diff options
Diffstat (limited to 'newlib/libc/stdlib/dtoa.c')
| -rw-r--r-- | newlib/libc/stdlib/dtoa.c | 854 |
1 files changed, 0 insertions, 854 deletions
diff --git a/newlib/libc/stdlib/dtoa.c b/newlib/libc/stdlib/dtoa.c deleted file mode 100644 index 62597c755..000000000 --- a/newlib/libc/stdlib/dtoa.c +++ /dev/null @@ -1,854 +0,0 @@ -/**************************************************************** - * - * 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 = NULL, *mhi, *S; - double ds; - char *s, *s0; - - d.d = _d; - - _REENT_CHECK_MP(ptr); - if (_REENT_MP_RESULT(ptr)) - { - _REENT_MP_RESULT(ptr)->_k = _REENT_MP_RESULT_K(ptr); - _REENT_MP_RESULT(ptr)->_maxwds = 1 << _REENT_MP_RESULT_K(ptr); - Bfree (ptr, _REENT_MP_RESULT(ptr)); - _REENT_MP_RESULT(ptr) = 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))) != 0) - { -#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; - ilim = ilim1 = -1; - switch (mode) - { - case 0: - case 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 (_REENT_MP_RESULT_K(ptr) = 0; sizeof (_Bigint) - sizeof (__ULong) + j <= i; - j <<= 1) - _REENT_MP_RESULT_K(ptr)++; - _REENT_MP_RESULT(ptr) = Balloc (ptr, _REENT_MP_RESULT_K(ptr)); - s = s0 = (char *) _REENT_MP_RESULT(ptr); - - 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) != 0) - { - 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) != 0) - 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. */ - - spec_case = 0; - 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; - } - } - - /* 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) != 0) - i = 32 - i; -#else - if ((i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0xf) != 0) - 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; -} |