374 lines
9.4 KiB
C
374 lines
9.4 KiB
C
/* fpconv_dtoa.c -- floating point conversion utilities.
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*
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* Fast and accurate double to string conversion based on Florian Loitsch's
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* Grisu-algorithm[1].
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*
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* [1] https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf
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* ----------------------------------------------------------------------------
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*
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* Copyright (c) 2013-2019, night-shift <as.smljk at gmail dot com>
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* Copyright (c) 2009, Florian Loitsch < florian.loitsch at inria dot fr >
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* All rights reserved.
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*
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* Boost Software License - Version 1.0 - August 17th, 2003
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*
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* Permission is hereby granted, free of charge, to any person or organization
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* obtaining a copy of the software and accompanying documentation covered by
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* this license (the "Software") to use, reproduce, display, distribute,
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* execute, and transmit the Software, and to prepare derivative works of the
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* Software, and to permit third-parties to whom the Software is furnished to
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* do so, all subject to the following:
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*
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* The copyright notices in the Software and this entire statement, including
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* the above license grant, this restriction and the following disclaimer,
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* must be included in all copies of the Software, in whole or in part, and
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* all derivative works of the Software, unless such copies or derivative
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* works are solely in the form of machine-executable object code generated by
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* a source language processor.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
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* SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
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* FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
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* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
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* DEALINGS IN THE SOFTWARE.
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*/
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#include "fpconv_dtoa.h"
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#include "fpconv_powers.h"
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#include <stdbool.h>
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#include <string.h>
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#define fracmask 0x000FFFFFFFFFFFFFU
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#define expmask 0x7FF0000000000000U
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#define hiddenbit 0x0010000000000000U
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#define signmask 0x8000000000000000U
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#define expbias (1023 + 52)
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#define absv(n) ((n) < 0 ? -(n) : (n))
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#define minv(a, b) ((a) < (b) ? (a) : (b))
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static uint64_t tens[] = { 10000000000000000000U,
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1000000000000000000U,
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100000000000000000U,
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10000000000000000U,
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1000000000000000U,
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100000000000000U,
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10000000000000U,
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1000000000000U,
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100000000000U,
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10000000000U,
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1000000000U,
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100000000U,
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10000000U,
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1000000U,
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100000U,
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10000U,
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1000U,
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100U,
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10U,
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1U };
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static inline uint64_t get_dbits(double d) {
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union
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{
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double dbl;
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uint64_t i;
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} dbl_bits = { d };
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return dbl_bits.i;
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}
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static Fp build_fp(double d) {
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uint64_t bits = get_dbits(d);
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Fp fp;
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fp.frac = bits & fracmask;
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fp.exp = (bits & expmask) >> 52;
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if (fp.exp) {
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fp.frac += hiddenbit;
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fp.exp -= expbias;
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} else {
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fp.exp = -expbias + 1;
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}
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return fp;
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}
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static void normalize(Fp *fp) {
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while ((fp->frac & hiddenbit) == 0) {
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fp->frac <<= 1;
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fp->exp--;
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}
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int shift = 64 - 52 - 1;
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fp->frac <<= shift;
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fp->exp -= shift;
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}
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static void get_normalized_boundaries(Fp *fp, Fp *lower, Fp *upper) {
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upper->frac = (fp->frac << 1) + 1;
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upper->exp = fp->exp - 1;
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while ((upper->frac & (hiddenbit << 1)) == 0) {
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upper->frac <<= 1;
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upper->exp--;
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}
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int u_shift = 64 - 52 - 2;
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upper->frac <<= u_shift;
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upper->exp = upper->exp - u_shift;
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int l_shift = fp->frac == hiddenbit ? 2 : 1;
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lower->frac = (fp->frac << l_shift) - 1;
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lower->exp = fp->exp - l_shift;
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lower->frac <<= lower->exp - upper->exp;
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lower->exp = upper->exp;
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}
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static Fp multiply(Fp *a, Fp *b) {
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const uint64_t lomask = 0x00000000FFFFFFFF;
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uint64_t ah_bl = (a->frac >> 32) * (b->frac & lomask);
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uint64_t al_bh = (a->frac & lomask) * (b->frac >> 32);
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uint64_t al_bl = (a->frac & lomask) * (b->frac & lomask);
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uint64_t ah_bh = (a->frac >> 32) * (b->frac >> 32);
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uint64_t tmp = (ah_bl & lomask) + (al_bh & lomask) + (al_bl >> 32);
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/* round up */
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tmp += 1U << 31;
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Fp fp = { ah_bh + (ah_bl >> 32) + (al_bh >> 32) + (tmp >> 32), a->exp + b->exp + 64 };
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return fp;
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}
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static void round_digit(char *digits,
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int ndigits,
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uint64_t delta,
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uint64_t rem,
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uint64_t kappa,
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uint64_t frac) {
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while (rem < frac && delta - rem >= kappa &&
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(rem + kappa < frac || frac - rem > rem + kappa - frac)) {
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digits[ndigits - 1]--;
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rem += kappa;
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}
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}
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static int generate_digits(Fp *fp, Fp *upper, Fp *lower, char *digits, int *K) {
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uint64_t wfrac = upper->frac - fp->frac;
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uint64_t delta = upper->frac - lower->frac;
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Fp one;
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one.frac = 1ULL << -upper->exp;
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one.exp = upper->exp;
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uint64_t part1 = upper->frac >> -one.exp;
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uint64_t part2 = upper->frac & (one.frac - 1);
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int idx = 0, kappa = 10;
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uint64_t *divp;
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/* 1000000000 */
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for (divp = tens + 10; kappa > 0; divp++) {
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uint64_t div = *divp;
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unsigned digit = part1 / div;
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if (digit || idx) {
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digits[idx++] = digit + '0';
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}
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part1 -= digit * div;
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kappa--;
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uint64_t tmp = (part1 << -one.exp) + part2;
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if (tmp <= delta) {
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*K += kappa;
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round_digit(digits, idx, delta, tmp, div << -one.exp, wfrac);
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return idx;
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}
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}
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/* 10 */
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uint64_t *unit = tens + 18;
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while (true) {
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part2 *= 10;
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delta *= 10;
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kappa--;
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unsigned digit = part2 >> -one.exp;
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if (digit || idx) {
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digits[idx++] = digit + '0';
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}
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part2 &= one.frac - 1;
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if (part2 < delta) {
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*K += kappa;
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round_digit(digits, idx, delta, part2, one.frac, wfrac * *unit);
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return idx;
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}
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unit--;
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}
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}
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static int grisu2(double d, char *digits, int *K) {
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Fp w = build_fp(d);
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Fp lower, upper;
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get_normalized_boundaries(&w, &lower, &upper);
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normalize(&w);
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int k;
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Fp cp = find_cachedpow10(upper.exp, &k);
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w = multiply(&w, &cp);
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upper = multiply(&upper, &cp);
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lower = multiply(&lower, &cp);
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lower.frac++;
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upper.frac--;
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*K = -k;
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return generate_digits(&w, &upper, &lower, digits, K);
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}
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static int emit_digits(char *digits, int ndigits, char *dest, int K, bool neg) {
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int exp = absv(K + ndigits - 1);
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/* write plain integer */
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if (K >= 0 && (exp < (ndigits + 7))) {
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memcpy(dest, digits, ndigits);
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memset(dest + ndigits, '0', K);
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return ndigits + K;
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}
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/* write decimal w/o scientific notation */
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if (K < 0 && (K > -7 || exp < 4)) {
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int offset = ndigits - absv(K);
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/* fp < 1.0 -> write leading zero */
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if (offset <= 0) {
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offset = -offset;
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dest[0] = '0';
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dest[1] = '.';
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memset(dest + 2, '0', offset);
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memcpy(dest + offset + 2, digits, ndigits);
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return ndigits + 2 + offset;
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/* fp > 1.0 */
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} else {
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memcpy(dest, digits, offset);
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dest[offset] = '.';
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memcpy(dest + offset + 1, digits + offset, ndigits - offset);
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return ndigits + 1;
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}
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}
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/* write decimal w/ scientific notation */
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ndigits = minv(ndigits, 18 - neg);
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int idx = 0;
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dest[idx++] = digits[0];
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if (ndigits > 1) {
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dest[idx++] = '.';
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memcpy(dest + idx, digits + 1, ndigits - 1);
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idx += ndigits - 1;
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}
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dest[idx++] = 'e';
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char sign = K + ndigits - 1 < 0 ? '-' : '+';
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dest[idx++] = sign;
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int cent = 0;
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if (exp > 99) {
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cent = exp / 100;
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dest[idx++] = cent + '0';
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exp -= cent * 100;
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}
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if (exp > 9) {
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int dec = exp / 10;
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dest[idx++] = dec + '0';
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exp -= dec * 10;
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} else if (cent) {
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dest[idx++] = '0';
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}
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dest[idx++] = exp % 10 + '0';
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return idx;
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}
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static int filter_special(double fp, char *dest) {
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if (fp == 0.0) {
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dest[0] = '0';
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return 1;
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}
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uint64_t bits = get_dbits(fp);
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bool nan = (bits & expmask) == expmask;
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if (!nan) {
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return 0;
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}
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if (bits & fracmask) {
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dest[0] = 'n';
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dest[1] = 'a';
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dest[2] = 'n';
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} else {
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dest[0] = 'i';
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dest[1] = 'n';
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dest[2] = 'f';
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}
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return 3;
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}
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int fpconv_dtoa(double d, char dest[24]) {
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char digits[18];
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int str_len = 0;
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bool neg = false;
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if (get_dbits(d) & signmask) {
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dest[0] = '-';
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str_len++;
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neg = true;
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}
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int spec = filter_special(d, dest + str_len);
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if (spec) {
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return str_len + spec;
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}
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int K = 0;
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int ndigits = grisu2(d, digits, &K);
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str_len += emit_digits(digits, ndigits, dest + str_len, K, neg);
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return str_len;
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}
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