grisu3.c

#include <math.h>
#include "grisu3.h"

/* This code is part of an implementation of the "grisu3" double to string
	conversion algorithm described in the research paper

	"Printing Floating-Point Numbers Quickly And Accurately with Integers"
	by Florian Loitsch, available at
	http://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf */

/* This grisu3 implementation is used by doubletoa() in MPFR.xs              */

/* See grisu3.h for definition of symbols and types                          */

static const power pow_cache[] =
{
  { 0xfa8fd5a0081c0288ULL, -1220, -348 },
  { 0xbaaee17fa23ebf76ULL, -1193, -340 },
  { 0x8b16fb203055ac76ULL, -1166, -332 },
  { 0xcf42894a5dce35eaULL, -1140, -324 },
  { 0x9a6bb0aa55653b2dULL, -1113, -316 },
  { 0xe61acf033d1a45dfULL, -1087, -308 },
  { 0xab70fe17c79ac6caULL, -1060, -300 },
  { 0xff77b1fcbebcdc4fULL, -1034, -292 },
  { 0xbe5691ef416bd60cULL, -1007, -284 },
  { 0x8dd01fad907ffc3cULL,  -980, -276 },
  { 0xd3515c2831559a83ULL,  -954, -268 },
  { 0x9d71ac8fada6c9b5ULL,  -927, -260 },
  { 0xea9c227723ee8bcbULL,  -901, -252 },
  { 0xaecc49914078536dULL,  -874, -244 },
  { 0x823c12795db6ce57ULL,  -847, -236 },
  { 0xc21094364dfb5637ULL,  -821, -228 },
  { 0x9096ea6f3848984fULL,  -794, -220 },
  { 0xd77485cb25823ac7ULL,  -768, -212 },
  { 0xa086cfcd97bf97f4ULL,  -741, -204 },
  { 0xef340a98172aace5ULL,  -715, -196 },
  { 0xb23867fb2a35b28eULL,  -688, -188 },
  { 0x84c8d4dfd2c63f3bULL,  -661, -180 },
  { 0xc5dd44271ad3cdbaULL,  -635, -172 },
  { 0x936b9fcebb25c996ULL,  -608, -164 },
  { 0xdbac6c247d62a584ULL,  -582, -156 },
  { 0xa3ab66580d5fdaf6ULL,  -555, -148 },
  { 0xf3e2f893dec3f126ULL,  -529, -140 },
  { 0xb5b5ada8aaff80b8ULL,  -502, -132 },
  { 0x87625f056c7c4a8bULL,  -475, -124 },
  { 0xc9bcff6034c13053ULL,  -449, -116 },
  { 0x964e858c91ba2655ULL,  -422, -108 },
  { 0xdff9772470297ebdULL,  -396, -100 },
  { 0xa6dfbd9fb8e5b88fULL,  -369,  -92 },
  { 0xf8a95fcf88747d94ULL,  -343,  -84 },
  { 0xb94470938fa89bcfULL,  -316,  -76 },
  { 0x8a08f0f8bf0f156bULL,  -289,  -68 },
  { 0xcdb02555653131b6ULL,  -263,  -60 },
  { 0x993fe2c6d07b7facULL,  -236,  -52 },
  { 0xe45c10c42a2b3b06ULL,  -210,  -44 },
  { 0xaa242499697392d3ULL,  -183,  -36 },
  { 0xfd87b5f28300ca0eULL,  -157,  -28 },
  { 0xbce5086492111aebULL,  -130,  -20 },
  { 0x8cbccc096f5088ccULL,  -103,  -12 },
  { 0xd1b71758e219652cULL,   -77,   -4 },
  { 0x9c40000000000000ULL,   -50,    4 },
  { 0xe8d4a51000000000ULL,   -24,   12 },
  { 0xad78ebc5ac620000ULL,     3,   20 },
  { 0x813f3978f8940984ULL,    30,   28 },
  { 0xc097ce7bc90715b3ULL,    56,   36 },
  { 0x8f7e32ce7bea5c70ULL,    83,   44 },
  { 0xd5d238a4abe98068ULL,   109,   52 },
  { 0x9f4f2726179a2245ULL,   136,   60 },
  { 0xed63a231d4c4fb27ULL,   162,   68 },
  { 0xb0de65388cc8ada8ULL,   189,   76 },
  { 0x83c7088e1aab65dbULL,   216,   84 },
  { 0xc45d1df942711d9aULL,   242,   92 },
  { 0x924d692ca61be758ULL,   269,  100 },
  { 0xda01ee641a708deaULL,   295,  108 },
  { 0xa26da3999aef774aULL,   322,  116 },
  { 0xf209787bb47d6b85ULL,   348,  124 },
  { 0xb454e4a179dd1877ULL,   375,  132 },
  { 0x865b86925b9bc5c2ULL,   402,  140 },
  { 0xc83553c5c8965d3dULL,   428,  148 },
  { 0x952ab45cfa97a0b3ULL,   455,  156 },
  { 0xde469fbd99a05fe3ULL,   481,  164 },
  { 0xa59bc234db398c25ULL,   508,  172 },
  { 0xf6c69a72a3989f5cULL,   534,  180 },
  { 0xb7dcbf5354e9beceULL,   561,  188 },
  { 0x88fcf317f22241e2ULL,   588,  196 },
  { 0xcc20ce9bd35c78a5ULL,   614,  204 },
  { 0x98165af37b2153dfULL,   641,  212 },
  { 0xe2a0b5dc971f303aULL,   667,  220 },
  { 0xa8d9d1535ce3b396ULL,   694,  228 },
  { 0xfb9b7cd9a4a7443cULL,   720,  236 },
  { 0xbb764c4ca7a44410ULL,   747,  244 },
  { 0x8bab8eefb6409c1aULL,   774,  252 },
  { 0xd01fef10a657842cULL,   800,  260 },
  { 0x9b10a4e5e9913129ULL,   827,  268 },
  { 0xe7109bfba19c0c9dULL,   853,  276 },
  { 0xac2820d9623bf429ULL,   880,  284 },
  { 0x80444b5e7aa7cf85ULL,   907,  292 },
  { 0xbf21e44003acdd2dULL,   933,  300 },
  { 0x8e679c2f5e44ff8fULL,   960,  308 },
  { 0xd433179d9c8cb841ULL,   986,  316 },
  { 0x9e19db92b4e31ba9ULL,  1013,  324 },
  { 0xeb96bf6ebadf77d9ULL,  1039,  332 },
  { 0xaf87023b9bf0ee6bULL,  1066,  340 }
};

/* pow10_cache[i] = 10^(i-1) */
static const unsigned int pow10_cache[] =
{ 0, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 };

static int cached_pow(int exp, diy_fp *p) {
  int k = (int)ceil((exp+DIYFP_FRACT_SIZE-1) * D_1_LOG2_10);
  int i = (k-MIN_CACHED_EXP-1) / CACHED_EXP_STEP + 1;
  p->f = pow_cache[i].fract;
  p->e = pow_cache[i].b_exp;
  return pow_cache[i].d_exp;
}

static diy_fp minus(diy_fp x, diy_fp y) {
  diy_fp d; d.f = x.f - y.f; d.e = x.e;
#ifdef DTOA_ASSERT
  if(x.e != y.e) croak("x.e != y.e");
  if(x.f < y.f) croak("x.f < y.f");
  /* assert(x.e == y.e && x.f >= y.f); */
#endif
  return d;
}

static diy_fp multiply(diy_fp x, diy_fp y) {
  uint64_t a, b, c, d, ac, bc, ad, bd, tmp;
  diy_fp r;
  a = x.f >> 32; b = x.f & MASK32;
  c = y.f >> 32; d = y.f & MASK32;
  ac = a*c; bc = b*c;
  ad = a*d; bd = b*d;
  tmp = (bd >> 32) + (ad & MASK32) + (bc & MASK32);
  tmp += 1U << 31; /* round */
  r.f = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32);
  r.e = x.e + y.e + 64;
  return r;
}

static diy_fp normalize_diy_fp(diy_fp n) {
#ifdef DTOA_ASSERT
  if(n.f == 0) croak("n.f == 0");
  /* assert(n.f != 0); */
#endif
  while(!(n.f & 0xFFC0000000000000ULL)) { n.f <<= 10; n.e -= 10; }
  while(!(n.f & D64_SIGN)) { n.f <<= 1; --n.e; }
  return n;
}

static diy_fp double2diy_fp(double d) {
  diy_fp fp;
  uint64_t u64 = CAST_U64(d);
  if(!(u64 & D64_EXP_MASK)) { fp.f = u64 & D64_FRACT_MASK; fp.e = 1 - D64_EXP_BIAS; }
  else { fp.f = (u64 & D64_FRACT_MASK) + D64_IMPLICIT_ONE; fp.e = (int)((u64 & D64_EXP_MASK) >> D64_EXP_POS) - D64_EXP_BIAS; }
  return fp;
}

static int largest_pow10(uint32_t n, int n_bits, uint32_t *power) {
  int guess = ((n_bits + 1) * 1233 >> 12) + 1/*skip first entry*/;
  if(n < pow10_cache[guess]) --guess; /* We don't have any guarantees that 2^n_bits <= n. */
  *power = pow10_cache[guess];
  return guess;
}

static int round_weed(char *buffer, int len, uint64_t wp_W, uint64_t delta, uint64_t rest, uint64_t ten_kappa, uint64_t ulp) {
  uint64_t wp_Wup = wp_W - ulp;
  uint64_t wp_Wdown = wp_W + ulp;
  while(rest < wp_Wup && delta - rest >= ten_kappa && (rest + ten_kappa < wp_Wup || wp_Wup - rest >= rest + ten_kappa - wp_Wup)) {
    --buffer[len-1];
    rest += ten_kappa;
  }
  if(rest < wp_Wdown && delta - rest >= ten_kappa && (rest + ten_kappa < wp_Wdown || wp_Wdown - rest > rest + ten_kappa - wp_Wdown))
    return 0;

  return 2*ulp <= rest && rest <= delta - 4*ulp;
}

static int digit_gen(diy_fp low, diy_fp w, diy_fp high, char *buffer, int *length, int *kappa) {
  uint64_t unit = 1;
  diy_fp too_low = { low.f - unit, low.e };
  diy_fp too_high = { high.f + unit, high.e };
  diy_fp unsafe_interval = minus(too_high, too_low);
  diy_fp one = { 1ULL << -w.e, w.e };
  uint32_t p1 = (uint32_t)(too_high.f >> -one.e);
  uint64_t p2 = too_high.f & (one.f - 1);
  uint32_t div;
  *kappa = largest_pow10(p1, DIYFP_FRACT_SIZE + one.e, &div);
  *length = 0;

  while(*kappa > 0) {
    uint64_t rest;
    int digit = p1 / div;
    buffer[*length] = (char)('0' + digit);
    ++*length;
    p1 %= div;
    --*kappa;
    rest = ((uint64_t)p1 << -one.e) + p2;
    if (rest < unsafe_interval.f) return round_weed(buffer, *length, minus(too_high, w).f, unsafe_interval.f, rest, (uint64_t)div << -one.e, unit);
    div /= 10;
  }

  for(;;) {
    int digit;
    p2 *= 10;
    unit *= 10;
    unsafe_interval.f *= 10;
    /* Integer division by one. */
    digit = (int)(p2 >> -one.e);
    buffer[*length] = (char)('0' + digit);
    ++*length;
    p2 &= one.f - 1;  /* Modulo by one. */
    --*kappa;
    if (p2 < unsafe_interval.f) return round_weed(buffer, *length, minus(too_high, w).f * unit, unsafe_interval.f, p2, one.f, unit);
  }
}

int grisu3(double v, char *buffer, int *length, int *d_exp) {
  int mk, kappa, success;
  diy_fp dfp = double2diy_fp(v);
  diy_fp w = normalize_diy_fp(dfp);

  /* normalize boundaries */
  diy_fp t = { (dfp.f << 1) + 1, dfp.e - 1 };
  diy_fp b_plus = normalize_diy_fp(t);
  diy_fp b_minus;
  diy_fp c_mk; /* Cached power of ten: 10^-k */
  uint64_t u64 = CAST_U64(v);
#ifdef DTOA_ASSERT
  if(v <= 0)
    croak("v <= 0, but Grisu only handles strictly positive finite numbers");
  if(v > 1.7976931348623157e308)
    croak("v > 1.7976931348623157e308, but Grisu only handles strictly positive finite numbers");
  /* assert(v > 0 && v <= 1.7976931348623157e308); *//* Grisu only handles strictly positive finite numbers. */
#endif
  if (!(u64 & D64_FRACT_MASK) && (u64 & D64_EXP_MASK) != 0) { b_minus.f = (dfp.f << 2) - 1; b_minus.e =  dfp.e - 2;} /* lower boundary is closer? */
  else { b_minus.f = (dfp.f << 1) - 1; b_minus.e = dfp.e - 1; }
  b_minus.f = b_minus.f << (b_minus.e - b_plus.e);
  b_minus.e = b_plus.e;

  mk = cached_pow(MIN_TARGET_EXP - DIYFP_FRACT_SIZE - w.e, &c_mk);

  w = multiply(w, c_mk);
  b_minus = multiply(b_minus, c_mk);
  b_plus  = multiply(b_plus,  c_mk);

  success = digit_gen(b_minus, w, b_plus, buffer, length, &kappa);
  *d_exp = kappa - mk;
  return success;
}

int i_to_str(int val, char *str) {
  int len, i;
  char *s;
  char *begin = str;

  if(val < 0) {
    *str++ = '-';
    val = -val;
    if(val < 10) *str++ = '0';
  }
  else { if (val) *str++ = '+'; }
  s = str;

  for(;;) {
    int ni = val / 10;
    int digit = val - ni*10;
    *s++ = (char)('0' + digit);
    if(ni == 0) break;
    val = ni;
  }

  *s = '\0';
  len = (int)(s - str);
  for(i = 0; i < len/2; ++i) {
    char ch = str[i];
    str[i] = str[len-1-i];
    str[len-1-i] = ch;
  }

  return (int)(s - begin);
}