2358 lines
72 KiB
C
2358 lines
72 KiB
C
/*
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Copyright (C) 1993 Free Software Foundation
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This file is part of the GNU IO Library. This library is free
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software; you can redistribute it and/or modify it under the
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terms of the GNU General Public License as published by the
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Free Software Foundation; either version 2, or (at your option)
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any later version.
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This library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with GNU CC; see the file COPYING. If not, write to
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the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
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As a special exception, if you link this library with files
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compiled with a GNU compiler to produce an executable, this does not cause
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the resulting executable to be covered by the GNU General Public License.
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This exception does not however invalidate any other reasons why
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the executable file might be covered by the GNU General Public License. */
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#include <libioP.h>
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#ifdef _IO_USE_DTOA
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/****************************************************************
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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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/* Some cleaning up by Per Bothner, bothner@cygnus.com, 1992, 1993.
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Re-written to not need static variables
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(except result, result_k, HIWORD, LOWORD). */
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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 KR_headers for old-style C function headers.
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*/
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#ifdef DEBUG
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#include <stdio.h>
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#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
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#endif
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#ifdef __STDC__
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#include <stdlib.h>
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#include <string.h>
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#include <float.h>
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#define CONST const
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#else
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#define CONST
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#define KR_headers
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/* In this case, we assume IEEE floats. */
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#define FLT_ROUNDS 1
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#define FLT_RADIX 2
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#define DBL_MANT_DIG 53
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#define DBL_DIG 15
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#define DBL_MAX_10_EXP 308
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#define DBL_MAX_EXP 1024
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#endif
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#include <errno.h>
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#ifndef __MATH_H__
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#include <math.h>
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#endif
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#ifdef Unsigned_Shifts
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#define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
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#else
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#define Sign_Extend(a,b) /*no-op*/
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#endif
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#if defined(__i386__) || defined(__i860__) || defined(clipper)
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#define IEEE_8087
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#endif
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#if defined(MIPSEL) || defined(__alpha__)
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#define IEEE_8087
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#endif
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#if defined(__sparc__) || defined(sparc) || defined(MIPSEB)
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#define IEEE_MC68k
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#endif
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#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
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#if FLT_RADIX==16
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#define IBM
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#else
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#if DBL_MANT_DIG==56
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#define VAX
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#else
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#if DBL_MANT_DIG==53 && DBL_MAX_10_EXP==308
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#define IEEE_Unknown
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#else
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Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
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#endif
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#endif
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#endif
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#endif
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typedef _G_uint32_t unsigned32;
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#ifdef IEEE_8087
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#define HIWORD 1
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#define LOWORD 0
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#define TEST_ENDIANNESS /* nothing */
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#else
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#if defined(IEEE_MC68k)
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#define HIWORD 0
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#define LOWORD 1
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#define TEST_ENDIANNESS /* nothing */
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#else
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static int HIWORD = -1, LOWORD;
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static void test_endianness()
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{
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union doubleword {
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double d;
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unsigned32 u[2];
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} dw;
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dw.d = 10;
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if (dw.u[0] != 0) /* big-endian */
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HIWORD=0, LOWORD=1;
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else
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HIWORD=1, LOWORD=0;
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}
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#define TEST_ENDIANNESS if (HIWORD<0) test_endianness();
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#endif
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#endif
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#if 0
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union {
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double d;
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unsigned32 x[2];
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} _temp;
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#endif
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#define word0(x) ((unsigned32 *)&x)[HIWORD]
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#if 0
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#define word0(X) (_temp.d = X, _temp.x[HIWORD])
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#define setword0(D,X) (_temp.d = D, _temp.x[HIWORD] = X, D = _temp.d)
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#endif
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#define word1(x) ((unsigned32 *)&x)[LOWORD]
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/* The following definition of Storeinc is appropriate for MIPS processors. */
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#if defined(IEEE_8087) + defined(VAX)
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#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
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((unsigned short *)a)[0] = (unsigned short)c, a++)
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#else
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#if defined(IEEE_MC68k)
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#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
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((unsigned short *)a)[1] = (unsigned short)c, a++)
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#else
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#define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
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#endif
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#endif
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/* #define P DBL_MANT_DIG */
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/* Ten_pmax = floor(P*log(2)/log(5)) */
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/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
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/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
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/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
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#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(IEEE_Unknown)
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#define Exp_shift 20
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#define Exp_shift1 20
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#define Exp_msk1 0x100000
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#define Exp_msk11 0x100000
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#define Exp_mask 0x7ff00000
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#define P 53
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#define Bias 1023
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#define IEEE_Arith
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#define Emin (-1022)
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#define Exp_1 0x3ff00000
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#define Exp_11 0x3ff00000
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#define Ebits 11
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#define Frac_mask 0xfffff
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#define Frac_mask1 0xfffff
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#define Ten_pmax 22
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#define Bletch 0x10
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#define Bndry_mask 0xfffff
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#define Bndry_mask1 0xfffff
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#define LSB 1
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#define Sign_bit 0x80000000
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#define Log2P 1
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#define Tiny0 0
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#define Tiny1 1
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#define Quick_max 14
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#define Int_max 14
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#define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
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#else
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#undef Sudden_Underflow
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#define Sudden_Underflow
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#ifdef IBM
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#define Exp_shift 24
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#define Exp_shift1 24
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#define Exp_msk1 0x1000000
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#define Exp_msk11 0x1000000
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#define Exp_mask 0x7f000000
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#define P 14
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#define Bias 65
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#define Exp_1 0x41000000
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#define Exp_11 0x41000000
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#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
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#define Frac_mask 0xffffff
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#define Frac_mask1 0xffffff
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#define Bletch 4
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#define Ten_pmax 22
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#define Bndry_mask 0xefffff
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#define Bndry_mask1 0xffffff
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#define LSB 1
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#define Sign_bit 0x80000000
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#define Log2P 4
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#define Tiny0 0x100000
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#define Tiny1 0
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#define Quick_max 14
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#define Int_max 15
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#else /* VAX */
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#define Exp_shift 23
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#define Exp_shift1 7
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#define Exp_msk1 0x80
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#define Exp_msk11 0x800000
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#define Exp_mask 0x7f80
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#define P 56
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#define Bias 129
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#define Exp_1 0x40800000
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#define Exp_11 0x4080
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#define Ebits 8
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#define Frac_mask 0x7fffff
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#define Frac_mask1 0xffff007f
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#define Ten_pmax 24
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#define Bletch 2
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#define Bndry_mask 0xffff007f
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#define Bndry_mask1 0xffff007f
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#define LSB 0x10000
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#define Sign_bit 0x8000
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#define Log2P 1
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#define Tiny0 0x80
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#define Tiny1 0
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#define Quick_max 15
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#define Int_max 15
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#endif
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#endif
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#ifndef IEEE_Arith
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#define ROUND_BIASED
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#endif
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#ifdef RND_PRODQUOT
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#define rounded_product(a,b) a = rnd_prod(a, b)
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#define rounded_quotient(a,b) a = rnd_quot(a, b)
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extern double rnd_prod(double, double), rnd_quot(double, double);
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#else
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#define rounded_product(a,b) a *= b
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#define rounded_quotient(a,b) a /= b
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#endif
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#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
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#define Big1 0xffffffff
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#define Kmax 15
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/* (1<<BIGINT_MINIMUM_K) is the minimum number of words to allocate
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in a Bigint. dtoa usually manages with 1<<2, and has not been
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known to need more than 1<<3. */
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#define BIGINT_MINIMUM_K 3
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struct Bigint {
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struct Bigint *next;
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int k; /* Parameter given to Balloc(k) */
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int maxwds; /* Allocated space: equals 1<<k. */
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short on_stack; /* 1 if stack-allocated. */
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short sign; /* 0 if value is positive or zero; 1 if negative. */
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int wds; /* Current length. */
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unsigned32 x[1<<BIGINT_MINIMUM_K]; /* Actually: x[maxwds] */
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};
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#define BIGINT_HEADER_SIZE \
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(sizeof(Bigint) - (1<<BIGINT_MINIMUM_K) * sizeof(unsigned32))
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typedef struct Bigint Bigint;
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/* Initialize a stack-allocated Bigint. */
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static Bigint *
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Binit
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#ifdef KR_headers
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(v) Bigint *v;
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#else
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(Bigint *v)
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#endif
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{
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v->on_stack = 1;
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v->k = BIGINT_MINIMUM_K;
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v->maxwds = 1 << BIGINT_MINIMUM_K;
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v->sign = v->wds = 0;
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return v;
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}
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/* Allocate a Bigint with '1<<k' big digits. */
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static Bigint *
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Balloc
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#ifdef KR_headers
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(k) int k;
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#else
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(int k)
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#endif
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{
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int x;
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Bigint *rv;
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if (k < BIGINT_MINIMUM_K)
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k = BIGINT_MINIMUM_K;
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x = 1 << k;
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rv = (Bigint *)
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malloc(BIGINT_HEADER_SIZE + x * sizeof(unsigned32));
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rv->k = k;
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rv->maxwds = x;
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rv->sign = rv->wds = 0;
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rv->on_stack = 0;
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return rv;
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}
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static void
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Bfree
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#ifdef KR_headers
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(v) Bigint *v;
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#else
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(Bigint *v)
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#endif
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{
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if (v && !v->on_stack)
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free (v);
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}
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static void
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Bcopy
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#ifdef KR_headers
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(x, y) Bigint *x, *y;
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#else
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(Bigint *x, Bigint *y)
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#endif
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{
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register unsigned32 *xp, *yp;
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register int i = y->wds;
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x->sign = y->sign;
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x->wds = i;
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for (xp = x->x, yp = y->x; --i >= 0; )
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*xp++ = *yp++;
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}
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|
|
/* Make sure b has room for at least 1<<k big digits. */
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|
|
static Bigint *
|
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Brealloc
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#ifdef KR_headers
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(b, k) Bigint *b; int k;
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#else
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(Bigint * b, int k)
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#endif
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{
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if (b == NULL)
|
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return Balloc(k);
|
|
if (b->k >= k)
|
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return b;
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else
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{
|
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Bigint *rv = Balloc (k);
|
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Bcopy(rv, b);
|
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Bfree(b);
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return rv;
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}
|
|
}
|
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|
|
/* Return b*m+a. b is modified.
|
|
Assumption: 0xFFFF*m+a fits in 32 bits. */
|
|
|
|
static Bigint *
|
|
multadd
|
|
#ifdef KR_headers
|
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(b, m, a) Bigint *b; int m, a;
|
|
#else
|
|
(Bigint *b, int m, int a)
|
|
#endif
|
|
{
|
|
int i, wds;
|
|
unsigned32 *x, y;
|
|
unsigned32 xi, z;
|
|
|
|
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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|
xi = *x;
|
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y = (xi & 0xffff) * m + a;
|
|
z = (xi >> 16) * m + (y >> 16);
|
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a = (int)(z >> 16);
|
|
*x++ = (z << 16) + (y & 0xffff);
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|
}
|
|
while(++i < wds);
|
|
if (a) {
|
|
if (wds >= b->maxwds)
|
|
b = Brealloc(b, b->k+1);
|
|
b->x[wds++] = a;
|
|
b->wds = wds;
|
|
}
|
|
return b;
|
|
}
|
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|
|
static Bigint *
|
|
s2b
|
|
#ifdef KR_headers
|
|
(result, s, nd0, nd, y9)
|
|
Bigint *result; CONST char *s; int nd0, nd; unsigned32 y9;
|
|
#else
|
|
(Bigint *result, CONST char *s, int nd0, int nd, unsigned32 y9)
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|
#endif
|
|
{
|
|
int i, k;
|
|
_G_int32_t x, y;
|
|
|
|
x = (nd + 8) / 9;
|
|
for(k = 0, y = 1; x > y; y <<= 1, k++) ;
|
|
result = Brealloc(result, k);
|
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result->x[0] = y9;
|
|
result->wds = 1;
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|
|
i = 9;
|
|
if (9 < nd0)
|
|
{
|
|
s += 9;
|
|
do
|
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result = multadd(result, 10, *s++ - '0');
|
|
while (++i < nd0);
|
|
s++;
|
|
}
|
|
else
|
|
s += 10;
|
|
for(; i < nd; i++)
|
|
result = multadd(result, 10, *s++ - '0');
|
|
return result;
|
|
}
|
|
|
|
static int
|
|
hi0bits
|
|
#ifdef KR_headers
|
|
(x) register unsigned32 x;
|
|
#else
|
|
(register unsigned32 x)
|
|
#endif
|
|
{
|
|
register int k = 0;
|
|
|
|
if (!(x & 0xffff0000)) {
|
|
k = 16;
|
|
x <<= 16;
|
|
}
|
|
if (!(x & 0xff000000)) {
|
|
k += 8;
|
|
x <<= 8;
|
|
}
|
|
if (!(x & 0xf0000000)) {
|
|
k += 4;
|
|
x <<= 4;
|
|
}
|
|
if (!(x & 0xc0000000)) {
|
|
k += 2;
|
|
x <<= 2;
|
|
}
|
|
if (!(x & 0x80000000)) {
|
|
k++;
|
|
if (!(x & 0x40000000))
|
|
return 32;
|
|
}
|
|
return k;
|
|
}
|
|
|
|
static int
|
|
lo0bits
|
|
#ifdef KR_headers
|
|
(y) unsigned32 *y;
|
|
#else
|
|
(unsigned32 *y)
|
|
#endif
|
|
{
|
|
register int k;
|
|
register unsigned32 x = *y;
|
|
|
|
if (x & 7) {
|
|
if (x & 1)
|
|
return 0;
|
|
if (x & 2) {
|
|
*y = x >> 1;
|
|
return 1;
|
|
}
|
|
*y = x >> 2;
|
|
return 2;
|
|
}
|
|
k = 0;
|
|
if (!(x & 0xffff)) {
|
|
k = 16;
|
|
x >>= 16;
|
|
}
|
|
if (!(x & 0xff)) {
|
|
k += 8;
|
|
x >>= 8;
|
|
}
|
|
if (!(x & 0xf)) {
|
|
k += 4;
|
|
x >>= 4;
|
|
}
|
|
if (!(x & 0x3)) {
|
|
k += 2;
|
|
x >>= 2;
|
|
}
|
|
if (!(x & 1)) {
|
|
k++;
|
|
x >>= 1;
|
|
if (!x & 1)
|
|
return 32;
|
|
}
|
|
*y = x;
|
|
return k;
|
|
}
|
|
|
|
static Bigint *
|
|
i2b
|
|
#ifdef KR_headers
|
|
(result, i) Bigint *result; int i;
|
|
#else
|
|
(Bigint* result, int i)
|
|
#endif
|
|
{
|
|
result = Brealloc(result, 1);
|
|
result->x[0] = i;
|
|
result->wds = 1;
|
|
return result;
|
|
}
|
|
|
|
/* Do: c = a * b. */
|
|
|
|
static Bigint *
|
|
mult
|
|
#ifdef KR_headers
|
|
(c, a, b) Bigint *a, *b, *c;
|
|
#else
|
|
(Bigint *c, Bigint *a, Bigint *b)
|
|
#endif
|
|
{
|
|
int k, wa, wb, wc;
|
|
unsigned32 carry, y, z;
|
|
unsigned32 *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
|
|
unsigned32 z2;
|
|
if (a->wds < b->wds) {
|
|
Bigint *tmp = a;
|
|
a = b;
|
|
b = tmp;
|
|
}
|
|
k = a->k;
|
|
wa = a->wds;
|
|
wb = b->wds;
|
|
wc = wa + wb;
|
|
if (wc > a->maxwds)
|
|
k++;
|
|
c = Brealloc(c, k);
|
|
for(x = c->x, xa = x + wc; x < xa; x++)
|
|
*x = 0;
|
|
xa = a->x;
|
|
xae = xa + wa;
|
|
xb = b->x;
|
|
xbe = xb + wb;
|
|
xc0 = c->x;
|
|
for(; xb < xbe; xb++, xc0++) {
|
|
if ((y = *xb & 0xffff)) {
|
|
x = xa;
|
|
xc = xc0;
|
|
carry = 0;
|
|
do {
|
|
z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
|
|
carry = z >> 16;
|
|
z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
|
|
carry = z2 >> 16;
|
|
Storeinc(xc, z2, z);
|
|
}
|
|
while(x < xae);
|
|
*xc = carry;
|
|
}
|
|
if ((y = *xb >> 16)) {
|
|
x = xa;
|
|
xc = xc0;
|
|
carry = 0;
|
|
z2 = *xc;
|
|
do {
|
|
z = (*x & 0xffff) * y + (*xc >> 16) + carry;
|
|
carry = z >> 16;
|
|
Storeinc(xc, z, z2);
|
|
z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
|
|
carry = z2 >> 16;
|
|
}
|
|
while(x < xae);
|
|
*xc = z2;
|
|
}
|
|
}
|
|
for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
|
|
c->wds = wc;
|
|
return c;
|
|
}
|
|
|
|
/* Returns b*(5**k). b is modified. */
|
|
/* Re-written by Per Bothner to not need a static list. */
|
|
|
|
static Bigint *
|
|
pow5mult
|
|
#ifdef KR_headers
|
|
(b, k) Bigint *b; int k;
|
|
#else
|
|
(Bigint *b, int k)
|
|
#endif
|
|
{
|
|
static int p05[6] = { 5, 25, 125, 625, 3125, 15625 };
|
|
|
|
for (; k > 6; k -= 6)
|
|
b = multadd(b, 15625, 0); /* b *= 5**6 */
|
|
if (k == 0)
|
|
return b;
|
|
else
|
|
return multadd(b, p05[k-1], 0);
|
|
}
|
|
|
|
/* Re-written by Per Bothner so shift can be in place. */
|
|
|
|
static Bigint *
|
|
lshift
|
|
#ifdef KR_headers
|
|
(b, k) Bigint *b; int k;
|
|
#else
|
|
(Bigint *b, int k)
|
|
#endif
|
|
{
|
|
int i;
|
|
unsigned32 *x, *x1, *xe;
|
|
int old_wds = b->wds;
|
|
int n = k >> 5;
|
|
int k1 = b->k;
|
|
int n1 = n + old_wds + 1;
|
|
|
|
if (k == 0)
|
|
return b;
|
|
|
|
for(i = b->maxwds; n1 > i; i <<= 1)
|
|
k1++;
|
|
b = Brealloc(b, k1);
|
|
|
|
xe = b->x; /* Source limit */
|
|
x = xe + old_wds; /* Source pointer */
|
|
x1 = x + n; /* Destination pointer */
|
|
if (k &= 0x1f) {
|
|
int k1 = 32 - k;
|
|
unsigned32 z = *--x;
|
|
if ((*x1 = (z >> k1)) != 0) {
|
|
++n1;
|
|
}
|
|
while (x > xe) {
|
|
unsigned32 w = *--x;
|
|
*--x1 = (z << k) | (w >> k1);
|
|
z = w;
|
|
}
|
|
*--x1 = z << k;
|
|
}
|
|
else
|
|
do {
|
|
*--x1 = *--x;
|
|
} while(x > xe);
|
|
while (x1 > xe)
|
|
*--x1 = 0;
|
|
b->wds = n1 - 1;
|
|
return b;
|
|
}
|
|
|
|
static int
|
|
cmp
|
|
#ifdef KR_headers
|
|
(a, b) Bigint *a, *b;
|
|
#else
|
|
(Bigint *a, Bigint *b)
|
|
#endif
|
|
{
|
|
unsigned32 *xa, *xa0, *xb, *xb0;
|
|
int i, j;
|
|
|
|
i = a->wds;
|
|
j = b->wds;
|
|
#ifdef DEBUG
|
|
if (i > 1 && !a->x[i-1])
|
|
Bug("cmp called with a->x[a->wds-1] == 0");
|
|
if (j > 1 && !b->x[j-1])
|
|
Bug("cmp called with b->x[b->wds-1] == 0");
|
|
#endif
|
|
if (i -= j)
|
|
return i;
|
|
xa0 = a->x;
|
|
xa = xa0 + j;
|
|
xb0 = b->x;
|
|
xb = xb0 + j;
|
|
for(;;) {
|
|
if (*--xa != *--xb)
|
|
return *xa < *xb ? -1 : 1;
|
|
if (xa <= xa0)
|
|
break;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
/* Do: c = a-b. */
|
|
|
|
static Bigint *
|
|
diff
|
|
#ifdef KR_headers
|
|
(c, a, b) Bigint *c, *a, *b;
|
|
#else
|
|
(Bigint *c, Bigint *a, Bigint *b)
|
|
#endif
|
|
{
|
|
int i, wa, wb;
|
|
_G_int32_t borrow, y; /* We need signed shifts here. */
|
|
unsigned32 *xa, *xae, *xb, *xbe, *xc;
|
|
_G_int32_t z;
|
|
|
|
i = cmp(a,b);
|
|
if (!i) {
|
|
c = Brealloc(c, 0);
|
|
c->wds = 1;
|
|
c->x[0] = 0;
|
|
return c;
|
|
}
|
|
if (i < 0) {
|
|
Bigint *tmp = a;
|
|
a = b;
|
|
b = tmp;
|
|
i = 1;
|
|
}
|
|
else
|
|
i = 0;
|
|
c = Brealloc(c, 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;
|
|
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);
|
|
}
|
|
while(!*--xc)
|
|
wa--;
|
|
c->wds = wa;
|
|
return c;
|
|
}
|
|
|
|
static double
|
|
ulp
|
|
#ifdef KR_headers
|
|
(x) double x;
|
|
#else
|
|
(double x)
|
|
#endif
|
|
{
|
|
register _G_int32_t L;
|
|
double a;
|
|
|
|
L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
|
|
#ifndef Sudden_Underflow
|
|
if (L > 0) {
|
|
#endif
|
|
#ifdef IBM
|
|
L |= Exp_msk1 >> 4;
|
|
#endif
|
|
word0(a) = L;
|
|
word1(a) = 0;
|
|
#ifndef Sudden_Underflow
|
|
}
|
|
else {
|
|
L = -L >> Exp_shift;
|
|
if (L < Exp_shift) {
|
|
word0(a) = 0x80000 >> L;
|
|
word1(a) = 0;
|
|
}
|
|
else {
|
|
word0(a) = 0;
|
|
L -= Exp_shift;
|
|
word1(a) = L >= 31 ? 1 : 1 << (31 - L);
|
|
}
|
|
}
|
|
#endif
|
|
return a;
|
|
}
|
|
|
|
static double
|
|
b2d
|
|
#ifdef KR_headers
|
|
(a, e) Bigint *a; int *e;
|
|
#else
|
|
(Bigint *a, int *e)
|
|
#endif
|
|
{
|
|
unsigned32 *xa, *xa0, w, y, z;
|
|
int k;
|
|
double d;
|
|
#ifdef VAX
|
|
unsigned32 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;
|
|
if (k < Ebits) {
|
|
d0 = Exp_1 | y >> (Ebits - k);
|
|
w = xa > xa0 ? *--xa : 0;
|
|
d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
|
|
goto ret_d;
|
|
}
|
|
z = xa > xa0 ? *--xa : 0;
|
|
if (k -= Ebits) {
|
|
d0 = Exp_1 | y << k | z >> (32 - k);
|
|
y = xa > xa0 ? *--xa : 0;
|
|
d1 = z << k | y >> (32 - k);
|
|
}
|
|
else {
|
|
d0 = Exp_1 | y;
|
|
d1 = z;
|
|
}
|
|
ret_d:
|
|
#ifdef VAX
|
|
word0(d) = d0 >> 16 | d0 << 16;
|
|
word1(d) = d1 >> 16 | d1 << 16;
|
|
#else
|
|
#undef d0
|
|
#undef d1
|
|
#endif
|
|
return d;
|
|
}
|
|
|
|
static Bigint *
|
|
d2b
|
|
#ifdef KR_headers
|
|
(result, d, e, bits) Bigint *result; double d; int *e, *bits;
|
|
#else
|
|
(Bigint *result, double d, int *e, int *bits)
|
|
#endif
|
|
{
|
|
int de, i, k;
|
|
unsigned32 *x, y, z;
|
|
#ifdef VAX
|
|
unsigned32 d0, d1;
|
|
d0 = word0(d) >> 16 | word0(d) << 16;
|
|
d1 = word1(d) >> 16 | word1(d) << 16;
|
|
#else
|
|
#define d0 word0(d)
|
|
#define d1 word1(d)
|
|
#endif
|
|
|
|
result = Brealloc(result, 1);
|
|
x = result->x;
|
|
|
|
z = d0 & Frac_mask;
|
|
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
|
|
|
|
de = (int)(d0 >> Exp_shift); /* The exponent part of d. */
|
|
|
|
/* Put back the suppressed high-order bit, if normalized. */
|
|
#ifndef IBM
|
|
#ifndef Sudden_Underflow
|
|
if (de)
|
|
#endif
|
|
z |= Exp_msk11;
|
|
#endif
|
|
|
|
if ((y = d1)) {
|
|
if ((k = lo0bits(&y))) {
|
|
x[0] = y | z << (32 - k);
|
|
z >>= k;
|
|
}
|
|
else
|
|
x[0] = y;
|
|
i = result->wds = (x[1] = z) ? 2 : 1;
|
|
}
|
|
else {
|
|
#ifdef DEBUG
|
|
if (!z)
|
|
Bug("Zero passed to d2b");
|
|
#endif
|
|
k = lo0bits(&z);
|
|
x[0] = z;
|
|
i = result->wds = 1;
|
|
k += 32;
|
|
}
|
|
#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;
|
|
*bits = 32*i - hi0bits(x[i-1]);
|
|
}
|
|
#endif
|
|
return result;
|
|
}
|
|
#undef d0
|
|
#undef d1
|
|
|
|
static double
|
|
ratio
|
|
#ifdef KR_headers
|
|
(a, b) Bigint *a, *b;
|
|
#else
|
|
(Bigint *a, Bigint *b)
|
|
#endif
|
|
{
|
|
double da, db;
|
|
int k, ka, kb;
|
|
|
|
da = b2d(a, &ka);
|
|
db = b2d(b, &kb);
|
|
k = ka - kb + 32*(a->wds - b->wds);
|
|
#ifdef IBM
|
|
if (k > 0) {
|
|
word0(da) += (k >> 2)*Exp_msk1;
|
|
if (k &= 3)
|
|
da *= 1 << k;
|
|
}
|
|
else {
|
|
k = -k;
|
|
word0(db) += (k >> 2)*Exp_msk1;
|
|
if (k &= 3)
|
|
db *= 1 << k;
|
|
}
|
|
#else
|
|
if (k > 0)
|
|
word0(da) += k*Exp_msk1;
|
|
else {
|
|
k = -k;
|
|
word0(db) += k*Exp_msk1;
|
|
}
|
|
#endif
|
|
return da / db;
|
|
}
|
|
|
|
static 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
|
|
#ifdef VAX
|
|
, 1e23, 1e24
|
|
#endif
|
|
};
|
|
|
|
static double
|
|
#ifdef IEEE_Arith
|
|
bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
|
|
static double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
|
|
#define n_bigtens 5
|
|
#else
|
|
#ifdef IBM
|
|
bigtens[] = { 1e16, 1e32, 1e64 };
|
|
static double tinytens[] = { 1e-16, 1e-32, 1e-64 };
|
|
#define n_bigtens 3
|
|
#else
|
|
bigtens[] = { 1e16, 1e32 };
|
|
static double tinytens[] = { 1e-16, 1e-32 };
|
|
#define n_bigtens 2
|
|
#endif
|
|
#endif
|
|
|
|
double
|
|
_IO_strtod
|
|
#ifdef KR_headers
|
|
(s00, se) CONST char *s00; char **se;
|
|
#else
|
|
(CONST char *s00, char **se)
|
|
#endif
|
|
{
|
|
int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
|
|
e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
|
|
CONST char *s, *s0, *s1;
|
|
double aadj, aadj1, adj, rv, rv0;
|
|
_G_int32_t L;
|
|
unsigned32 y, z;
|
|
Bigint _bb, _b_avail, _bd, _bd0, _bs, _delta;
|
|
Bigint *bb = Binit(&_bb);
|
|
Bigint *bd = Binit(&_bd);
|
|
Bigint *bd0 = Binit(&_bd0);
|
|
Bigint *bs = Binit(&_bs);
|
|
Bigint *b_avail = Binit(&_b_avail);
|
|
Bigint *delta = Binit(&_delta);
|
|
|
|
TEST_ENDIANNESS;
|
|
sign = nz0 = nz = 0;
|
|
rv = 0.;
|
|
for(s = s00;;s++) switch(*s) {
|
|
case '-':
|
|
sign = 1;
|
|
/* no break */
|
|
case '+':
|
|
if (*++s)
|
|
goto break2;
|
|
/* no break */
|
|
case 0:
|
|
/* "+" and "-" should be reported as an error? */
|
|
sign = 0;
|
|
s = s00;
|
|
goto ret;
|
|
case '\t':
|
|
case '\n':
|
|
case '\v':
|
|
case '\f':
|
|
case '\r':
|
|
case ' ':
|
|
continue;
|
|
default:
|
|
goto break2;
|
|
}
|
|
break2:
|
|
if (*s == '0') {
|
|
nz0 = 1;
|
|
while(*++s == '0') ;
|
|
if (!*s)
|
|
goto ret;
|
|
}
|
|
s0 = s;
|
|
y = z = 0;
|
|
for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
|
|
if (nd < 9)
|
|
y = 10*y + c - '0';
|
|
else if (nd < 16)
|
|
z = 10*z + c - '0';
|
|
nd0 = nd;
|
|
if (c == '.') {
|
|
c = *++s;
|
|
if (!nd) {
|
|
for(; c == '0'; c = *++s)
|
|
nz++;
|
|
if (c > '0' && c <= '9') {
|
|
s0 = s;
|
|
nf += nz;
|
|
nz = 0;
|
|
goto have_dig;
|
|
}
|
|
goto dig_done;
|
|
}
|
|
for(; c >= '0' && c <= '9'; c = *++s) {
|
|
have_dig:
|
|
nz++;
|
|
if (c -= '0') {
|
|
nf += nz;
|
|
for(i = 1; i < nz; i++)
|
|
if (nd++ < 9)
|
|
y *= 10;
|
|
else if (nd <= DBL_DIG + 1)
|
|
z *= 10;
|
|
if (nd++ < 9)
|
|
y = 10*y + c;
|
|
else if (nd <= DBL_DIG + 1)
|
|
z = 10*z + c;
|
|
nz = 0;
|
|
}
|
|
}
|
|
}
|
|
dig_done:
|
|
e = 0;
|
|
if (c == 'e' || c == 'E') {
|
|
if (!nd && !nz && !nz0) {
|
|
s = s00;
|
|
goto ret;
|
|
}
|
|
s00 = s;
|
|
esign = 0;
|
|
switch(c = *++s) {
|
|
case '-':
|
|
esign = 1;
|
|
case '+':
|
|
c = *++s;
|
|
}
|
|
if (c >= '0' && c <= '9') {
|
|
while(c == '0')
|
|
c = *++s;
|
|
if (c > '0' && c <= '9') {
|
|
e = c - '0';
|
|
s1 = s;
|
|
while((c = *++s) >= '0' && c <= '9')
|
|
e = 10*e + c - '0';
|
|
if (s - s1 > 8)
|
|
/* Avoid confusion from exponents
|
|
* so large that e might overflow.
|
|
*/
|
|
e = 9999999;
|
|
if (esign)
|
|
e = -e;
|
|
}
|
|
else
|
|
e = 0;
|
|
}
|
|
else
|
|
s = s00;
|
|
}
|
|
if (!nd) {
|
|
if (!nz && !nz0)
|
|
s = s00;
|
|
goto ret;
|
|
}
|
|
e1 = e -= nf;
|
|
|
|
/* Now we have nd0 digits, starting at s0, followed by a
|
|
* decimal point, followed by nd-nd0 digits. The number we're
|
|
* after is the integer represented by those digits times
|
|
* 10**e */
|
|
|
|
if (!nd0)
|
|
nd0 = nd;
|
|
k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
|
|
rv = y;
|
|
if (k > 9)
|
|
rv = tens[k - 9] * rv + z;
|
|
if (nd <= DBL_DIG
|
|
#ifndef RND_PRODQUOT
|
|
&& FLT_ROUNDS == 1
|
|
#endif
|
|
) {
|
|
if (!e)
|
|
goto ret;
|
|
if (e > 0) {
|
|
if (e <= Ten_pmax) {
|
|
#ifdef VAX
|
|
goto vax_ovfl_check;
|
|
#else
|
|
/* rv = */ rounded_product(rv, tens[e]);
|
|
goto ret;
|
|
#endif
|
|
}
|
|
i = DBL_DIG - nd;
|
|
if (e <= Ten_pmax + i) {
|
|
/* A fancier test would sometimes let us do
|
|
* this for larger i values.
|
|
*/
|
|
e -= i;
|
|
rv *= tens[i];
|
|
#ifdef VAX
|
|
/* VAX exponent range is so narrow we must
|
|
* worry about overflow here...
|
|
*/
|
|
vax_ovfl_check:
|
|
word0(rv) -= P*Exp_msk1;
|
|
/* rv = */ rounded_product(rv, tens[e]);
|
|
if ((word0(rv) & Exp_mask)
|
|
> Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
|
|
goto ovfl;
|
|
word0(rv) += P*Exp_msk1;
|
|
#else
|
|
/* rv = */ rounded_product(rv, tens[e]);
|
|
#endif
|
|
goto ret;
|
|
}
|
|
}
|
|
#ifndef Inaccurate_Divide
|
|
else if (e >= -Ten_pmax) {
|
|
/* rv = */ rounded_quotient(rv, tens[-e]);
|
|
goto ret;
|
|
}
|
|
#endif
|
|
}
|
|
e1 += nd - k;
|
|
|
|
/* Get starting approximation = rv * 10**e1 */
|
|
|
|
if (e1 > 0) {
|
|
if ((i = e1 & 15))
|
|
rv *= tens[i];
|
|
if (e1 &= ~15) {
|
|
if (e1 > DBL_MAX_10_EXP) {
|
|
ovfl:
|
|
errno = ERANGE;
|
|
#if defined(sun) && !defined(__svr4__)
|
|
/* SunOS defines HUGE_VAL as __infinity(), which is in libm. */
|
|
#undef HUGE_VAL
|
|
#endif
|
|
#ifndef HUGE_VAL
|
|
#define HUGE_VAL 1.7976931348623157E+308
|
|
#endif
|
|
rv = HUGE_VAL;
|
|
goto ret;
|
|
}
|
|
if (e1 >>= 4) {
|
|
for(j = 0; e1 > 1; j++, e1 >>= 1)
|
|
if (e1 & 1)
|
|
rv *= bigtens[j];
|
|
/* The last multiplication could overflow. */
|
|
word0(rv) -= P*Exp_msk1;
|
|
rv *= bigtens[j];
|
|
if ((z = word0(rv) & Exp_mask)
|
|
> Exp_msk1*(DBL_MAX_EXP+Bias-P))
|
|
goto ovfl;
|
|
if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
|
|
/* set to largest number */
|
|
/* (Can't trust DBL_MAX) */
|
|
word0(rv) = Big0;
|
|
word1(rv) = Big1;
|
|
}
|
|
else
|
|
word0(rv) += P*Exp_msk1;
|
|
}
|
|
|
|
}
|
|
}
|
|
else if (e1 < 0) {
|
|
e1 = -e1;
|
|
if ((i = e1 & 15))
|
|
rv /= tens[i];
|
|
if (e1 &= ~15) {
|
|
e1 >>= 4;
|
|
for(j = 0; e1 > 1; j++, e1 >>= 1)
|
|
if (e1 & 1)
|
|
rv *= tinytens[j];
|
|
/* The last multiplication could underflow. */
|
|
rv0 = rv;
|
|
rv *= tinytens[j];
|
|
if (!rv) {
|
|
rv = 2.*rv0;
|
|
rv *= tinytens[j];
|
|
if (!rv) {
|
|
undfl:
|
|
rv = 0.;
|
|
errno = ERANGE;
|
|
goto ret;
|
|
}
|
|
word0(rv) = Tiny0;
|
|
word1(rv) = Tiny1;
|
|
/* The refinement below will clean
|
|
* this approximation up.
|
|
*/
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Now the hard part -- adjusting rv to the correct value.*/
|
|
|
|
/* Put digits into bd: true value = bd * 10^e */
|
|
|
|
bd0 = s2b(bd0, s0, nd0, nd, y);
|
|
bd = Brealloc(bd, bd0->k);
|
|
|
|
for(;;) {
|
|
Bcopy(bd, bd0);
|
|
bb = d2b(bb, rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
|
|
bs = i2b(bs, 1);
|
|
|
|
if (e >= 0) {
|
|
bb2 = bb5 = 0;
|
|
bd2 = bd5 = e;
|
|
}
|
|
else {
|
|
bb2 = bb5 = -e;
|
|
bd2 = bd5 = 0;
|
|
}
|
|
if (bbe >= 0)
|
|
bb2 += bbe;
|
|
else
|
|
bd2 -= bbe;
|
|
bs2 = bb2;
|
|
#ifdef Sudden_Underflow
|
|
#ifdef IBM
|
|
j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
|
|
#else
|
|
j = P + 1 - bbbits;
|
|
#endif
|
|
#else
|
|
i = bbe + bbbits - 1; /* logb(rv) */
|
|
if (i < Emin) /* denormal */
|
|
j = bbe + (P-Emin);
|
|
else
|
|
j = P + 1 - bbbits;
|
|
#endif
|
|
bb2 += j;
|
|
bd2 += j;
|
|
i = bb2 < bd2 ? bb2 : bd2;
|
|
if (i > bs2)
|
|
i = bs2;
|
|
if (i > 0) {
|
|
bb2 -= i;
|
|
bd2 -= i;
|
|
bs2 -= i;
|
|
}
|
|
if (bb5 > 0) {
|
|
Bigint *b_tmp;
|
|
bs = pow5mult(bs, bb5);
|
|
b_tmp = mult(b_avail, bs, bb);
|
|
b_avail = bb;
|
|
bb = b_tmp;
|
|
}
|
|
if (bb2 > 0)
|
|
bb = lshift(bb, bb2);
|
|
if (bd5 > 0)
|
|
bd = pow5mult(bd, bd5);
|
|
if (bd2 > 0)
|
|
bd = lshift(bd, bd2);
|
|
if (bs2 > 0)
|
|
bs = lshift(bs, bs2);
|
|
delta = diff(delta, bb, bd);
|
|
dsign = delta->sign;
|
|
delta->sign = 0;
|
|
i = cmp(delta, bs);
|
|
if (i < 0) {
|
|
/* Error is less than half an ulp -- check for
|
|
* special case of mantissa a power of two.
|
|
*/
|
|
if (dsign || word1(rv) || word0(rv) & Bndry_mask)
|
|
break;
|
|
delta = lshift(delta,Log2P);
|
|
if (cmp(delta, bs) > 0)
|
|
goto drop_down;
|
|
break;
|
|
}
|
|
if (i == 0) {
|
|
/* exactly half-way between */
|
|
if (dsign) {
|
|
if ((word0(rv) & Bndry_mask1) == Bndry_mask1
|
|
&& word1(rv) == 0xffffffff) {
|
|
/*boundary case -- increment exponent*/
|
|
word0(rv) = (word0(rv) & Exp_mask)
|
|
+ Exp_msk1
|
|
#ifdef IBM
|
|
| Exp_msk1 >> 4
|
|
#endif
|
|
;
|
|
word1(rv) = 0;
|
|
break;
|
|
}
|
|
}
|
|
else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
|
|
drop_down:
|
|
/* boundary case -- decrement exponent */
|
|
#ifdef Sudden_Underflow
|
|
L = word0(rv) & Exp_mask;
|
|
#ifdef IBM
|
|
if (L < Exp_msk1)
|
|
#else
|
|
if (L <= Exp_msk1)
|
|
#endif
|
|
goto undfl;
|
|
L -= Exp_msk1;
|
|
#else
|
|
L = (word0(rv) & Exp_mask) - Exp_msk1;
|
|
#endif
|
|
word0(rv) = L | Bndry_mask1;
|
|
word1(rv) = 0xffffffff;
|
|
#ifdef IBM
|
|
continue;
|
|
#else
|
|
break;
|
|
#endif
|
|
}
|
|
#ifndef ROUND_BIASED
|
|
if (!(word1(rv) & LSB))
|
|
break;
|
|
#endif
|
|
if (dsign)
|
|
rv += ulp(rv);
|
|
#ifndef ROUND_BIASED
|
|
else {
|
|
rv -= ulp(rv);
|
|
#ifndef Sudden_Underflow
|
|
if (!rv)
|
|
goto undfl;
|
|
#endif
|
|
}
|
|
#endif
|
|
break;
|
|
}
|
|
if ((aadj = ratio(delta, bs)) <= 2.) {
|
|
if (dsign)
|
|
aadj = aadj1 = 1.;
|
|
else if (word1(rv) || word0(rv) & Bndry_mask) {
|
|
#ifndef Sudden_Underflow
|
|
if (word1(rv) == Tiny1 && !word0(rv))
|
|
goto undfl;
|
|
#endif
|
|
aadj = 1.;
|
|
aadj1 = -1.;
|
|
}
|
|
else {
|
|
/* special case -- power of FLT_RADIX to be */
|
|
/* rounded down... */
|
|
|
|
if (aadj < 2./FLT_RADIX)
|
|
aadj = 1./FLT_RADIX;
|
|
else
|
|
aadj *= 0.5;
|
|
aadj1 = -aadj;
|
|
}
|
|
}
|
|
else {
|
|
aadj *= 0.5;
|
|
aadj1 = dsign ? aadj : -aadj;
|
|
#ifdef Check_FLT_ROUNDS
|
|
switch(FLT_ROUNDS) {
|
|
case 2: /* towards +infinity */
|
|
aadj1 -= 0.5;
|
|
break;
|
|
case 0: /* towards 0 */
|
|
case 3: /* towards -infinity */
|
|
aadj1 += 0.5;
|
|
}
|
|
#else
|
|
if (FLT_ROUNDS == 0)
|
|
aadj1 += 0.5;
|
|
#endif
|
|
}
|
|
y = word0(rv) & Exp_mask;
|
|
|
|
/* Check for overflow */
|
|
|
|
if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
|
|
rv0 = rv;
|
|
word0(rv) -= P*Exp_msk1;
|
|
adj = aadj1 * ulp(rv);
|
|
rv += adj;
|
|
if ((word0(rv) & Exp_mask) >=
|
|
Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
|
|
if (word0(rv0) == Big0 && word1(rv0) == Big1)
|
|
goto ovfl;
|
|
word0(rv) = Big0;
|
|
word1(rv) = Big1;
|
|
continue;
|
|
}
|
|
else
|
|
word0(rv) += P*Exp_msk1;
|
|
}
|
|
else {
|
|
#ifdef Sudden_Underflow
|
|
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
|
|
rv0 = rv;
|
|
word0(rv) += P*Exp_msk1;
|
|
adj = aadj1 * ulp(rv);
|
|
rv += adj;
|
|
#ifdef IBM
|
|
if ((word0(rv) & Exp_mask) < P*Exp_msk1)
|
|
#else
|
|
if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
|
|
#endif
|
|
{
|
|
if (word0(rv0) == Tiny0
|
|
&& word1(rv0) == Tiny1)
|
|
goto undfl;
|
|
word0(rv) = Tiny0;
|
|
word1(rv) = Tiny1;
|
|
continue;
|
|
}
|
|
else
|
|
word0(rv) -= P*Exp_msk1;
|
|
}
|
|
else {
|
|
adj = aadj1 * ulp(rv);
|
|
rv += adj;
|
|
}
|
|
#else
|
|
/* Compute adj so that the IEEE rounding rules will
|
|
* correctly round rv + adj in some half-way cases.
|
|
* If rv * ulp(rv) is denormalized (i.e.,
|
|
* y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
|
|
* trouble from bits lost to denormalization;
|
|
* example: 1.2e-307 .
|
|
*/
|
|
if (y <= (P-1)*Exp_msk1 && aadj >= 1.) {
|
|
aadj1 = (double)(int)(aadj + 0.5);
|
|
if (!dsign)
|
|
aadj1 = -aadj1;
|
|
}
|
|
adj = aadj1 * ulp(rv);
|
|
rv += adj;
|
|
#endif
|
|
}
|
|
z = word0(rv) & Exp_mask;
|
|
if (y == z) {
|
|
/* Can we stop now? */
|
|
L = (_G_int32_t)aadj;
|
|
aadj -= L;
|
|
/* The tolerances below are conservative. */
|
|
if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
|
|
if (aadj < .4999999 || aadj > .5000001)
|
|
break;
|
|
}
|
|
else if (aadj < .4999999/FLT_RADIX)
|
|
break;
|
|
}
|
|
}
|
|
Bfree(bb);
|
|
Bfree(bd);
|
|
Bfree(bs);
|
|
Bfree(bd0);
|
|
Bfree(delta);
|
|
Bfree(b_avail);
|
|
ret:
|
|
if (se)
|
|
*se = (char *)s;
|
|
return sign ? -rv : rv;
|
|
}
|
|
|
|
static int
|
|
quorem
|
|
#ifdef KR_headers
|
|
(b, S) Bigint *b, *S;
|
|
#else
|
|
(Bigint *b, Bigint *S)
|
|
#endif
|
|
{
|
|
int n;
|
|
_G_int32_t borrow, y;
|
|
unsigned32 carry, q, ys;
|
|
unsigned32 *bx, *bxe, *sx, *sxe;
|
|
_G_int32_t z;
|
|
unsigned32 si, zs;
|
|
|
|
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 {
|
|
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);
|
|
}
|
|
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 {
|
|
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);
|
|
}
|
|
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 *
|
|
_IO_dtoa
|
|
#ifdef KR_headers
|
|
(d, mode, ndigits, decpt, sign, rve)
|
|
double d; int mode, ndigits, *decpt, *sign; char **rve;
|
|
#else
|
|
(double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
|
|
#endif
|
|
{
|
|
/* 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;
|
|
_G_int32_t L;
|
|
#ifndef Sudden_Underflow
|
|
int denorm;
|
|
#endif
|
|
Bigint _b_avail, _b, _mhi, _mlo, _S;
|
|
Bigint *b_avail = Binit(&_b_avail);
|
|
Bigint *b = Binit(&_b);
|
|
Bigint *S = Binit(&_S);
|
|
/* mhi and mlo are only set and used if leftright. */
|
|
Bigint *mhi = NULL, *mlo = NULL;
|
|
double d2, ds, eps;
|
|
char *s, *s0;
|
|
static Bigint *result = NULL;
|
|
static int result_k;
|
|
|
|
TEST_ENDIANNESS;
|
|
if (result) {
|
|
/* result is contains a string, so its fields (interpreted
|
|
as a Bigint have been trashed. Restore them.
|
|
This is a really ugly interface - result should
|
|
not be static, since that is not thread-safe. FIXME. */
|
|
result->k = result_k;
|
|
result->maxwds = 1 << result_k;
|
|
result->on_stack = 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;
|
|
#ifdef IEEE_Arith
|
|
if (!word1(d) && !(word0(d) & 0xfffff))
|
|
{
|
|
s = "Infinity";
|
|
if (rve)
|
|
*rve = s + 8;
|
|
}
|
|
else
|
|
#endif
|
|
{
|
|
s = "NaN";
|
|
if (rve)
|
|
*rve = s +3;
|
|
}
|
|
return s;
|
|
}
|
|
#endif
|
|
#ifdef IBM
|
|
d += 0; /* normalize */
|
|
#endif
|
|
if (!d) {
|
|
*decpt = 1;
|
|
s = "0";
|
|
if (rve)
|
|
*rve = s + 1;
|
|
return s;
|
|
}
|
|
|
|
b = d2b(b, d, &be, &bbits);
|
|
i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
|
|
#ifndef Sudden_Underflow
|
|
if (i) {
|
|
#endif
|
|
d2 = d;
|
|
word0(d2) &= Frac_mask1;
|
|
word0(d2) |= Exp_11;
|
|
#ifdef IBM
|
|
if (j = 11 - hi0bits(word0(d2) & Frac_mask))
|
|
d2 /= 1 << j;
|
|
#endif
|
|
|
|
i -= Bias;
|
|
#ifdef IBM
|
|
i <<= 2;
|
|
i += j;
|
|
#endif
|
|
#ifndef Sudden_Underflow
|
|
denorm = 0;
|
|
}
|
|
else {
|
|
/* d is denormalized */
|
|
unsigned32 x;
|
|
|
|
i = bbits + be + (Bias + (P-1) - 1);
|
|
x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
|
|
: word1(d) << (32 - i);
|
|
d2 = x;
|
|
word0(d2) -= 31*Exp_msk1; /* adjust exponent */
|
|
i -= (Bias + (P-1) - 1) + 1;
|
|
denorm = 1;
|
|
}
|
|
#endif
|
|
|
|
/* Now i is the unbiased base-2 exponent. */
|
|
|
|
/* 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*log(2)/log(10) + log10(d2)
|
|
*
|
|
* This suggests computing an approximation k to log10(d) by
|
|
*
|
|
* k = i*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) by 0.301029995663981; since |i| <= 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.)
|
|
*/
|
|
|
|
ds = (d2-1.5)*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 < 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;
|
|
}
|
|
/* i is now an upper bound of the number of digits to generate. */
|
|
j = sizeof(unsigned32) * (1<<BIGINT_MINIMUM_K);
|
|
/* The test is <= so as to allow room for the final '\0'. */
|
|
for(result_k = BIGINT_MINIMUM_K; BIGINT_HEADER_SIZE + j <= i;
|
|
j <<= 1) result_k++;
|
|
if (!result || result_k > result->k)
|
|
{
|
|
Bfree (result);
|
|
result = Balloc(result_k);
|
|
}
|
|
s = s0 = (char *)result;
|
|
|
|
if (ilim >= 0 && ilim <= Quick_max && try_quick) {
|
|
|
|
/* Try to get by with floating-point arithmetic. */
|
|
|
|
i = 0;
|
|
d2 = 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 /= bigtens[n_bigtens-1];
|
|
ieps++;
|
|
}
|
|
for(; j; j >>= 1, i++)
|
|
if (j & 1) {
|
|
ieps++;
|
|
ds *= bigtens[i];
|
|
}
|
|
d /= ds;
|
|
}
|
|
else if ((j1 = -k)) {
|
|
d *= tens[j1 & 0xf];
|
|
for(j = j1 >> 4; j; j >>= 1, i++)
|
|
if (j & 1) {
|
|
ieps++;
|
|
d *= bigtens[i];
|
|
}
|
|
}
|
|
if (k_check && d < 1. && ilim > 0) {
|
|
if (ilim1 <= 0)
|
|
goto fast_failed;
|
|
ilim = ilim1;
|
|
k--;
|
|
d *= 10.;
|
|
ieps++;
|
|
}
|
|
eps = ieps*d + 7.;
|
|
word0(eps) -= (P-1)*Exp_msk1;
|
|
if (ilim == 0) {
|
|
d -= 5.;
|
|
if (d > eps)
|
|
goto one_digit;
|
|
if (d < -eps)
|
|
goto no_digits;
|
|
goto fast_failed;
|
|
}
|
|
#ifndef No_leftright
|
|
if (leftright) {
|
|
/* Use Steele & White method of only
|
|
* generating digits needed.
|
|
*/
|
|
eps = 0.5/tens[ilim-1] - eps;
|
|
for(i = 0;;) {
|
|
L = (_G_int32_t)d;
|
|
d -= L;
|
|
*s++ = '0' + (int)L;
|
|
if (d < eps)
|
|
goto ret1;
|
|
if (1. - d < eps)
|
|
goto bump_up;
|
|
if (++i >= ilim)
|
|
break;
|
|
eps *= 10.;
|
|
d *= 10.;
|
|
}
|
|
}
|
|
else {
|
|
#endif
|
|
/* Generate ilim digits, then fix them up. */
|
|
eps *= tens[ilim-1];
|
|
for(i = 1;; i++, d *= 10.) {
|
|
L = (_G_int32_t)d;
|
|
d -= L;
|
|
*s++ = '0' + (int)L;
|
|
if (i == ilim) {
|
|
if (d > 0.5 + eps)
|
|
goto bump_up;
|
|
else if (d < 0.5 - eps) {
|
|
while(*--s == '0');
|
|
s++;
|
|
goto ret1;
|
|
}
|
|
break;
|
|
}
|
|
}
|
|
#ifndef No_leftright
|
|
}
|
|
#endif
|
|
fast_failed:
|
|
s = s0;
|
|
d = d2;
|
|
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) {
|
|
if (ilim < 0 || d <= 5*ds)
|
|
goto no_digits;
|
|
goto one_digit;
|
|
}
|
|
for(i = 1;; i++) {
|
|
L = (_G_int32_t)(d / ds);
|
|
d -= L*ds;
|
|
#ifdef Check_FLT_ROUNDS
|
|
/* If FLT_ROUNDS == 2, L will usually be high by 1 */
|
|
if (d < 0) {
|
|
L--;
|
|
d += ds;
|
|
}
|
|
#endif
|
|
*s++ = '0' + (int)L;
|
|
if (i == ilim) {
|
|
d += d;
|
|
if (d > ds || (d == ds && L & 1)) {
|
|
bump_up:
|
|
while(*--s == '9')
|
|
if (s == s0) {
|
|
k++;
|
|
*s = '0';
|
|
break;
|
|
}
|
|
++*s++;
|
|
}
|
|
break;
|
|
}
|
|
if (!(d *= 10.))
|
|
break;
|
|
}
|
|
goto ret1;
|
|
}
|
|
|
|
m2 = b2;
|
|
m5 = b5;
|
|
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(Binit(&_mhi), 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) {
|
|
Bigint *b_tmp;
|
|
mhi = pow5mult(mhi, m5);
|
|
b_tmp = mult(b_avail, mhi, b);
|
|
b_avail = b;
|
|
b = b_tmp;
|
|
}
|
|
if ((j = b5 - m5))
|
|
b = pow5mult(b, j);
|
|
}
|
|
else
|
|
b = pow5mult(b, b5);
|
|
}
|
|
S = i2b(S, 1);
|
|
if (s5 > 0)
|
|
S = pow5mult(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.
|
|
*/
|
|
if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
|
|
i = 32 - i;
|
|
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(b, b2);
|
|
if (s2 > 0)
|
|
S = lshift(S, s2);
|
|
if (k_check) {
|
|
if (cmp(b,S) < 0) {
|
|
k--;
|
|
b = multadd(b, 10, 0); /* we botched the k estimate */
|
|
if (leftright)
|
|
mhi = multadd(mhi, 10, 0);
|
|
ilim = ilim1;
|
|
}
|
|
}
|
|
if (ilim <= 0 && mode > 2) {
|
|
if (ilim < 0 || cmp(b,S = multadd(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(mhi, m2);
|
|
|
|
/* Compute mlo -- check for special case
|
|
* that d is a normalized power of 2.
|
|
*/
|
|
|
|
if (spec_case) {
|
|
mlo = Brealloc(Binit(&_mlo), mhi->k);
|
|
Bcopy(mlo, mhi);
|
|
mhi = lshift(mhi, Log2P);
|
|
}
|
|
else
|
|
mlo = mhi;
|
|
|
|
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);
|
|
b_avail = diff(b_avail, S, mhi); /* b_avail = S - mi */
|
|
j1 = b_avail->sign ? 1 : cmp(b, b_avail);
|
|
#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(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(b, 10, 0);
|
|
if (mlo == mhi)
|
|
mlo = mhi = multadd(mhi, 10, 0);
|
|
else {
|
|
mlo = multadd(mlo, 10, 0);
|
|
mhi = multadd(mhi, 10, 0);
|
|
}
|
|
}
|
|
}
|
|
else
|
|
for(i = 1;; i++) {
|
|
*s++ = dig = quorem(b,S) + '0';
|
|
if (i >= ilim)
|
|
break;
|
|
b = multadd(b, 10, 0);
|
|
}
|
|
|
|
/* Round off last digit */
|
|
|
|
b = lshift(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(b_avail);
|
|
Bfree(S);
|
|
if (mhi) {
|
|
if (mlo && mlo != mhi)
|
|
Bfree(mlo);
|
|
Bfree(mhi);
|
|
}
|
|
ret1:
|
|
Bfree(b);
|
|
*s = 0;
|
|
*decpt = k + 1;
|
|
if (rve)
|
|
*rve = s;
|
|
return s0;
|
|
}
|
|
#endif /* _IO_USE_DTOA */
|