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)
213#if defined(HAVE_STDCKDINT_H) || !defined(__has_include)
214#elif __has_include(<stdckdint.h>)
215# define HAVE_STDCKDINT_H 1
217#ifdef HAVE_STDCKDINT_H
218# include <stdckdint.h>
223ckd_add(
int *result,
int x,
int y)
226 if (y < INT_MIN - x)
return 1;
229 if (y > INT_MAX - x)
return 1;
237extern void *MALLOC(
size_t);
242extern void FREE(
void*);
247#define NO_SANITIZE(x, y) y
251#undef Avoid_Underflow
252#ifdef IEEE_BIG_ENDIAN
255#ifdef IEEE_LITTLE_ENDIAN
263#define DBL_MAX_10_EXP 308
264#define DBL_MAX_EXP 1024
270#define DBL_MAX_10_EXP 75
271#define DBL_MAX_EXP 63
273#define DBL_MAX 7.2370055773322621e+75
278#define DBL_MAX_10_EXP 38
279#define DBL_MAX_EXP 127
281#define DBL_MAX 1.7014118346046923e+38
285#define LONG_MAX 2147483647
302static const char hexdigit[] =
"0123456789abcdef0123456789ABCDEF";
305#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1
306Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
309typedef union {
double d; ULong L[2]; }
U;
314# ifdef IEEE_LITTLE_ENDIAN
315# define word0(x) (((ULong *)&(x))[1])
316# define word1(x) (((ULong *)&(x))[0])
318# define word0(x) (((ULong *)&(x))[0])
319# define word1(x) (((ULong *)&(x))[1])
323# ifdef IEEE_LITTLE_ENDIAN
324# define word0(x) ((x).L[1])
325# define word1(x) ((x).L[0])
327# define word0(x) ((x).L[0])
328# define word1(x) ((x).L[1])
330# define dval(x) ((x).d)
337#if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
338#define Storeinc(a,b,c) (((unsigned short *)(a))[1] = (unsigned short)(b), \
339((unsigned short *)(a))[0] = (unsigned short)(c), (a)++)
341#define Storeinc(a,b,c) (((unsigned short *)(a))[0] = (unsigned short)(b), \
342((unsigned short *)(a))[1] = (unsigned short)(c), (a)++)
354#define Exp_msk1 0x100000
355#define Exp_msk11 0x100000
356#define Exp_mask 0x7ff00000
360#define Exp_1 0x3ff00000
361#define Exp_11 0x3ff00000
363#define Frac_mask 0xfffff
364#define Frac_mask1 0xfffff
367#define Bndry_mask 0xfffff
368#define Bndry_mask1 0xfffff
370#define Sign_bit 0x80000000
377#define Avoid_Underflow
379#undef Sudden_Underflow
385#define Flt_Rounds FLT_ROUNDS
391#ifdef Honor_FLT_ROUNDS
392#define Rounding rounding
393#undef Check_FLT_ROUNDS
394#define Check_FLT_ROUNDS
396#define Rounding Flt_Rounds
400#undef Check_FLT_ROUNDS
401#undef Honor_FLT_ROUNDS
403#undef Sudden_Underflow
404#define Sudden_Underflow
410#define Exp_msk1 0x1000000
411#define Exp_msk11 0x1000000
412#define Exp_mask 0x7f000000
415#define Exp_1 0x41000000
416#define Exp_11 0x41000000
418#define Frac_mask 0xffffff
419#define Frac_mask1 0xffffff
422#define Bndry_mask 0xefffff
423#define Bndry_mask1 0xffffff
425#define Sign_bit 0x80000000
427#define Tiny0 0x100000
437#define Exp_msk11 0x800000
438#define Exp_mask 0x7f80
441#define Exp_1 0x40800000
444#define Frac_mask 0x7fffff
445#define Frac_mask1 0xffff007f
448#define Bndry_mask 0xffff007f
449#define Bndry_mask1 0xffff007f
451#define Sign_bit 0x8000
465#define rounded_product(a,b) ((a) = rnd_prod((a), (b)))
466#define rounded_quotient(a,b) ((a) = rnd_quot((a), (b)))
467extern double rnd_prod(
double,
double), rnd_quot(
double,
double);
469#define rounded_product(a,b) ((a) *= (b))
470#define rounded_quotient(a,b) ((a) /= (b))
473#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
474#define Big1 0xffffffff
480#define FFFFFFFF 0xffffffffUL
494#define Llong long long
497#define ULLong unsigned Llong
501#define MULTIPLE_THREADS 1
503#ifndef MULTIPLE_THREADS
504#define ACQUIRE_DTOA_LOCK(n)
505#define FREE_DTOA_LOCK(n)
507#define ACQUIRE_DTOA_LOCK(n)
508#define FREE_DTOA_LOCK(n)
511#ifndef ATOMIC_PTR_CAS
512#define ATOMIC_PTR_CAS(var, old, new) ((var) = (new), (void *)(old))
518#define UNLIKELY(x) (x)
521#define ASSUME(x) (void)(x)
528 int k, maxwds, sign, wds;
541 rv = (
Bigint *)MALLOC(
sizeof(
Bigint) + (x-1)*
sizeof(ULong));
542 if (!rv)
return NULL;
545 rv->sign = rv->wds = 0;
555#define Bcopy(x,y) memcpy((char *)&(x)->sign, (char *)&(y)->sign, \
556(y)->wds*sizeof(Long) + 2*sizeof(int))
559multadd(
Bigint *b,
int m,
int a)
579 y = *x * (ULLong)m + carry;
581 *x++ = (ULong)(y & FFFFFFFF);
585 y = (xi & 0xffff) * m + carry;
586 z = (xi >> 16) * m + (y >> 16);
588 *x++ = (z << 16) + (y & 0xffff);
597 if (wds >= b->maxwds) {
607 b->x[wds++] = (ULong)carry;
614s2b(
const char *s,
int nd0,
int nd, ULong y9)
621 for (k = 0, y = 1; x > y; y <<= 1, k++) ;
630 b->x[0] = y9 & 0xffff;
631 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
638 b = multadd(b, 10, *s++ -
'0');
645 for (; i < nd; i++) {
646 b = multadd(b, 10, *s++ -
'0');
653hi0bits(
register ULong x)
657 if (!(x & 0xffff0000)) {
661 if (!(x & 0xff000000)) {
665 if (!(x & 0xf0000000)) {
669 if (!(x & 0xc0000000)) {
673 if (!(x & 0x80000000)) {
675 if (!(x & 0x40000000))
685 register ULong x = *y;
736#define Bzero_p(b) (!(b)->x[0] && (b)->wds <= 1)
743 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
754 if (Bzero_p(a) || Bzero_p(b)) {
762 if (a->wds < b->wds) {
775 for (x = c->x, xa = x + wc; x < xa; x++)
783 for (; xb < xbe; xc0++) {
784 if ((y = *xb++) != 0) {
789 z = *x++ * (ULLong)y + *xc + carry;
791 *xc++ = (ULong)(z & FFFFFFFF);
798 for (; xb < xbe; xb++, xc0++) {
799 if ((y = *xb & 0xffff) != 0) {
804 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
806 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
812 if ((y = *xb >> 16) != 0) {
818 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
821 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
828 for (; xb < xbe; xc0++) {
834 z = *x++ * y + *xc + carry;
843 for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
855 static const int p05[3] = { 5, 25, 125 };
857 if ((i = k & 3) != 0) {
858 b = multadd(b, p05[i-1], 0);
862#define b_cache(var, addr, new_expr) \
863 if ((var = addr) != 0) {} else { \
865 ACQUIRE_DTOA_LOCK(1); \
866 if (!(var = addr) && (var = (new_expr)) != 0) { \
868 tmp = ATOMIC_PTR_CAS(addr, NULL, var); \
871 if (UNLIKELY(tmp)) { \
884 b_cache(p5, p5s, i2b(625));
894 b_cache(p51, p5->next, mult(p5, p5));
905 ULong *x, *x1, *xe, z;
907 if (!k || Bzero_p(b))
return b;
916 for (i = b->maxwds; n1 > i; i <<= 1)
924 for (i = 0; i < n; i++)
944 *x1++ = *x << k & 0xffff | z;
963 ULong *xa, *xa0, *xb, *xb0;
969 if (i > 1 && !a->x[i-1])
970 Bug(
"cmp called with a->x[a->wds-1] == 0");
971 if (j > 1 && !b->x[j-1])
972 Bug(
"cmp called with b->x[b->wds-1] == 0");
982 return *xa < *xb ? -1 : 1;
995 ULong *xa, *xae, *xb, *xbe, *xc;
1008 if (!c)
return NULL;
1022 if (!c)
return NULL;
1034 y = (ULLong)*xa++ - *xb++ - borrow;
1035 borrow = y >> 32 & (ULong)1;
1036 *xc++ = (ULong)(y & FFFFFFFF);
1040 borrow = y >> 32 & (ULong)1;
1041 *xc++ = (ULong)(y & FFFFFFFF);
1046 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1047 borrow = (y & 0x10000) >> 16;
1048 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1049 borrow = (z & 0x10000) >> 16;
1053 y = (*xa & 0xffff) - borrow;
1054 borrow = (y & 0x10000) >> 16;
1055 z = (*xa++ >> 16) - borrow;
1056 borrow = (z & 0x10000) >> 16;
1061 y = *xa++ - *xb++ - borrow;
1062 borrow = (y & 0x10000) >> 16;
1067 borrow = (y & 0x10000) >> 16;
1085 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1086#ifndef Avoid_Underflow
1087#ifndef Sudden_Underflow
1096#ifndef Avoid_Underflow
1097#ifndef Sudden_Underflow
1100 L = -L >> Exp_shift;
1101 if (L < Exp_shift) {
1102 word0(a) = 0x80000 >> L;
1108 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1119 ULong *xa, *xa0, w, y, z;
1133 if (!y) Bug(
"zero y in b2d");
1139 d0 = Exp_1 | y >> (Ebits - k);
1140 w = xa > xa0 ? *--xa : 0;
1141 d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1144 z = xa > xa0 ? *--xa : 0;
1146 d0 = Exp_1 | y << k | z >> (32 - k);
1147 y = xa > xa0 ? *--xa : 0;
1148 d1 = z << k | y >> (32 - k);
1155 if (k < Ebits + 16) {
1156 z = xa > xa0 ? *--xa : 0;
1157 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1158 w = xa > xa0 ? *--xa : 0;
1159 y = xa > xa0 ? *--xa : 0;
1160 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1163 z = xa > xa0 ? *--xa : 0;
1164 w = xa > xa0 ? *--xa : 0;
1166 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1167 y = xa > xa0 ? *--xa : 0;
1168 d1 = w << k + 16 | y << k;
1172 word0(d) = d0 >> 16 | d0 << 16;
1173 word1(d) = d1 >> 16 | d1 << 16;
1182d2b(
double d_,
int *e,
int *bits)
1188#ifndef Sudden_Underflow
1196 d0 = word0(d) >> 16 | word0(d) << 16;
1197 d1 = word1(d) >> 16 | word1(d) << 16;
1208 if (!b)
return NULL;
1213#ifdef Sudden_Underflow
1214 de = (int)(d0 >> Exp_shift);
1219 if ((de = (
int)(d0 >> Exp_shift)) != 0)
1223 if ((y = d1) != 0) {
1224 if ((k = lo0bits(&y)) != 0) {
1225 x[0] = y | z << (32 - k);
1230#ifndef Sudden_Underflow
1233 b->wds = (x[1] = z) ? 2 : 1;
1238 Bug(
"Zero passed to d2b");
1242#ifndef Sudden_Underflow
1250 if (k = lo0bits(&y))
1252 x[0] = y | z << 32 - k & 0xffff;
1253 x[1] = z >> k - 16 & 0xffff;
1259 x[1] = y >> 16 | z << 16 - k & 0xffff;
1260 x[2] = z >> k & 0xffff;
1275 Bug(
"Zero passed to d2b");
1293#ifndef Sudden_Underflow
1297 *e = (de - Bias - (P-1) << 2) + k;
1298 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1300 *e = de - Bias - (P-1) + k;
1303#ifndef Sudden_Underflow
1306 *e = de - Bias - (P-1) + 1 + k;
1308 *bits = 32*i - hi0bits(x[i-1]);
1310 *bits = (i+2)*16 - hi0bits(x[i]);
1325 dval(da) = b2d(a, &ka);
1326 dval(db) = b2d(b, &kb);
1328 k = ka - kb + 32*(a->wds - b->wds);
1330 k = ka - kb + 16*(a->wds - b->wds);
1334 word0(da) += (k >> 2)*Exp_msk1;
1340 word0(db) += (k >> 2)*Exp_msk1;
1346 word0(da) += k*Exp_msk1;
1349 word0(db) += k*Exp_msk1;
1352 return dval(da) / dval(db);
1357 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1358 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1367bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1368static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1369#ifdef Avoid_Underflow
1370 9007199254740992.*9007199254740992.e-256
1378#define Scale_Bit 0x10
1382bigtens[] = { 1e16, 1e32, 1e64 };
1383static const double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1386bigtens[] = { 1e16, 1e32 };
1387static const double tinytens[] = { 1e-16, 1e-32 };
1399#define NAN_WORD0 0x7ff80000
1407match(
const char **sp,
char *t)
1410 const char *s = *sp;
1413 if ((c = *++s) >=
'A' && c <=
'Z')
1424hexnan(
double *rvp,
const char **sp)
1428 int havedig, udx0, xshift;
1431 havedig = xshift = 0;
1434 while (c = *(
const unsigned char*)++s) {
1435 if (c >=
'0' && c <=
'9')
1437 else if (c >=
'a' && c <=
'f')
1439 else if (c >=
'A' && c <=
'F')
1441 else if (c <=
' ') {
1442 if (udx0 && havedig) {
1448 else if ( c ==
')' && havedig) {
1461 x[0] = (x[0] << 4) | (x[1] >> 28);
1462 x[1] = (x[1] << 4) | c;
1464 if ((x[0] &= 0xfffff) || x[1]) {
1465 word0(*rvp) = Exp_mask | x[0];
1472NO_SANITIZE(
"unsigned-integer-overflow",
double strtod(
const char *s00,
char **se));
1474strtod(
const char *s00,
char **se)
1476#ifdef Avoid_Underflow
1479 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1480 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1481 const char *s, *s0, *s1;
1486 Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1488 int inexact, oldinexact;
1490#ifdef Honor_FLT_ROUNDS
1498 sign = nz0 = nz = 0;
1523 if (s[1] ==
'x' || s[1] ==
'X') {
1529 if (!*++s || (!(s1 = strchr(hexdigit, *s)) && *s !=
'.'))
goto ret0;
1531 while (*++s ==
'0');
1533 s1 = strchr(hexdigit, *s);
1537 adj += aadj * ((s1 - hexdigit) & 15);
1540 }
while (*++s && (s1 = strchr(hexdigit, *s)));
1543 if ((*s ==
'.') && *++s && (s1 = strchr(hexdigit, *s))) {
1550 for (; *s && (s1 = strchr(hexdigit, *s)); ++s) {
1551 adj += aadj * ((s1 - hexdigit) & 15);
1552 if ((aadj /= 16) == 0.0) {
1553 while (*++s && strchr(hexdigit, *s));
1559 if (*s ==
'P' || *s ==
'p') {
1560 dsign = 0x2C - *++s;
1561 if (abs(dsign) == 1) s++;
1566 if (c <
'0' ||
'9' < c)
goto ret0;
1573 if (nd + dsign * nd0 > 2095) {
1574 while (
'0' <= c && c <=
'9') c = *++s;
1577 }
while (
'0' <= c && c <=
'9');
1580 dval(rv) = ldexp(adj, nd0);
1584 while (*++s ==
'0') ;
1590 for (nd = nf = 0; (c = *s) >=
'0' && c <=
'9'; nd++, s++)
1593 else if (nd < DBL_DIG + 2)
1597 s1 = localeconv()->decimal_point;
1620 for (; c ==
'0'; c = *++s)
1622 if (c >
'0' && c <=
'9') {
1630 for (; c >=
'0' && c <=
'9'; c = *++s) {
1633 if (nd > DBL_DIG * 4) {
1638 for (i = 1; i < nz; i++)
1641 else if (nd <= DBL_DIG + 2)
1645 else if (nd <= DBL_DIG + 2)
1653 if (c ==
'e' || c ==
'E') {
1654 if (!nd && !nz && !nz0) {
1665 if (c >=
'0' && c <=
'9') {
1668 if (c >
'0' && c <=
'9') {
1671 while ((c = *++s) >=
'0' && c <=
'9')
1673 if (s - s1 > 8 || L > 19999)
1696 if (match(&s,
"nf")) {
1698 if (!match(&s,
"inity"))
1700 word0(rv) = 0x7ff00000;
1707 if (match(&s,
"an")) {
1708 word0(rv) = NAN_WORD0;
1709 word1(rv) = NAN_WORD1;
1733 k = nd < DBL_DIG + 2 ? nd : DBL_DIG + 2;
1738 oldinexact = get_inexact();
1740 dval(rv) = tens[k - 9] * dval(rv) + z;
1742 bd0 = bb = bd = bs = delta = 0;
1745#ifndef Honor_FLT_ROUNDS
1753 if (e <= Ten_pmax) {
1755 goto vax_ovfl_check;
1757#ifdef Honor_FLT_ROUNDS
1760 dval(rv) = -dval(rv);
1764 rounded_product(dval(rv), tens[e]);
1769 if (e <= Ten_pmax + i) {
1773#ifdef Honor_FLT_ROUNDS
1776 dval(rv) = -dval(rv);
1781 dval(rv) *= tens[i];
1787 word0(rv) -= P*Exp_msk1;
1788 rounded_product(dval(rv), tens[e]);
1789 if ((word0(rv) & Exp_mask)
1790 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1792 word0(rv) += P*Exp_msk1;
1794 rounded_product(dval(rv), tens[e]);
1799#ifndef Inaccurate_Divide
1800 else if (e >= -Ten_pmax) {
1801#ifdef Honor_FLT_ROUNDS
1804 dval(rv) = -dval(rv);
1808 rounded_quotient(dval(rv), tens[-e]);
1819 oldinexact = get_inexact();
1821#ifdef Avoid_Underflow
1824#ifdef Honor_FLT_ROUNDS
1825 if ((rounding = Flt_Rounds) >= 2) {
1827 rounding = rounding == 2 ? 0 : 2;
1838 if ((i = e1 & 15) != 0)
1839 dval(rv) *= tens[i];
1841 if (e1 > DBL_MAX_10_EXP) {
1848#ifdef Honor_FLT_ROUNDS
1856 word0(rv) = Exp_mask;
1860 word0(rv) = Exp_mask;
1866 dval(rv0) *= dval(rv0);
1877 for (j = 0; e1 > 1; j++, e1 >>= 1)
1879 dval(rv) *= bigtens[j];
1881 word0(rv) -= P*Exp_msk1;
1882 dval(rv) *= bigtens[j];
1883 if ((z = word0(rv) & Exp_mask)
1884 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1886 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1893 word0(rv) += P*Exp_msk1;
1898 if ((i = e1 & 15) != 0)
1899 dval(rv) /= tens[i];
1901 if (e1 >= 1 << n_bigtens)
1903#ifdef Avoid_Underflow
1906 for (j = 0; e1 > 0; j++, e1 >>= 1)
1908 dval(rv) *= tinytens[j];
1909 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1910 >> Exp_shift)) > 0) {
1915 word0(rv) = (P+2)*Exp_msk1;
1917 word0(rv) &= 0xffffffff << (j-32);
1920 word1(rv) &= 0xffffffff << j;
1923 for (j = 0; e1 > 1; j++, e1 >>= 1)
1925 dval(rv) *= tinytens[j];
1927 dval(rv0) = dval(rv);
1928 dval(rv) *= tinytens[j];
1930 dval(rv) = 2.*dval(rv0);
1931 dval(rv) *= tinytens[j];
1943#ifndef Avoid_Underflow
1958 bd0 = s2b(s0, nd0, nd, y);
1962 bd = Balloc(bd0->k);
1963 if (!bd)
goto retfree;
1965 bb = d2b(dval(rv), &bbe, &bbbits);
1966 if (!bb)
goto retfree;
1968 if (!bs)
goto retfree;
1983#ifdef Honor_FLT_ROUNDS
1987#ifdef Avoid_Underflow
1995#ifdef Sudden_Underflow
1997 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
2012#ifdef Avoid_Underflow
2015 i = bb2 < bd2 ? bb2 : bd2;
2024 bs = pow5mult(bs, bb5);
2025 if (!bs)
goto retfree;
2029 if (!bb)
goto retfree;
2032 bb = lshift(bb, bb2);
2033 if (!bb)
goto retfree;
2036 bd = pow5mult(bd, bd5);
2037 if (!bd)
goto retfree;
2040 bd = lshift(bd, bd2);
2041 if (!bd)
goto retfree;
2044 bs = lshift(bs, bs2);
2045 if (!bs)
goto retfree;
2047 delta = diff(bb, bd);
2048 if (!delta)
goto retfree;
2049 dsign = delta->sign;
2052#ifdef Honor_FLT_ROUNDS
2053 if (rounding != 1) {
2056 if (!delta->x[0] && delta->wds <= 1) {
2072 && !(word0(rv) & Frac_mask)) {
2073 y = word0(rv) & Exp_mask;
2074#ifdef Avoid_Underflow
2075 if (!scale || y > 2*P*Exp_msk1)
2080 delta = lshift(delta,Log2P);
2081 if (!delta)
goto nomem;
2082 if (cmp(delta, bs) <= 0)
2087#ifdef Avoid_Underflow
2088 if (scale && (y = word0(rv) & Exp_mask)
2090 word0(adj) += (2*P+1)*Exp_msk1 - y;
2092#ifdef Sudden_Underflow
2093 if ((word0(rv) & Exp_mask) <=
2095 word0(rv) += P*Exp_msk1;
2096 dval(rv) += adj*ulp(dval(rv));
2097 word0(rv) -= P*Exp_msk1;
2102 dval(rv) += adj*ulp(dval(rv));
2106 adj = ratio(delta, bs);
2109 if (adj <= 0x7ffffffe) {
2113 if (!((rounding>>1) ^ dsign))
2118#ifdef Avoid_Underflow
2119 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2120 word0(adj) += (2*P+1)*Exp_msk1 - y;
2122#ifdef Sudden_Underflow
2123 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2124 word0(rv) += P*Exp_msk1;
2125 adj *= ulp(dval(rv));
2130 word0(rv) -= P*Exp_msk1;
2135 adj *= ulp(dval(rv));
2148 if (dsign || word1(rv) || word0(rv) & Bndry_mask
2150#ifdef Avoid_Underflow
2151 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2153 || (word0(rv) & Exp_mask) <= Exp_msk1
2158 if (!delta->x[0] && delta->wds <= 1)
2163 if (!delta->x[0] && delta->wds <= 1) {
2170 delta = lshift(delta,Log2P);
2171 if (!delta)
goto retfree;
2172 if (cmp(delta, bs) > 0)
2179 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2181#ifdef Avoid_Underflow
2182 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2183 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2187 word0(rv) = (word0(rv) & Exp_mask)
2194#ifdef Avoid_Underflow
2200 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2203#ifdef Sudden_Underflow
2204 L = word0(rv) & Exp_mask;
2208#ifdef Avoid_Underflow
2209 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2217#ifdef Avoid_Underflow
2219 L = word0(rv) & Exp_mask;
2220 if (L <= (2*P+1)*Exp_msk1) {
2221 if (L > (P+2)*Exp_msk1)
2230 L = (word0(rv) & Exp_mask) - Exp_msk1;
2232 word0(rv) = L | Bndry_mask1;
2233 word1(rv) = 0xffffffff;
2241 if (!(word1(rv) & LSB))
2245 dval(rv) += ulp(dval(rv));
2248 dval(rv) -= ulp(dval(rv));
2249#ifndef Sudden_Underflow
2254#ifdef Avoid_Underflow
2260 if ((aadj = ratio(delta, bs)) <= 2.) {
2262 aadj = dval(aadj1) = 1.;
2263 else if (word1(rv) || word0(rv) & Bndry_mask) {
2264#ifndef Sudden_Underflow
2265 if (word1(rv) == Tiny1 && !word0(rv))
2275 if (aadj < 2./FLT_RADIX)
2276 aadj = 1./FLT_RADIX;
2279 dval(aadj1) = -aadj;
2284 dval(aadj1) = dsign ? aadj : -aadj;
2285#ifdef Check_FLT_ROUNDS
2295 if (Flt_Rounds == 0)
2299 y = word0(rv) & Exp_mask;
2303 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2304 dval(rv0) = dval(rv);
2305 word0(rv) -= P*Exp_msk1;
2306 adj = dval(aadj1) * ulp(dval(rv));
2308 if ((word0(rv) & Exp_mask) >=
2309 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2310 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2317 word0(rv) += P*Exp_msk1;
2320#ifdef Avoid_Underflow
2321 if (scale && y <= 2*P*Exp_msk1) {
2322 if (aadj <= 0x7fffffff) {
2323 if ((z = (
int)aadj) <= 0)
2326 dval(aadj1) = dsign ? aadj : -aadj;
2328 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2330 adj = dval(aadj1) * ulp(dval(rv));
2333#ifdef Sudden_Underflow
2334 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2335 dval(rv0) = dval(rv);
2336 word0(rv) += P*Exp_msk1;
2337 adj = dval(aadj1) * ulp(dval(rv));
2340 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2342 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2345 if (word0(rv0) == Tiny0 && word1(rv0) == Tiny1)
2352 word0(rv) -= P*Exp_msk1;
2355 adj = dval(aadj1) * ulp(dval(rv));
2366 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2367 dval(aadj1) = (double)(
int)(aadj + 0.5);
2369 dval(aadj1) = -dval(aadj1);
2371 adj = dval(aadj1) * ulp(dval(rv));
2376 z = word0(rv) & Exp_mask;
2378#ifdef Avoid_Underflow
2386 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2387 if (aadj < .4999999 || aadj > .5000001)
2390 else if (aadj < .4999999/FLT_RADIX)
2403 word0(rv0) = Exp_1 + (70 << Exp_shift);
2408 else if (!oldinexact)
2411#ifdef Avoid_Underflow
2413 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2415 dval(rv) *= dval(rv0);
2418 if (word0(rv) == 0 && word1(rv) == 0)
2424 if (inexact && !(word0(rv) & Exp_mask)) {
2427 dval(rv0) *= dval(rv0);
2439 return sign ? -dval(rv) : dval(rv);
2442NO_SANITIZE(
"unsigned-integer-overflow",
static int quorem(
Bigint *b,
Bigint *S));
2447 ULong *bx, *bxe, q, *sx, *sxe;
2449 ULLong borrow, carry, y, ys;
2451 ULong borrow, carry, y, ys;
2460 Bug(
"oversize b in quorem");
2468 q = *bxe / (*sxe + 1);
2471 Bug(
"oversized quotient in quorem");
2478 ys = *sx++ * (ULLong)q + carry;
2480 y = *bx - (ys & FFFFFFFF) - borrow;
2481 borrow = y >> 32 & (ULong)1;
2482 *bx++ = (ULong)(y & FFFFFFFF);
2486 ys = (si & 0xffff) * q + carry;
2487 zs = (si >> 16) * q + (ys >> 16);
2489 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2490 borrow = (y & 0x10000) >> 16;
2491 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2492 borrow = (z & 0x10000) >> 16;
2495 ys = *sx++ * q + carry;
2497 y = *bx - (ys & 0xffff) - borrow;
2498 borrow = (y & 0x10000) >> 16;
2502 }
while (sx <= sxe);
2505 while (--bxe > bx && !*bxe)
2510 if (cmp(b, S) >= 0) {
2520 y = *bx - (ys & FFFFFFFF) - borrow;
2521 borrow = y >> 32 & (ULong)1;
2522 *bx++ = (ULong)(y & FFFFFFFF);
2526 ys = (si & 0xffff) + carry;
2527 zs = (si >> 16) + (ys >> 16);
2529 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2530 borrow = (y & 0x10000) >> 16;
2531 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2532 borrow = (z & 0x10000) >> 16;
2537 y = *bx - (ys & 0xffff) - borrow;
2538 borrow = (y & 0x10000) >> 16;
2542 }
while (sx <= sxe);
2546 while (--bxe > bx && !*bxe)
2554#ifndef MULTIPLE_THREADS
2555static char *dtoa_result;
2558#ifndef MULTIPLE_THREADS
2562 return dtoa_result = MALLOC(i);
2565#define rv_alloc(i) MALLOC(i)
2569nrv_alloc(
const char *s,
char **rve,
size_t n)
2573 t = rv = rv_alloc(n);
2574 if (!rv)
return NULL;
2575 while ((*t = *s++) != 0) t++;
2581#define rv_strdup(s, rve) nrv_alloc((s), (rve), strlen(s)+1)
2583#ifndef MULTIPLE_THREADS
2597static const char INFSTR[] =
"Infinity";
2598static const char NANSTR[] =
"NaN";
2599static const char ZEROSTR[] =
"0";
2636dtoa(
double d_,
int mode,
int ndigits,
int *decpt,
int *sign,
char **rve)
2672 int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
2673 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2674 spec_case, try_quick, half = 0;
2676#ifndef Sudden_Underflow
2680 Bigint *b, *b1, *delta, *mlo = 0, *mhi = 0, *S;
2684#ifdef Honor_FLT_ROUNDS
2688 int inexact, oldinexact;
2693#ifndef MULTIPLE_THREADS
2695 freedtoa(dtoa_result);
2700 if (word0(d) & Sign_bit) {
2703 word0(d) &= ~Sign_bit;
2708#if defined(IEEE_Arith) + defined(VAX)
2710 if ((word0(d) & Exp_mask) == Exp_mask)
2712 if (word0(d) == 0x8000)
2718 if (!word1(d) && !(word0(d) & 0xfffff))
2719 return rv_strdup(INFSTR, rve);
2721 return rv_strdup(NANSTR, rve);
2729 return rv_strdup(ZEROSTR, rve);
2733 try_quick = oldinexact = get_inexact();
2736#ifdef Honor_FLT_ROUNDS
2737 if ((rounding = Flt_Rounds) >= 2) {
2739 rounding = rounding == 2 ? 0 : 2;
2746 b = d2b(dval(d), &be, &bbits);
2747 if (!b)
return NULL;
2748#ifdef Sudden_Underflow
2749 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2751 if ((i = (
int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
2754 word0(d2) &= Frac_mask1;
2755 word0(d2) |= Exp_11;
2757 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2788#ifndef Sudden_Underflow
2794 i = bbits + be + (Bias + (P-1) - 1);
2795 x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
2796 : word1(d) << (32 - i);
2798 word0(d2) -= 31*Exp_msk1;
2799 i -= (Bias + (P-1) - 1) + 1;
2803 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2805 if (ds < 0. && ds != k)
2808 if (k >= 0 && k <= Ten_pmax) {
2809 if (dval(d) < tens[k])
2832 if (mode < 0 || mode > 9)
2836#ifdef Check_FLT_ROUNDS
2837 try_quick = Rounding == 1;
2861 ilim = ilim1 = i = ndigits;
2867 if (ckd_add(&i, ndigits, k + 1)) {
2876 s = s0 = rv_alloc(i+1);
2882#ifdef Honor_FLT_ROUNDS
2883 if (mode > 1 && rounding != 1)
2887 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2902 dval(d) /= bigtens[n_bigtens-1];
2905 for (; j; j >>= 1, i++)
2912 else if ((j1 = -k) != 0) {
2913 dval(d) *= tens[j1 & 0xf];
2914 for (j = j1 >> 4; j; j >>= 1, i++)
2917 dval(d) *= bigtens[i];
2920 if (k_check && dval(d) < 1. && ilim > 0) {
2928 dval(eps) = ieps*dval(d) + 7.;
2929 word0(eps) -= (P-1)*Exp_msk1;
2933 if (dval(d) > dval(eps))
2935 if (dval(d) < -dval(eps))
2944 dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2948 *s++ =
'0' + (int)L;
2949 if (dval(d) < dval(eps))
2951 if (1. - dval(d) < dval(eps))
2962 dval(eps) *= tens[ilim-1];
2963 for (i = 1;; i++, dval(d) *= 10.) {
2964 L = (Long)(dval(d));
2965 if (!(dval(d) -= L))
2967 *s++ =
'0' + (int)L;
2969 if (dval(d) > 0.5 + dval(eps))
2971 else if (dval(d) < 0.5 - dval(eps)) {
2972 while (*--s ==
'0') ;
2977 if ((*(s-1) -
'0') & 1) {
2995 if (be >= 0 && k <= Int_max) {
2998 if (ndigits < 0 && ilim <= 0) {
3000 if (ilim < 0 || dval(d) <= 5*ds)
3004 for (i = 1;; i++, dval(d) *= 10.) {
3005 L = (Long)(dval(d) / ds);
3007#ifdef Check_FLT_ROUNDS
3014 *s++ =
'0' + (int)L;
3022#ifdef Honor_FLT_ROUNDS
3026 case 2:
goto bump_up;
3030 if (dval(d) > ds || (dval(d) == ds && (L & 1))) {
3050#ifndef Sudden_Underflow
3051 denorm ? be + (Bias + (P-1) - 1 + 1) :
3054 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
3061 if (!mhi)
goto nomem;
3063 if (m2 > 0 && s2 > 0) {
3064 i = m2 < s2 ? m2 : s2;
3072 mhi = pow5mult(mhi, m5);
3073 if (!mhi)
goto nomem;
3079 if ((j = b5 - m5) != 0) {
3085 b = pow5mult(b, b5);
3092 S = pow5mult(S, s5);
3099 if ((mode < 2 || leftright)
3100#ifdef Honor_FLT_ROUNDS
3104 if (!word1(d) && !(word0(d) & Bndry_mask)
3105#ifndef Sudden_Underflow
3106 && word0(d) & (Exp_mask & ~Exp_msk1)
3124 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0)
3127 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) != 0)
3153 b = multadd(b, 10, 0);
3156 mhi = multadd(mhi, 10, 0);
3157 if (!mhi)
goto nomem;
3162 if (ilim <= 0 && (mode == 3 || mode == 5)) {
3163 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3176 mhi = lshift(mhi, m2);
3177 if (!mhi)
goto nomem;
3186 mhi = Balloc(mhi->k);
3187 if (!mhi)
goto nomem;
3189 mhi = lshift(mhi, Log2P);
3190 if (!mhi)
goto nomem;
3194 dig = quorem(b,S) +
'0';
3199 delta = diff(S, mhi);
3200 if (!delta)
goto nomem;
3201 j1 = delta->sign ? 1 : cmp(b, delta);
3204 if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3205#ifdef Honor_FLT_ROUNDS
3214 else if (!b->x[0] && b->wds <= 1)
3221 if (j < 0 || (j == 0 && mode != 1
3226 if (!b->x[0] && b->wds <= 1) {
3232#ifdef Honor_FLT_ROUNDS
3235 case 0:
goto accept_dig;
3236 case 2:
goto keep_dig;
3243 if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ ==
'9')
3251#ifdef Honor_FLT_ROUNDS
3263#ifdef Honor_FLT_ROUNDS
3269 b = multadd(b, 10, 0);
3272 mlo = mhi = multadd(mhi, 10, 0);
3273 if (!mlo)
goto nomem;
3276 mlo = multadd(mlo, 10, 0);
3277 if (!mlo)
goto nomem;
3278 mhi = multadd(mhi, 10, 0);
3279 if (!mhi)
goto nomem;
3285 *s++ = dig = quorem(b,S) +
'0';
3286 if (!b->x[0] && b->wds <= 1) {
3294 b = multadd(b, 10, 0);
3300#ifdef Honor_FLT_ROUNDS
3302 case 0:
goto trimzeros;
3303 case 2:
goto roundoff;
3309 if (j > 0 || (j == 0 && (dig & 1))) {
3317 if (!half || (*s -
'0') & 1)
3321 while (*--s ==
'0') ;
3327 if (mlo && mlo != mhi)
3335 word0(d) = Exp_1 + (70 << Exp_shift);
3340 else if (!oldinexact)
3352 if (mlo && mlo != mhi)
3387#define DBL_MANH_SIZE 20
3388#define DBL_MANL_SIZE 32
3389#define DBL_ADJ (DBL_MAX_EXP - 2)
3390#define SIGFIGS ((DBL_MANT_DIG + 3) / 4 + 1)
3391#define dexp_get(u) ((int)(word0(u) >> Exp_shift) & ~Exp_msk1)
3392#define dexp_set(u,v) (word0(u) = (((int)(word0(u)) & ~Exp_mask) | ((v) << Exp_shift)))
3393#define dmanh_get(u) ((uint32_t)(word0(u) & Frac_mask))
3394#define dmanl_get(u) ((uint32_t)word1(u))
3422hdtoa(
double d,
const char *xdigs,
int ndigits,
int *decpt,
int *sign,
char **rve)
3427 uint32_t manh, manl;
3430 if (word0(u) & Sign_bit) {
3433 word0(u) &= ~Sign_bit;
3440 return rv_strdup(INFSTR, rve);
3442 else if (isnan(d)) {
3444 return rv_strdup(NANSTR, rve);
3446 else if (d == 0.0) {
3448 return rv_strdup(ZEROSTR, rve);
3450 else if (dexp_get(u)) {
3451 *decpt = dexp_get(u) - DBL_ADJ;
3454 u.d *= 5.363123171977039e+154 ;
3455 *decpt = dexp_get(u) - (514 + DBL_ADJ);
3465 bufsize = (ndigits > 0) ? ndigits : SIGFIGS;
3466 s0 = rv_alloc(bufsize+1);
3467 if (!s0)
return NULL;
3470 if (SIGFIGS > ndigits && ndigits > 0) {
3472 int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG;
3473 dexp_set(u, offset);
3476 *decpt += dexp_get(u) - offset;
3479 manh = dmanh_get(u);
3480 manl = dmanl_get(u);
3482 for (s = s0 + 1; s < s0 + bufsize; s++) {
3483 *s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf];
3484 manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4));
3490 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.