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- /*
- * This file is part of the UCB release of Plan 9. It is subject to the license
- * terms in the LICENSE file found in the top-level directory of this
- * distribution and at http://akaros.cs.berkeley.edu/files/Plan9License. No
- * part of the UCB release of Plan 9, including this file, may be copied,
- * modified, propagated, or distributed except according to the terms contained
- * in the LICENSE file.
- */
- /* derived from /netlib/fp/dtoa.c assuming IEEE, Standard C */
- /* kudos to dmg@bell-labs.com, gripes to ehg@bell-labs.com */
- /* Let x be the exact mathematical number defined by a decimal
- * string s. Then atof(s) is the round-nearest-even IEEE
- * floating point value.
- * Let y be an IEEE floating point value and let s be the string
- * printed as %.17g. Then atof(s) is exactly y.
- */
- #include <u.h>
- #include <libc.h>
- static Lock _dtoalk[2];
- #define ACQUIRE_DTOA_LOCK(n) lock(&_dtoalk[n])
- #define FREE_DTOA_LOCK(n) unlock(&_dtoalk[n])
- #define PRIVATE_mem ((2000+sizeof(double)-1)/sizeof(double))
- static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
- #define FLT_ROUNDS 1
- #define DBL_DIG 15
- #define DBL_MAX_10_EXP 308
- #define DBL_MAX_EXP 1024
- #define FLT_RADIX 2
- #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
- /* Ten_pmax = floor(P*log(2)/log(5)) */
- /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
- /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
- /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
- #define Exp_shift 20
- #define Exp_shift1 20
- #define Exp_msk1 0x100000
- #define Exp_msk11 0x100000
- #define Exp_mask 0x7ff00000
- #define P 53
- #define Bias 1023
- #define Emin (-1022)
- #define Exp_1 0x3ff00000
- #define Exp_11 0x3ff00000
- #define Ebits 11
- #define Frac_mask 0xfffff
- #define Frac_mask1 0xfffff
- #define Ten_pmax 22
- #define Bletch 0x10
- #define Bndry_mask 0xfffff
- #define Bndry_mask1 0xfffff
- #define LSB 1
- #define Sign_bit 0x80000000
- #define Log2P 1
- #define Tiny0 0
- #define Tiny1 1
- #define Quick_max 14
- #define Int_max 14
- #define Avoid_Underflow
- #define rounded_product(a,b) a *= b
- #define rounded_quotient(a,b) a /= b
- #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
- #define Big1 0xffffffff
- #define FFFFFFFF 0xffffffffUL
- #define Kmax 15
- typedef struct Bigint Bigint;
- typedef struct Ulongs Ulongs;
- struct Bigint {
- Bigint *next;
- int k, maxwds, sign, wds;
- unsigned x[1];
- };
- struct Ulongs {
- uint32_t hi;
- uint32_t lo;
- };
- static Bigint *freelist[Kmax+1];
- Ulongs
- double2ulongs(double d)
- {
- FPdbleword dw;
- Ulongs uls;
- dw.x = d;
- uls.hi = dw.hi;
- uls.lo = dw.lo;
- return uls;
- }
- double
- ulongs2double(Ulongs uls)
- {
- FPdbleword dw;
- dw.hi = uls.hi;
- dw.lo = uls.lo;
- return dw.x;
- }
- static Bigint *
- Balloc(int k)
- {
- int x;
- Bigint * rv;
- unsigned int len;
- ACQUIRE_DTOA_LOCK(0);
- if (rv = freelist[k]) {
- freelist[k] = rv->next;
- } else {
- x = 1 << k;
- len = (sizeof(Bigint) + (x - 1) * sizeof(unsigned int) + sizeof(double) -1)
- / sizeof(double);
- if (pmem_next - private_mem + len <= PRIVATE_mem) {
- rv = (Bigint * )pmem_next;
- pmem_next += len;
- } else
- rv = (Bigint * )malloc(len * sizeof(double));
- rv->k = k;
- rv->maxwds = x;
- }
- FREE_DTOA_LOCK(0);
- rv->sign = rv->wds = 0;
- return rv;
- }
- static void
- Bfree(Bigint *v)
- {
- if (v) {
- ACQUIRE_DTOA_LOCK(0);
- v->next = freelist[v->k];
- freelist[v->k] = v;
- FREE_DTOA_LOCK(0);
- }
- }
- #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
- y->wds*sizeof(int) + 2*sizeof(int))
- static Bigint *
- multadd(Bigint *b, int m, int a) /* multiply by m and add a */
- {
- int i, wds;
- unsigned int carry, *x, y;
- unsigned int xi, z;
- Bigint * b1;
- wds = b->wds;
- x = b->x;
- i = 0;
- carry = a;
- do {
- xi = *x;
- y = (xi & 0xffff) * m + carry;
- z = (xi >> 16) * m + (y >> 16);
- carry = z >> 16;
- *x++ = (z << 16) + (y & 0xffff);
- } while (++i < wds);
- if (carry) {
- if (wds >= b->maxwds) {
- b1 = Balloc(b->k + 1);
- Bcopy(b1, b);
- Bfree(b);
- b = b1;
- }
- b->x[wds++] = carry;
- b->wds = wds;
- }
- return b;
- }
- static Bigint *
- s2b(const char *s, int nd0, int nd, unsigned int y9)
- {
- Bigint * b;
- int i, k;
- int x, y;
- x = (nd + 8) / 9;
- for (k = 0, y = 1; x > y; y <<= 1, k++)
- ;
- b = Balloc(k);
- b->x[0] = y9;
- b->wds = 1;
- i = 9;
- if (9 < nd0) {
- s += 9;
- do
- b = multadd(b, 10, *s++ - '0');
- while (++i < nd0);
- s++;
- } else
- s += 10;
- for (; i < nd; i++)
- b = multadd(b, 10, *s++ - '0');
- return b;
- }
- static int
- hi0bits(register unsigned int x)
- {
- register int k = 0;
- if (!(x & 0xffff0000)) {
- k = 16;
- x <<= 16;
- }
- if (!(x & 0xff000000)) {
- k += 8;
- x <<= 8;
- }
- if (!(x & 0xf0000000)) {
- k += 4;
- x <<= 4;
- }
- if (!(x & 0xc0000000)) {
- k += 2;
- x <<= 2;
- }
- if (!(x & 0x80000000)) {
- k++;
- if (!(x & 0x40000000))
- return 32;
- }
- return k;
- }
- static int
- lo0bits(unsigned int *y)
- {
- register int k;
- register unsigned int x = *y;
- if (x & 7) {
- if (x & 1)
- return 0;
- if (x & 2) {
- *y = x >> 1;
- return 1;
- }
- *y = x >> 2;
- return 2;
- }
- k = 0;
- if (!(x & 0xffff)) {
- k = 16;
- x >>= 16;
- }
- if (!(x & 0xff)) {
- k += 8;
- x >>= 8;
- }
- if (!(x & 0xf)) {
- k += 4;
- x >>= 4;
- }
- if (!(x & 0x3)) {
- k += 2;
- x >>= 2;
- }
- if (!(x & 1)) {
- k++;
- x >>= 1;
- if (!x & 1)
- return 32;
- }
- *y = x;
- return k;
- }
- static Bigint *
- i2b(int i)
- {
- Bigint * b;
- b = Balloc(1);
- b->x[0] = i;
- b->wds = 1;
- return b;
- }
- static Bigint *
- mult(Bigint *a, Bigint *b)
- {
- Bigint * c;
- int k, wa, wb, wc;
- unsigned int * x, *xa, *xae, *xb, *xbe, *xc, *xc0;
- unsigned int y;
- unsigned int carry, z;
- unsigned int z2;
- if (a->wds < b->wds) {
- c = a;
- a = b;
- b = c;
- }
- k = a->k;
- wa = a->wds;
- wb = b->wds;
- wc = wa + wb;
- if (wc > a->maxwds)
- k++;
- c = Balloc(k);
- for (x = c->x, xa = x + wc; x < xa; x++)
- *x = 0;
- xa = a->x;
- xae = xa + wa;
- xb = b->x;
- xbe = xb + wb;
- xc0 = c->x;
- for (; xb < xbe; xb++, xc0++) {
- if (y = *xb & 0xffff) {
- x = xa;
- xc = xc0;
- carry = 0;
- do {
- z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
- carry = z >> 16;
- z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
- carry = z2 >> 16;
- Storeinc(xc, z2, z);
- } while (x < xae);
- *xc = carry;
- }
- if (y = *xb >> 16) {
- x = xa;
- xc = xc0;
- carry = 0;
- z2 = *xc;
- do {
- z = (*x & 0xffff) * y + (*xc >> 16) + carry;
- carry = z >> 16;
- Storeinc(xc, z, z2);
- z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
- carry = z2 >> 16;
- } while (x < xae);
- *xc = z2;
- }
- }
- for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc)
- ;
- c->wds = wc;
- return c;
- }
- static Bigint *p5s;
- static Bigint *
- pow5mult(Bigint *b, int k)
- {
- Bigint * b1, *p5, *p51;
- int i;
- static int p05[3] = {
- 5, 25, 125 };
- if (i = k & 3)
- b = multadd(b, p05[i-1], 0);
- if (!(k >>= 2))
- return b;
- if (!(p5 = p5s)) {
- /* first time */
- ACQUIRE_DTOA_LOCK(1);
- if (!(p5 = p5s)) {
- p5 = p5s = i2b(625);
- p5->next = 0;
- }
- FREE_DTOA_LOCK(1);
- }
- for (; ; ) {
- if (k & 1) {
- b1 = mult(b, p5);
- Bfree(b);
- b = b1;
- }
- if (!(k >>= 1))
- break;
- if (!(p51 = p5->next)) {
- ACQUIRE_DTOA_LOCK(1);
- if (!(p51 = p5->next)) {
- p51 = p5->next = mult(p5, p5);
- p51->next = 0;
- }
- FREE_DTOA_LOCK(1);
- }
- p5 = p51;
- }
- return b;
- }
- static Bigint *
- lshift(Bigint *b, int k)
- {
- int i, k1, n, n1;
- Bigint * b1;
- unsigned int * x, *x1, *xe, z;
- n = k >> 5;
- k1 = b->k;
- n1 = n + b->wds + 1;
- for (i = b->maxwds; n1 > i; i <<= 1)
- k1++;
- b1 = Balloc(k1);
- x1 = b1->x;
- for (i = 0; i < n; i++)
- *x1++ = 0;
- x = b->x;
- xe = x + b->wds;
- if (k &= 0x1f) {
- k1 = 32 - k;
- z = 0;
- do {
- *x1++ = *x << k | z;
- z = *x++ >> k1;
- } while (x < xe);
- if (*x1 = z)
- ++n1;
- } else
- do
- *x1++ = *x++;
- while (x < xe);
- b1->wds = n1 - 1;
- Bfree(b);
- return b1;
- }
- static int
- cmp(Bigint *a, Bigint *b)
- {
- unsigned int * xa, *xa0, *xb, *xb0;
- int i, j;
- i = a->wds;
- j = b->wds;
- if (i -= j)
- return i;
- xa0 = a->x;
- xa = xa0 + j;
- xb0 = b->x;
- xb = xb0 + j;
- for (; ; ) {
- if (*--xa != *--xb)
- return * xa < *xb ? -1 : 1;
- if (xa <= xa0)
- break;
- }
- return 0;
- }
- static Bigint *
- diff(Bigint *a, Bigint *b)
- {
- Bigint * c;
- int i, wa, wb;
- unsigned int * xa, *xae, *xb, *xbe, *xc;
- unsigned int borrow, y;
- unsigned int z;
- i = cmp(a, b);
- if (!i) {
- c = Balloc(0);
- c->wds = 1;
- c->x[0] = 0;
- return c;
- }
- if (i < 0) {
- c = a;
- a = b;
- b = c;
- i = 1;
- } else
- i = 0;
- c = Balloc(a->k);
- c->sign = i;
- wa = a->wds;
- xa = a->x;
- xae = xa + wa;
- wb = b->wds;
- xb = b->x;
- xbe = xb + wb;
- xc = c->x;
- borrow = 0;
- do {
- y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
- borrow = (y & 0x10000) >> 16;
- z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
- borrow = (z & 0x10000) >> 16;
- Storeinc(xc, z, y);
- } while (xb < xbe);
- while (xa < xae) {
- y = (*xa & 0xffff) - borrow;
- borrow = (y & 0x10000) >> 16;
- z = (*xa++ >> 16) - borrow;
- borrow = (z & 0x10000) >> 16;
- Storeinc(xc, z, y);
- }
- while (!*--xc)
- wa--;
- c->wds = wa;
- return c;
- }
- static double
- ulp(double x)
- {
- uint32_t L;
- Ulongs uls;
- uls = double2ulongs(x);
- L = (uls.hi & Exp_mask) - (P - 1) * Exp_msk1;
- return ulongs2double((Ulongs){L, 0});
- }
- static double
- b2d(Bigint *a, int *e)
- {
- unsigned *xa, *xa0, w, y, z;
- int k;
- uint32_t d0, d1;
- xa0 = a->x;
- xa = xa0 + a->wds;
- y = *--xa;
- k = hi0bits(y);
- *e = 32 - k;
- if (k < Ebits) {
- w = xa > xa0 ? *--xa : 0;
- d1 = y << (32 - Ebits) + k | w >> Ebits - k;
- return ulongs2double((Ulongs){Exp_1 | y >> Ebits - k, d1});
- }
- z = xa > xa0 ? *--xa : 0;
- if (k -= Ebits) {
- d0 = Exp_1 | y << k | z >> 32 - k;
- y = xa > xa0 ? *--xa : 0;
- d1 = z << k | y >> 32 - k;
- } else {
- d0 = Exp_1 | y;
- d1 = z;
- }
- return ulongs2double((Ulongs){d0, d1});
- }
- static Bigint *
- d2b(double d, int *e, int *bits)
- {
- Bigint * b;
- int de, i, k;
- unsigned *x, y, z;
- Ulongs uls;
- b = Balloc(1);
- x = b->x;
- uls = double2ulongs(d);
- z = uls.hi & Frac_mask;
- uls.hi &= 0x7fffffff; /* clear sign bit, which we ignore */
- de = (int)(uls.hi >> Exp_shift);
- z |= Exp_msk11;
- if (y = uls.lo) { /* assignment = */
- if (k = lo0bits(&y)) { /* assignment = */
- x[0] = y | z << 32 - k;
- z >>= k;
- } else
- x[0] = y;
- i = b->wds = (x[1] = z) ? 2 : 1;
- } else {
- k = lo0bits(&z);
- x[0] = z;
- i = b->wds = 1;
- k += 32;
- }
- USED(i);
- *e = de - Bias - (P - 1) + k;
- *bits = P - k;
- return b;
- }
- static double
- ratio(Bigint *a, Bigint *b)
- {
- double da, db;
- int k, ka, kb;
- Ulongs uls;
- da = b2d(a, &ka);
- db = b2d(b, &kb);
- k = ka - kb + 32 * (a->wds - b->wds);
- if (k > 0) {
- uls = double2ulongs(da);
- uls.hi += k * Exp_msk1;
- da = ulongs2double(uls);
- } else {
- k = -k;
- uls = double2ulongs(db);
- uls.hi += k * Exp_msk1;
- db = ulongs2double(uls);
- }
- return da / db;
- }
- static const double
- tens[] = {
- 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
- 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
- 1e20, 1e21, 1e22
- };
- static const double
- bigtens[] = {
- 1e16, 1e32, 1e64, 1e128, 1e256 };
- #define Scale_Bit 0x10
- #define n_bigtens 5
- #define NAN_WORD0 0x7ff80000
- #define NAN_WORD1 0
- static int
- match(const char **sp, char *t)
- {
- int c, d;
- const char * s = *sp;
- while (d = *t++) {
- if ((c = *++s) >= 'A' && c <= 'Z')
- c += 'a' - 'A';
- if (c != d)
- return 0;
- }
- *sp = s + 1;
- return 1;
- }
- static void
- gethex(double *rvp, const char **sp)
- {
- unsigned int c, x[2];
- const char * s;
- int havedig, udx0, xshift;
- x[0] = x[1] = 0;
- havedig = xshift = 0;
- udx0 = 1;
- s = *sp;
- while (c = *(const unsigned char * )++s) {
- if (c >= '0' && c <= '9')
- c -= '0';
- else if (c >= 'a' && c <= 'f')
- c += 10 - 'a';
- else if (c >= 'A' && c <= 'F')
- c += 10 - 'A';
- else if (c <= ' ') {
- if (udx0 && havedig) {
- udx0 = 0;
- xshift = 1;
- }
- continue;
- } else if (/*(*/ c == ')') {
- *sp = s + 1;
- break;
- } else
- return; /* invalid form: don't change *sp */
- havedig = 1;
- if (xshift) {
- xshift = 0;
- x[0] = x[1];
- x[1] = 0;
- }
- if (udx0)
- x[0] = (x[0] << 4) | (x[1] >> 28);
- x[1] = (x[1] << 4) | c;
- }
- if ((x[0] &= 0xfffff) || x[1])
- *rvp = ulongs2double((Ulongs){Exp_mask | x[0], x[1]});
- }
- static int
- quorem(Bigint *b, Bigint *S)
- {
- int n;
- unsigned int * bx, *bxe, q, *sx, *sxe;
- unsigned int borrow, carry, y, ys;
- unsigned int si, z, zs;
- n = S->wds;
- if (b->wds < n)
- return 0;
- sx = S->x;
- sxe = sx + --n;
- bx = b->x;
- bxe = bx + n;
- q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
- if (q) {
- borrow = 0;
- carry = 0;
- do {
- si = *sx++;
- ys = (si & 0xffff) * q + carry;
- zs = (si >> 16) * q + (ys >> 16);
- carry = zs >> 16;
- y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
- borrow = (y & 0x10000) >> 16;
- z = (*bx >> 16) - (zs & 0xffff) - borrow;
- borrow = (z & 0x10000) >> 16;
- Storeinc(bx, z, y);
- } while (sx <= sxe);
- if (!*bxe) {
- bx = b->x;
- while (--bxe > bx && !*bxe)
- --n;
- b->wds = n;
- }
- }
- if (cmp(b, S) >= 0) {
- q++;
- borrow = 0;
- carry = 0;
- bx = b->x;
- sx = S->x;
- do {
- si = *sx++;
- ys = (si & 0xffff) + carry;
- zs = (si >> 16) + (ys >> 16);
- carry = zs >> 16;
- y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
- borrow = (y & 0x10000) >> 16;
- z = (*bx >> 16) - (zs & 0xffff) - borrow;
- borrow = (z & 0x10000) >> 16;
- Storeinc(bx, z, y);
- } while (sx <= sxe);
- bx = b->x;
- bxe = bx + n;
- if (!*bxe) {
- while (--bxe > bx && !*bxe)
- --n;
- b->wds = n;
- }
- }
- return q;
- }
- static char *
- rv_alloc(int i)
- {
- int j, k, *r;
- j = sizeof(unsigned int);
- for (k = 0;
- sizeof(Bigint) - sizeof(unsigned int) - sizeof(int) + j <= i;
- j <<= 1)
- k++;
- r = (int * )Balloc(k);
- *r = k;
- return
- (char *)(r + 1);
- }
- static char *
- nrv_alloc(char *s, char **rve, int n)
- {
- char *rv, *t;
- t = rv = rv_alloc(n);
- while (*t = *s++)
- t++;
- if (rve)
- *rve = t;
- return rv;
- }
- /* freedtoa(s) must be used to free values s returned by dtoa
- * when MULTIPLE_THREADS is #defined. It should be used in all cases,
- * but for consistency with earlier versions of dtoa, it is optional
- * when MULTIPLE_THREADS is not defined.
- */
- void
- freedtoa(char *s)
- {
- Bigint * b = (Bigint * )((int *)s - 1);
- b->maxwds = 1 << (b->k = *(int * )b);
- Bfree(b);
- }
- /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
- *
- * Inspired by "How to Print Floating-Point Numbers Accurately" by
- * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
- *
- * Modifications:
- * 1. Rather than iterating, we use a simple numeric overestimate
- * to determine k = floor(log10(d)). We scale relevant
- * quantities using O(log2(k)) rather than O(k) multiplications.
- * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
- * try to generate digits strictly left to right. Instead, we
- * compute with fewer bits and propagate the carry if necessary
- * when rounding the final digit up. This is often faster.
- * 3. Under the assumption that input will be rounded nearest,
- * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
- * That is, we allow equality in stopping tests when the
- * round-nearest rule will give the same floating-point value
- * as would satisfaction of the stopping test with strict
- * inequality.
- * 4. We remove common factors of powers of 2 from relevant
- * quantities.
- * 5. When converting floating-point integers less than 1e16,
- * we use floating-point arithmetic rather than resorting
- * to multiple-precision integers.
- * 6. When asked to produce fewer than 15 digits, we first try
- * to get by with floating-point arithmetic; we resort to
- * multiple-precision integer arithmetic only if we cannot
- * guarantee that the floating-point calculation has given
- * the correctly rounded result. For k requested digits and
- * "uniformly" distributed input, the probability is
- * something like 10^(k-15) that we must resort to the int
- * calculation.
- */
- char *
- dtoa(double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
- {
- /* Arguments ndigits, decpt, sign are similar to those
- of ecvt and fcvt; trailing zeros are suppressed from
- the returned string. If not null, *rve is set to point
- to the end of the return value. If d is +-Infinity or NaN,
- then *decpt is set to 9999.
- mode:
- 0 ==> shortest string that yields d when read in
- and rounded to nearest.
- 1 ==> like 0, but with Steele & White stopping rule;
- e.g. with IEEE P754 arithmetic , mode 0 gives
- 1e23 whereas mode 1 gives 9.999999999999999e22.
- 2 ==> max(1,ndigits) significant digits. This gives a
- return value similar to that of ecvt, except
- that trailing zeros are suppressed.
- 3 ==> through ndigits past the decimal point. This
- gives a return value similar to that from fcvt,
- except that trailing zeros are suppressed, and
- ndigits can be negative.
- 4-9 should give the same return values as 2-3, i.e.,
- 4 <= mode <= 9 ==> same return as mode
- 2 + (mode & 1). These modes are mainly for
- debugging; often they run slower but sometimes
- faster than modes 2-3.
- 4,5,8,9 ==> left-to-right digit generation.
- 6-9 ==> don't try fast floating-point estimate
- (if applicable).
- Values of mode other than 0-9 are treated as mode 0.
- Sufficient space is allocated to the return value
- to hold the suppressed trailing zeros.
- */
- int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
- j, j1, k, k0, k_check, L, leftright, m2, m5, s2, s5,
- spec_case, try_quick;
- Bigint * b, *b1, *delta, *mlo=nil, *mhi, *S;
- double d2, ds, eps;
- char *s, *s0;
- Ulongs ulsd, ulsd2;
- ulsd = double2ulongs(d);
- if (ulsd.hi & Sign_bit) {
- /* set sign for everything, including 0's and NaNs */
- *sign = 1;
- ulsd.hi &= ~Sign_bit; /* clear sign bit */
- } else
- *sign = 0;
- if ((ulsd.hi & Exp_mask) == Exp_mask) {
- /* Infinity or NaN */
- *decpt = 9999;
- if (!ulsd.lo && !(ulsd.hi & 0xfffff))
- return nrv_alloc("Infinity", rve, 8);
- return nrv_alloc("NaN", rve, 3);
- }
- d = ulongs2double(ulsd);
- if (!d) {
- *decpt = 1;
- return nrv_alloc("0", rve, 1);
- }
- b = d2b(d, &be, &bbits);
- i = (int)(ulsd.hi >> Exp_shift1 & (Exp_mask >> Exp_shift1));
- ulsd2 = ulsd;
- ulsd2.hi &= Frac_mask1;
- ulsd2.hi |= Exp_11;
- d2 = ulongs2double(ulsd2);
- /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
- * log10(x) = log(x) / log(10)
- * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
- * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
- *
- * This suggests computing an approximation k to log10(d) by
- *
- * k = (i - Bias)*0.301029995663981
- * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
- *
- * We want k to be too large rather than too small.
- * The error in the first-order Taylor series approximation
- * is in our favor, so we just round up the constant enough
- * to compensate for any error in the multiplication of
- * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
- * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
- * adding 1e-13 to the constant term more than suffices.
- * Hence we adjust the constant term to 0.1760912590558.
- * (We could get a more accurate k by invoking log10,
- * but this is probably not worthwhile.)
- */
- i -= Bias;
- ds = (d2 - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
- k = (int)ds;
- if (ds < 0. && ds != k)
- k--; /* want k = floor(ds) */
- k_check = 1;
- if (k >= 0 && k <= Ten_pmax) {
- if (d < tens[k])
- k--;
- k_check = 0;
- }
- j = bbits - i - 1;
- if (j >= 0) {
- b2 = 0;
- s2 = j;
- } else {
- b2 = -j;
- s2 = 0;
- }
- if (k >= 0) {
- b5 = 0;
- s5 = k;
- s2 += k;
- } else {
- b2 -= k;
- b5 = -k;
- s5 = 0;
- }
- if (mode < 0 || mode > 9)
- mode = 0;
- try_quick = 1;
- if (mode > 5) {
- mode -= 4;
- try_quick = 0;
- }
- leftright = 1;
- switch (mode) {
- case 0:
- case 1:
- default:
- ilim = ilim1 = -1;
- i = 18;
- ndigits = 0;
- break;
- case 2:
- leftright = 0;
- /* no break */
- case 4:
- if (ndigits <= 0)
- ndigits = 1;
- ilim = ilim1 = i = ndigits;
- break;
- case 3:
- leftright = 0;
- /* no break */
- case 5:
- i = ndigits + k + 1;
- ilim = i;
- ilim1 = i - 1;
- if (i <= 0)
- i = 1;
- }
- s = s0 = rv_alloc(i);
- if (ilim >= 0 && ilim <= Quick_max && try_quick) {
- /* Try to get by with floating-point arithmetic. */
- i = 0;
- d2 = d;
- k0 = k;
- ilim0 = ilim;
- ieps = 2; /* conservative */
- if (k > 0) {
- ds = tens[k&0xf];
- j = k >> 4;
- if (j & Bletch) {
- /* prevent overflows */
- j &= Bletch - 1;
- d /= bigtens[n_bigtens-1];
- ieps++;
- }
- for (; j; j >>= 1, i++)
- if (j & 1) {
- ieps++;
- ds *= bigtens[i];
- }
- d /= ds;
- } else if (j1 = -k) {
- d *= tens[j1 & 0xf];
- for (j = j1 >> 4; j; j >>= 1, i++)
- if (j & 1) {
- ieps++;
- d *= bigtens[i];
- }
- }
- if (k_check && d < 1. && ilim > 0) {
- if (ilim1 <= 0)
- goto fast_failed;
- ilim = ilim1;
- k--;
- d *= 10.;
- ieps++;
- }
- eps = ieps * d + 7.;
- ulsd = double2ulongs(eps);
- ulsd.hi -= (P - 1) * Exp_msk1;
- eps = ulongs2double(ulsd);
- if (ilim == 0) {
- S = mhi = 0;
- d -= 5.;
- if (d > eps)
- goto one_digit;
- if (d < -eps)
- goto no_digits;
- goto fast_failed;
- }
- /* Generate ilim digits, then fix them up. */
- eps *= tens[ilim-1];
- for (i = 1; ; i++, d *= 10.) {
- L = d;
- // assert(L < 10);
- d -= L;
- *s++ = '0' + (int)L;
- if (i == ilim) {
- if (d > 0.5 + eps)
- goto bump_up;
- else if (d < 0.5 - eps) {
- while (*--s == '0')
- ;
- s++;
- goto ret1;
- }
- break;
- }
- }
- fast_failed:
- s = s0;
- d = d2;
- k = k0;
- ilim = ilim0;
- }
- /* Do we have a "small" integer? */
- if (be >= 0 && k <= Int_max) {
- /* Yes. */
- ds = tens[k];
- if (ndigits < 0 && ilim <= 0) {
- S = mhi = 0;
- if (ilim < 0 || d <= 5 * ds)
- goto no_digits;
- goto one_digit;
- }
- for (i = 1; ; i++) {
- L = d / ds;
- d -= L * ds;
- *s++ = '0' + (int)L;
- if (i == ilim) {
- d += d;
- if (d > ds || d == ds && L & 1) {
- bump_up:
- while (*--s == '9')
- if (s == s0) {
- k++;
- *s = '0';
- break;
- }
- ++ * s++;
- }
- break;
- }
- if (!(d *= 10.))
- break;
- }
- goto ret1;
- }
- m2 = b2;
- m5 = b5;
- mhi = mlo = 0;
- if (leftright) {
- if (mode < 2) {
- i =
- 1 + P - bbits;
- } else {
- j = ilim - 1;
- if (m5 >= j)
- m5 -= j;
- else {
- s5 += j -= m5;
- b5 += j;
- m5 = 0;
- }
- if ((i = ilim) < 0) {
- m2 -= i;
- i = 0;
- }
- }
- b2 += i;
- s2 += i;
- mhi = i2b(1);
- }
- if (m2 > 0 && s2 > 0) {
- i = m2 < s2 ? m2 : s2;
- b2 -= i;
- m2 -= i;
- s2 -= i;
- }
- if (b5 > 0) {
- if (leftright) {
- if (m5 > 0) {
- mhi = pow5mult(mhi, m5);
- b1 = mult(mhi, b);
- Bfree(b);
- b = b1;
- }
- if (j = b5 - m5)
- b = pow5mult(b, j);
- } else
- b = pow5mult(b, b5);
- }
- S = i2b(1);
- if (s5 > 0)
- S = pow5mult(S, s5);
- /* Check for special case that d is a normalized power of 2. */
- spec_case = 0;
- if (mode < 2) {
- ulsd = double2ulongs(d);
- if (!ulsd.lo && !(ulsd.hi & Bndry_mask)) {
- /* The special case */
- b2 += Log2P;
- s2 += Log2P;
- spec_case = 1;
- }
- }
- /* Arrange for convenient computation of quotients:
- * shift left if necessary so divisor has 4 leading 0 bits.
- *
- * Perhaps we should just compute leading 28 bits of S once
- * and for all and pass them and a shift to quorem, so it
- * can do shifts and ors to compute the numerator for q.
- */
- if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)
- i = 32 - i;
- if (i > 4) {
- i -= 4;
- b2 += i;
- m2 += i;
- s2 += i;
- } else if (i < 4) {
- i += 28;
- b2 += i;
- m2 += i;
- s2 += i;
- }
- if (b2 > 0)
- b = lshift(b, b2);
- if (s2 > 0)
- S = lshift(S, s2);
- if (k_check) {
- if (cmp(b, S) < 0) {
- k--;
- b = multadd(b, 10, 0); /* we botched the k estimate */
- if (leftright)
- mhi = multadd(mhi, 10, 0);
- ilim = ilim1;
- }
- }
- if (ilim <= 0 && mode > 2) {
- if (ilim < 0 || cmp(b, S = multadd(S, 5, 0)) <= 0) {
- /* no digits, fcvt style */
- no_digits:
- k = -1 - ndigits;
- goto ret;
- }
- one_digit:
- *s++ = '1';
- k++;
- goto ret;
- }
- if (leftright) {
- if (m2 > 0)
- mhi = lshift(mhi, m2);
- /* Compute mlo -- check for special case
- * that d is a normalized power of 2.
- */
- mlo = mhi;
- if (spec_case) {
- mhi = Balloc(mhi->k);
- Bcopy(mhi, mlo);
- mhi = lshift(mhi, Log2P);
- }
- for (i = 1; ; i++) {
- dig = quorem(b, S) + '0';
- /* Do we yet have the shortest decimal string
- * that will round to d?
- */
- j = cmp(b, mlo);
- delta = diff(S, mhi);
- j1 = delta->sign ? 1 : cmp(b, delta);
- Bfree(delta);
- ulsd = double2ulongs(d);
- if (j1 == 0 && !mode && !(ulsd.lo & 1)) {
- if (dig == '9')
- goto round_9_up;
- if (j > 0)
- dig++;
- *s++ = dig;
- goto ret;
- }
- if (j < 0 || j == 0 && !mode && !(ulsd.lo & 1)) {
- if (j1 > 0) {
- b = lshift(b, 1);
- j1 = cmp(b, S);
- if ((j1 > 0 || j1 == 0 && dig & 1)
- && dig++ == '9')
- goto round_9_up;
- }
- *s++ = dig;
- goto ret;
- }
- if (j1 > 0) {
- if (dig == '9') { /* possible if i == 1 */
- round_9_up:
- *s++ = '9';
- goto roundoff;
- }
- *s++ = dig + 1;
- goto ret;
- }
- *s++ = dig;
- if (i == ilim)
- break;
- b = multadd(b, 10, 0);
- if (mlo == mhi)
- mlo = mhi = multadd(mhi, 10, 0);
- else {
- mlo = multadd(mlo, 10, 0);
- mhi = multadd(mhi, 10, 0);
- }
- }
- } else
- for (i = 1; ; i++) {
- *s++ = dig = quorem(b, S) + '0';
- if (i >= ilim)
- break;
- b = multadd(b, 10, 0);
- }
- /* Round off last digit */
- b = lshift(b, 1);
- j = cmp(b, S);
- if (j > 0 || j == 0 && dig & 1) {
- roundoff:
- while (*--s == '9')
- if (s == s0) {
- k++;
- *s++ = '1';
- goto ret;
- }
- ++ * s++;
- } else {
- while (*--s == '0')
- ;
- s++;
- }
- ret:
- Bfree(S);
- if (mhi) {
- if (mlo && mlo != mhi)
- Bfree(mlo);
- Bfree(mhi);
- }
- ret1:
- Bfree(b);
- *s = 0;
- *decpt = k + 1;
- if (rve)
- *rve = s;
- return s0;
- }
|