959 lines
18 KiB
C
959 lines
18 KiB
C
/****************************************************************
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*
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* The author of this software is David M. Gay.
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*
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* Copyright (c) 1991 by AT&T.
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose without fee is hereby granted, provided that this entire notice
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* is included in all copies of any software which is or includes a copy
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* or modification of this software and in all copies of the supporting
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* documentation for such software.
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*
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* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
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* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
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* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
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* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
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*
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***************************************************************/
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/* Please send bug reports to
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David M. Gay
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AT&T Bell Laboratories, Room 2C-463
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600 Mountain Avenue
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Murray Hill, NJ 07974-2070
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U.S.A.
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dmg@research.att.com or research!dmg
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*/
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/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
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*
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* This strtod returns a nearest machine number to the input decimal
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* string (or sets errno to ERANGE). With IEEE arithmetic, ties are
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* broken by the IEEE round-even rule. Otherwise ties are broken by
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* biased rounding (add half and chop).
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*
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* Inspired loosely by William D. Clinger's paper "How to Read Floating
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* Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
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*
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* Modifications:
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*
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* 1. We only require IEEE, IBM, or VAX double-precision
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* arithmetic (not IEEE double-extended).
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* 2. We get by with floating-point arithmetic in a case that
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* Clinger missed -- when we're computing d * 10^n
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* for a small integer d and the integer n is not too
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* much larger than 22 (the maximum integer k for which
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* we can represent 10^k exactly), we may be able to
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* compute (d*10^k) * 10^(e-k) with just one roundoff.
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* 3. Rather than a bit-at-a-time adjustment of the binary
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* result in the hard case, we use floating-point
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* arithmetic to determine the adjustment to within
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* one bit; only in really hard cases do we need to
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* compute a second residual.
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* 4. Because of 3., we don't need a large table of powers of 10
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* for ten-to-e (just some small tables, e.g. of 10^k
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* for 0 <= k <= 22).
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*/
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/*
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* #define IEEE_8087 for IEEE-arithmetic machines where the least
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* significant byte has the lowest address.
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* #define IEEE_MC68k for IEEE-arithmetic machines where the most
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* significant byte has the lowest address.
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* #define Sudden_Underflow for IEEE-format machines without gradual
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* underflow (i.e., that flush to zero on underflow).
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* #define IBM for IBM mainframe-style floating-point arithmetic.
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* #define VAX for VAX-style floating-point arithmetic.
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* #define Unsigned_Shifts if >> does treats its left operand as unsigned.
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* #define No_leftright to omit left-right logic in fast floating-point
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* computation of dtoa.
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* #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
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* #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
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* that use extended-precision instructions to compute rounded
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* products and quotients) with IBM.
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* #define ROUND_BIASED for IEEE-format with biased rounding.
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* #define Inaccurate_Divide for IEEE-format with correctly rounded
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* products but inaccurate quotients, e.g., for Intel i860.
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* #define Just_16 to store 16 bits per 32-bit long when doing high-precision
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* integer arithmetic. Whether this speeds things up or slows things
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* down depends on the machine and the number being converted.
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*/
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#include <stdlib.h>
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#include <string.h>
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#include <java-assert.h>
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#include "mprec.h"
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/* reent.c knows this value */
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#define _Kmax 15
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#include <stdio.h>
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_Jv_Bigint *
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_DEFUN (Balloc, (ptr, k), struct _Jv_reent *ptr _AND int k)
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{
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_Jv_Bigint *rv = NULL;
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int i = 0;
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int j = 1;
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JvAssert ((1 << k) < MAX_BIGNUM_WDS);
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while ((ptr->_allocation_map & j) && i < MAX_BIGNUMS)
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i++, j <<= 1;
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JvAssert (i < MAX_BIGNUMS);
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if (i >= MAX_BIGNUMS)
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return NULL;
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ptr->_allocation_map |= j;
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rv = &ptr->_freelist[i];
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rv->_k = k;
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rv->_maxwds = 32;
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return rv;
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}
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void
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_DEFUN (Bfree, (ptr, v), struct _Jv_reent *ptr _AND _Jv_Bigint * v)
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{
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long i;
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i = v - ptr->_freelist;
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JvAssert (i >= 0 && i < MAX_BIGNUMS);
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if (i >= 0 && i < MAX_BIGNUMS)
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ptr->_allocation_map &= ~ (1 << i);
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}
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_Jv_Bigint *
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_DEFUN (multadd, (ptr, b, m, a),
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struct _Jv_reent *ptr _AND
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_Jv_Bigint * b _AND
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int m _AND
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int a)
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{
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int i, wds;
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unsigned long *x, y;
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#ifdef Pack_32
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unsigned long xi, z;
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#endif
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_Jv_Bigint *b1;
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wds = b->_wds;
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x = b->_x;
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i = 0;
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do
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{
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#ifdef Pack_32
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xi = *x;
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y = (xi & 0xffff) * m + a;
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z = (xi >> 16) * m + (y >> 16);
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a = (int) (z >> 16);
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*x++ = (z << 16) + (y & 0xffff);
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#else
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y = *x * m + a;
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a = (int) (y >> 16);
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*x++ = y & 0xffff;
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#endif
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}
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while (++i < wds);
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if (a)
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{
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if (wds >= b->_maxwds)
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{
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b1 = Balloc (ptr, b->_k + 1);
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Bcopy (b1, b);
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Bfree (ptr, b);
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b = b1;
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}
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b->_x[wds++] = a;
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b->_wds = wds;
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}
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return b;
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}
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_Jv_Bigint *
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_DEFUN (s2b, (ptr, s, nd0, nd, y9),
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struct _Jv_reent * ptr _AND
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_CONST char *s _AND
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int nd0 _AND
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int nd _AND
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unsigned long y9)
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{
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_Jv_Bigint *b;
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int i, k;
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long x, y;
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x = (nd + 8) / 9;
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for (k = 0, y = 1; x > y; y <<= 1, k++);
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#ifdef Pack_32
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b = Balloc (ptr, k);
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b->_x[0] = y9;
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b->_wds = 1;
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#else
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b = Balloc (ptr, k + 1);
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b->_x[0] = y9 & 0xffff;
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b->_wds = (b->_x[1] = y9 >> 16) ? 2 : 1;
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#endif
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i = 9;
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if (9 < nd0)
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{
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s += 9;
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do
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b = multadd (ptr, b, 10, *s++ - '0');
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while (++i < nd0);
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s++;
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}
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else
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s += 10;
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for (; i < nd; i++)
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b = multadd (ptr, b, 10, *s++ - '0');
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return b;
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}
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int
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_DEFUN (hi0bits,
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(x), register unsigned long x)
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{
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register int k = 0;
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if (!(x & 0xffff0000))
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{
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k = 16;
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x <<= 16;
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}
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if (!(x & 0xff000000))
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{
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k += 8;
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x <<= 8;
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}
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if (!(x & 0xf0000000))
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{
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k += 4;
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x <<= 4;
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}
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if (!(x & 0xc0000000))
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{
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k += 2;
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x <<= 2;
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}
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if (!(x & 0x80000000))
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{
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k++;
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if (!(x & 0x40000000))
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return 32;
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}
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return k;
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}
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int
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_DEFUN (lo0bits, (y), unsigned long *y)
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{
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register int k;
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register unsigned long x = *y;
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if (x & 7)
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{
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if (x & 1)
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return 0;
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if (x & 2)
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{
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*y = x >> 1;
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return 1;
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}
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*y = x >> 2;
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return 2;
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}
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k = 0;
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if (!(x & 0xffff))
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{
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k = 16;
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x >>= 16;
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}
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if (!(x & 0xff))
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{
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k += 8;
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x >>= 8;
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}
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if (!(x & 0xf))
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{
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k += 4;
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x >>= 4;
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}
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if (!(x & 0x3))
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{
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k += 2;
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x >>= 2;
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}
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if (!(x & 1))
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{
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k++;
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x >>= 1;
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if (!x & 1)
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return 32;
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}
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*y = x;
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return k;
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}
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_Jv_Bigint *
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_DEFUN (i2b, (ptr, i), struct _Jv_reent * ptr _AND int i)
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{
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_Jv_Bigint *b;
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b = Balloc (ptr, 1);
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b->_x[0] = i;
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b->_wds = 1;
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return b;
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}
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_Jv_Bigint *
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_DEFUN (mult, (ptr, a, b), struct _Jv_reent * ptr _AND _Jv_Bigint * a _AND _Jv_Bigint * b)
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{
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_Jv_Bigint *c;
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int k, wa, wb, wc;
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unsigned long carry, y, z;
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unsigned long *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
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#ifdef Pack_32
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unsigned long z2;
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#endif
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if (a->_wds < b->_wds)
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{
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c = a;
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a = b;
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b = c;
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}
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k = a->_k;
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wa = a->_wds;
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wb = b->_wds;
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wc = wa + wb;
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if (wc > a->_maxwds)
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k++;
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c = Balloc (ptr, k);
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for (x = c->_x, xa = x + wc; x < xa; x++)
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*x = 0;
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xa = a->_x;
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xae = xa + wa;
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xb = b->_x;
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xbe = xb + wb;
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xc0 = c->_x;
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#ifdef Pack_32
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for (; xb < xbe; xb++, xc0++)
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{
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if ((y = *xb & 0xffff))
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{
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x = xa;
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xc = xc0;
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carry = 0;
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do
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{
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z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
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carry = z >> 16;
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z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
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carry = z2 >> 16;
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Storeinc (xc, z2, z);
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}
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while (x < xae);
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*xc = carry;
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}
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if ((y = *xb >> 16))
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{
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x = xa;
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xc = xc0;
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carry = 0;
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z2 = *xc;
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do
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{
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z = (*x & 0xffff) * y + (*xc >> 16) + carry;
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carry = z >> 16;
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Storeinc (xc, z, z2);
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z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
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carry = z2 >> 16;
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}
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while (x < xae);
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*xc = z2;
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}
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}
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#else
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for (; xb < xbe; xc0++)
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{
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if (y = *xb++)
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{
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x = xa;
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xc = xc0;
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carry = 0;
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do
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{
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z = *x++ * y + *xc + carry;
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carry = z >> 16;
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*xc++ = z & 0xffff;
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}
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while (x < xae);
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*xc = carry;
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}
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}
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#endif
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for (xc0 = c->_x, xc = xc0 + wc; wc > 0 && !*--xc; --wc);
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c->_wds = wc;
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return c;
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}
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_Jv_Bigint *
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_DEFUN (pow5mult,
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(ptr, b, k), struct _Jv_reent * ptr _AND _Jv_Bigint * b _AND int k)
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{
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_Jv_Bigint *b1, *p5, *p51;
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int i;
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static _CONST int p05[3] = {5, 25, 125};
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if ((i = k & 3))
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b = multadd (ptr, b, p05[i - 1], 0);
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if (!(k >>= 2))
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return b;
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if (!(p5 = ptr->_p5s))
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{
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/* first time */
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p5 = ptr->_p5s = i2b (ptr, 625);
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p5->_next = 0;
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}
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for (;;)
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{
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if (k & 1)
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{
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b1 = mult (ptr, b, p5);
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Bfree (ptr, b);
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b = b1;
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}
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if (!(k >>= 1))
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break;
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if (!(p51 = p5->_next))
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{
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p51 = p5->_next = mult (ptr, p5, p5);
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p51->_next = 0;
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}
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p5 = p51;
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}
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return b;
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}
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_Jv_Bigint *
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_DEFUN (lshift, (ptr, b, k), struct _Jv_reent * ptr _AND _Jv_Bigint * b _AND int k)
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{
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int i, k1, n, n1;
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_Jv_Bigint *b1;
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unsigned long *x, *x1, *xe, z;
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#ifdef Pack_32
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n = k >> 5;
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#else
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n = k >> 4;
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#endif
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k1 = b->_k;
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n1 = n + b->_wds + 1;
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for (i = b->_maxwds; n1 > i; i <<= 1)
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k1++;
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b1 = Balloc (ptr, k1);
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x1 = b1->_x;
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for (i = 0; i < n; i++)
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*x1++ = 0;
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x = b->_x;
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xe = x + b->_wds;
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#ifdef Pack_32
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if (k &= 0x1f)
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{
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k1 = 32 - k;
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z = 0;
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do
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{
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*x1++ = *x << k | z;
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z = *x++ >> k1;
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}
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while (x < xe);
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if ((*x1 = z))
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++n1;
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}
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#else
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if (k &= 0xf)
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{
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k1 = 16 - k;
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z = 0;
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do
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|
{
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*x1++ = *x << k & 0xffff | z;
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z = *x++ >> k1;
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}
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while (x < xe);
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if (*x1 = z)
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++n1;
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}
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#endif
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else
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do
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*x1++ = *x++;
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while (x < xe);
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b1->_wds = n1 - 1;
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Bfree (ptr, b);
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return b1;
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}
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int
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_DEFUN (cmp, (a, b), _Jv_Bigint * a _AND _Jv_Bigint * b)
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|
{
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unsigned long *xa, *xa0, *xb, *xb0;
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int i, j;
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i = a->_wds;
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j = b->_wds;
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#ifdef DEBUG
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if (i > 1 && !a->_x[i - 1])
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Bug ("cmp called with a->_x[a->_wds-1] == 0");
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if (j > 1 && !b->_x[j - 1])
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Bug ("cmp called with b->_x[b->_wds-1] == 0");
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#endif
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if (i -= j)
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return i;
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xa0 = a->_x;
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xa = xa0 + j;
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xb0 = b->_x;
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xb = xb0 + j;
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for (;;)
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{
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if (*--xa != *--xb)
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return *xa < *xb ? -1 : 1;
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if (xa <= xa0)
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break;
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}
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return 0;
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}
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_Jv_Bigint *
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_DEFUN (diff, (ptr, a, b), struct _Jv_reent * ptr _AND
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_Jv_Bigint * a _AND _Jv_Bigint * b)
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|
{
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_Jv_Bigint *c;
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|
int i, wa, wb;
|
|
long borrow, y; /* We need signed shifts here. */
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|
unsigned long *xa, *xae, *xb, *xbe, *xc;
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#ifdef Pack_32
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long z;
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#endif
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i = cmp (a, b);
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if (!i)
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{
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c = Balloc (ptr, 0);
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c->_wds = 1;
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c->_x[0] = 0;
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return c;
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}
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if (i < 0)
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{
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|
c = a;
|
|
a = b;
|
|
b = c;
|
|
i = 1;
|
|
}
|
|
else
|
|
i = 0;
|
|
c = Balloc (ptr, 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;
|
|
#ifdef Pack_32
|
|
do
|
|
{
|
|
y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
|
|
borrow = y >> 16;
|
|
Sign_Extend (borrow, y);
|
|
z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
|
|
borrow = z >> 16;
|
|
Sign_Extend (borrow, z);
|
|
Storeinc (xc, z, y);
|
|
}
|
|
while (xb < xbe);
|
|
while (xa < xae)
|
|
{
|
|
y = (*xa & 0xffff) + borrow;
|
|
borrow = y >> 16;
|
|
Sign_Extend (borrow, y);
|
|
z = (*xa++ >> 16) + borrow;
|
|
borrow = z >> 16;
|
|
Sign_Extend (borrow, z);
|
|
Storeinc (xc, z, y);
|
|
}
|
|
#else
|
|
do
|
|
{
|
|
y = *xa++ - *xb++ + borrow;
|
|
borrow = y >> 16;
|
|
Sign_Extend (borrow, y);
|
|
*xc++ = y & 0xffff;
|
|
}
|
|
while (xb < xbe);
|
|
while (xa < xae)
|
|
{
|
|
y = *xa++ + borrow;
|
|
borrow = y >> 16;
|
|
Sign_Extend (borrow, y);
|
|
*xc++ = y & 0xffff;
|
|
}
|
|
#endif
|
|
while (!*--xc)
|
|
wa--;
|
|
c->_wds = wa;
|
|
return c;
|
|
}
|
|
|
|
double
|
|
_DEFUN (ulp, (_x), double _x)
|
|
{
|
|
union double_union x, a;
|
|
register long L;
|
|
|
|
x.d = _x;
|
|
|
|
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;
|
|
#ifndef _DOUBLE_IS_32BITS
|
|
word1 (a) = 0;
|
|
#endif
|
|
|
|
#ifndef Sudden_Underflow
|
|
}
|
|
else
|
|
{
|
|
L = -L >> Exp_shift;
|
|
if (L < Exp_shift)
|
|
{
|
|
word0 (a) = 0x80000 >> L;
|
|
#ifndef _DOUBLE_IS_32BITS
|
|
word1 (a) = 0;
|
|
#endif
|
|
}
|
|
else
|
|
{
|
|
word0 (a) = 0;
|
|
L -= Exp_shift;
|
|
#ifndef _DOUBLE_IS_32BITS
|
|
word1 (a) = L >= 31 ? 1 : 1 << (31 - L);
|
|
#endif
|
|
}
|
|
}
|
|
#endif
|
|
return a.d;
|
|
}
|
|
|
|
double
|
|
_DEFUN (b2d, (a, e),
|
|
_Jv_Bigint * a _AND int *e)
|
|
{
|
|
unsigned long *xa, *xa0, w, y, z;
|
|
int k;
|
|
union double_union 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;
|
|
#ifndef _DOUBLE_IS_32BITS
|
|
d1 = y << (32 - Ebits + k) | w >> (Ebits - k);
|
|
#endif
|
|
goto ret_d;
|
|
}
|
|
z = xa > xa0 ? *--xa : 0;
|
|
if (k -= Ebits)
|
|
{
|
|
d0 = Exp_1 | y << k | z >> (32 - k);
|
|
y = xa > xa0 ? *--xa : 0;
|
|
#ifndef _DOUBLE_IS_32BITS
|
|
d1 = z << k | y >> (32 - k);
|
|
#endif
|
|
}
|
|
else
|
|
{
|
|
d0 = Exp_1 | y;
|
|
#ifndef _DOUBLE_IS_32BITS
|
|
d1 = z;
|
|
#endif
|
|
}
|
|
#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;
|
|
}
|
|
|
|
_Jv_Bigint *
|
|
_DEFUN (d2b,
|
|
(ptr, _d, e, bits),
|
|
struct _Jv_reent * ptr _AND
|
|
double _d _AND
|
|
int *e _AND
|
|
int *bits)
|
|
|
|
{
|
|
union double_union d;
|
|
_Jv_Bigint *b;
|
|
int de, i, k;
|
|
unsigned long *x, y, z;
|
|
#ifdef VAX
|
|
unsigned long d0, d1;
|
|
d.d = _d;
|
|
d0 = word0 (d) >> 16 | word0 (d) << 16;
|
|
d1 = word1 (d) >> 16 | word1 (d) << 16;
|
|
#else
|
|
#define d0 word0(d)
|
|
#define d1 word1(d)
|
|
d.d = _d;
|
|
#endif
|
|
|
|
#ifdef Pack_32
|
|
b = Balloc (ptr, 1);
|
|
#else
|
|
b = Balloc (ptr, 2);
|
|
#endif
|
|
x = b->_x;
|
|
|
|
z = d0 & Frac_mask;
|
|
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
|
|
#ifdef Sudden_Underflow
|
|
de = (int) (d0 >> Exp_shift);
|
|
#ifndef IBM
|
|
z |= Exp_msk11;
|
|
#endif
|
|
#else
|
|
if ((de = (int) (d0 >> Exp_shift)))
|
|
z |= Exp_msk1;
|
|
#endif
|
|
#ifdef Pack_32
|
|
#ifndef _DOUBLE_IS_32BITS
|
|
if ((y = d1))
|
|
{
|
|
if ((k = lo0bits (&y)))
|
|
{
|
|
x[0] = y | z << (32 - k);
|
|
z >>= k;
|
|
}
|
|
else
|
|
x[0] = y;
|
|
i = b->_wds = (x[1] = z) ? 2 : 1;
|
|
}
|
|
else
|
|
#endif
|
|
{
|
|
#ifdef DEBUG
|
|
if (!z)
|
|
Bug ("Zero passed to d2b");
|
|
#endif
|
|
k = lo0bits (&z);
|
|
x[0] = z;
|
|
i = b->_wds = 1;
|
|
#ifndef _DOUBLE_IS_32BITS
|
|
k += 32;
|
|
#endif
|
|
}
|
|
#else
|
|
if (y = d1)
|
|
{
|
|
if (k = lo0bits (&y))
|
|
if (k >= 16)
|
|
{
|
|
x[0] = y | z << 32 - k & 0xffff;
|
|
x[1] = z >> k - 16 & 0xffff;
|
|
x[2] = z >> k;
|
|
i = 2;
|
|
}
|
|
else
|
|
{
|
|
x[0] = y & 0xffff;
|
|
x[1] = y >> 16 | z << 16 - k & 0xffff;
|
|
x[2] = z >> k & 0xffff;
|
|
x[3] = z >> k + 16;
|
|
i = 3;
|
|
}
|
|
else
|
|
{
|
|
x[0] = y & 0xffff;
|
|
x[1] = y >> 16;
|
|
x[2] = z & 0xffff;
|
|
x[3] = z >> 16;
|
|
i = 3;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
#ifdef DEBUG
|
|
if (!z)
|
|
Bug ("Zero passed to d2b");
|
|
#endif
|
|
k = lo0bits (&z);
|
|
if (k >= 16)
|
|
{
|
|
x[0] = z;
|
|
i = 0;
|
|
}
|
|
else
|
|
{
|
|
x[0] = z & 0xffff;
|
|
x[1] = z >> 16;
|
|
i = 1;
|
|
}
|
|
k += 32;
|
|
}
|
|
while (!x[i])
|
|
--i;
|
|
b->_wds = i + 1;
|
|
#endif
|
|
#ifndef Sudden_Underflow
|
|
if (de)
|
|
{
|
|
#endif
|
|
#ifdef IBM
|
|
*e = (de - Bias - (P - 1) << 2) + k;
|
|
*bits = 4 * P + 8 - k - hi0bits (word0 (d) & Frac_mask);
|
|
#else
|
|
*e = de - Bias - (P - 1) + k;
|
|
*bits = P - k;
|
|
#endif
|
|
#ifndef Sudden_Underflow
|
|
}
|
|
else
|
|
{
|
|
*e = de - Bias - (P - 1) + 1 + k;
|
|
#ifdef Pack_32
|
|
*bits = 32 * i - hi0bits (x[i - 1]);
|
|
#else
|
|
*bits = (i + 2) * 16 - hi0bits (x[i]);
|
|
#endif
|
|
}
|
|
#endif
|
|
return b;
|
|
}
|
|
#undef d0
|
|
#undef d1
|
|
|
|
double
|
|
_DEFUN (ratio, (a, b), _Jv_Bigint * a _AND _Jv_Bigint * b)
|
|
|
|
{
|
|
union double_union 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.d *= 1 << k;
|
|
}
|
|
else
|
|
{
|
|
k = -k;
|
|
word0 (db) += (k >> 2) * Exp_msk1;
|
|
if (k &= 3)
|
|
db.d *= 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;
|
|
}
|
|
|
|
|
|
_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, 1e23, 1e24
|
|
|
|
};
|
|
|
|
#if !defined(_DOUBLE_IS_32BITS) && !defined(__v800)
|
|
_CONST double bigtens[] =
|
|
{1e16, 1e32, 1e64, 1e128, 1e256};
|
|
|
|
_CONST double tinytens[] =
|
|
{1e-16, 1e-32, 1e-64, 1e-128, 1e-256};
|
|
#else
|
|
_CONST double bigtens[] =
|
|
{1e16, 1e32};
|
|
|
|
_CONST double tinytens[] =
|
|
{1e-16, 1e-32};
|
|
#endif
|
|
|
|
|