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Diffstat (limited to 'newlib/libc/stdlib/dtoa.c')
| -rw-r--r-- | newlib/libc/stdlib/dtoa.c | 854 |
1 files changed, 854 insertions, 0 deletions
diff --git a/newlib/libc/stdlib/dtoa.c b/newlib/libc/stdlib/dtoa.c new file mode 100644 index 0000000..3911f0e --- /dev/null +++ b/newlib/libc/stdlib/dtoa.c @@ -0,0 +1,854 @@ +/**************************************************************** + * + * The author of this software is David M. Gay. + * + * Copyright (c) 1991 by AT&T. + * + * Permission to use, copy, modify, and distribute this software for any + * purpose without fee is hereby granted, provided that this entire notice + * is included in all copies of any software which is or includes a copy + * or modification of this software and in all copies of the supporting + * documentation for such software. + * + * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED + * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY + * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY + * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. + * + ***************************************************************/ + +/* Please send bug reports to + David M. Gay + AT&T Bell Laboratories, Room 2C-463 + 600 Mountain Avenue + Murray Hill, NJ 07974-2070 + U.S.A. + dmg@research.att.com or research!dmg + */ + +#include <_ansi.h> +#include <stdlib.h> +#include <reent.h> +#include <string.h> +#include "mprec.h" + +static int +_DEFUN (quorem, + (b, S), + _Bigint * b _AND _Bigint * S) +{ + int n; + __Long borrow, y; + __ULong carry, q, ys; + __ULong *bx, *bxe, *sx, *sxe; +#ifdef Pack_32 + __Long z; + __ULong si, zs; +#endif + + n = S->_wds; +#ifdef DEBUG + /*debug*/ if (b->_wds > n) + /*debug*/ Bug ("oversize b in quorem"); +#endif + 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 */ +#ifdef DEBUG + /*debug*/ if (q > 9) + /*debug*/ Bug ("oversized quotient in quorem"); +#endif + if (q) + { + borrow = 0; + carry = 0; + do + { +#ifdef Pack_32 + si = *sx++; + ys = (si & 0xffff) * q + carry; + zs = (si >> 16) * q + (ys >> 16); + carry = zs >> 16; + y = (*bx & 0xffff) - (ys & 0xffff) + borrow; + borrow = y >> 16; + Sign_Extend (borrow, y); + z = (*bx >> 16) - (zs & 0xffff) + borrow; + borrow = z >> 16; + Sign_Extend (borrow, z); + Storeinc (bx, z, y); +#else + ys = *sx++ * q + carry; + carry = ys >> 16; + y = *bx - (ys & 0xffff) + borrow; + borrow = y >> 16; + Sign_Extend (borrow, y); + *bx++ = y & 0xffff; +#endif + } + 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 + { +#ifdef Pack_32 + si = *sx++; + ys = (si & 0xffff) + carry; + zs = (si >> 16) + (ys >> 16); + carry = zs >> 16; + y = (*bx & 0xffff) - (ys & 0xffff) + borrow; + borrow = y >> 16; + Sign_Extend (borrow, y); + z = (*bx >> 16) - (zs & 0xffff) + borrow; + borrow = z >> 16; + Sign_Extend (borrow, z); + Storeinc (bx, z, y); +#else + ys = *sx++ + carry; + carry = ys >> 16; + y = *bx - (ys & 0xffff) + borrow; + borrow = y >> 16; + Sign_Extend (borrow, y); + *bx++ = y & 0xffff; +#endif + } + while (sx <= sxe); + bx = b->_x; + bxe = bx + n; + if (!*bxe) + { + while (--bxe > bx && !*bxe) + --n; + b->_wds = n; + } + } + return q; +} + +/* 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 long + * calculation. + */ + + +char * +_DEFUN (_dtoa_r, + (ptr, _d, mode, ndigits, decpt, sign, rve), + struct _reent *ptr _AND + double _d _AND + int mode _AND + int ndigits _AND + int *decpt _AND + int *sign _AND + 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, leftright, m2, m5, s2, s5, spec_case, try_quick; + union double_union d, d2, eps; + __Long L; +#ifndef Sudden_Underflow + int denorm; + __ULong x; +#endif + _Bigint *b, *b1, *delta, *mlo, *mhi, *S; + double ds; + char *s, *s0; + + d.d = _d; + + if (ptr->_result) + { + ptr->_result->_k = ptr->_result_k; + ptr->_result->_maxwds = 1 << ptr->_result_k; + Bfree (ptr, ptr->_result); + ptr->_result = 0; + } + + if (word0 (d) & Sign_bit) + { + /* set sign for everything, including 0's and NaNs */ + *sign = 1; + word0 (d) &= ~Sign_bit; /* clear sign bit */ + } + else + *sign = 0; + +#if defined(IEEE_Arith) + defined(VAX) +#ifdef IEEE_Arith + if ((word0 (d) & Exp_mask) == Exp_mask) +#else + if (word0 (d) == 0x8000) +#endif + { + /* Infinity or NaN */ + *decpt = 9999; + s = +#ifdef IEEE_Arith + !word1 (d) && !(word0 (d) & 0xfffff) ? "Infinity" : +#endif + "NaN"; + if (rve) + *rve = +#ifdef IEEE_Arith + s[3] ? s + 8 : +#endif + s + 3; + return s; + } +#endif +#ifdef IBM + d.d += 0; /* normalize */ +#endif + if (!d.d) + { + *decpt = 1; + s = "0"; + if (rve) + *rve = s + 1; + return s; + } + + b = d2b (ptr, d.d, &be, &bbits); +#ifdef Sudden_Underflow + i = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1)); +#else + if (i = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1))) + { +#endif + d2.d = d.d; + word0 (d2) &= Frac_mask1; + word0 (d2) |= Exp_11; +#ifdef IBM + if (j = 11 - hi0bits (word0 (d2) & Frac_mask)) + d2.d /= 1 << j; +#endif + + /* 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; +#ifdef IBM + i <<= 2; + i += j; +#endif +#ifndef Sudden_Underflow + denorm = 0; + } + else + { + /* d is denormalized */ + + i = bbits + be + (Bias + (P - 1) - 1); + x = i > 32 ? word0 (d) << 64 - i | word1 (d) >> i - 32 + : word1 (d) << 32 - i; + d2.d = x; + word0 (d2) -= 31 * Exp_msk1; /* adjust exponent */ + i -= (Bias + (P - 1) - 1) + 1; + denorm = 1; + } +#endif + ds = (d2.d - 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.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: + 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; + } + j = sizeof (__ULong); + for (ptr->_result_k = 0; sizeof (_Bigint) - sizeof (__ULong) + j <= i; + j <<= 1) + ptr->_result_k++; + ptr->_result = Balloc (ptr, ptr->_result_k); + s = s0 = (char *) ptr->_result; + + if (ilim >= 0 && ilim <= Quick_max && try_quick) + { + /* Try to get by with floating-point arithmetic. */ + + i = 0; + d2.d = d.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.d /= bigtens[n_bigtens - 1]; + ieps++; + } + for (; j; j >>= 1, i++) + if (j & 1) + { + ieps++; + ds *= bigtens[i]; + } + d.d /= ds; + } + else if (j1 = -k) + { + d.d *= tens[j1 & 0xf]; + for (j = j1 >> 4; j; j >>= 1, i++) + if (j & 1) + { + ieps++; + d.d *= bigtens[i]; + } + } + if (k_check && d.d < 1. && ilim > 0) + { + if (ilim1 <= 0) + goto fast_failed; + ilim = ilim1; + k--; + d.d *= 10.; + ieps++; + } + eps.d = ieps * d.d + 7.; + word0 (eps) -= (P - 1) * Exp_msk1; + if (ilim == 0) + { + S = mhi = 0; + d.d -= 5.; + if (d.d > eps.d) + goto one_digit; + if (d.d < -eps.d) + goto no_digits; + goto fast_failed; + } +#ifndef No_leftright + if (leftright) + { + /* Use Steele & White method of only + * generating digits needed. + */ + eps.d = 0.5 / tens[ilim - 1] - eps.d; + for (i = 0;;) + { + L = d.d; + d.d -= L; + *s++ = '0' + (int) L; + if (d.d < eps.d) + goto ret1; + if (1. - d.d < eps.d) + goto bump_up; + if (++i >= ilim) + break; + eps.d *= 10.; + d.d *= 10.; + } + } + else + { +#endif + /* Generate ilim digits, then fix them up. */ + eps.d *= tens[ilim - 1]; + for (i = 1;; i++, d.d *= 10.) + { + L = d.d; + d.d -= L; + *s++ = '0' + (int) L; + if (i == ilim) + { + if (d.d > 0.5 + eps.d) + goto bump_up; + else if (d.d < 0.5 - eps.d) + { + while (*--s == '0'); + s++; + goto ret1; + } + break; + } + } +#ifndef No_leftright + } +#endif + fast_failed: + s = s0; + d.d = d2.d; + 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.d <= 5 * ds) + goto no_digits; + goto one_digit; + } + for (i = 1;; i++) + { + L = d.d / ds; + d.d -= L * ds; +#ifdef Check_FLT_ROUNDS + /* If FLT_ROUNDS == 2, L will usually be high by 1 */ + if (d.d < 0) + { + L--; + d.d += ds; + } +#endif + *s++ = '0' + (int) L; + if (i == ilim) + { + d.d += d.d; + if (d.d > ds || d.d == ds && L & 1) + { + bump_up: + while (*--s == '9') + if (s == s0) + { + k++; + *s = '0'; + break; + } + ++*s++; + } + break; + } + if (!(d.d *= 10.)) + break; + } + goto ret1; + } + + m2 = b2; + m5 = b5; + mhi = mlo = 0; + if (leftright) + { + if (mode < 2) + { + i = +#ifndef Sudden_Underflow + denorm ? be + (Bias + (P - 1) - 1 + 1) : +#endif +#ifdef IBM + 1 + 4 * P - 3 - bbits + ((bbits + be - 1) & 3); +#else + 1 + P - bbits; +#endif + } + 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 (ptr, 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 (ptr, mhi, m5); + b1 = mult (ptr, mhi, b); + Bfree (ptr, b); + b = b1; + } + if (j = b5 - m5) + b = pow5mult (ptr, b, j); + } + else + b = pow5mult (ptr, b, b5); + } + S = i2b (ptr, 1); + if (s5 > 0) + S = pow5mult (ptr, S, s5); + + /* Check for special case that d is a normalized power of 2. */ + + if (mode < 2) + { + if (!word1 (d) && !(word0 (d) & Bndry_mask) +#ifndef Sudden_Underflow + && word0 (d) & Exp_mask +#endif + ) + { + /* The special case */ + b2 += Log2P; + s2 += Log2P; + spec_case = 1; + } + else + spec_case = 0; + } + + /* 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. + */ + +#ifdef Pack_32 + if (i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0x1f) + i = 32 - i; +#else + if (i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0xf) + i = 16 - i; +#endif + 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 (ptr, b, b2); + if (s2 > 0) + S = lshift (ptr, S, s2); + if (k_check) + { + if (cmp (b, S) < 0) + { + k--; + b = multadd (ptr, b, 10, 0); /* we botched the k estimate */ + if (leftright) + mhi = multadd (ptr, mhi, 10, 0); + ilim = ilim1; + } + } + if (ilim <= 0 && mode > 2) + { + if (ilim < 0 || cmp (b, S = multadd (ptr, 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 (ptr, mhi, m2); + + /* Compute mlo -- check for special case + * that d is a normalized power of 2. + */ + + mlo = mhi; + if (spec_case) + { + mhi = Balloc (ptr, mhi->_k); + Bcopy (mhi, mlo); + mhi = lshift (ptr, 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 (ptr, S, mhi); + j1 = delta->_sign ? 1 : cmp (b, delta); + Bfree (ptr, delta); +#ifndef ROUND_BIASED + if (j1 == 0 && !mode && !(word1 (d) & 1)) + { + if (dig == '9') + goto round_9_up; + if (j > 0) + dig++; + *s++ = dig; + goto ret; + } +#endif + if (j < 0 || j == 0 && !mode +#ifndef ROUND_BIASED + && !(word1 (d) & 1) +#endif + ) + { + if (j1 > 0) + { + b = lshift (ptr, 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 (ptr, b, 10, 0); + if (mlo == mhi) + mlo = mhi = multadd (ptr, mhi, 10, 0); + else + { + mlo = multadd (ptr, mlo, 10, 0); + mhi = multadd (ptr, mhi, 10, 0); + } + } + } + else + for (i = 1;; i++) + { + *s++ = dig = quorem (b, S) + '0'; + if (i >= ilim) + break; + b = multadd (ptr, b, 10, 0); + } + + /* Round off last digit */ + + b = lshift (ptr, 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 (ptr, S); + if (mhi) + { + if (mlo && mlo != mhi) + Bfree (ptr, mlo); + Bfree (ptr, mhi); + } +ret1: + Bfree (ptr, b); + *s = 0; + *decpt = k + 1; + if (rve) + *rve = s; + return s0; +} |