155#ifdef WORDS_BIGENDIAN
156#define IEEE_BIG_ENDIAN
158#define IEEE_LITTLE_ENDIAN
163#undef IEEE_BIG_ENDIAN
164#undef IEEE_LITTLE_ENDIAN
167#if defined(__arm__) && !defined(__VFP_FP__)
168#define IEEE_BIG_ENDIAN
169#undef IEEE_LITTLE_ENDIAN
180#if (INT_MAX >> 30) && !(INT_MAX >> 31)
182#define ULong unsigned int
183#elif (LONG_MAX >> 30) && !(LONG_MAX >> 31)
185#define ULong unsigned long int
187#error No 32bit integer
190#if defined(HAVE_LONG_LONG) && (HAVE_LONG_LONG)
191#define Llong LONG_LONG
198#define Bug(x) {fprintf(stderr, "%s\n", (x)); exit(EXIT_FAILURE);}
203#define ISDIGIT(c) isdigit(c)
214extern void *MALLOC(
size_t);
219extern void FREE(
void*);
224#define NO_SANITIZE(x, y) y
228#undef Avoid_Underflow
229#ifdef IEEE_BIG_ENDIAN
232#ifdef IEEE_LITTLE_ENDIAN
240#define DBL_MAX_10_EXP 308
241#define DBL_MAX_EXP 1024
247#define DBL_MAX_10_EXP 75
248#define DBL_MAX_EXP 63
250#define DBL_MAX 7.2370055773322621e+75
255#define DBL_MAX_10_EXP 38
256#define DBL_MAX_EXP 127
258#define DBL_MAX 1.7014118346046923e+38
262#define LONG_MAX 2147483647
279static const char hexdigit[] =
"0123456789abcdef0123456789ABCDEF";
282#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1
283Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
286typedef union {
double d; ULong L[2]; }
U;
291# ifdef IEEE_LITTLE_ENDIAN
292# define word0(x) (((ULong *)&(x))[1])
293# define word1(x) (((ULong *)&(x))[0])
295# define word0(x) (((ULong *)&(x))[0])
296# define word1(x) (((ULong *)&(x))[1])
300# ifdef IEEE_LITTLE_ENDIAN
301# define word0(x) ((x).L[1])
302# define word1(x) ((x).L[0])
304# define word0(x) ((x).L[0])
305# define word1(x) ((x).L[1])
307# define dval(x) ((x).d)
314#if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
315#define Storeinc(a,b,c) (((unsigned short *)(a))[1] = (unsigned short)(b), \
316((unsigned short *)(a))[0] = (unsigned short)(c), (a)++)
318#define Storeinc(a,b,c) (((unsigned short *)(a))[0] = (unsigned short)(b), \
319((unsigned short *)(a))[1] = (unsigned short)(c), (a)++)
331#define Exp_msk1 0x100000
332#define Exp_msk11 0x100000
333#define Exp_mask 0x7ff00000
337#define Exp_1 0x3ff00000
338#define Exp_11 0x3ff00000
340#define Frac_mask 0xfffff
341#define Frac_mask1 0xfffff
344#define Bndry_mask 0xfffff
345#define Bndry_mask1 0xfffff
347#define Sign_bit 0x80000000
354#define Avoid_Underflow
356#undef Sudden_Underflow
362#define Flt_Rounds FLT_ROUNDS
368#ifdef Honor_FLT_ROUNDS
369#define Rounding rounding
370#undef Check_FLT_ROUNDS
371#define Check_FLT_ROUNDS
373#define Rounding Flt_Rounds
377#undef Check_FLT_ROUNDS
378#undef Honor_FLT_ROUNDS
380#undef Sudden_Underflow
381#define Sudden_Underflow
387#define Exp_msk1 0x1000000
388#define Exp_msk11 0x1000000
389#define Exp_mask 0x7f000000
392#define Exp_1 0x41000000
393#define Exp_11 0x41000000
395#define Frac_mask 0xffffff
396#define Frac_mask1 0xffffff
399#define Bndry_mask 0xefffff
400#define Bndry_mask1 0xffffff
402#define Sign_bit 0x80000000
404#define Tiny0 0x100000
414#define Exp_msk11 0x800000
415#define Exp_mask 0x7f80
418#define Exp_1 0x40800000
421#define Frac_mask 0x7fffff
422#define Frac_mask1 0xffff007f
425#define Bndry_mask 0xffff007f
426#define Bndry_mask1 0xffff007f
428#define Sign_bit 0x8000
442#define rounded_product(a,b) ((a) = rnd_prod((a), (b)))
443#define rounded_quotient(a,b) ((a) = rnd_quot((a), (b)))
444extern double rnd_prod(
double,
double), rnd_quot(
double,
double);
446#define rounded_product(a,b) ((a) *= (b))
447#define rounded_quotient(a,b) ((a) /= (b))
450#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
451#define Big1 0xffffffff
457#define FFFFFFFF 0xffffffffUL
471#define Llong long long
474#define ULLong unsigned Llong
478#define MULTIPLE_THREADS 1
480#ifndef MULTIPLE_THREADS
481#define ACQUIRE_DTOA_LOCK(n)
482#define FREE_DTOA_LOCK(n)
484#define ACQUIRE_DTOA_LOCK(n)
485#define FREE_DTOA_LOCK(n)
488#ifndef ATOMIC_PTR_CAS
489#define ATOMIC_PTR_CAS(var, old, new) ((var) = (new), (void *)(old))
495#define UNLIKELY(x) (x)
498#define ASSUME(x) (void)(x)
505 int k, maxwds, sign, wds;
518 rv = (
Bigint *)MALLOC(
sizeof(
Bigint) + (x-1)*
sizeof(ULong));
521 rv->sign = rv->wds = 0;
531#define Bcopy(x,y) memcpy((char *)&(x)->sign, (char *)&(y)->sign, \
532(y)->wds*sizeof(Long) + 2*sizeof(int))
535multadd(
Bigint *b,
int m,
int a)
555 y = *x * (ULLong)m + carry;
557 *x++ = (ULong)(y & FFFFFFFF);
561 y = (xi & 0xffff) * m + carry;
562 z = (xi >> 16) * m + (y >> 16);
564 *x++ = (z << 16) + (y & 0xffff);
573 if (wds >= b->maxwds) {
579 b->x[wds++] = (ULong)carry;
586s2b(
const char *s,
int nd0,
int nd, ULong y9)
593 for (k = 0, y = 1; x > y; y <<= 1, k++) ;
600 b->x[0] = y9 & 0xffff;
601 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
608 b = multadd(b, 10, *s++ -
'0');
615 b = multadd(b, 10, *s++ -
'0');
620hi0bits(
register ULong x)
624 if (!(x & 0xffff0000)) {
628 if (!(x & 0xff000000)) {
632 if (!(x & 0xf0000000)) {
636 if (!(x & 0xc0000000)) {
640 if (!(x & 0x80000000)) {
642 if (!(x & 0x40000000))
652 register ULong x = *y;
707 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
718 if (a->wds < b->wds) {
730 for (x = c->x, xa = x + wc; x < xa; x++)
738 for (; xb < xbe; xc0++) {
739 if ((y = *xb++) != 0) {
744 z = *x++ * (ULLong)y + *xc + carry;
746 *xc++ = (ULong)(z & FFFFFFFF);
753 for (; xb < xbe; xb++, xc0++) {
754 if ((y = *xb & 0xffff) != 0) {
759 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
761 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
767 if ((y = *xb >> 16) != 0) {
773 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
776 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
783 for (; xb < xbe; xc0++) {
789 z = *x++ * y + *xc + carry;
798 for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
811 static const int p05[3] = { 5, 25, 125 };
813 if ((i = k & 3) != 0)
814 b = multadd(b, p05[i-1], 0);
820 ACQUIRE_DTOA_LOCK(1);
824 p5tmp = ATOMIC_PTR_CAS(p5s, NULL, p5);
825 if (UNLIKELY(p5tmp)) {
840 if (!(p51 = p5->next)) {
841 ACQUIRE_DTOA_LOCK(1);
842 if (!(p51 = p5->next)) {
845 p5tmp = ATOMIC_PTR_CAS(p5->next, NULL, p51);
846 if (UNLIKELY(p5tmp)) {
863 ULong *x, *x1, *xe, z;
872 for (i = b->maxwds; n1 > i; i <<= 1)
876 for (i = 0; i < n; i++)
896 *x1++ = *x << k & 0xffff | z;
915 ULong *xa, *xa0, *xb, *xb0;
921 if (i > 1 && !a->x[i-1])
922 Bug(
"cmp called with a->x[a->wds-1] == 0");
923 if (j > 1 && !b->x[j-1])
924 Bug(
"cmp called with b->x[b->wds-1] == 0");
934 return *xa < *xb ? -1 : 1;
947 ULong *xa, *xae, *xb, *xbe, *xc;
984 y = (ULLong)*xa++ - *xb++ - borrow;
985 borrow = y >> 32 & (ULong)1;
986 *xc++ = (ULong)(y & FFFFFFFF);
990 borrow = y >> 32 & (ULong)1;
991 *xc++ = (ULong)(y & FFFFFFFF);
996 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
997 borrow = (y & 0x10000) >> 16;
998 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
999 borrow = (z & 0x10000) >> 16;
1003 y = (*xa & 0xffff) - borrow;
1004 borrow = (y & 0x10000) >> 16;
1005 z = (*xa++ >> 16) - borrow;
1006 borrow = (z & 0x10000) >> 16;
1011 y = *xa++ - *xb++ - borrow;
1012 borrow = (y & 0x10000) >> 16;
1017 borrow = (y & 0x10000) >> 16;
1035 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1036#ifndef Avoid_Underflow
1037#ifndef Sudden_Underflow
1046#ifndef Avoid_Underflow
1047#ifndef Sudden_Underflow
1050 L = -L >> Exp_shift;
1051 if (L < Exp_shift) {
1052 word0(a) = 0x80000 >> L;
1058 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1069 ULong *xa, *xa0, w, y, z;
1083 if (!y) Bug(
"zero y in b2d");
1089 d0 = Exp_1 | y >> (Ebits - k);
1090 w = xa > xa0 ? *--xa : 0;
1091 d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1094 z = xa > xa0 ? *--xa : 0;
1096 d0 = Exp_1 | y << k | z >> (32 - k);
1097 y = xa > xa0 ? *--xa : 0;
1098 d1 = z << k | y >> (32 - k);
1105 if (k < Ebits + 16) {
1106 z = xa > xa0 ? *--xa : 0;
1107 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1108 w = xa > xa0 ? *--xa : 0;
1109 y = xa > xa0 ? *--xa : 0;
1110 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1113 z = xa > xa0 ? *--xa : 0;
1114 w = xa > xa0 ? *--xa : 0;
1116 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1117 y = xa > xa0 ? *--xa : 0;
1118 d1 = w << k + 16 | y << k;
1122 word0(d) = d0 >> 16 | d0 << 16;
1123 word1(d) = d1 >> 16 | d1 << 16;
1132d2b(
double d_,
int *e,
int *bits)
1138#ifndef Sudden_Underflow
1146 d0 = word0(d) >> 16 | word0(d) << 16;
1147 d1 = word1(d) >> 16 | word1(d) << 16;
1162#ifdef Sudden_Underflow
1163 de = (int)(d0 >> Exp_shift);
1168 if ((de = (
int)(d0 >> Exp_shift)) != 0)
1172 if ((y = d1) != 0) {
1173 if ((k = lo0bits(&y)) != 0) {
1174 x[0] = y | z << (32 - k);
1179#ifndef Sudden_Underflow
1182 b->wds = (x[1] = z) ? 2 : 1;
1187 Bug(
"Zero passed to d2b");
1191#ifndef Sudden_Underflow
1199 if (k = lo0bits(&y))
1201 x[0] = y | z << 32 - k & 0xffff;
1202 x[1] = z >> k - 16 & 0xffff;
1208 x[1] = y >> 16 | z << 16 - k & 0xffff;
1209 x[2] = z >> k & 0xffff;
1224 Bug(
"Zero passed to d2b");
1242#ifndef Sudden_Underflow
1246 *e = (de - Bias - (P-1) << 2) + k;
1247 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1249 *e = de - Bias - (P-1) + k;
1252#ifndef Sudden_Underflow
1255 *e = de - Bias - (P-1) + 1 + k;
1257 *bits = 32*i - hi0bits(x[i-1]);
1259 *bits = (i+2)*16 - hi0bits(x[i]);
1274 dval(da) = b2d(a, &ka);
1275 dval(db) = b2d(b, &kb);
1277 k = ka - kb + 32*(a->wds - b->wds);
1279 k = ka - kb + 16*(a->wds - b->wds);
1283 word0(da) += (k >> 2)*Exp_msk1;
1289 word0(db) += (k >> 2)*Exp_msk1;
1295 word0(da) += k*Exp_msk1;
1298 word0(db) += k*Exp_msk1;
1301 return dval(da) / dval(db);
1306 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1307 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1316bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1317static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1318#ifdef Avoid_Underflow
1319 9007199254740992.*9007199254740992.e-256
1327#define Scale_Bit 0x10
1331bigtens[] = { 1e16, 1e32, 1e64 };
1332static const double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1335bigtens[] = { 1e16, 1e32 };
1336static const double tinytens[] = { 1e-16, 1e-32 };
1348#define NAN_WORD0 0x7ff80000
1356match(
const char **sp,
char *t)
1359 const char *s = *sp;
1362 if ((c = *++s) >=
'A' && c <=
'Z')
1373hexnan(
double *rvp,
const char **sp)
1377 int havedig, udx0, xshift;
1380 havedig = xshift = 0;
1383 while (c = *(
const unsigned char*)++s) {
1384 if (c >=
'0' && c <=
'9')
1386 else if (c >=
'a' && c <=
'f')
1388 else if (c >=
'A' && c <=
'F')
1390 else if (c <=
' ') {
1391 if (udx0 && havedig) {
1397 else if ( c ==
')' && havedig) {
1410 x[0] = (x[0] << 4) | (x[1] >> 28);
1411 x[1] = (x[1] << 4) | c;
1413 if ((x[0] &= 0xfffff) || x[1]) {
1414 word0(*rvp) = Exp_mask | x[0];
1421NO_SANITIZE(
"unsigned-integer-overflow",
double strtod(
const char *s00,
char **se));
1423strtod(
const char *s00,
char **se)
1425#ifdef Avoid_Underflow
1428 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1429 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1430 const char *s, *s0, *s1;
1435 Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1437 int inexact, oldinexact;
1439#ifdef Honor_FLT_ROUNDS
1447 sign = nz0 = nz = 0;
1472 if (s[1] ==
'x' || s[1] ==
'X') {
1478 if (!*++s || (!(s1 = strchr(hexdigit, *s)) && *s !=
'.'))
goto ret0;
1480 while (*++s ==
'0');
1482 s1 = strchr(hexdigit, *s);
1486 adj += aadj * ((s1 - hexdigit) & 15);
1489 }
while (*++s && (s1 = strchr(hexdigit, *s)));
1492 if ((*s ==
'.') && *++s && (s1 = strchr(hexdigit, *s))) {
1499 for (; *s && (s1 = strchr(hexdigit, *s)); ++s) {
1500 adj += aadj * ((s1 - hexdigit) & 15);
1501 if ((aadj /= 16) == 0.0) {
1502 while (*++s && strchr(hexdigit, *s));
1508 if (*s ==
'P' || *s ==
'p') {
1509 dsign = 0x2C - *++s;
1510 if (abs(dsign) == 1) s++;
1515 if (c <
'0' ||
'9' < c)
goto ret0;
1522 if (nd + dsign * nd0 > 2095) {
1523 while (
'0' <= c && c <=
'9') c = *++s;
1526 }
while (
'0' <= c && c <=
'9');
1529 dval(rv) = ldexp(adj, nd0);
1533 while (*++s ==
'0') ;
1539 for (nd = nf = 0; (c = *s) >=
'0' && c <=
'9'; nd++, s++)
1542 else if (nd < DBL_DIG + 2)
1546 s1 = localeconv()->decimal_point;
1569 for (; c ==
'0'; c = *++s)
1571 if (c >
'0' && c <=
'9') {
1579 for (; c >=
'0' && c <=
'9'; c = *++s) {
1582 if (nd > DBL_DIG * 4) {
1587 for (i = 1; i < nz; i++)
1590 else if (nd <= DBL_DIG + 2)
1594 else if (nd <= DBL_DIG + 2)
1602 if (c ==
'e' || c ==
'E') {
1603 if (!nd && !nz && !nz0) {
1614 if (c >=
'0' && c <=
'9') {
1617 if (c >
'0' && c <=
'9') {
1620 while ((c = *++s) >=
'0' && c <=
'9')
1622 if (s - s1 > 8 || L > 19999)
1645 if (match(&s,
"nf")) {
1647 if (!match(&s,
"inity"))
1649 word0(rv) = 0x7ff00000;
1656 if (match(&s,
"an")) {
1657 word0(rv) = NAN_WORD0;
1658 word1(rv) = NAN_WORD1;
1682 k = nd < DBL_DIG + 2 ? nd : DBL_DIG + 2;
1687 oldinexact = get_inexact();
1689 dval(rv) = tens[k - 9] * dval(rv) + z;
1691 bd0 = bb = bd = bs = delta = 0;
1694#ifndef Honor_FLT_ROUNDS
1702 if (e <= Ten_pmax) {
1704 goto vax_ovfl_check;
1706#ifdef Honor_FLT_ROUNDS
1709 dval(rv) = -dval(rv);
1713 rounded_product(dval(rv), tens[e]);
1718 if (e <= Ten_pmax + i) {
1722#ifdef Honor_FLT_ROUNDS
1725 dval(rv) = -dval(rv);
1730 dval(rv) *= tens[i];
1736 word0(rv) -= P*Exp_msk1;
1737 rounded_product(dval(rv), tens[e]);
1738 if ((word0(rv) & Exp_mask)
1739 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1741 word0(rv) += P*Exp_msk1;
1743 rounded_product(dval(rv), tens[e]);
1748#ifndef Inaccurate_Divide
1749 else if (e >= -Ten_pmax) {
1750#ifdef Honor_FLT_ROUNDS
1753 dval(rv) = -dval(rv);
1757 rounded_quotient(dval(rv), tens[-e]);
1768 oldinexact = get_inexact();
1770#ifdef Avoid_Underflow
1773#ifdef Honor_FLT_ROUNDS
1774 if ((rounding = Flt_Rounds) >= 2) {
1776 rounding = rounding == 2 ? 0 : 2;
1787 if ((i = e1 & 15) != 0)
1788 dval(rv) *= tens[i];
1790 if (e1 > DBL_MAX_10_EXP) {
1797#ifdef Honor_FLT_ROUNDS
1805 word0(rv) = Exp_mask;
1809 word0(rv) = Exp_mask;
1815 dval(rv0) *= dval(rv0);
1826 for (j = 0; e1 > 1; j++, e1 >>= 1)
1828 dval(rv) *= bigtens[j];
1830 word0(rv) -= P*Exp_msk1;
1831 dval(rv) *= bigtens[j];
1832 if ((z = word0(rv) & Exp_mask)
1833 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1835 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1842 word0(rv) += P*Exp_msk1;
1847 if ((i = e1 & 15) != 0)
1848 dval(rv) /= tens[i];
1850 if (e1 >= 1 << n_bigtens)
1852#ifdef Avoid_Underflow
1855 for (j = 0; e1 > 0; j++, e1 >>= 1)
1857 dval(rv) *= tinytens[j];
1858 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1859 >> Exp_shift)) > 0) {
1864 word0(rv) = (P+2)*Exp_msk1;
1866 word0(rv) &= 0xffffffff << (j-32);
1869 word1(rv) &= 0xffffffff << j;
1872 for (j = 0; e1 > 1; j++, e1 >>= 1)
1874 dval(rv) *= tinytens[j];
1876 dval(rv0) = dval(rv);
1877 dval(rv) *= tinytens[j];
1879 dval(rv) = 2.*dval(rv0);
1880 dval(rv) *= tinytens[j];
1892#ifndef Avoid_Underflow
1907 bd0 = s2b(s0, nd0, nd, y);
1910 bd = Balloc(bd0->k);
1912 bb = d2b(dval(rv), &bbe, &bbbits);
1928#ifdef Honor_FLT_ROUNDS
1932#ifdef Avoid_Underflow
1940#ifdef Sudden_Underflow
1942 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1957#ifdef Avoid_Underflow
1960 i = bb2 < bd2 ? bb2 : bd2;
1969 bs = pow5mult(bs, bb5);
1975 bb = lshift(bb, bb2);
1977 bd = pow5mult(bd, bd5);
1979 bd = lshift(bd, bd2);
1981 bs = lshift(bs, bs2);
1982 delta = diff(bb, bd);
1983 dsign = delta->sign;
1986#ifdef Honor_FLT_ROUNDS
1987 if (rounding != 1) {
1990 if (!delta->x[0] && delta->wds <= 1) {
2006 && !(word0(rv) & Frac_mask)) {
2007 y = word0(rv) & Exp_mask;
2008#ifdef Avoid_Underflow
2009 if (!scale || y > 2*P*Exp_msk1)
2014 delta = lshift(delta,Log2P);
2015 if (cmp(delta, bs) <= 0)
2020#ifdef Avoid_Underflow
2021 if (scale && (y = word0(rv) & Exp_mask)
2023 word0(adj) += (2*P+1)*Exp_msk1 - y;
2025#ifdef Sudden_Underflow
2026 if ((word0(rv) & Exp_mask) <=
2028 word0(rv) += P*Exp_msk1;
2029 dval(rv) += adj*ulp(dval(rv));
2030 word0(rv) -= P*Exp_msk1;
2035 dval(rv) += adj*ulp(dval(rv));
2039 adj = ratio(delta, bs);
2042 if (adj <= 0x7ffffffe) {
2046 if (!((rounding>>1) ^ dsign))
2051#ifdef Avoid_Underflow
2052 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2053 word0(adj) += (2*P+1)*Exp_msk1 - y;
2055#ifdef Sudden_Underflow
2056 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2057 word0(rv) += P*Exp_msk1;
2058 adj *= ulp(dval(rv));
2063 word0(rv) -= P*Exp_msk1;
2068 adj *= ulp(dval(rv));
2081 if (dsign || word1(rv) || word0(rv) & Bndry_mask
2083#ifdef Avoid_Underflow
2084 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2086 || (word0(rv) & Exp_mask) <= Exp_msk1
2091 if (!delta->x[0] && delta->wds <= 1)
2096 if (!delta->x[0] && delta->wds <= 1) {
2103 delta = lshift(delta,Log2P);
2104 if (cmp(delta, bs) > 0)
2111 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2113#ifdef Avoid_Underflow
2114 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2115 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2119 word0(rv) = (word0(rv) & Exp_mask)
2126#ifdef Avoid_Underflow
2132 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2135#ifdef Sudden_Underflow
2136 L = word0(rv) & Exp_mask;
2140#ifdef Avoid_Underflow
2141 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2149#ifdef Avoid_Underflow
2151 L = word0(rv) & Exp_mask;
2152 if (L <= (2*P+1)*Exp_msk1) {
2153 if (L > (P+2)*Exp_msk1)
2162 L = (word0(rv) & Exp_mask) - Exp_msk1;
2164 word0(rv) = L | Bndry_mask1;
2165 word1(rv) = 0xffffffff;
2173 if (!(word1(rv) & LSB))
2177 dval(rv) += ulp(dval(rv));
2180 dval(rv) -= ulp(dval(rv));
2181#ifndef Sudden_Underflow
2186#ifdef Avoid_Underflow
2192 if ((aadj = ratio(delta, bs)) <= 2.) {
2194 aadj = dval(aadj1) = 1.;
2195 else if (word1(rv) || word0(rv) & Bndry_mask) {
2196#ifndef Sudden_Underflow
2197 if (word1(rv) == Tiny1 && !word0(rv))
2207 if (aadj < 2./FLT_RADIX)
2208 aadj = 1./FLT_RADIX;
2211 dval(aadj1) = -aadj;
2216 dval(aadj1) = dsign ? aadj : -aadj;
2217#ifdef Check_FLT_ROUNDS
2227 if (Flt_Rounds == 0)
2231 y = word0(rv) & Exp_mask;
2235 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2236 dval(rv0) = dval(rv);
2237 word0(rv) -= P*Exp_msk1;
2238 adj = dval(aadj1) * ulp(dval(rv));
2240 if ((word0(rv) & Exp_mask) >=
2241 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2242 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2249 word0(rv) += P*Exp_msk1;
2252#ifdef Avoid_Underflow
2253 if (scale && y <= 2*P*Exp_msk1) {
2254 if (aadj <= 0x7fffffff) {
2255 if ((z = (
int)aadj) <= 0)
2258 dval(aadj1) = dsign ? aadj : -aadj;
2260 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2262 adj = dval(aadj1) * ulp(dval(rv));
2265#ifdef Sudden_Underflow
2266 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2267 dval(rv0) = dval(rv);
2268 word0(rv) += P*Exp_msk1;
2269 adj = dval(aadj1) * ulp(dval(rv));
2272 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2274 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2277 if (word0(rv0) == Tiny0 && word1(rv0) == Tiny1)
2284 word0(rv) -= P*Exp_msk1;
2287 adj = dval(aadj1) * ulp(dval(rv));
2298 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2299 dval(aadj1) = (double)(
int)(aadj + 0.5);
2301 dval(aadj1) = -dval(aadj1);
2303 adj = dval(aadj1) * ulp(dval(rv));
2308 z = word0(rv) & Exp_mask;
2310#ifdef Avoid_Underflow
2318 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2319 if (aadj < .4999999 || aadj > .5000001)
2322 else if (aadj < .4999999/FLT_RADIX)
2335 word0(rv0) = Exp_1 + (70 << Exp_shift);
2340 else if (!oldinexact)
2343#ifdef Avoid_Underflow
2345 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2347 dval(rv) *= dval(rv0);
2350 if (word0(rv) == 0 && word1(rv) == 0)
2356 if (inexact && !(word0(rv) & Exp_mask)) {
2359 dval(rv0) *= dval(rv0);
2371 return sign ? -dval(rv) : dval(rv);
2374NO_SANITIZE(
"unsigned-integer-overflow",
static int quorem(
Bigint *b,
Bigint *S));
2379 ULong *bx, *bxe, q, *sx, *sxe;
2381 ULLong borrow, carry, y, ys;
2383 ULong borrow, carry, y, ys;
2392 Bug(
"oversize b in quorem");
2400 q = *bxe / (*sxe + 1);
2403 Bug(
"oversized quotient in quorem");
2410 ys = *sx++ * (ULLong)q + carry;
2412 y = *bx - (ys & FFFFFFFF) - borrow;
2413 borrow = y >> 32 & (ULong)1;
2414 *bx++ = (ULong)(y & FFFFFFFF);
2418 ys = (si & 0xffff) * q + carry;
2419 zs = (si >> 16) * q + (ys >> 16);
2421 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2422 borrow = (y & 0x10000) >> 16;
2423 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2424 borrow = (z & 0x10000) >> 16;
2427 ys = *sx++ * q + carry;
2429 y = *bx - (ys & 0xffff) - borrow;
2430 borrow = (y & 0x10000) >> 16;
2434 }
while (sx <= sxe);
2437 while (--bxe > bx && !*bxe)
2442 if (cmp(b, S) >= 0) {
2452 y = *bx - (ys & FFFFFFFF) - borrow;
2453 borrow = y >> 32 & (ULong)1;
2454 *bx++ = (ULong)(y & FFFFFFFF);
2458 ys = (si & 0xffff) + carry;
2459 zs = (si >> 16) + (ys >> 16);
2461 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2462 borrow = (y & 0x10000) >> 16;
2463 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2464 borrow = (z & 0x10000) >> 16;
2469 y = *bx - (ys & 0xffff) - borrow;
2470 borrow = (y & 0x10000) >> 16;
2474 }
while (sx <= sxe);
2478 while (--bxe > bx && !*bxe)
2486#ifndef MULTIPLE_THREADS
2487static char *dtoa_result;
2490#ifndef MULTIPLE_THREADS
2494 return dtoa_result = MALLOC(i);
2497#define rv_alloc(i) MALLOC(i)
2501nrv_alloc(
const char *s,
char **rve,
size_t n)
2505 t = rv = rv_alloc(n);
2506 while ((*t = *s++) != 0) t++;
2512#define rv_strdup(s, rve) nrv_alloc((s), (rve), strlen(s)+1)
2514#ifndef MULTIPLE_THREADS
2528static const char INFSTR[] =
"Infinity";
2529static const char NANSTR[] =
"NaN";
2530static const char ZEROSTR[] =
"0";
2567dtoa(
double d_,
int mode,
int ndigits,
int *decpt,
int *sign,
char **rve)
2603 int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
2604 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2605 spec_case, try_quick, half = 0;
2607#ifndef Sudden_Underflow
2611 Bigint *b, *b1, *delta, *mlo = 0, *mhi = 0, *S;
2615#ifdef Honor_FLT_ROUNDS
2619 int inexact, oldinexact;
2624#ifndef MULTIPLE_THREADS
2626 freedtoa(dtoa_result);
2631 if (word0(d) & Sign_bit) {
2634 word0(d) &= ~Sign_bit;
2639#if defined(IEEE_Arith) + defined(VAX)
2641 if ((word0(d) & Exp_mask) == Exp_mask)
2643 if (word0(d) == 0x8000)
2649 if (!word1(d) && !(word0(d) & 0xfffff))
2650 return rv_strdup(INFSTR, rve);
2652 return rv_strdup(NANSTR, rve);
2660 return rv_strdup(ZEROSTR, rve);
2664 try_quick = oldinexact = get_inexact();
2667#ifdef Honor_FLT_ROUNDS
2668 if ((rounding = Flt_Rounds) >= 2) {
2670 rounding = rounding == 2 ? 0 : 2;
2677 b = d2b(dval(d), &be, &bbits);
2678#ifdef Sudden_Underflow
2679 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2681 if ((i = (
int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
2684 word0(d2) &= Frac_mask1;
2685 word0(d2) |= Exp_11;
2687 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2718#ifndef Sudden_Underflow
2724 i = bbits + be + (Bias + (P-1) - 1);
2725 x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
2726 : word1(d) << (32 - i);
2728 word0(d2) -= 31*Exp_msk1;
2729 i -= (Bias + (P-1) - 1) + 1;
2733 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2735 if (ds < 0. && ds != k)
2738 if (k >= 0 && k <= Ten_pmax) {
2739 if (dval(d) < tens[k])
2762 if (mode < 0 || mode > 9)
2766#ifdef Check_FLT_ROUNDS
2767 try_quick = Rounding == 1;
2791 ilim = ilim1 = i = ndigits;
2797 i = ndigits + k + 1;
2803 s = s0 = rv_alloc(i+1);
2805#ifdef Honor_FLT_ROUNDS
2806 if (mode > 1 && rounding != 1)
2810 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2825 dval(d) /= bigtens[n_bigtens-1];
2828 for (; j; j >>= 1, i++)
2835 else if ((j1 = -k) != 0) {
2836 dval(d) *= tens[j1 & 0xf];
2837 for (j = j1 >> 4; j; j >>= 1, i++)
2840 dval(d) *= bigtens[i];
2843 if (k_check && dval(d) < 1. && ilim > 0) {
2851 dval(eps) = ieps*dval(d) + 7.;
2852 word0(eps) -= (P-1)*Exp_msk1;
2856 if (dval(d) > dval(eps))
2858 if (dval(d) < -dval(eps))
2867 dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2871 *s++ =
'0' + (int)L;
2872 if (dval(d) < dval(eps))
2874 if (1. - dval(d) < dval(eps))
2885 dval(eps) *= tens[ilim-1];
2886 for (i = 1;; i++, dval(d) *= 10.) {
2887 L = (Long)(dval(d));
2888 if (!(dval(d) -= L))
2890 *s++ =
'0' + (int)L;
2892 if (dval(d) > 0.5 + dval(eps))
2894 else if (dval(d) < 0.5 - dval(eps)) {
2895 while (*--s ==
'0') ;
2900 if ((*(s-1) -
'0') & 1) {
2918 if (be >= 0 && k <= Int_max) {
2921 if (ndigits < 0 && ilim <= 0) {
2923 if (ilim < 0 || dval(d) <= 5*ds)
2927 for (i = 1;; i++, dval(d) *= 10.) {
2928 L = (Long)(dval(d) / ds);
2930#ifdef Check_FLT_ROUNDS
2937 *s++ =
'0' + (int)L;
2945#ifdef Honor_FLT_ROUNDS
2949 case 2:
goto bump_up;
2953 if (dval(d) > ds || (dval(d) == ds && (L & 1))) {
2973#ifndef Sudden_Underflow
2974 denorm ? be + (Bias + (P-1) - 1 + 1) :
2977 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
2985 if (m2 > 0 && s2 > 0) {
2986 i = m2 < s2 ? m2 : s2;
2994 mhi = pow5mult(mhi, m5);
2999 if ((j = b5 - m5) != 0)
3003 b = pow5mult(b, b5);
3007 S = pow5mult(S, s5);
3012 if ((mode < 2 || leftright)
3013#ifdef Honor_FLT_ROUNDS
3017 if (!word1(d) && !(word0(d) & Bndry_mask)
3018#ifndef Sudden_Underflow
3019 && word0(d) & (Exp_mask & ~Exp_msk1)
3037 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0)
3040 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) != 0)
3062 b = multadd(b, 10, 0);
3064 mhi = multadd(mhi, 10, 0);
3068 if (ilim <= 0 && (mode == 3 || mode == 5)) {
3069 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3082 mhi = lshift(mhi, m2);
3090 mhi = Balloc(mhi->k);
3092 mhi = lshift(mhi, Log2P);
3096 dig = quorem(b,S) +
'0';
3101 delta = diff(S, mhi);
3102 j1 = delta->sign ? 1 : cmp(b, delta);
3105 if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3106#ifdef Honor_FLT_ROUNDS
3115 else if (!b->x[0] && b->wds <= 1)
3122 if (j < 0 || (j == 0 && mode != 1
3127 if (!b->x[0] && b->wds <= 1) {
3133#ifdef Honor_FLT_ROUNDS
3136 case 0:
goto accept_dig;
3137 case 2:
goto keep_dig;
3143 if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ ==
'9')
3151#ifdef Honor_FLT_ROUNDS
3163#ifdef Honor_FLT_ROUNDS
3169 b = multadd(b, 10, 0);
3171 mlo = mhi = multadd(mhi, 10, 0);
3173 mlo = multadd(mlo, 10, 0);
3174 mhi = multadd(mhi, 10, 0);
3180 *s++ = dig = quorem(b,S) +
'0';
3181 if (!b->x[0] && b->wds <= 1) {
3189 b = multadd(b, 10, 0);
3194#ifdef Honor_FLT_ROUNDS
3196 case 0:
goto trimzeros;
3197 case 2:
goto roundoff;
3202 if (j > 0 || (j == 0 && (dig & 1))) {
3210 if (!half || (*s -
'0') & 1)
3214 while (*--s ==
'0') ;
3220 if (mlo && mlo != mhi)
3228 word0(d) = Exp_1 + (70 << Exp_shift);
3233 else if (!oldinexact)
3270#define DBL_MANH_SIZE 20
3271#define DBL_MANL_SIZE 32
3272#define DBL_ADJ (DBL_MAX_EXP - 2)
3273#define SIGFIGS ((DBL_MANT_DIG + 3) / 4 + 1)
3274#define dexp_get(u) ((int)(word0(u) >> Exp_shift) & ~Exp_msk1)
3275#define dexp_set(u,v) (word0(u) = (((int)(word0(u)) & ~Exp_mask) | ((v) << Exp_shift)))
3276#define dmanh_get(u) ((uint32_t)(word0(u) & Frac_mask))
3277#define dmanl_get(u) ((uint32_t)word1(u))
3305hdtoa(
double d,
const char *xdigs,
int ndigits,
int *decpt,
int *sign,
char **rve)
3310 uint32_t manh, manl;
3313 if (word0(u) & Sign_bit) {
3316 word0(u) &= ~Sign_bit;
3323 return rv_strdup(INFSTR, rve);
3325 else if (isnan(d)) {
3327 return rv_strdup(NANSTR, rve);
3329 else if (d == 0.0) {
3331 return rv_strdup(ZEROSTR, rve);
3333 else if (dexp_get(u)) {
3334 *decpt = dexp_get(u) - DBL_ADJ;
3337 u.d *= 5.363123171977039e+154 ;
3338 *decpt = dexp_get(u) - (514 + DBL_ADJ);
3348 bufsize = (ndigits > 0) ? ndigits : SIGFIGS;
3349 s0 = rv_alloc(bufsize+1);
3352 if (SIGFIGS > ndigits && ndigits > 0) {
3354 int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG;
3355 dexp_set(u, offset);
3358 *decpt += dexp_get(u) - offset;
3361 manh = dmanh_get(u);
3362 manl = dmanl_get(u);
3364 for (s = s0 + 1; s < s0 + bufsize; s++) {
3365 *s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf];
3366 manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4));
3372 for (ndigits = SIGFIGS; s0[ndigits - 1] ==
'0'; ndigits--)
#define ISDIGIT
Old name of rb_isdigit.
#define strtod(s, e)
Just another name of ruby_strtod.
#define errno
Ractor-aware version of errno.