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tippecanoe/milo/dtoa_milo.h
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Claude 7127e49c86 Replace the Grisu2 float formatter with a C++ port of rsc/fpfmt 
Tippecanoe formatted every double it wrote through milo::dtoa_milo, a
vendored Grisu2. Grisu2 is fast, but it guarantees neither the shortest
digit string nor the correctly rounded one: it only guarantees that what
it prints parses back to the value it came from. In practice it prints a
digit more than necessary about 0.16% of the time, and picks a neighbor
of the correctly rounded digits about 32% of the time.

This ports Russ Cox's fpfmt (https://github.com/rsc/fpfmt) to C++ in
fpfmt/ and formats through it instead. fpfmt is both shortest and
correctly rounded, and it is faster:

  full std::string formatting     Grisu2      fpfmt   speedup
  random bit patterns          156.62 ns   66.83 ns     2.34x
  geo coordinates              124.07 ns   58.62 ns     2.12x
  short decimals                69.37 ns   49.16 ns     1.41x
  small integers                44.18 ns   38.06 ns     1.16x

  digit generation only           Grisu2      fpfmt   speedup
  random bit patterns           90.07 ns   20.81 ns     4.33x
  geo coordinates               80.64 ns   20.18 ns     4.00x
  short decimals                55.61 ns   21.90 ns     2.54x
  small integers                40.23 ns   22.50 ns     1.79x

(Intel Xeon @ 2.80GHz, g++ 13.3 -O3. `make fpfmt-bench` reproduces this,
and `./fpfmt-bench -check` reruns the correctness sweep, which is why
milo/dtoa_milo.h is kept even though nothing links it any more.)

The port is deliberately literal, so it can be diffed against fpfmt.go.
Its Short() agrees bit for bit with the Go original's on 445,640 values
covering powers of ten, small integers and reciprocals, subnormals, and
random bit patterns. Over 38.5 million values, fpfmt::dtoa always round
trips, is never longer than Grisu2's output, and is shorter 61,329 times.

Output is otherwise formatted exactly as before, including the choice
between plain and exponential notation, so 26 expected test outputs
change: some numbers lose digits (-26.170044999999999 becomes
-26.170045), and some have a corrected final digit (9.823748927348929e+55
becomes 9.823748927348928e+55). Every changed token was checked to parse
back to the identical double; none of the values themselves moved.

milo/milo.h, whose only job was to declare the C shim jsonpull calls, is
replaced by fpfmt/fpfmt.h, and the shim is renamed dtoa_shortest.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_014wJRAuhMninQE4wK2TUfuZ
2026-08-31 00:22:35 +00:00

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// Grisu2, from https://github.com/miloyip/dtoa-benchmark.
//
// Tippecanoe no longer formats numbers with this; fpfmt::dtoa() (fpfmt/) has
// replaced it. The header is kept only as the baseline for fpfmt/bench.cpp,
// so the correctness and speed comparison between the two stays reproducible.
#pragma once
#include <assert.h>
#include <math.h>
#include <cmath>
#if defined(_MSC_VER)
#include "msinttypes/stdint.h"
#include <intrin.h>
#else
#include <stdint.h>
#endif
namespace milo {
#define UINT64_C2(h, l) ((static_cast<uint64_t>(h) << 32) | static_cast<uint64_t>(l))
struct DiyFp {
DiyFp() {}
DiyFp(uint64_t ff, int ee) : f(ff), e(ee) {}
DiyFp(double d) {
union {
double d;
uint64_t u64;
} u = { d };
int biased_e = (u.u64 & kDpExponentMask) >> kDpSignificandSize;
uint64_t significand = (u.u64 & kDpSignificandMask);
if (biased_e != 0) {
f = significand + kDpHiddenBit;
e = biased_e - kDpExponentBias;
}
else {
f = significand;
e = kDpMinExponent + 1;
}
}
DiyFp operator-(const DiyFp& rhs) const {
assert(e == rhs.e);
assert(f >= rhs.f);
return DiyFp(f - rhs.f, e);
}
DiyFp operator*(const DiyFp& rhs) const {
#if defined(_MSC_VER) && defined(_M_AMD64)
uint64_t h;
uint64_t l = _umul128(f, rhs.f, &h);
if (l & (uint64_t(1) << 63)) // rounding
h++;
return DiyFp(h, e + rhs.e + 64);
#elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && defined(__x86_64__)
unsigned __int128 p = static_cast<unsigned __int128>(f) * static_cast<unsigned __int128>(rhs.f);
uint64_t h = p >> 64;
uint64_t l = static_cast<uint64_t>(p);
if (l & (uint64_t(1) << 63)) // rounding
h++;
return DiyFp(h, e + rhs.e + 64);
#else
const uint64_t M32 = 0xFFFFFFFF;
const uint64_t a = f >> 32;
const uint64_t b = f & M32;
const uint64_t c = rhs.f >> 32;
const uint64_t d = rhs.f & M32;
const uint64_t ac = a * c;
const uint64_t bc = b * c;
const uint64_t ad = a * d;
const uint64_t bd = b * d;
uint64_t tmp = (bd >> 32) + (ad & M32) + (bc & M32);
tmp += 1U << 31; /// mult_round
return DiyFp(ac + (ad >> 32) + (bc >> 32) + (tmp >> 32), e + rhs.e + 64);
#endif
}
DiyFp Normalize() const {
#if defined(_MSC_VER) && defined(_M_AMD64)
unsigned long index;
_BitScanReverse64(&index, f);
return DiyFp(f << (63 - index), e - (63 - index));
#elif defined(__GNUC__)
int s = __builtin_clzll(f);
return DiyFp(f << s, e - s);
#else
DiyFp res = *this;
while (!(res.f & kDpHiddenBit)) {
res.f <<= 1;
res.e--;
}
res.f <<= (kDiySignificandSize - kDpSignificandSize - 1);
res.e = res.e - (kDiySignificandSize - kDpSignificandSize - 1);
return res;
#endif
}
DiyFp NormalizeBoundary() const {
#if defined(_MSC_VER) && defined(_M_AMD64)
unsigned long index;
_BitScanReverse64(&index, f);
return DiyFp (f << (63 - index), e - (63 - index));
#else
DiyFp res = *this;
while (!(res.f & (kDpHiddenBit << 1))) {
res.f <<= 1;
res.e--;
}
res.f <<= (kDiySignificandSize - kDpSignificandSize - 2);
res.e = res.e - (kDiySignificandSize - kDpSignificandSize - 2);
return res;
#endif
}
void NormalizedBoundaries(DiyFp* minus, DiyFp* plus) const {
DiyFp pl = DiyFp((f << 1) + 1, e - 1).NormalizeBoundary();
DiyFp mi = (f == kDpHiddenBit) ? DiyFp((f << 2) - 1, e - 2) : DiyFp((f << 1) - 1, e - 1);
mi.f <<= mi.e - pl.e;
mi.e = pl.e;
*plus = pl;
*minus = mi;
}
static const int kDiySignificandSize = 64;
static const int kDpSignificandSize = 52;
static const int kDpExponentBias = 0x3FF + kDpSignificandSize;
static const int kDpMinExponent = -kDpExponentBias;
static const uint64_t kDpExponentMask = UINT64_C2(0x7FF00000, 0x00000000);
static const uint64_t kDpSignificandMask = UINT64_C2(0x000FFFFF, 0xFFFFFFFF);
static const uint64_t kDpHiddenBit = UINT64_C2(0x00100000, 0x00000000);
uint64_t f;
int e;
};
inline DiyFp GetCachedPower(int e, int* K) {
// 10^-348, 10^-340, ..., 10^340
static const uint64_t kCachedPowers_F[] = {
UINT64_C2(0xfa8fd5a0, 0x081c0288), UINT64_C2(0xbaaee17f, 0xa23ebf76),
UINT64_C2(0x8b16fb20, 0x3055ac76), UINT64_C2(0xcf42894a, 0x5dce35ea),
UINT64_C2(0x9a6bb0aa, 0x55653b2d), UINT64_C2(0xe61acf03, 0x3d1a45df),
UINT64_C2(0xab70fe17, 0xc79ac6ca), UINT64_C2(0xff77b1fc, 0xbebcdc4f),
UINT64_C2(0xbe5691ef, 0x416bd60c), UINT64_C2(0x8dd01fad, 0x907ffc3c),
UINT64_C2(0xd3515c28, 0x31559a83), UINT64_C2(0x9d71ac8f, 0xada6c9b5),
UINT64_C2(0xea9c2277, 0x23ee8bcb), UINT64_C2(0xaecc4991, 0x4078536d),
UINT64_C2(0x823c1279, 0x5db6ce57), UINT64_C2(0xc2109436, 0x4dfb5637),
UINT64_C2(0x9096ea6f, 0x3848984f), UINT64_C2(0xd77485cb, 0x25823ac7),
UINT64_C2(0xa086cfcd, 0x97bf97f4), UINT64_C2(0xef340a98, 0x172aace5),
UINT64_C2(0xb23867fb, 0x2a35b28e), UINT64_C2(0x84c8d4df, 0xd2c63f3b),
UINT64_C2(0xc5dd4427, 0x1ad3cdba), UINT64_C2(0x936b9fce, 0xbb25c996),
UINT64_C2(0xdbac6c24, 0x7d62a584), UINT64_C2(0xa3ab6658, 0x0d5fdaf6),
UINT64_C2(0xf3e2f893, 0xdec3f126), UINT64_C2(0xb5b5ada8, 0xaaff80b8),
UINT64_C2(0x87625f05, 0x6c7c4a8b), UINT64_C2(0xc9bcff60, 0x34c13053),
UINT64_C2(0x964e858c, 0x91ba2655), UINT64_C2(0xdff97724, 0x70297ebd),
UINT64_C2(0xa6dfbd9f, 0xb8e5b88f), UINT64_C2(0xf8a95fcf, 0x88747d94),
UINT64_C2(0xb9447093, 0x8fa89bcf), UINT64_C2(0x8a08f0f8, 0xbf0f156b),
UINT64_C2(0xcdb02555, 0x653131b6), UINT64_C2(0x993fe2c6, 0xd07b7fac),
UINT64_C2(0xe45c10c4, 0x2a2b3b06), UINT64_C2(0xaa242499, 0x697392d3),
UINT64_C2(0xfd87b5f2, 0x8300ca0e), UINT64_C2(0xbce50864, 0x92111aeb),
UINT64_C2(0x8cbccc09, 0x6f5088cc), UINT64_C2(0xd1b71758, 0xe219652c),
UINT64_C2(0x9c400000, 0x00000000), UINT64_C2(0xe8d4a510, 0x00000000),
UINT64_C2(0xad78ebc5, 0xac620000), UINT64_C2(0x813f3978, 0xf8940984),
UINT64_C2(0xc097ce7b, 0xc90715b3), UINT64_C2(0x8f7e32ce, 0x7bea5c70),
UINT64_C2(0xd5d238a4, 0xabe98068), UINT64_C2(0x9f4f2726, 0x179a2245),
UINT64_C2(0xed63a231, 0xd4c4fb27), UINT64_C2(0xb0de6538, 0x8cc8ada8),
UINT64_C2(0x83c7088e, 0x1aab65db), UINT64_C2(0xc45d1df9, 0x42711d9a),
UINT64_C2(0x924d692c, 0xa61be758), UINT64_C2(0xda01ee64, 0x1a708dea),
UINT64_C2(0xa26da399, 0x9aef774a), UINT64_C2(0xf209787b, 0xb47d6b85),
UINT64_C2(0xb454e4a1, 0x79dd1877), UINT64_C2(0x865b8692, 0x5b9bc5c2),
UINT64_C2(0xc83553c5, 0xc8965d3d), UINT64_C2(0x952ab45c, 0xfa97a0b3),
UINT64_C2(0xde469fbd, 0x99a05fe3), UINT64_C2(0xa59bc234, 0xdb398c25),
UINT64_C2(0xf6c69a72, 0xa3989f5c), UINT64_C2(0xb7dcbf53, 0x54e9bece),
UINT64_C2(0x88fcf317, 0xf22241e2), UINT64_C2(0xcc20ce9b, 0xd35c78a5),
UINT64_C2(0x98165af3, 0x7b2153df), UINT64_C2(0xe2a0b5dc, 0x971f303a),
UINT64_C2(0xa8d9d153, 0x5ce3b396), UINT64_C2(0xfb9b7cd9, 0xa4a7443c),
UINT64_C2(0xbb764c4c, 0xa7a44410), UINT64_C2(0x8bab8eef, 0xb6409c1a),
UINT64_C2(0xd01fef10, 0xa657842c), UINT64_C2(0x9b10a4e5, 0xe9913129),
UINT64_C2(0xe7109bfb, 0xa19c0c9d), UINT64_C2(0xac2820d9, 0x623bf429),
UINT64_C2(0x80444b5e, 0x7aa7cf85), UINT64_C2(0xbf21e440, 0x03acdd2d),
UINT64_C2(0x8e679c2f, 0x5e44ff8f), UINT64_C2(0xd433179d, 0x9c8cb841),
UINT64_C2(0x9e19db92, 0xb4e31ba9), UINT64_C2(0xeb96bf6e, 0xbadf77d9),
UINT64_C2(0xaf87023b, 0x9bf0ee6b)
};
static const int16_t kCachedPowers_E[] = {
-1220, -1193, -1166, -1140, -1113, -1087, -1060, -1034, -1007, -980,
-954, -927, -901, -874, -847, -821, -794, -768, -741, -715,
-688, -661, -635, -608, -582, -555, -529, -502, -475, -449,
-422, -396, -369, -343, -316, -289, -263, -236, -210, -183,
-157, -130, -103, -77, -50, -24, 3, 30, 56, 83,
109, 136, 162, 189, 216, 242, 269, 295, 322, 348,
375, 402, 428, 455, 481, 508, 534, 561, 588, 614,
641, 667, 694, 720, 747, 774, 800, 827, 853, 880,
907, 933, 960, 986, 1013, 1039, 1066
};
//int k = static_cast<int>(ceil((-61 - e) * 0.30102999566398114)) + 374;
double dk = (-61 - e) * 0.30102999566398114 + 347; // dk must be positive, so can do ceiling in positive
int k = static_cast<int>(dk);
if (k != dk)
k++;
unsigned index = static_cast<unsigned>((k >> 3) + 1);
*K = -(-348 + static_cast<int>(index << 3)); // decimal exponent no need lookup table
assert(index < sizeof(kCachedPowers_F) / sizeof(kCachedPowers_F[0]));
return DiyFp(kCachedPowers_F[index], kCachedPowers_E[index]);
}
inline void GrisuRound(std::string &buffer, int len, uint64_t delta, uint64_t rest, uint64_t ten_kappa, uint64_t wp_w) {
while (rest < wp_w && delta - rest >= ten_kappa &&
(rest + ten_kappa < wp_w || /// closer
wp_w - rest > rest + ten_kappa - wp_w)) {
buffer[len - 1]--;
rest += ten_kappa;
}
}
inline unsigned CountDecimalDigit32(uint32_t n) {
// Simple pure C++ implementation was faster than __builtin_clz version in this situation.
if (n < 10) return 1;
if (n < 100) return 2;
if (n < 1000) return 3;
if (n < 10000) return 4;
if (n < 100000) return 5;
if (n < 1000000) return 6;
if (n < 10000000) return 7;
if (n < 100000000) return 8;
if (n < 1000000000) return 9;
return 10;
}
inline void DigitGen(const DiyFp& W, const DiyFp& Mp, uint64_t delta, std::string &buffer, int* len, int* K) {
static const uint32_t kPow10[] = { 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 };
const DiyFp one(uint64_t(1) << -Mp.e, Mp.e);
const DiyFp wp_w = Mp - W;
uint32_t p1 = static_cast<uint32_t>(Mp.f >> -one.e);
uint64_t p2 = Mp.f & (one.f - 1);
int kappa = static_cast<int>(CountDecimalDigit32(p1));
*len = 0;
while (kappa > 0) {
uint32_t d;
switch (kappa) {
case 10: d = p1 / 1000000000; p1 %= 1000000000; break;
case 9: d = p1 / 100000000; p1 %= 100000000; break;
case 8: d = p1 / 10000000; p1 %= 10000000; break;
case 7: d = p1 / 1000000; p1 %= 1000000; break;
case 6: d = p1 / 100000; p1 %= 100000; break;
case 5: d = p1 / 10000; p1 %= 10000; break;
case 4: d = p1 / 1000; p1 %= 1000; break;
case 3: d = p1 / 100; p1 %= 100; break;
case 2: d = p1 / 10; p1 %= 10; break;
case 1: d = p1; p1 = 0; break;
default:
#if defined(_MSC_VER)
__assume(0);
#elif __GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 5)
__builtin_unreachable();
#else
d = 0;
#endif
}
if (d || *len) {
buffer.push_back('0' + static_cast<char>(d));
(*len)++;
}
kappa--;
uint64_t tmp = (static_cast<uint64_t>(p1) << -one.e) + p2;
if (tmp <= delta) {
*K += kappa;
GrisuRound(buffer, *len, delta, tmp, static_cast<uint64_t>(kPow10[kappa]) << -one.e, wp_w.f);
return;
}
}
// kappa = 0
for (;;) {
p2 *= 10;
delta *= 10;
char d = static_cast<char>(p2 >> -one.e);
if (d || *len) {
buffer.push_back('0' + d);
(*len)++;
}
p2 &= one.f - 1;
kappa--;
if (p2 < delta) {
*K += kappa;
int index = -static_cast<int>(kappa);
GrisuRound(buffer, *len, delta, p2, one.f, wp_w.f * (index < 9 ? kPow10[-static_cast<int>(kappa)] : 0));
return;
}
}
}
inline void Grisu2(double value, std::string &buffer, int* length, int* K) {
const DiyFp v(value);
DiyFp w_m, w_p;
v.NormalizedBoundaries(&w_m, &w_p);
const DiyFp c_mk = GetCachedPower(w_p.e, K);
const DiyFp W = v.Normalize() * c_mk;
DiyFp Wp = w_p * c_mk;
DiyFp Wm = w_m * c_mk;
Wm.f++;
Wp.f--;
DigitGen(W, Wp, Wp.f - Wm.f, buffer, length, K);
}
inline const char* GetDigitsLut() {
static const char cDigitsLut[200] = {
'0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
'1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
'2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
'3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
'4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
'5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
'6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
'7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
'8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
'9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
};
return cDigitsLut;
}
inline void WriteExponent(int K, std::string &buffer) {
if (K < 0) {
buffer.push_back('-');
K = -K;
} else {
buffer.push_back('+');
}
if (K >= 100) {
buffer.push_back('0' + static_cast<char>(K / 100));
K %= 100;
const char* d = GetDigitsLut() + K * 2;
buffer.push_back(d[0]);
buffer.push_back(d[1]);
}
else if (K >= 10) {
const char* d = GetDigitsLut() + K * 2;
buffer.push_back(d[0]);
buffer.push_back(d[1]);
}
else
buffer.push_back('0' + static_cast<char>(K));
}
inline void Prettify(std::string &buffer, int length, int k) {
const int kk = length + k; // 10^(kk-1) <= v < 10^kk
if (length <= kk && kk <= 21) {
// 1234e7 -> 12340000000
for (int i = length; i < kk; i++)
buffer.push_back('0');
}
else if (0 < kk && kk <= 21) {
// 1234e-2 -> 12.34
buffer.insert(buffer.begin() + kk, '.');
}
else if (-6 < kk && kk <= 0) {
// 1234e-6 -> 0.001234
const int offset = 2 - kk;
buffer.insert(buffer.begin(), '0');
buffer.insert(buffer.begin() + 1, '.');
for (int i = 2; i < offset; i++)
buffer.insert(buffer.begin() + 2, '0');
}
else if (length == 1) {
// 1e30
buffer.push_back('e');
WriteExponent(kk - 1, buffer);
}
else {
// 1234e30 -> 1.234e33
buffer.insert(buffer.begin() + 1, '.');
buffer.push_back('e');
WriteExponent(kk - 1, buffer);
}
}
inline std::string dtoa_milo(double value) {
std::string buffer;
if (std::isnan(value)) {
return "nan";
}
if (std::isinf(value)) {
if (value < 0) {
return "-inf";
} else {
return "inf";
}
}
if (value == 0) {
buffer = "0";
}
else {
bool minus = false;
if (value < 0) {
minus = true;
value = -value;
}
int length, K;
Grisu2(value, buffer, &length, &K);
Prettify(buffer, length, K);
if (minus) {
buffer.insert(buffer.begin(), '-');
}
}
return buffer;
}
}
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