[ruby/json] Faster float formatting

This commit provides an alternative implementation for a float → decimal conversion.

It integrates a C implementation of Fabian Loitsch's Grisu-algorithm [[pdf]](http://florian.loitsch.com/publications/dtoa-pldi2010.pdf), extracted from https://github.com/night-shift/fpconv. The relevant files are added in this PR, they are, as is all of https://github.com/night-shift/fpconv, available under a MIT License.

As a result, I see a speedup of 900% on Apple Silicon M1 for a float set of benchmarks.

floats don't have a single correct  string representation: a float like `1000.0` can be represented as "1000", "1e3", "1000.0" (and more).

The Grisu algorithm converts floating point numbers to an optimal decimal string representation without loss of precision. As a result, a float that is exactly an integer (like `Float(10)`) will be converted by that algorithm into `"10"`. While technically correct – the JSON format treats floats and integers identically –, this differs from the current behaviour of the `"json"` gem. To address this, the integration checks for that case, and explicitely adds a ".0" suffix in those cases.

This is sufficient to meet all existing tests; there is, however, a chance that the current implementation and this implementation occasionally encode floats differently.

```
== Encoding floats (4179311 bytes)
ruby 3.4.1 (2024-12-25 revision ruby/json@48d4efcb85) +YJIT +PRISM [arm64-darwin24]
Warming up --------------------------------------
        json (local)     4.000 i/100ms
Calculating -------------------------------------
        json (local)     46.046 (± 2.2%) i/s   (21.72 ms/i) -    232.000 in   5.039611s

Normalize to 2090234 byte
== Encoding floats (4179242 bytes)
ruby 3.4.1 (2024-12-25 revision ruby/json@48d4efcb85) +YJIT +PRISM [arm64-darwin24]
Warming up --------------------------------------
       json (2.10.2)     1.000 i/100ms
Calculating -------------------------------------
       json (2.10.2)      4.614 (± 0.0%) i/s  (216.74 ms/i) -     24.000 in   5.201871s
```

These benchmarks are run via a script ([link](https://gist.github.com/radiospiel/04019402726a28b31616df3d0c17bd1c)) which is based on the gem's `benchmark/encoder.rb` file. There are probably better ways to run benchmarks :) My version allows to combine multiple test cases into a single one.

The `dumps` benchmark, which covers the JSON files in `benchmark/data/*.json` – with the exception of `canada.json` – , reported a minor speedup within statistical uncertainty.

ruby/json@7d77415108

Author: radiospiel

ext/json/ext/vendor/fpconv/README.md

@@ -0,0 +1,3 @@
+The contents of this directory is extracted from https://github.com/night-shift/fpconv
+
+It is licensed under the provisions of the Boost Software License - Version 1.0 - August 17th, 2003. See the ./license file for details.

ext/json/ext/vendor/fpconv/license

@@ -0,0 +1,23 @@
+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.

ext/json/ext/vendor/fpconv/src/fpconv.c

@@ -0,0 +1,339 @@
+#include <stdbool.h>
+#include <string.h>
+
+#include "fpconv.h"
+#include "powers.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 = (unsigned) (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 = (unsigned) (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);
+
+    int max_trailing_zeros = 7;
+
+    if(neg) {
+        max_trailing_zeros -= 1;
+    }
+
+    /* write plain integer */
+    if(K >= 0 && (exp < (ndigits + max_trailing_zeros))) {
+
+        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;
+}