+++ /dev/null
-/****************************************************************
- *
- * 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 "mprec.h"
-#include <string.h>
-
-static int
-_DEFUN (quorem,
- (b, S),
- _Jv_Bigint * b _AND _Jv_Bigint * S)
-{
- int n;
- long borrow, y;
- unsigned long carry, q, ys;
- unsigned long *bx, *bxe, *sx, *sxe;
-#ifdef Pack_32
- long z;
- unsigned long 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;
-}
-
-#ifdef DEBUG
-#include <stdio.h>
-
-void
-print (_Jv_Bigint * b)
-{
- int i, wds;
- unsigned long *x, y;
- wds = b->_wds;
- x = b->_x+wds;
- i = 0;
- do
- {
- x--;
- fprintf (stderr, "%08x", *x);
- }
- while (++i < wds);
- fprintf (stderr, "\n");
-}
-#endif
-
-/* 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, float_type),
- struct _Jv_reent *ptr _AND
- double _d _AND
- int mode _AND
- int ndigits _AND
- int *decpt _AND
- int *sign _AND
- char **rve _AND
- int float_type)
-{
- /*
- float_type == 0 for double precision, 1 for float.
-
- 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).
-
- > 16 ==> Floating-point arg is treated as single precision.
-
- 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;
- unsigned long x;
-#endif
- _Jv_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 (unsigned long);
- for (ptr->_result_k = 0; (int) (sizeof (_Jv_Bigint) - sizeof (unsigned long)) + 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);
-
- /* Single precision case, */
- if (float_type)
- mhi = lshift (ptr, mhi, 29);
-
- /* 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;
-}
-
-
-_VOID
-_DEFUN (_dtoa,
- (_d, mode, ndigits, decpt, sign, rve, buf, float_type),
- double _d _AND
- int mode _AND
- int ndigits _AND
- int *decpt _AND
- int *sign _AND
- char **rve _AND
- char *buf _AND
- int float_type)
-{
- struct _Jv_reent reent;
- char *p;
- memset (&reent, 0, sizeof reent);
-
- p = _dtoa_r (&reent, _d, mode, ndigits, decpt, sign, rve, float_type);
- strcpy (buf, p);
-
- return;
-}
projects / msp430-gcc.git / blobdiff