Plan 9 from Bell Labs’s /usr/web/sources/plan9/sys/src/libstdio/dtoa.c

 ``` /* 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 #include 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 { ulong hi; ulong 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) { ulong 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; ulong 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 }; static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 9007199254740992.e-256 }; /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ /* flag unnecessarily. It leads to a song and dance at the end of strtod. */ #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; } ```