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266 lines
8.9 KiB
C
266 lines
8.9 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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/*
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* Extracted from MathGeoLib.
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*
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* mikkelfj:
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* - Fixed final output when printing single digit negative exponent to
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* have leading zero (important for JSON).
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* - Changed formatting to prefer 0.012 over 1.2-e-2.
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*
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* Large portions of the original grisu3.c file has been moved to
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* grisu3_math.h, the rest is placed here.
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*
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* See also comments in grisu3_math.h.
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*
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* MatGeoLib grisu3.c comment:
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*
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* This file is part of an implementation of the "grisu3" double to string
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* conversion algorithm described in the research paper
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*
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* "Printing Floating-Point Numbers Quickly And Accurately with Integers"
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* by Florian Loitsch, available at
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* http://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf
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*/
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#ifndef GRISU3_PRINT_H
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#define GRISU3_PRINT_H
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include <stdio.h> /* sprintf, only needed for fallback printing */
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#include <assert.h> /* assert */
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#include "grisu3_math.h"
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/*
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* The lightweight "portable" C library recognizes grisu3 support if
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* included first.
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*/
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#define grisu3_print_double_is_defined 1
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/*
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* Not sure we have an exact definition, but we get up to 23
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* emperically. There is some math ensuring it does not go awol though,
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* like 18 digits + exponent or so.
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* This max should be safe size buffer for printing, including zero term.
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*/
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#define GRISU3_PRINT_MAX 30
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static int grisu3_round_weed(char *buffer, int len, uint64_t wp_W, uint64_t delta, uint64_t rest, uint64_t ten_kappa, uint64_t ulp)
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{
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uint64_t wp_Wup = wp_W - ulp;
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uint64_t wp_Wdown = wp_W + ulp;
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while(rest < wp_Wup && delta - rest >= ten_kappa
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&& (rest + ten_kappa < wp_Wup || wp_Wup - rest >= rest + ten_kappa - wp_Wup))
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{
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--buffer[len-1];
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rest += ten_kappa;
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}
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if (rest < wp_Wdown && delta - rest >= ten_kappa
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&& (rest + ten_kappa < wp_Wdown || wp_Wdown - rest > rest + ten_kappa - wp_Wdown))
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return 0;
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return 2*ulp <= rest && rest <= delta - 4*ulp;
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}
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static int grisu3_digit_gen(grisu3_diy_fp_t low, grisu3_diy_fp_t w, grisu3_diy_fp_t high, char *buffer, int *length, int *kappa)
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{
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uint64_t unit = 1;
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grisu3_diy_fp_t too_low = { low.f - unit, low.e };
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grisu3_diy_fp_t too_high = { high.f + unit, high.e };
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grisu3_diy_fp_t unsafe_interval = grisu3_diy_fp_minus(too_high, too_low);
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grisu3_diy_fp_t one = { 1ULL << -w.e, w.e };
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uint32_t p1 = (uint32_t)(too_high.f >> -one.e);
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uint64_t p2 = too_high.f & (one.f - 1);
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uint32_t div;
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*kappa = grisu3_largest_pow10(p1, GRISU3_DIY_FP_FRACT_SIZE + one.e, &div);
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*length = 0;
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while(*kappa > 0)
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{
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uint64_t rest;
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char digit = (char)(p1 / div);
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buffer[*length] = '0' + digit;
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++*length;
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p1 %= div;
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--*kappa;
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rest = ((uint64_t)p1 << -one.e) + p2;
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if (rest < unsafe_interval.f) return grisu3_round_weed(buffer, *length, grisu3_diy_fp_minus(too_high, w).f, unsafe_interval.f, rest, (uint64_t)div << -one.e, unit);
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div /= 10;
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}
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for(;;)
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{
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char digit;
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p2 *= 10;
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unit *= 10;
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unsafe_interval.f *= 10;
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/* Integer division by one. */
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digit = (char)(p2 >> -one.e);
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buffer[*length] = '0' + digit;
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++*length;
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p2 &= one.f - 1; /* Modulo by one. */
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--*kappa;
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if (p2 < unsafe_interval.f) return grisu3_round_weed(buffer, *length, grisu3_diy_fp_minus(too_high, w).f * unit, unsafe_interval.f, p2, one.f, unit);
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}
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}
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static int grisu3(double v, char *buffer, int *length, int *d_exp)
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{
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int mk, kappa, success;
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grisu3_diy_fp_t dfp = grisu3_cast_diy_fp_from_double(v);
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grisu3_diy_fp_t w = grisu3_diy_fp_normalize(dfp);
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/* normalize boundaries */
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grisu3_diy_fp_t t = { (dfp.f << 1) + 1, dfp.e - 1 };
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grisu3_diy_fp_t b_plus = grisu3_diy_fp_normalize(t);
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grisu3_diy_fp_t b_minus;
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grisu3_diy_fp_t c_mk; /* Cached power of ten: 10^-k */
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uint64_t u64 = grisu3_cast_uint64_from_double(v);
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assert(v > 0 && v <= 1.7976931348623157e308); /* Grisu only handles strictly positive finite numbers. */
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if (!(u64 & GRISU3_D64_FRACT_MASK) && (u64 & GRISU3_D64_EXP_MASK) != 0) { b_minus.f = (dfp.f << 2) - 1; b_minus.e = dfp.e - 2;} /* lower boundary is closer? */
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else { b_minus.f = (dfp.f << 1) - 1; b_minus.e = dfp.e - 1; }
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b_minus.f = b_minus.f << (b_minus.e - b_plus.e);
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b_minus.e = b_plus.e;
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mk = grisu3_diy_fp_cached_pow(GRISU3_MIN_TARGET_EXP - GRISU3_DIY_FP_FRACT_SIZE - w.e, &c_mk);
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w = grisu3_diy_fp_multiply(w, c_mk);
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b_minus = grisu3_diy_fp_multiply(b_minus, c_mk);
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b_plus = grisu3_diy_fp_multiply(b_plus, c_mk);
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success = grisu3_digit_gen(b_minus, w, b_plus, buffer, length, &kappa);
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*d_exp = kappa - mk;
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return success;
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}
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static int grisu3_i_to_str(int val, char *str)
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{
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int len, i;
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char *s;
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char *begin = str;
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if (val < 0) { *str++ = '-'; val = -val; }
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s = str;
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for(;;)
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{
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int ni = val / 10;
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int digit = val - ni*10;
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*s++ = (char)('0' + digit);
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if (ni == 0)
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break;
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val = ni;
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}
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*s = '\0';
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len = (int)(s - str);
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for(i = 0; i < len/2; ++i)
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{
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char ch = str[i];
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str[i] = str[len-1-i];
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str[len-1-i] = ch;
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}
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return (int)(s - begin);
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}
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static int grisu3_print_nan(uint64_t v, char *dst)
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{
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static char hexdigits[16] = "0123456789ABCDEF";
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int i = 0;
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dst[0] = 'N';
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dst[1] = 'a';
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dst[2] = 'N';
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dst[3] = '(';
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dst[20] = ')';
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dst[21] = '\0';
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dst += 4;
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for (i = 15; i >= 0; --i) {
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dst[i] = hexdigits[v & 0x0F];
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v >>= 4;
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}
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return 21;
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}
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static int grisu3_print_double(double v, char *dst)
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{
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int d_exp, len, success, decimals, i;
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uint64_t u64 = grisu3_cast_uint64_from_double(v);
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char *s2 = dst;
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assert(dst);
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/* Prehandle NaNs */
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if ((u64 << 1) > 0xFFE0000000000000ULL) return grisu3_print_nan(u64, dst);
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/* Prehandle negative values. */
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if ((u64 & GRISU3_D64_SIGN) != 0) { *s2++ = '-'; v = -v; u64 ^= GRISU3_D64_SIGN; }
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/* Prehandle zero. */
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if (!u64) { *s2++ = '0'; *s2 = '\0'; return (int)(s2 - dst); }
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/* Prehandle infinity. */
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if (u64 == GRISU3_D64_EXP_MASK) { *s2++ = 'i'; *s2++ = 'n'; *s2++ = 'f'; *s2 = '\0'; return (int)(s2 - dst); }
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success = grisu3(v, s2, &len, &d_exp);
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/* If grisu3 was not able to convert the number to a string, then use old sprintf (suboptimal). */
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if (!success) return sprintf(s2, "%.17g", v) + (int)(s2 - dst);
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/* We now have an integer string of form "151324135" and a base-10 exponent for that number. */
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/* Next, decide the best presentation for that string by whether to use a decimal point, or the scientific exponent notation 'e'. */
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/* We don't pick the absolute shortest representation, but pick a balance between readability and shortness, e.g. */
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/* 1.545056189557677e-308 could be represented in a shorter form */
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/* 1545056189557677e-323 but that would be somewhat unreadable. */
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decimals = GRISU3_MIN(-d_exp, GRISU3_MAX(1, len-1));
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/* mikkelfj:
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* fix zero prefix .1 => 0.1, important for JSON export.
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* prefer unscientific notation at same length:
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* -1.2345e-4 over -1.00012345,
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* -1.0012345 over -1.2345e-3
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*/
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if (d_exp < 0 && (len + d_exp) > -3 && len <= -d_exp)
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{
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/* mikkelfj: fix zero prefix .1 => 0.1, and short exponents 1.3e-2 => 0.013. */
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memmove(s2 + 2 - d_exp - len, s2, (size_t)len);
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s2[0] = '0';
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s2[1] = '.';
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for (i = 2; i < 2-d_exp-len; ++i) s2[i] = '0';
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len += i;
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}
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else if (d_exp < 0 && len > 1) /* Add decimal point? */
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{
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for(i = 0; i < decimals; ++i) s2[len-i] = s2[len-i-1];
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s2[len++ - decimals] = '.';
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d_exp += decimals;
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/* Need scientific notation as well? */
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if (d_exp != 0) { s2[len++] = 'e'; len += grisu3_i_to_str(d_exp, s2+len); }
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}
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/* Add scientific notation? */
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else if (d_exp < 0 || d_exp > 2) { s2[len++] = 'e'; len += grisu3_i_to_str(d_exp, s2+len); }
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/* Add zeroes instead of scientific notation? */
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else if (d_exp > 0) { while(d_exp-- > 0) s2[len++] = '0'; }
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s2[len] = '\0'; /* grisu3 doesn't null terminate, so ensure termination. */
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return (int)(s2+len-dst);
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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_PRINT_H */
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