fpconv_dtoa.c

/* fpconv_dtoa.c -- 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) 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 "fpconv_dtoa.h"

#include "fpconv_powers.h"

#include <stdbool.h>
#include <string.h>

#define fracmask 0x000FFFFFFFFFFFFFU
#define expmask 0x7FF0000000000000U
#define hiddenbit 0x0010000000000000U
#define signmask 0x8000000000000000U
#define expbias (1023 + 52)

#define absv(n) ((n) < 0 ? -(n) : (n))
#define minv(a, b) ((a) < (b) ? (a) : (b))

static uint64_t tens[] = { 10000000000000000000U,
                           1000000000000000000U,
                           100000000000000000U,
                           10000000000000000U,
                           1000000000000000U,
                           100000000000000U,
                           10000000000000U,
                           1000000000000U,
                           100000000000U,
                           10000000000U,
                           1000000000U,
                           100000000U,
                           10000000U,
                           1000000U,
                           100000U,
                           10000U,
                           1000U,
                           100U,
                           10U,
                           1U };

static inline uint64_t get_dbits(double d) {
    union
    {
        double dbl;
        uint64_t i;
    } dbl_bits = { d };

    return dbl_bits.i;
}

static Fp build_fp(double d) {
    uint64_t bits = get_dbits(d);

    Fp fp;
    fp.frac = bits & fracmask;
    fp.exp = (bits & expmask) >> 52;

    if (fp.exp) {
        fp.frac += hiddenbit;
        fp.exp -= expbias;

    } else {
        fp.exp = -expbias + 1;
    }

    return fp;
}

static void normalize(Fp *fp) {
    while ((fp->frac & hiddenbit) == 0) {
        fp->frac <<= 1;
        fp->exp--;
    }

    int shift = 64 - 52 - 1;
    fp->frac <<= shift;
    fp->exp -= shift;
}

static void get_normalized_boundaries(Fp *fp, Fp *lower, Fp *upper) {
    upper->frac = (fp->frac << 1) + 1;
    upper->exp = fp->exp - 1;

    while ((upper->frac & (hiddenbit << 1)) == 0) {
        upper->frac <<= 1;
        upper->exp--;
    }

    int u_shift = 64 - 52 - 2;

    upper->frac <<= u_shift;
    upper->exp = upper->exp - u_shift;

    int l_shift = fp->frac == hiddenbit ? 2 : 1;

    lower->frac = (fp->frac << l_shift) - 1;
    lower->exp = fp->exp - l_shift;

    lower->frac <<= lower->exp - upper->exp;
    lower->exp = upper->exp;
}

static Fp multiply(Fp *a, Fp *b) {
    const uint64_t lomask = 0x00000000FFFFFFFF;

    uint64_t ah_bl = (a->frac >> 32) * (b->frac & lomask);
    uint64_t al_bh = (a->frac & lomask) * (b->frac >> 32);
    uint64_t al_bl = (a->frac & lomask) * (b->frac & lomask);
    uint64_t ah_bh = (a->frac >> 32) * (b->frac >> 32);

    uint64_t tmp = (ah_bl & lomask) + (al_bh & lomask) + (al_bl >> 32);
    /* round up */
    tmp += 1U << 31;

    Fp fp = { ah_bh + (ah_bl >> 32) + (al_bh >> 32) + (tmp >> 32), a->exp + b->exp + 64 };

    return fp;
}

static void round_digit(char *digits,
                        int ndigits,
                        uint64_t delta,
                        uint64_t rem,
                        uint64_t kappa,
                        uint64_t frac) {
    while (rem < frac && delta - rem >= kappa &&
           (rem + kappa < frac || frac - rem > rem + kappa - frac)) {
        digits[ndigits - 1]--;
        rem += kappa;
    }
}

static int generate_digits(Fp *fp, Fp *upper, Fp *lower, char *digits, int *K) {
    uint64_t wfrac = upper->frac - fp->frac;
    uint64_t delta = upper->frac - lower->frac;

    Fp one;
    one.frac = 1ULL << -upper->exp;
    one.exp = upper->exp;

    uint64_t part1 = upper->frac >> -one.exp;
    uint64_t part2 = upper->frac & (one.frac - 1);

    int idx = 0, kappa = 10;
    uint64_t *divp;
    /* 1000000000 */
    for (divp = tens + 10; kappa > 0; divp++) {
        uint64_t div = *divp;
        unsigned digit = part1 / div;

        if (digit || idx) {
            digits[idx++] = digit + '0';
        }

        part1 -= digit * div;
        kappa--;

        uint64_t tmp = (part1 << -one.exp) + part2;
        if (tmp <= delta) {
            *K += kappa;
            round_digit(digits, idx, delta, tmp, div << -one.exp, wfrac);

            return idx;
        }
    }

    /* 10 */
    uint64_t *unit = tens + 18;

    while (true) {
        part2 *= 10;
        delta *= 10;
        kappa--;

        unsigned digit = part2 >> -one.exp;
        if (digit || idx) {
            digits[idx++] = digit + '0';
        }

        part2 &= one.frac - 1;
        if (part2 < delta) {
            *K += kappa;
            round_digit(digits, idx, delta, part2, one.frac, wfrac * *unit);

            return idx;
        }

        unit--;
    }
}

static int grisu2(double d, char *digits, int *K) {
    Fp w = build_fp(d);

    Fp lower, upper;
    get_normalized_boundaries(&w, &lower, &upper);

    normalize(&w);

    int k;
    Fp cp = find_cachedpow10(upper.exp, &k);

    w = multiply(&w, &cp);
    upper = multiply(&upper, &cp);
    lower = multiply(&lower, &cp);

    lower.frac++;
    upper.frac--;

    *K = -k;

    return generate_digits(&w, &upper, &lower, digits, K);
}

static int emit_digits(char *digits, int ndigits, char *dest, int K, bool neg) {
    int exp = absv(K + ndigits - 1);

    /* write plain integer */
    if (K >= 0 && (exp < (ndigits + 7))) {
        memcpy(dest, digits, ndigits);
        memset(dest + ndigits, '0', K);

        return ndigits + K;
    }

    /* write decimal w/o scientific notation */
    if (K < 0 && (K > -7 || exp < 4)) {
        int offset = ndigits - absv(K);
        /* fp < 1.0 -> write leading zero */
        if (offset <= 0) {
            offset = -offset;
            dest[0] = '0';
            dest[1] = '.';
            memset(dest + 2, '0', offset);
            memcpy(dest + offset + 2, digits, ndigits);

            return ndigits + 2 + offset;

            /* fp > 1.0 */
        } else {
            memcpy(dest, digits, offset);
            dest[offset] = '.';
            memcpy(dest + offset + 1, digits + offset, ndigits - offset);

            return ndigits + 1;
        }
    }

    /* write decimal w/ scientific notation */
    ndigits = minv(ndigits, 18 - neg);

    int idx = 0;
    dest[idx++] = digits[0];

    if (ndigits > 1) {
        dest[idx++] = '.';
        memcpy(dest + idx, digits + 1, ndigits - 1);
        idx += ndigits - 1;
    }

    dest[idx++] = 'e';

    char sign = K + ndigits - 1 < 0 ? '-' : '+';
    dest[idx++] = sign;

    int cent = 0;

    if (exp > 99) {
        cent = exp / 100;
        dest[idx++] = cent + '0';
        exp -= cent * 100;
    }
    if (exp > 9) {
        int dec = exp / 10;
        dest[idx++] = dec + '0';
        exp -= dec * 10;

    } else if (cent) {
        dest[idx++] = '0';
    }

    dest[idx++] = exp % 10 + '0';

    return idx;
}

static int filter_special(double fp, char *dest) {
    if (fp == 0.0) {
        dest[0] = '0';
        return 1;
    }

    uint64_t bits = get_dbits(fp);

    bool nan = (bits & expmask) == expmask;

    if (!nan) {
        return 0;
    }

    if (bits & fracmask) {
        dest[0] = 'n';
        dest[1] = 'a';
        dest[2] = 'n';

    } else {
        dest[0] = 'i';
        dest[1] = 'n';
        dest[2] = 'f';
    }

    return 3;
}

int fpconv_dtoa(double d, char dest[24]) {
    char digits[18];

    int str_len = 0;
    bool neg = false;

    if (get_dbits(d) & signmask) {
        dest[0] = '-';
        str_len++;
        neg = true;
    }

    int spec = filter_special(d, dest + str_len);

    if (spec) {
        return str_len + spec;
    }

    int K = 0;
    int ndigits = grisu2(d, digits, &K);

    str_len += emit_digits(digits, ndigits, dest + str_len, K, neg);

    return str_len;
}