkel F. Jørgensen, dvide.com
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* Copyright author of MathGeoLib (https://github.com/juj)
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License. http://www.apache.org/licenses/LICENSE-2.0
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*/
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/* 2016-02-02: Updated by mikkelfj
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*
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* Extracted from MatGeoLib grisu3.c, Apache 2.0 license, and extended.
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*
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* This file is usually include via grisu3_print.h or grisu3_parse.h.
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*
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* The original MatGeoLib dtoa_grisu3 implementation is largely
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* unchanged except for the uint64 to double cast. The remaining changes
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* are file structure, name changes, and new additions for parsing:
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*
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* - Split into header files only:
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* grisu3_math.h, grisu3_print.h, (added grisu3_parse.h)
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*
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* - names prefixed with grisu3_, grisu3_diy_fp_, GRISU3_.
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* - added static to all functions.
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* - disabled clang unused function warnings.
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* - guarded <stdint.h> to allow for alternative impl.
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* - added extra numeric constants needed for parsing.
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* - added dec_pow, cast_double_from_diy_fp.
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* - changed some function names for consistency.
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* - moved printing specific grisu3 functions to grisu3_print.h.
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* - changed double to uint64 cast to avoid aliasing.
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* - added new grisu3_parse.h for parsing doubles.
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* - grisu3_print_double (dtoa_grisu3) format .1 as 0.1 needed for valid JSON output
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* and grisu3_parse_double wouldn't consume it.
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* - grsu3_print_double changed formatting to prefer 0.012 over 1.2e-2.
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*
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* These changes make it possible to include the files as headers only
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* in other software libraries without risking name conflicts, and to
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* extend the implementation with a port of Googles Double Conversion
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* strtod functionality for parsing doubles.
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*
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* Extracted from: rev. 915501a / Dec 22, 2015
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* <https://github.com/juj/MathGeoLib/blob/master/src/Math/grisu3.c>
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* MathGeoLib License: http://www.apache.org/licenses/LICENSE-2.0.html
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*/
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#ifndef GRISU3_MATH_H
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#define GRISU3_MATH_H
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#ifdef __cplusplus
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extern "C" {
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#endif
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/* Guarded to allow inclusion of pstdint.h first, if stdint.h is not supported. */
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#ifndef UINT8_MAX
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#include <stdint.h> /* uint64_t etc. */
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#endif
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#ifdef GRISU3_NO_ASSERT
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#undef GRISU3_ASSERT
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#define GRISU3_ASSERT(x) ((void)0)
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#endif
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#ifndef GRISU3_ASSERT
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#include <assert.h> /* assert */
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#define GRISU3_ASSERT(x) assert(x)
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#endif
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#ifdef _MSC_VER
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#pragma warning(disable : 4204) /* nonstandard extension used : non-constant aggregate initializer */
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#endif
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#define GRISU3_D64_SIGN 0x8000000000000000ULL
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#define GRISU3_D64_EXP_MASK 0x7FF0000000000000ULL
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#define GRISU3_D64_FRACT_MASK 0x000FFFFFFFFFFFFFULL
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#define GRISU3_D64_IMPLICIT_ONE 0x0010000000000000ULL
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#define GRISU3_D64_EXP_POS 52
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#define GRISU3_D64_EXP_BIAS 1075
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#define GRISU3_D64_DENORM_EXP (-GRISU3_D64_EXP_BIAS + 1)
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#define GRISU3_DIY_FP_FRACT_SIZE 64
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#define GRISU3_D_1_LOG2_10 0.30102999566398114 /* 1 / lg(10) */
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#define GRISU3_MIN_TARGET_EXP -60
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#define GRISU3_MASK32 0xFFFFFFFFULL
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#define GRISU3_MIN_CACHED_EXP -348
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#define GRISU3_MAX_CACHED_EXP 340
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#define GRISU3_CACHED_EXP_STEP 8
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#define GRISU3_D64_MAX_DEC_EXP 309
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#define GRISU3_D64_MIN_DEC_EXP -324
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#define GRISU3_D64_INF GRISU3_D64_EXP_MASK
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#define GRISU3_MIN(x,y) ((x) <= (y) ? (x) : (y))
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#define GRISU3_MAX(x,y) ((x) >= (y) ? (x) : (y))
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typedef struct grisu3_diy_fp
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{
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uint64_t f;
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int e;
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} grisu3_diy_fp_t;
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typedef struct grisu3_diy_fp_power
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{
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uint64_t fract;
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int16_t b_exp, d_exp;
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} grisu3_diy_fp_power_t;
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typedef union {
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uint64_t u64;
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double d64;
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} grisu3_cast_double_t;
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static uint64_t grisu3_cast_uint64_from_double(double d)
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{
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grisu3_cast_double_t cd;
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cd.d64 = d;
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return cd.u64;
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}
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static double grisu3_cast_double_from_uint64(uint64_t u)
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{
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grisu3_cast_double_t cd;
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cd.u64 = u;
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return cd.d64;
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}
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#define grisu3_double_infinity grisu3_cast_double_from_uint64(GRISU3_D64_INF)
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#define grisu3_double_nan grisu3_cast_double_from_uint64(GRISU3_D64_INF + 1)
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static const grisu3_diy_fp_power_t grisu3_diy_fp_pow_cache[] =
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{
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{ 0xfa8fd5a0081c0288ULL, -1220, -348 },
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{ 0xbaaee17fa23ebf76ULL, -1193, -340 },
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{ 0x8b16fb203055ac76ULL, -1166, -332 },
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{ 0xcf42894a5dce35eaULL, -1140, -324 },
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{ 0x9a6bb0aa55653b2dULL, -1113, -316 },
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{ 0xe61acf033d1a45dfULL, -1087, -308 },
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{ 0xab70fe17c79ac6caULL, -1060, -300 },
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{ 0xff77b1fcbebcdc4fULL, -1034, -292 },
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{ 0xbe5691ef416bd60cULL, -1007, -284 },
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{ 0x8dd01fad907ffc3cULL, -980, -276 },
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{ 0xd3515c2831559a83ULL, -954, -268 },
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{ 0x9d71ac8fada6c9b5ULL, -927, -260 },
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{ 0xea9c227723ee8bcbULL, -901, -252 },
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{ 0xaecc49914078536dULL, -874, -244 },
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{ 0x823c12795db6ce57ULL, -847, -236 },
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{ 0xc21094364dfb5637ULL, -821, -228 },
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{ 0x9096ea6f3848984fULL, -794, -220 },
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{ 0xd77485cb25823ac7ULL, -768, -212 },
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{ 0xa086cfcd97bf97f4ULL, -741, -204 },
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{ 0xef340a98172aace5ULL, -715, -196 },
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{ 0xb23867fb2a35b28eULL, -688, -188 },
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{ 0x84c8d4dfd2c63f3bULL, -661, -180 },
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{ 0xc5dd44271ad3cdbaULL, -635, -172 },
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{ 0x936b9fcebb25c996ULL, -608, -164 },
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{ 0xdbac6c247d62a584ULL, -582, -156 },
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{ 0xa3ab66580d5fdaf6ULL, -555, -148 },
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{ 0xf3e2f893dec3f126ULL, -529, -140 },
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{ 0xb5b5ada8aaff80b8ULL, -502, -132 },
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{ 0x87625f056c7c4a8bULL, -475, -124 },
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{ 0xc9bcff6034c13053ULL, -449, -116 },
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{ 0x964e858c91ba2655ULL, -422, -108 },
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{ 0xdff9772470297ebdULL, -396, -100 },
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{ 0xa6dfbd9fb8e5b88fULL, -369, -92 },
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{ 0xf8a95fcf88747d94ULL, -343, -84 },
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{ 0xb94470938fa89bcfULL, -316, -76 },
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{ 0x8a08f0f8bf0f156bULL, -289, -68 },
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{ 0xcdb02555653131b6ULL, -263, -60 },
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{ 0x993fe2c6d07b7facULL, -236, -52 },
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{ 0xe45c10c42a2b3b06ULL, -210, -44 },
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{ 0xaa242499697392d3ULL, -183, -36 },
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{ 0xfd87b5f28300ca0eULL, -157, -28 },
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{ 0xbce5086492111aebULL, -130, -20 },
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{ 0x8cbccc096f5088ccULL, -103, -12 },
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{ 0xd1b71758e219652cULL, -77, -4 },
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{ 0x9c40000000000000ULL, -50, 4 },
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{ 0xe8d4a51000000000ULL, -24, 12 },
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{ 0xad78ebc5ac620000ULL, 3, 20 },
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{ 0x813f3978f8940984ULL, 30, 28 },
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{ 0xc097ce7bc90715b3ULL, 56, 36 },
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{ 0x8f7e32ce7bea5c70ULL, 83, 44 },
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{ 0xd5d238a4abe98068ULL, 109, 52 },
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{ 0x9f4f2726179a2245ULL, 136, 60 },
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{ 0xed63a231d4c4fb27ULL, 162, 68 },
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{ 0xb0de65388cc8ada8ULL, 189, 76 },
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{ 0x83c7088e1aab65dbULL, 216, 84 },
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{ 0xc45d1df942711d9aULL, 242, 92 },
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{ 0x924d692ca61be758ULL, 269, 100 },
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{ 0xda01ee641a708deaULL, 295, 108 },
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{ 0xa26da3999aef774aULL, 322, 116 },
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{ 0xf209787bb47d6b85ULL, 348, 124 },
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{ 0xb454e4a179dd1877ULL, 375, 132 },
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{ 0x865b86925b9bc5c2ULL, 402, 140 },
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{ 0xc83553c5c8965d3dULL, 428, 148 },
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{ 0x952ab45cfa97a0b3ULL, 455, 156 },
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{ 0xde469fbd99a05fe3ULL, 481, 164 },
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{ 0xa59bc234db398c25ULL, 508, 172 },
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{ 0xf6c69a72a3989f5cULL, 534, 180 },
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{ 0xb7dcbf5354e9beceULL, 561, 188 },
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{ 0x88fcf317f22241e2ULL, 588, 196 },
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{ 0xcc20ce9bd35c78a5ULL, 614, 204 },
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{ 0x98165af37b2153dfULL, 641, 212 },
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{ 0xe2a0b5dc971f303aULL, 667, 220 },
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{ 0xa8d9d1535ce3b396ULL, 694, 228 },
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{ 0xfb9b7cd9a4a7443cULL, 720, 236 },
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{ 0xbb764c4ca7a44410ULL, 747, 244 },
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{ 0x8bab8eefb6409c1aULL, 774, 252 },
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{ 0xd01fef10a657842cULL, 800, 260 },
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{ 0x9b10a4e5e9913129ULL, 827, 268 },
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{ 0xe7109bfba19c0c9dULL, 853, 276 },
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{ 0xac2820d9623bf429ULL, 880, 284 },
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{ 0x80444b5e7aa7cf85ULL, 907, 292 },
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{ 0xbf21e44003acdd2dULL, 933, 300 },
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{ 0x8e679c2f5e44ff8fULL, 960, 308 },
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{ 0xd433179d9c8cb841ULL, 986, 316 },
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{ 0x9e19db92b4e31ba9ULL, 1013, 324 },
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{ 0xeb96bf6ebadf77d9ULL, 1039, 332 },
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{ 0xaf87023b9bf0ee6bULL, 1066, 340 }
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};
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/* Avoid dependence on lib math to get (int)ceil(v) */
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static int grisu3_iceil(double v)
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{
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int k = (int)v;
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if (v < 0) return k;
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return v - k == 0 ? k : k + 1;
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}
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static int grisu3_diy_fp_cached_pow(int exp, grisu3_diy_fp_t *p)
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{
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int k = grisu3_iceil((exp+GRISU3_DIY_FP_FRACT_SIZE-1) * GRISU3_D_1_LOG2_10);
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int i = (k-GRISU3_MIN_CACHED_EXP-1) / GRISU3_CACHED_EXP_STEP + 1;
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p->f = grisu3_diy_fp_pow_cache[i].fract;
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p->e = grisu3_diy_fp_pow_cache[i].b_exp;
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return grisu3_diy_fp_pow_cache[i].d_exp;
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}
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static grisu3_diy_fp_t grisu3_diy_fp_minus(grisu3_diy_fp_t x, grisu3_diy_fp_t y)
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{
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grisu3_diy_fp_t d; d.f = x.f - y.f; d.e = x.e;
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GRISU3_ASSERT(x.e == y.e && x.f >= y.f);
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return d;
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}
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static grisu3_diy_fp_t grisu3_diy_fp_multiply(grisu3_diy_fp_t x, grisu3_diy_fp_t y)
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{
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uint64_t a, b, c, d, ac, bc, ad, bd, tmp;
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grisu3_diy_fp_t r;
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a = x.f >> 32; b = x.f & GRISU3_MASK32;
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c = y.f >> 32; d = y.f & GRISU3_MASK32;
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ac = a*c; bc = b*c;
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ad = a*d; bd = b*d;
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tmp = (bd >> 32) + (ad & GRISU3_MASK32) + (bc & GRISU3_MASK32);
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tmp += 1U << 31; /* round */
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r.f = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32);
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r.e = x.e + y.e + 64;
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return r;
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}
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static grisu3_diy_fp_t grisu3_diy_fp_normalize(grisu3_diy_fp_t n)
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{
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GRISU3_ASSERT(n.f != 0);
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while(!(n.f & 0xFFC0000000000000ULL)) { n.f <<= 10; n.e -= 10; }
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while(!(n.f & GRISU3_D64_SIGN)) { n.f <<= 1; --n.e; }
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return n;
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}
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static grisu3_diy_fp_t grisu3_cast_diy_fp_from_double(double d)
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{
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grisu3_diy_fp_t fp;
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uint64_t u64 = grisu3_cast_uint64_from_double(d);
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if (!(u64 & GRISU3_D64_EXP_MASK)) { fp.f = u64 & GRISU3_D64_FRACT_MASK; fp.e = 1 - GRISU3_D64_EXP_BIAS; }
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else { fp.f = (u64 & GRISU3_D64_FRACT_MASK) + GRISU3_D64_IMPLICIT_ONE; fp.e = (int)((u64 & GRISU3_D64_EXP_MASK) >> GRISU3_D64_EXP_POS) - GRISU3_D64_EXP_BIAS; }
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return fp;
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}
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static double grisu3_cast_double_from_diy_fp(grisu3_diy_fp_t n)
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{
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const uint64_t hidden_bit = GRISU3_D64_IMPLICIT_ONE;
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const uint64_t frac_mask = GRISU3_D64_FRACT_MASK;
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const int denorm_exp = GRISU3_D64_DENORM_EXP;
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const int exp_bias = GRISU3_D64_EXP_BIAS;
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const int exp_pos = GRISU3_D64_EXP_POS;
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grisu3_diy_fp_t v = n;
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uint64_t e_biased;
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while (v.f > hidden_bit + frac_mask) {
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v.f >>= 1;
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++v.e;
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}
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if (v.e < denorm_exp) {
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return 0.0;
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}
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while (v.e > denorm_exp && (v.f & hidden_bit) == 0) {
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v.f <<= 1;
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--v.e;
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}
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if (v.e == denorm_exp && (v.f & hidden_bit) == 0) {
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e_biased = 0;
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} else {
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e_biased = (uint64_t)(v.e + exp_bias);
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}
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return grisu3_cast_double_from_uint64((v.f & frac_mask) | (e_biased << exp_pos));
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}
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/* pow10_cache[i] = 10^(i-1) */
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static const unsigned int grisu3_pow10_cache[] = { 0, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 };
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static int grisu3_largest_pow10(uint32_t n, int n_bits, uint32_t *power)
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{
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int guess = ((n_bits + 1) * 1233 >> 12) + 1/*skip first entry*/;
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if (n < grisu3_pow10_cache[guess]) --guess; /* We don't have any guarantees that 2^n_bits <= n. */
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*power = grisu3_pow10_cache[guess];
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return guess;
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}
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#ifdef __cplusplus
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}
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#endif
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#endif /* GRISU3_MATH_H */
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