ref: 1d891d163e814a93ee5346cf05b4fac297bf3a5c
dir: /sys/src/ape/lib/ap/stdio/strtod.c/
#include "fconv.h" /* strtod for IEEE-, VAX-, and IBM-arithmetic machines (dmg). * * This strtod returns a nearest machine number to the input decimal * string (or sets errno to ERANGE). With IEEE arithmetic, ties are * broken by the IEEE round-even rule. Otherwise ties are broken by * biased rounding (add half and chop). * * Inspired loosely by William D. Clinger's paper "How to Read Floating * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. * * Modifications: * * 1. We only require IEEE, IBM, or VAX double-precision * arithmetic (not IEEE double-extended). * 2. We get by with floating-point arithmetic in a case that * Clinger missed -- when we're computing d * 10^n * for a small integer d and the integer n is not too * much larger than 22 (the maximum integer k for which * we can represent 10^k exactly), we may be able to * compute (d*10^k) * 10^(e-k) with just one roundoff. * 3. Rather than a bit-at-a-time adjustment of the binary * result in the hard case, we use floating-point * arithmetic to determine the adjustment to within * one bit; only in really hard cases do we need to * compute a second residual. * 4. Because of 3., we don't need a large table of powers of 10 * for ten-to-e (just some small tables, e.g. of 10^k * for 0 <= k <= 22). */ #ifdef RND_PRODQUOT #define rounded_product(a,b) a = rnd_prod(a, b) #define rounded_quotient(a,b) a = rnd_quot(a, b) extern double rnd_prod(double, double), rnd_quot(double, double); #else #define rounded_product(a,b) a *= b #define rounded_quotient(a,b) a /= b #endif static double ulp(double xarg) { register long L; Dul a; Dul x; x.d = xarg; L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; #ifndef Sudden_Underflow if (L > 0) { #endif #ifdef IBM L |= Exp_msk1 >> 4; #endif word0(a) = L; word1(a) = 0; #ifndef Sudden_Underflow } else { L = -L >> Exp_shift; if (L < Exp_shift) { word0(a) = 0x80000 >> L; word1(a) = 0; } else { word0(a) = 0; L -= Exp_shift; word1(a) = L >= 31 ? 1 : 1 << 31 - L; } } #endif return a.d; } static Bigint * s2b(CONST char *s, int nd0, int nd, unsigned long y9) { Bigint *b; int i, k; long x, y; x = (nd + 8) / 9; for(k = 0, y = 1; x > y; y <<= 1, k++) ; #ifdef Pack_32 b = Balloc(k); b->x[0] = y9; b->wds = 1; #else b = Balloc(k+1); b->x[0] = y9 & 0xffff; b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; #endif 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 double b2d(Bigint *a, int *e) { unsigned long *xa, *xa0, w, y, z; int k; Dul d; #ifdef VAX unsigned long d0, d1; #else #define d0 word0(d) #define d1 word1(d) #endif xa0 = a->x; xa = xa0 + a->wds; y = *--xa; #ifdef DEBUG if (!y) Bug("zero y in b2d"); #endif k = hi0bits(y); *e = 32 - k; #ifdef Pack_32 if (k < Ebits) { d0 = Exp_1 | y >> Ebits - k; w = xa > xa0 ? *--xa : 0; d1 = y << (32-Ebits) + k | w >> Ebits - k; goto ret_d; } 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; } #else if (k < Ebits + 16) { z = xa > xa0 ? *--xa : 0; d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; w = xa > xa0 ? *--xa : 0; y = xa > xa0 ? *--xa : 0; d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; goto ret_d; } z = xa > xa0 ? *--xa : 0; w = xa > xa0 ? *--xa : 0; k -= Ebits + 16; d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; y = xa > xa0 ? *--xa : 0; d1 = w << k + 16 | y << k; #endif ret_d: #ifdef VAX word0(d) = d0 >> 16 | d0 << 16; word1(d) = d1 >> 16 | d1 << 16; #else #undef d0 #undef d1 #endif return d.d; } static double ratio(Bigint *a, Bigint *b) { Dul da, db; int k, ka, kb; da.d = b2d(a, &ka); db.d = b2d(b, &kb); #ifdef Pack_32 k = ka - kb + 32*(a->wds - b->wds); #else k = ka - kb + 16*(a->wds - b->wds); #endif #ifdef IBM if (k > 0) { word0(da) += (k >> 2)*Exp_msk1; if (k &= 3) da *= 1 << k; } else { k = -k; word0(db) += (k >> 2)*Exp_msk1; if (k &= 3) db *= 1 << k; } #else if (k > 0) word0(da) += k*Exp_msk1; else { k = -k; word0(db) += k*Exp_msk1; } #endif return da.d / db.d; } double strtod(CONST char *s00, char **se) { int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign; CONST char *s, *s0, *s1; double aadj, aadj1, adj; Dul rv, rv0; long L; unsigned long y, z; Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; sign = nz0 = nz = 0; rv.d = 0.; for(s = s00;;s++) switch(*s) { case '-': sign = 1; /* no break */ case '+': if (*++s) goto break2; /* no break */ case 0: s = s00; goto ret; case '\t': case '\n': case '\v': case '\f': case '\r': case ' ': continue; default: goto break2; } break2: if (*s == '0') { nz0 = 1; while(*++s == '0') ; if (!*s) goto ret; } s0 = s; y = z = 0; for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) if (nd < 9) y = 10*y + c - '0'; else if (nd < 16) z = 10*z + c - '0'; nd0 = nd; if (c == '.') { c = *++s; if (!nd) { for(; c == '0'; c = *++s) nz++; if (c > '0' && c <= '9') { s0 = s; nf += nz; nz = 0; goto have_dig; } goto dig_done; } for(; c >= '0' && c <= '9'; c = *++s) { have_dig: nz++; if (c -= '0') { nf += nz; for(i = 1; i < nz; i++) if (nd++ < 9) y *= 10; else if (nd <= DBL_DIG + 1) z *= 10; if (nd++ < 9) y = 10*y + c; else if (nd <= DBL_DIG + 1) z = 10*z + c; nz = 0; } } } dig_done: e = 0; if (c == 'e' || c == 'E') { if (!nd && !nz && !nz0) { s = s00; goto ret; } s00 = s; esign = 0; switch(c = *++s) { case '-': esign = 1; case '+': c = *++s; } if (c >= '0' && c <= '9') { while(c == '0') c = *++s; if (c > '0' && c <= '9') { e = c - '0'; s1 = s; while((c = *++s) >= '0' && c <= '9') e = 10*e + c - '0'; if (s - s1 > 8) /* Avoid confusion from exponents * so large that e might overflow. */ e = 9999999; if (esign) e = -e; } else e = 0; } else s = s00; } if (!nd) { if (!nz && !nz0) s = s00; goto ret; } e1 = e -= nf; /* Now we have nd0 digits, starting at s0, followed by a * decimal point, followed by nd-nd0 digits. The number we're * after is the integer represented by those digits times * 10**e */ if (!nd0) nd0 = nd; k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; rv.d = y; if (k > 9) rv.d = tens[k - 9] * rv.d + z; bd0 = 0; if (nd <= DBL_DIG #ifndef RND_PRODQUOT && FLT_ROUNDS == 1 #endif ) { if (!e) goto ret; if (e > 0) { if (e <= Ten_pmax) { #ifdef VAX goto vax_ovfl_check; #else /* rv = */ rounded_product(rv.d, tens[e]); goto ret; #endif } i = DBL_DIG - nd; if (e <= Ten_pmax + i) { /* A fancier test would sometimes let us do * this for larger i values. */ e -= i; rv.d *= tens[i]; #ifdef VAX /* VAX exponent range is so narrow we must * worry about overflow here... */ vax_ovfl_check: word0(rv) -= P*Exp_msk1; /* rv = */ rounded_product(rv.d, tens[e]); if ((word0(rv) & Exp_mask) > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) goto ovfl; word0(rv) += P*Exp_msk1; #else /* rv = */ rounded_product(rv.d, tens[e]); #endif goto ret; } } else if (e >= -Ten_pmax) { /* rv = */ rounded_quotient(rv.d, tens[-e]); goto ret; } } e1 += nd - k; /* Get starting approximation = rv * 10**e1 */ if (e1 > 0) { if (nd0 + e1 - 1 > DBL_MAX_10_EXP) goto ovfl; if (i = e1 & 15) rv.d *= tens[i]; if (e1 &= ~15) { if (e1 > DBL_MAX_10_EXP) { ovfl: errno = ERANGE; rv.d = HUGE_VAL; if (bd0) goto retfree; goto ret; } if (e1 >>= 4) { for(j = 0; e1 > 1; j++, e1 >>= 1) if (e1 & 1) rv.d *= bigtens[j]; /* The last multiplication could overflow. */ word0(rv) -= P*Exp_msk1; rv.d *= bigtens[j]; if ((z = word0(rv) & Exp_mask) > Exp_msk1*(DBL_MAX_EXP+Bias-P)) goto ovfl; if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { /* set to largest number */ /* (Can't trust DBL_MAX) */ word0(rv) = Big0; word1(rv) = Big1; } else word0(rv) += P*Exp_msk1; } } } else if (e1 < 0) { e1 = -e1; if (i = e1 & 15) rv.d /= tens[i]; if (e1 &= ~15) { e1 >>= 4; if (e1 >= 1 << n_bigtens) goto undfl; for(j = 0; e1 > 1; j++, e1 >>= 1) if (e1 & 1) rv.d *= tinytens[j]; /* The last multiplication could underflow. */ rv0.d = rv.d; rv.d *= tinytens[j]; if (rv.d == 0) { rv.d = 2.*rv0.d; rv.d *= tinytens[j]; if (rv.d == 0) { undfl: rv.d = 0.; errno = ERANGE; if (bd0) goto retfree; goto ret; } word0(rv) = Tiny0; word1(rv) = Tiny1; /* The refinement below will clean * this approximation up. */ } } } /* Now the hard part -- adjusting rv to the correct value.*/ /* Put digits into bd: true value = bd * 10^e */ bd0 = s2b(s0, nd0, nd, y); for(;;) { bd = Balloc(bd0->k); Bcopy(bd, bd0); bb = d2b(rv.d, &bbe, &bbbits); /* rv = bb * 2^bbe */ bs = i2b(1); if (e >= 0) { bb2 = bb5 = 0; bd2 = bd5 = e; } else { bb2 = bb5 = -e; bd2 = bd5 = 0; } if (bbe >= 0) bb2 += bbe; else bd2 -= bbe; bs2 = bb2; #ifdef Sudden_Underflow #ifdef IBM j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); #else j = P + 1 - bbbits; #endif #else i = bbe + bbbits - 1; /* logb(rv) */ if (i < Emin) /* denormal */ j = bbe + (P-Emin); else j = P + 1 - bbbits; #endif bb2 += j; bd2 += j; i = bb2 < bd2 ? bb2 : bd2; if (i > bs2) i = bs2; if (i > 0) { bb2 -= i; bd2 -= i; bs2 -= i; } if (bb5 > 0) { bs = pow5mult(bs, bb5); bb1 = mult(bs, bb); Bfree(bb); bb = bb1; } if (bb2 > 0) bb = lshift(bb, bb2); if (bd5 > 0) bd = pow5mult(bd, bd5); if (bd2 > 0) bd = lshift(bd, bd2); if (bs2 > 0) bs = lshift(bs, bs2); delta = diff(bb, bd); dsign = delta->sign; delta->sign = 0; i = cmp(delta, bs); if (i < 0) { /* Error is less than half an ulp -- check for * special case of mantissa a power of two. */ if (dsign || word1(rv) || word0(rv) & Bndry_mask) break; delta = lshift(delta,Log2P); if (cmp(delta, bs) > 0) goto drop_down; break; } if (i == 0) { /* exactly half-way between */ if (dsign) { if ((word0(rv) & Bndry_mask1) == Bndry_mask1 && word1(rv) == 0xffffffff) { /*boundary case -- increment exponent*/ word0(rv) = (word0(rv) & Exp_mask) + Exp_msk1 #ifdef IBM | Exp_msk1 >> 4 #endif ; word1(rv) = 0; break; } } else if (!(word0(rv) & Bndry_mask) && !word1(rv)) { drop_down: /* boundary case -- decrement exponent */ #ifdef Sudden_Underflow L = word0(rv) & Exp_mask; #ifdef IBM if (L < Exp_msk1) #else if (L <= Exp_msk1) #endif goto undfl; L -= Exp_msk1; #else L = (word0(rv) & Exp_mask) - Exp_msk1; #endif word0(rv) = L | Bndry_mask1; word1(rv) = 0xffffffff; #ifdef IBM goto cont; #else break; #endif } #ifndef ROUND_BIASED if (!(word1(rv) & LSB)) break; #endif if (dsign) rv.d += ulp(rv.d); #ifndef ROUND_BIASED else { rv.d -= ulp(rv.d); #ifndef Sudden_Underflow if (rv.d == 0) goto undfl; #endif } #endif break; } if ((aadj = ratio(delta, bs)) <= 2.) { if (dsign) aadj = aadj1 = 1.; else if (word1(rv) || word0(rv) & Bndry_mask) { #ifndef Sudden_Underflow if (word1(rv) == Tiny1 && !word0(rv)) goto undfl; #endif aadj = 1.; aadj1 = -1.; } else { /* special case -- power of FLT_RADIX to be */ /* rounded down... */ if (aadj < 2./FLT_RADIX) aadj = 1./FLT_RADIX; else aadj *= 0.5; aadj1 = -aadj; } } else { aadj *= 0.5; aadj1 = dsign ? aadj : -aadj; #ifdef Check_FLT_ROUNDS switch(FLT_ROUNDS) { case 2: /* towards +infinity */ aadj1 -= 0.5; break; case 0: /* towards 0 */ case 3: /* towards -infinity */ aadj1 += 0.5; } #else if (FLT_ROUNDS == 0) aadj1 += 0.5; #endif } y = word0(rv) & Exp_mask; /* Check for overflow */ if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { rv0.d = rv.d; word0(rv) -= P*Exp_msk1; adj = aadj1 * ulp(rv.d); rv.d += adj; if ((word0(rv) & Exp_mask) >= Exp_msk1*(DBL_MAX_EXP+Bias-P)) { if (word0(rv0) == Big0 && word1(rv0) == Big1) goto ovfl; word0(rv) = Big0; word1(rv) = Big1; goto cont; } else word0(rv) += P*Exp_msk1; } else { #ifdef Sudden_Underflow if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { rv0.d = rv.d; word0(rv) += P*Exp_msk1; adj = aadj1 * ulp(rv.d); rv.d += adj; #ifdef IBM if ((word0(rv) & Exp_mask) < P*Exp_msk1) #else if ((word0(rv) & Exp_mask) <= P*Exp_msk1) #endif { if (word0(rv0) == Tiny0 && word1(rv0) == Tiny1) goto undfl; word0(rv) = Tiny0; word1(rv) = Tiny1; goto cont; } else word0(rv) -= P*Exp_msk1; } else { adj = aadj1 * ulp(rv.d); rv.d += adj; } #else /* Compute adj so that the IEEE rounding rules will * correctly round rv + adj in some half-way cases. * If rv * ulp(rv) is denormalized (i.e., * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid * trouble from bits lost to denormalization; * example: 1.2e-307 . */ if (y <= (P-1)*Exp_msk1 && aadj >= 1.) { aadj1 = (double)(int)(aadj + 0.5); if (!dsign) aadj1 = -aadj1; } adj = aadj1 * ulp(rv.d); rv.d += adj; #endif } z = word0(rv) & Exp_mask; if (y == z) { /* Can we stop now? */ L = aadj; aadj -= L; /* The tolerances below are conservative. */ if (dsign || word1(rv) || word0(rv) & Bndry_mask) { if (aadj < .4999999 || aadj > .5000001) break; } else if (aadj < .4999999/FLT_RADIX) break; } cont: Bfree(bb); Bfree(bd); Bfree(bs); Bfree(delta); } retfree: Bfree(bb); Bfree(bd); Bfree(bs); Bfree(bd0); Bfree(delta); ret: if (se) *se = (char *)s; return sign ? -rv.d : rv.d; }