[444] | 1 | /**************************************************************** |
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| 2 | * |
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| 3 | * The author of this software is David M. Gay. |
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| 4 | * |
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| 5 | * Copyright (c) 1991 by AT&T. |
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| 6 | * |
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| 7 | * Permission to use, copy, modify, and distribute this software for any |
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| 8 | * purpose without fee is hereby granted, provided that this entire notice |
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| 9 | * is included in all copies of any software which is or includes a copy |
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| 10 | * or modification of this software and in all copies of the supporting |
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| 11 | * documentation for such software. |
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| 12 | * |
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| 13 | * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED |
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| 14 | * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY |
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| 15 | * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY |
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| 16 | * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. |
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| 17 | * |
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| 18 | ***************************************************************/ |
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| 19 | |
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| 20 | /* Please send bug reports to |
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| 21 | David M. Gay |
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| 22 | AT&T Bell Laboratories, Room 2C-463 |
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| 23 | 600 Mountain Avenue |
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| 24 | Murray Hill, NJ 07974-2070 |
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| 25 | U.S.A. |
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| 26 | dmg@research.att.com or research!dmg |
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| 27 | */ |
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| 28 | |
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| 29 | /* strtod for IEEE-, VAX-, and IBM-arithmetic machines. |
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| 30 | * |
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| 31 | * This strtod returns a nearest machine number to the input decimal |
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| 32 | * string (or sets errno to ERANGE). With IEEE arithmetic, ties are |
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| 33 | * broken by the IEEE round-even rule. Otherwise ties are broken by |
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| 34 | * biased rounding (add half and chop). |
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| 35 | * |
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| 36 | * Inspired loosely by William D. Clinger's paper "How to Read Floating |
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| 37 | * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. |
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| 38 | * |
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| 39 | * Modifications: |
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| 40 | * |
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| 41 | * 1. We only require IEEE, IBM, or VAX double-precision |
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| 42 | * arithmetic (not IEEE double-extended). |
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| 43 | * 2. We get by with floating-point arithmetic in a case that |
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| 44 | * Clinger missed -- when we're computing d * 10^n |
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| 45 | * for a small integer d and the integer n is not too |
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| 46 | * much larger than 22 (the maximum integer k for which |
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| 47 | * we can represent 10^k exactly), we may be able to |
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| 48 | * compute (d*10^k) * 10^(e-k) with just one roundoff. |
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| 49 | * 3. Rather than a bit-at-a-time adjustment of the binary |
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| 50 | * result in the hard case, we use floating-point |
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| 51 | * arithmetic to determine the adjustment to within |
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| 52 | * one bit; only in really hard cases do we need to |
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| 53 | * compute a second residual. |
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| 54 | * 4. Because of 3., we don't need a large table of powers of 10 |
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| 55 | * for ten-to-e (just some small tables, e.g. of 10^k |
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| 56 | * for 0 <= k <= 22). |
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| 57 | */ |
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| 58 | |
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| 59 | /* |
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| 60 | * #define IEEE_8087 for IEEE-arithmetic machines where the least |
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| 61 | * significant byte has the lowest address. |
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| 62 | * #define IEEE_MC68k for IEEE-arithmetic machines where the most |
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| 63 | * significant byte has the lowest address. |
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| 64 | * #define Sudden_Underflow for IEEE-format machines without gradual |
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| 65 | * underflow (i.e., that flush to zero on underflow). |
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| 66 | * #define IBM for IBM mainframe-style floating-point arithmetic. |
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| 67 | * #define VAX for VAX-style floating-point arithmetic. |
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| 68 | * #define Unsigned_Shifts if >> does treats its left operand as unsigned. |
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| 69 | * #define No_leftright to omit left-right logic in fast floating-point |
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| 70 | * computation of dtoa. |
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| 71 | * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3. |
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| 72 | * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines |
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| 73 | * that use extended-precision instructions to compute rounded |
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| 74 | * products and quotients) with IBM. |
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| 75 | * #define ROUND_BIASED for IEEE-format with biased rounding. |
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| 76 | * #define Inaccurate_Divide for IEEE-format with correctly rounded |
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| 77 | * products but inaccurate quotients, e.g., for Intel i860. |
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| 78 | * #define Just_16 to store 16 bits per 32-bit long when doing high-precision |
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| 79 | * integer arithmetic. Whether this speeds things up or slows things |
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| 80 | * down depends on the machine and the number being converted. |
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| 81 | */ |
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| 82 | |
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| 83 | #include <_ansi.h> |
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| 84 | #include <stdlib.h> |
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| 85 | #include <string.h> |
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| 86 | #include <reent.h> |
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| 87 | #include "mprec.h" |
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| 88 | |
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| 89 | /* This is defined in sys/reent.h as (sizeof (size_t) << 3) now, as in NetBSD. |
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| 90 | The old value of 15 was wrong and made newlib vulnerable against buffer |
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| 91 | overrun attacks (CVE-2009-0689), same as other implementations of gdtoa |
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| 92 | based on BSD code. |
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| 93 | #define _Kmax 15 |
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| 94 | */ |
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| 95 | |
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| 96 | _Bigint * |
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| 97 | Balloc (struct _reent *ptr, int k) |
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| 98 | { |
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| 99 | int x; |
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| 100 | _Bigint *rv ; |
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| 101 | |
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| 102 | _REENT_CHECK_MP(ptr); |
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| 103 | if (_REENT_MP_FREELIST(ptr) == NULL) |
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| 104 | { |
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| 105 | /* Allocate a list of pointers to the mprec objects */ |
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| 106 | _REENT_MP_FREELIST(ptr) = (struct _Bigint **) _calloc_r (ptr, |
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| 107 | sizeof (struct _Bigint *), |
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| 108 | _Kmax + 1); |
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| 109 | if (_REENT_MP_FREELIST(ptr) == NULL) |
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| 110 | { |
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| 111 | return NULL; |
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| 112 | } |
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| 113 | } |
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| 114 | |
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| 115 | if ((rv = _REENT_MP_FREELIST(ptr)[k]) != 0) |
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| 116 | { |
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| 117 | _REENT_MP_FREELIST(ptr)[k] = rv->_next; |
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| 118 | } |
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| 119 | else |
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| 120 | { |
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| 121 | x = 1 << k; |
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| 122 | /* Allocate an mprec Bigint and stick in in the freelist */ |
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| 123 | rv = (_Bigint *) _calloc_r (ptr, |
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| 124 | 1, |
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| 125 | sizeof (_Bigint) + |
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| 126 | (x-1) * sizeof(rv->_x)); |
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| 127 | if (rv == NULL) return NULL; |
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| 128 | rv->_k = k; |
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| 129 | rv->_maxwds = x; |
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| 130 | } |
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| 131 | rv->_sign = rv->_wds = 0; |
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| 132 | return rv; |
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| 133 | } |
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| 134 | |
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| 135 | void |
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| 136 | Bfree (struct _reent *ptr, _Bigint * v) |
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| 137 | { |
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| 138 | _REENT_CHECK_MP(ptr); |
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| 139 | if (v) |
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| 140 | { |
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| 141 | v->_next = _REENT_MP_FREELIST(ptr)[v->_k]; |
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| 142 | _REENT_MP_FREELIST(ptr)[v->_k] = v; |
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| 143 | } |
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| 144 | } |
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| 145 | |
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| 146 | _Bigint * |
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| 147 | multadd (struct _reent *ptr, |
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| 148 | _Bigint * b, |
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| 149 | int m, |
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| 150 | int a) |
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| 151 | { |
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| 152 | int i, wds; |
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| 153 | __ULong *x, y; |
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| 154 | #ifdef Pack_32 |
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| 155 | __ULong xi, z; |
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| 156 | #endif |
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| 157 | _Bigint *b1; |
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| 158 | |
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| 159 | wds = b->_wds; |
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| 160 | x = b->_x; |
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| 161 | i = 0; |
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| 162 | do |
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| 163 | { |
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| 164 | #ifdef Pack_32 |
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| 165 | xi = *x; |
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| 166 | y = (xi & 0xffff) * m + a; |
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| 167 | z = (xi >> 16) * m + (y >> 16); |
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| 168 | a = (int) (z >> 16); |
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| 169 | *x++ = (z << 16) + (y & 0xffff); |
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| 170 | #else |
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| 171 | y = *x * m + a; |
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| 172 | a = (int) (y >> 16); |
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| 173 | *x++ = y & 0xffff; |
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| 174 | #endif |
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| 175 | } |
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| 176 | while (++i < wds); |
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| 177 | if (a) |
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| 178 | { |
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| 179 | if (wds >= b->_maxwds) |
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| 180 | { |
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| 181 | b1 = Balloc (ptr, b->_k + 1); |
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| 182 | Bcopy (b1, b); |
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| 183 | Bfree (ptr, b); |
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| 184 | b = b1; |
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| 185 | } |
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| 186 | b->_x[wds++] = a; |
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| 187 | b->_wds = wds; |
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| 188 | } |
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| 189 | return b; |
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| 190 | } |
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| 191 | |
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| 192 | _Bigint * |
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| 193 | s2b (struct _reent * ptr, |
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| 194 | const char *s, |
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| 195 | int nd0, |
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| 196 | int nd, |
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| 197 | __ULong y9) |
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| 198 | { |
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| 199 | _Bigint *b; |
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| 200 | int i, k; |
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| 201 | __Long x, y; |
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| 202 | |
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| 203 | x = (nd + 8) / 9; |
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| 204 | for (k = 0, y = 1; x > y; y <<= 1, k++); |
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| 205 | #ifdef Pack_32 |
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| 206 | b = Balloc (ptr, k); |
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| 207 | b->_x[0] = y9; |
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| 208 | b->_wds = 1; |
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| 209 | #else |
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| 210 | b = Balloc (ptr, k + 1); |
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| 211 | b->_x[0] = y9 & 0xffff; |
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| 212 | b->_wds = (b->_x[1] = y9 >> 16) ? 2 : 1; |
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| 213 | #endif |
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| 214 | |
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| 215 | i = 9; |
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| 216 | if (9 < nd0) |
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| 217 | { |
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| 218 | s += 9; |
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| 219 | do |
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| 220 | b = multadd (ptr, b, 10, *s++ - '0'); |
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| 221 | while (++i < nd0); |
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| 222 | s++; |
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| 223 | } |
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| 224 | else |
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| 225 | s += 10; |
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| 226 | for (; i < nd; i++) |
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| 227 | b = multadd (ptr, b, 10, *s++ - '0'); |
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| 228 | return b; |
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| 229 | } |
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| 230 | |
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| 231 | int |
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| 232 | hi0bits (register __ULong x) |
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| 233 | { |
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| 234 | register int k = 0; |
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| 235 | |
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| 236 | if (!(x & 0xffff0000)) |
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| 237 | { |
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| 238 | k = 16; |
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| 239 | x <<= 16; |
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| 240 | } |
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| 241 | if (!(x & 0xff000000)) |
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| 242 | { |
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| 243 | k += 8; |
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| 244 | x <<= 8; |
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| 245 | } |
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| 246 | if (!(x & 0xf0000000)) |
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| 247 | { |
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| 248 | k += 4; |
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| 249 | x <<= 4; |
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| 250 | } |
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| 251 | if (!(x & 0xc0000000)) |
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| 252 | { |
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| 253 | k += 2; |
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| 254 | x <<= 2; |
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| 255 | } |
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| 256 | if (!(x & 0x80000000)) |
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| 257 | { |
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| 258 | k++; |
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| 259 | if (!(x & 0x40000000)) |
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| 260 | return 32; |
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| 261 | } |
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| 262 | return k; |
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| 263 | } |
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| 264 | |
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| 265 | int |
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| 266 | lo0bits (__ULong *y) |
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| 267 | { |
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| 268 | register int k; |
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| 269 | register __ULong x = *y; |
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| 270 | |
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| 271 | if (x & 7) |
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| 272 | { |
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| 273 | if (x & 1) |
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| 274 | return 0; |
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| 275 | if (x & 2) |
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| 276 | { |
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| 277 | *y = x >> 1; |
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| 278 | return 1; |
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| 279 | } |
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| 280 | *y = x >> 2; |
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| 281 | return 2; |
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| 282 | } |
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| 283 | k = 0; |
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| 284 | if (!(x & 0xffff)) |
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| 285 | { |
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| 286 | k = 16; |
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| 287 | x >>= 16; |
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| 288 | } |
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| 289 | if (!(x & 0xff)) |
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| 290 | { |
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| 291 | k += 8; |
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| 292 | x >>= 8; |
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| 293 | } |
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| 294 | if (!(x & 0xf)) |
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| 295 | { |
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| 296 | k += 4; |
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| 297 | x >>= 4; |
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| 298 | } |
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| 299 | if (!(x & 0x3)) |
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| 300 | { |
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| 301 | k += 2; |
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| 302 | x >>= 2; |
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| 303 | } |
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| 304 | if (!(x & 1)) |
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| 305 | { |
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| 306 | k++; |
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| 307 | x >>= 1; |
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| 308 | if (!x & 1) |
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| 309 | return 32; |
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| 310 | } |
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| 311 | *y = x; |
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| 312 | return k; |
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| 313 | } |
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| 314 | |
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| 315 | _Bigint * |
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| 316 | i2b (struct _reent * ptr, int i) |
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| 317 | { |
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| 318 | _Bigint *b; |
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| 319 | |
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| 320 | b = Balloc (ptr, 1); |
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| 321 | b->_x[0] = i; |
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| 322 | b->_wds = 1; |
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| 323 | return b; |
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| 324 | } |
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| 325 | |
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| 326 | _Bigint * |
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| 327 | mult (struct _reent * ptr, _Bigint * a, _Bigint * b) |
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| 328 | { |
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| 329 | _Bigint *c; |
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| 330 | int k, wa, wb, wc; |
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| 331 | __ULong carry, y, z; |
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| 332 | __ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; |
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| 333 | #ifdef Pack_32 |
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| 334 | __ULong z2; |
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| 335 | #endif |
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| 336 | |
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| 337 | if (a->_wds < b->_wds) |
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| 338 | { |
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| 339 | c = a; |
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| 340 | a = b; |
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| 341 | b = c; |
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| 342 | } |
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| 343 | k = a->_k; |
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| 344 | wa = a->_wds; |
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| 345 | wb = b->_wds; |
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| 346 | wc = wa + wb; |
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| 347 | if (wc > a->_maxwds) |
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| 348 | k++; |
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| 349 | c = Balloc (ptr, k); |
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| 350 | for (x = c->_x, xa = x + wc; x < xa; x++) |
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| 351 | *x = 0; |
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| 352 | xa = a->_x; |
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| 353 | xae = xa + wa; |
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| 354 | xb = b->_x; |
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| 355 | xbe = xb + wb; |
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| 356 | xc0 = c->_x; |
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| 357 | #ifdef Pack_32 |
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| 358 | for (; xb < xbe; xb++, xc0++) |
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| 359 | { |
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| 360 | if ((y = *xb & 0xffff) != 0) |
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| 361 | { |
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| 362 | x = xa; |
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| 363 | xc = xc0; |
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| 364 | carry = 0; |
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| 365 | do |
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| 366 | { |
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| 367 | z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; |
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| 368 | carry = z >> 16; |
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| 369 | z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; |
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| 370 | carry = z2 >> 16; |
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| 371 | Storeinc (xc, z2, z); |
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| 372 | } |
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| 373 | while (x < xae); |
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| 374 | *xc = carry; |
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| 375 | } |
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| 376 | if ((y = *xb >> 16) != 0) |
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| 377 | { |
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| 378 | x = xa; |
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| 379 | xc = xc0; |
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| 380 | carry = 0; |
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| 381 | z2 = *xc; |
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| 382 | do |
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| 383 | { |
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| 384 | z = (*x & 0xffff) * y + (*xc >> 16) + carry; |
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| 385 | carry = z >> 16; |
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| 386 | Storeinc (xc, z, z2); |
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| 387 | z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; |
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| 388 | carry = z2 >> 16; |
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| 389 | } |
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| 390 | while (x < xae); |
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| 391 | *xc = z2; |
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| 392 | } |
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| 393 | } |
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| 394 | #else |
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| 395 | for (; xb < xbe; xc0++) |
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| 396 | { |
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| 397 | if (y = *xb++) |
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| 398 | { |
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| 399 | x = xa; |
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| 400 | xc = xc0; |
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| 401 | carry = 0; |
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| 402 | do |
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| 403 | { |
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| 404 | z = *x++ * y + *xc + carry; |
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| 405 | carry = z >> 16; |
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| 406 | *xc++ = z & 0xffff; |
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| 407 | } |
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| 408 | while (x < xae); |
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| 409 | *xc = carry; |
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| 410 | } |
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| 411 | } |
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| 412 | #endif |
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| 413 | for (xc0 = c->_x, xc = xc0 + wc; wc > 0 && !*--xc; --wc); |
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| 414 | c->_wds = wc; |
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| 415 | return c; |
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| 416 | } |
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| 417 | |
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| 418 | _Bigint * |
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| 419 | pow5mult (struct _reent * ptr, _Bigint * b, int k) |
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| 420 | { |
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| 421 | _Bigint *b1, *p5, *p51; |
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| 422 | int i; |
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| 423 | static const int p05[3] = {5, 25, 125}; |
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| 424 | |
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| 425 | if ((i = k & 3) != 0) |
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| 426 | b = multadd (ptr, b, p05[i - 1], 0); |
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| 427 | |
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| 428 | if (!(k >>= 2)) |
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| 429 | return b; |
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| 430 | _REENT_CHECK_MP(ptr); |
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| 431 | if (!(p5 = _REENT_MP_P5S(ptr))) |
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| 432 | { |
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| 433 | /* first time */ |
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| 434 | p5 = _REENT_MP_P5S(ptr) = i2b (ptr, 625); |
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| 435 | p5->_next = 0; |
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| 436 | } |
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| 437 | for (;;) |
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| 438 | { |
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| 439 | if (k & 1) |
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| 440 | { |
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| 441 | b1 = mult (ptr, b, p5); |
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| 442 | Bfree (ptr, b); |
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| 443 | b = b1; |
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| 444 | } |
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| 445 | if (!(k >>= 1)) |
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| 446 | break; |
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| 447 | if (!(p51 = p5->_next)) |
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| 448 | { |
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| 449 | p51 = p5->_next = mult (ptr, p5, p5); |
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| 450 | p51->_next = 0; |
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| 451 | } |
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| 452 | p5 = p51; |
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| 453 | } |
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| 454 | return b; |
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| 455 | } |
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| 456 | |
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| 457 | _Bigint * |
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| 458 | lshift (struct _reent * ptr, _Bigint * b, int k) |
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| 459 | { |
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| 460 | int i, k1, n, n1; |
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| 461 | _Bigint *b1; |
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| 462 | __ULong *x, *x1, *xe, z; |
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| 463 | |
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| 464 | #ifdef Pack_32 |
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| 465 | n = k >> 5; |
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| 466 | #else |
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| 467 | n = k >> 4; |
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| 468 | #endif |
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| 469 | k1 = b->_k; |
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| 470 | n1 = n + b->_wds + 1; |
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| 471 | for (i = b->_maxwds; n1 > i; i <<= 1) |
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| 472 | k1++; |
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| 473 | b1 = Balloc (ptr, k1); |
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| 474 | x1 = b1->_x; |
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| 475 | for (i = 0; i < n; i++) |
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| 476 | *x1++ = 0; |
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| 477 | x = b->_x; |
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| 478 | xe = x + b->_wds; |
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| 479 | #ifdef Pack_32 |
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| 480 | if (k &= 0x1f) |
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| 481 | { |
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| 482 | k1 = 32 - k; |
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| 483 | z = 0; |
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| 484 | do |
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| 485 | { |
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| 486 | *x1++ = *x << k | z; |
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| 487 | z = *x++ >> k1; |
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| 488 | } |
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| 489 | while (x < xe); |
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| 490 | if ((*x1 = z) != 0) |
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| 491 | ++n1; |
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| 492 | } |
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| 493 | #else |
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| 494 | if (k &= 0xf) |
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| 495 | { |
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| 496 | k1 = 16 - k; |
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| 497 | z = 0; |
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| 498 | do |
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| 499 | { |
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| 500 | *x1++ = *x << k & 0xffff | z; |
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| 501 | z = *x++ >> k1; |
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| 502 | } |
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| 503 | while (x < xe); |
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| 504 | if (*x1 = z) |
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| 505 | ++n1; |
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| 506 | } |
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| 507 | #endif |
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| 508 | else |
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| 509 | do |
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| 510 | *x1++ = *x++; |
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| 511 | while (x < xe); |
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| 512 | b1->_wds = n1 - 1; |
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| 513 | Bfree (ptr, b); |
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| 514 | return b1; |
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| 515 | } |
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| 516 | |
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| 517 | int |
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| 518 | cmp (_Bigint * a, _Bigint * b) |
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| 519 | { |
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| 520 | __ULong *xa, *xa0, *xb, *xb0; |
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| 521 | int i, j; |
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| 522 | |
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| 523 | i = a->_wds; |
---|
| 524 | j = b->_wds; |
---|
| 525 | #ifdef DEBUG |
---|
| 526 | if (i > 1 && !a->_x[i - 1]) |
---|
| 527 | Bug ("cmp called with a->_x[a->_wds-1] == 0"); |
---|
| 528 | if (j > 1 && !b->_x[j - 1]) |
---|
| 529 | Bug ("cmp called with b->_x[b->_wds-1] == 0"); |
---|
| 530 | #endif |
---|
| 531 | if (i -= j) |
---|
| 532 | return i; |
---|
| 533 | xa0 = a->_x; |
---|
| 534 | xa = xa0 + j; |
---|
| 535 | xb0 = b->_x; |
---|
| 536 | xb = xb0 + j; |
---|
| 537 | for (;;) |
---|
| 538 | { |
---|
| 539 | if (*--xa != *--xb) |
---|
| 540 | return *xa < *xb ? -1 : 1; |
---|
| 541 | if (xa <= xa0) |
---|
| 542 | break; |
---|
| 543 | } |
---|
| 544 | return 0; |
---|
| 545 | } |
---|
| 546 | |
---|
| 547 | _Bigint * |
---|
| 548 | diff (struct _reent * ptr, |
---|
| 549 | _Bigint * a, _Bigint * b) |
---|
| 550 | { |
---|
| 551 | _Bigint *c; |
---|
| 552 | int i, wa, wb; |
---|
| 553 | __Long borrow, y; /* We need signed shifts here. */ |
---|
| 554 | __ULong *xa, *xae, *xb, *xbe, *xc; |
---|
| 555 | #ifdef Pack_32 |
---|
| 556 | __Long z; |
---|
| 557 | #endif |
---|
| 558 | |
---|
| 559 | i = cmp (a, b); |
---|
| 560 | if (!i) |
---|
| 561 | { |
---|
| 562 | c = Balloc (ptr, 0); |
---|
| 563 | c->_wds = 1; |
---|
| 564 | c->_x[0] = 0; |
---|
| 565 | return c; |
---|
| 566 | } |
---|
| 567 | if (i < 0) |
---|
| 568 | { |
---|
| 569 | c = a; |
---|
| 570 | a = b; |
---|
| 571 | b = c; |
---|
| 572 | i = 1; |
---|
| 573 | } |
---|
| 574 | else |
---|
| 575 | i = 0; |
---|
| 576 | c = Balloc (ptr, a->_k); |
---|
| 577 | c->_sign = i; |
---|
| 578 | wa = a->_wds; |
---|
| 579 | xa = a->_x; |
---|
| 580 | xae = xa + wa; |
---|
| 581 | wb = b->_wds; |
---|
| 582 | xb = b->_x; |
---|
| 583 | xbe = xb + wb; |
---|
| 584 | xc = c->_x; |
---|
| 585 | borrow = 0; |
---|
| 586 | #ifdef Pack_32 |
---|
| 587 | do |
---|
| 588 | { |
---|
| 589 | y = (*xa & 0xffff) - (*xb & 0xffff) + borrow; |
---|
| 590 | borrow = y >> 16; |
---|
| 591 | Sign_Extend (borrow, y); |
---|
| 592 | z = (*xa++ >> 16) - (*xb++ >> 16) + borrow; |
---|
| 593 | borrow = z >> 16; |
---|
| 594 | Sign_Extend (borrow, z); |
---|
| 595 | Storeinc (xc, z, y); |
---|
| 596 | } |
---|
| 597 | while (xb < xbe); |
---|
| 598 | while (xa < xae) |
---|
| 599 | { |
---|
| 600 | y = (*xa & 0xffff) + borrow; |
---|
| 601 | borrow = y >> 16; |
---|
| 602 | Sign_Extend (borrow, y); |
---|
| 603 | z = (*xa++ >> 16) + borrow; |
---|
| 604 | borrow = z >> 16; |
---|
| 605 | Sign_Extend (borrow, z); |
---|
| 606 | Storeinc (xc, z, y); |
---|
| 607 | } |
---|
| 608 | #else |
---|
| 609 | do |
---|
| 610 | { |
---|
| 611 | y = *xa++ - *xb++ + borrow; |
---|
| 612 | borrow = y >> 16; |
---|
| 613 | Sign_Extend (borrow, y); |
---|
| 614 | *xc++ = y & 0xffff; |
---|
| 615 | } |
---|
| 616 | while (xb < xbe); |
---|
| 617 | while (xa < xae) |
---|
| 618 | { |
---|
| 619 | y = *xa++ + borrow; |
---|
| 620 | borrow = y >> 16; |
---|
| 621 | Sign_Extend (borrow, y); |
---|
| 622 | *xc++ = y & 0xffff; |
---|
| 623 | } |
---|
| 624 | #endif |
---|
| 625 | while (!*--xc) |
---|
| 626 | wa--; |
---|
| 627 | c->_wds = wa; |
---|
| 628 | return c; |
---|
| 629 | } |
---|
| 630 | |
---|
| 631 | double |
---|
| 632 | ulp (double _x) |
---|
| 633 | { |
---|
| 634 | union double_union x, a; |
---|
| 635 | register __Long L; |
---|
| 636 | |
---|
| 637 | x.d = _x; |
---|
| 638 | |
---|
| 639 | L = (word0 (x) & Exp_mask) - (P - 1) * Exp_msk1; |
---|
| 640 | #ifndef Sudden_Underflow |
---|
| 641 | if (L > 0) |
---|
| 642 | { |
---|
| 643 | #endif |
---|
| 644 | #ifdef IBM |
---|
| 645 | L |= Exp_msk1 >> 4; |
---|
| 646 | #endif |
---|
| 647 | word0 (a) = L; |
---|
| 648 | #ifndef _DOUBLE_IS_32BITS |
---|
| 649 | word1 (a) = 0; |
---|
| 650 | #endif |
---|
| 651 | |
---|
| 652 | #ifndef Sudden_Underflow |
---|
| 653 | } |
---|
| 654 | else |
---|
| 655 | { |
---|
| 656 | L = -L >> Exp_shift; |
---|
| 657 | if (L < Exp_shift) |
---|
| 658 | { |
---|
| 659 | word0 (a) = 0x80000 >> L; |
---|
| 660 | #ifndef _DOUBLE_IS_32BITS |
---|
| 661 | word1 (a) = 0; |
---|
| 662 | #endif |
---|
| 663 | } |
---|
| 664 | else |
---|
| 665 | { |
---|
| 666 | word0 (a) = 0; |
---|
| 667 | L -= Exp_shift; |
---|
| 668 | #ifndef _DOUBLE_IS_32BITS |
---|
| 669 | word1 (a) = L >= 31 ? 1 : 1 << (31 - L); |
---|
| 670 | #endif |
---|
| 671 | } |
---|
| 672 | } |
---|
| 673 | #endif |
---|
| 674 | return a.d; |
---|
| 675 | } |
---|
| 676 | |
---|
| 677 | double |
---|
| 678 | b2d (_Bigint * a, int *e) |
---|
| 679 | { |
---|
| 680 | __ULong *xa, *xa0, w, y, z; |
---|
| 681 | int k; |
---|
| 682 | union double_union d; |
---|
| 683 | #ifdef VAX |
---|
| 684 | __ULong d0, d1; |
---|
| 685 | #else |
---|
| 686 | #define d0 word0(d) |
---|
| 687 | #define d1 word1(d) |
---|
| 688 | #endif |
---|
| 689 | |
---|
| 690 | xa0 = a->_x; |
---|
| 691 | xa = xa0 + a->_wds; |
---|
| 692 | y = *--xa; |
---|
| 693 | #ifdef DEBUG |
---|
| 694 | if (!y) |
---|
| 695 | Bug ("zero y in b2d"); |
---|
| 696 | #endif |
---|
| 697 | k = hi0bits (y); |
---|
| 698 | *e = 32 - k; |
---|
| 699 | #ifdef Pack_32 |
---|
| 700 | if (k < Ebits) |
---|
| 701 | { |
---|
| 702 | d0 = Exp_1 | y >> (Ebits - k); |
---|
| 703 | w = xa > xa0 ? *--xa : 0; |
---|
| 704 | #ifndef _DOUBLE_IS_32BITS |
---|
| 705 | d1 = y << ((32 - Ebits) + k) | w >> (Ebits - k); |
---|
| 706 | #endif |
---|
| 707 | goto ret_d; |
---|
| 708 | } |
---|
| 709 | z = xa > xa0 ? *--xa : 0; |
---|
| 710 | if (k -= Ebits) |
---|
| 711 | { |
---|
| 712 | d0 = Exp_1 | y << k | z >> (32 - k); |
---|
| 713 | y = xa > xa0 ? *--xa : 0; |
---|
| 714 | #ifndef _DOUBLE_IS_32BITS |
---|
| 715 | d1 = z << k | y >> (32 - k); |
---|
| 716 | #endif |
---|
| 717 | } |
---|
| 718 | else |
---|
| 719 | { |
---|
| 720 | d0 = Exp_1 | y; |
---|
| 721 | #ifndef _DOUBLE_IS_32BITS |
---|
| 722 | d1 = z; |
---|
| 723 | #endif |
---|
| 724 | } |
---|
| 725 | #else |
---|
| 726 | if (k < Ebits + 16) |
---|
| 727 | { |
---|
| 728 | z = xa > xa0 ? *--xa : 0; |
---|
| 729 | d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; |
---|
| 730 | w = xa > xa0 ? *--xa : 0; |
---|
| 731 | y = xa > xa0 ? *--xa : 0; |
---|
| 732 | d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; |
---|
| 733 | goto ret_d; |
---|
| 734 | } |
---|
| 735 | z = xa > xa0 ? *--xa : 0; |
---|
| 736 | w = xa > xa0 ? *--xa : 0; |
---|
| 737 | k -= Ebits + 16; |
---|
| 738 | d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; |
---|
| 739 | y = xa > xa0 ? *--xa : 0; |
---|
| 740 | d1 = w << k + 16 | y << k; |
---|
| 741 | #endif |
---|
| 742 | ret_d: |
---|
| 743 | #ifdef VAX |
---|
| 744 | word0 (d) = d0 >> 16 | d0 << 16; |
---|
| 745 | word1 (d) = d1 >> 16 | d1 << 16; |
---|
| 746 | #else |
---|
| 747 | #undef d0 |
---|
| 748 | #undef d1 |
---|
| 749 | #endif |
---|
| 750 | return d.d; |
---|
| 751 | } |
---|
| 752 | |
---|
| 753 | _Bigint * |
---|
| 754 | d2b (struct _reent * ptr, |
---|
| 755 | double _d, |
---|
| 756 | int *e, |
---|
| 757 | int *bits) |
---|
| 758 | |
---|
| 759 | { |
---|
| 760 | union double_union d; |
---|
| 761 | _Bigint *b; |
---|
| 762 | int de, i, k; |
---|
| 763 | __ULong *x, y, z; |
---|
| 764 | #ifdef VAX |
---|
| 765 | __ULong d0, d1; |
---|
| 766 | #endif |
---|
| 767 | d.d = _d; |
---|
| 768 | #ifdef VAX |
---|
| 769 | d0 = word0 (d) >> 16 | word0 (d) << 16; |
---|
| 770 | d1 = word1 (d) >> 16 | word1 (d) << 16; |
---|
| 771 | #else |
---|
| 772 | #define d0 word0(d) |
---|
| 773 | #define d1 word1(d) |
---|
| 774 | d.d = _d; |
---|
| 775 | #endif |
---|
| 776 | |
---|
| 777 | #ifdef Pack_32 |
---|
| 778 | b = Balloc (ptr, 1); |
---|
| 779 | #else |
---|
| 780 | b = Balloc (ptr, 2); |
---|
| 781 | #endif |
---|
| 782 | x = b->_x; |
---|
| 783 | |
---|
| 784 | z = d0 & Frac_mask; |
---|
| 785 | d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ |
---|
| 786 | #ifdef Sudden_Underflow |
---|
| 787 | de = (int) (d0 >> Exp_shift); |
---|
| 788 | #ifndef IBM |
---|
| 789 | z |= Exp_msk11; |
---|
| 790 | #endif |
---|
| 791 | #else |
---|
| 792 | if ((de = (int) (d0 >> Exp_shift)) != 0) |
---|
| 793 | z |= Exp_msk1; |
---|
| 794 | #endif |
---|
| 795 | #ifdef Pack_32 |
---|
| 796 | #ifndef _DOUBLE_IS_32BITS |
---|
| 797 | if (d1) |
---|
| 798 | { |
---|
| 799 | y = d1; |
---|
| 800 | k = lo0bits (&y); |
---|
| 801 | if (k) |
---|
| 802 | { |
---|
| 803 | x[0] = y | z << (32 - k); |
---|
| 804 | z >>= k; |
---|
| 805 | } |
---|
| 806 | else |
---|
| 807 | x[0] = y; |
---|
| 808 | i = b->_wds = (x[1] = z) ? 2 : 1; |
---|
| 809 | } |
---|
| 810 | else |
---|
| 811 | #endif |
---|
| 812 | { |
---|
| 813 | #ifdef DEBUG |
---|
| 814 | if (!z) |
---|
| 815 | Bug ("Zero passed to d2b"); |
---|
| 816 | #endif |
---|
| 817 | k = lo0bits (&z); |
---|
| 818 | x[0] = z; |
---|
| 819 | i = b->_wds = 1; |
---|
| 820 | #ifndef _DOUBLE_IS_32BITS |
---|
| 821 | k += 32; |
---|
| 822 | #endif |
---|
| 823 | } |
---|
| 824 | #else |
---|
| 825 | if (d1) |
---|
| 826 | { |
---|
| 827 | y = d1; |
---|
| 828 | k = lo0bits (&y); |
---|
| 829 | if (k) |
---|
| 830 | if (k >= 16) |
---|
| 831 | { |
---|
| 832 | x[0] = y | z << 32 - k & 0xffff; |
---|
| 833 | x[1] = z >> k - 16 & 0xffff; |
---|
| 834 | x[2] = z >> k; |
---|
| 835 | i = 2; |
---|
| 836 | } |
---|
| 837 | else |
---|
| 838 | { |
---|
| 839 | x[0] = y & 0xffff; |
---|
| 840 | x[1] = y >> 16 | z << 16 - k & 0xffff; |
---|
| 841 | x[2] = z >> k & 0xffff; |
---|
| 842 | x[3] = z >> k + 16; |
---|
| 843 | i = 3; |
---|
| 844 | } |
---|
| 845 | else |
---|
| 846 | { |
---|
| 847 | x[0] = y & 0xffff; |
---|
| 848 | x[1] = y >> 16; |
---|
| 849 | x[2] = z & 0xffff; |
---|
| 850 | x[3] = z >> 16; |
---|
| 851 | i = 3; |
---|
| 852 | } |
---|
| 853 | } |
---|
| 854 | else |
---|
| 855 | { |
---|
| 856 | #ifdef DEBUG |
---|
| 857 | if (!z) |
---|
| 858 | Bug ("Zero passed to d2b"); |
---|
| 859 | #endif |
---|
| 860 | k = lo0bits (&z); |
---|
| 861 | if (k >= 16) |
---|
| 862 | { |
---|
| 863 | x[0] = z; |
---|
| 864 | i = 0; |
---|
| 865 | } |
---|
| 866 | else |
---|
| 867 | { |
---|
| 868 | x[0] = z & 0xffff; |
---|
| 869 | x[1] = z >> 16; |
---|
| 870 | i = 1; |
---|
| 871 | } |
---|
| 872 | k += 32; |
---|
| 873 | } |
---|
| 874 | while (!x[i]) |
---|
| 875 | --i; |
---|
| 876 | b->_wds = i + 1; |
---|
| 877 | #endif |
---|
| 878 | #ifndef Sudden_Underflow |
---|
| 879 | if (de) |
---|
| 880 | { |
---|
| 881 | #endif |
---|
| 882 | #ifdef IBM |
---|
| 883 | *e = (de - Bias - (P - 1) << 2) + k; |
---|
| 884 | *bits = 4 * P + 8 - k - hi0bits (word0 (d) & Frac_mask); |
---|
| 885 | #else |
---|
| 886 | *e = de - Bias - (P - 1) + k; |
---|
| 887 | *bits = P - k; |
---|
| 888 | #endif |
---|
| 889 | #ifndef Sudden_Underflow |
---|
| 890 | } |
---|
| 891 | else |
---|
| 892 | { |
---|
| 893 | *e = de - Bias - (P - 1) + 1 + k; |
---|
| 894 | #ifdef Pack_32 |
---|
| 895 | *bits = 32 * i - hi0bits (x[i - 1]); |
---|
| 896 | #else |
---|
| 897 | *bits = (i + 2) * 16 - hi0bits (x[i]); |
---|
| 898 | #endif |
---|
| 899 | } |
---|
| 900 | #endif |
---|
| 901 | return b; |
---|
| 902 | } |
---|
| 903 | #undef d0 |
---|
| 904 | #undef d1 |
---|
| 905 | |
---|
| 906 | double |
---|
| 907 | ratio (_Bigint * a, _Bigint * b) |
---|
| 908 | |
---|
| 909 | { |
---|
| 910 | union double_union da, db; |
---|
| 911 | int k, ka, kb; |
---|
| 912 | |
---|
| 913 | da.d = b2d (a, &ka); |
---|
| 914 | db.d = b2d (b, &kb); |
---|
| 915 | #ifdef Pack_32 |
---|
| 916 | k = ka - kb + 32 * (a->_wds - b->_wds); |
---|
| 917 | #else |
---|
| 918 | k = ka - kb + 16 * (a->_wds - b->_wds); |
---|
| 919 | #endif |
---|
| 920 | #ifdef IBM |
---|
| 921 | if (k > 0) |
---|
| 922 | { |
---|
| 923 | word0 (da) += (k >> 2) * Exp_msk1; |
---|
| 924 | if (k &= 3) |
---|
| 925 | da.d *= 1 << k; |
---|
| 926 | } |
---|
| 927 | else |
---|
| 928 | { |
---|
| 929 | k = -k; |
---|
| 930 | word0 (db) += (k >> 2) * Exp_msk1; |
---|
| 931 | if (k &= 3) |
---|
| 932 | db.d *= 1 << k; |
---|
| 933 | } |
---|
| 934 | #else |
---|
| 935 | if (k > 0) |
---|
| 936 | word0 (da) += k * Exp_msk1; |
---|
| 937 | else |
---|
| 938 | { |
---|
| 939 | k = -k; |
---|
| 940 | word0 (db) += k * Exp_msk1; |
---|
| 941 | } |
---|
| 942 | #endif |
---|
| 943 | return da.d / db.d; |
---|
| 944 | } |
---|
| 945 | |
---|
| 946 | |
---|
| 947 | const double |
---|
| 948 | tens[] = |
---|
| 949 | { |
---|
| 950 | 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, |
---|
| 951 | 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, |
---|
| 952 | 1e20, 1e21, 1e22, 1e23, 1e24 |
---|
| 953 | |
---|
| 954 | }; |
---|
| 955 | |
---|
| 956 | #if !defined(_DOUBLE_IS_32BITS) && !defined(__v800) |
---|
| 957 | const double bigtens[] = |
---|
| 958 | {1e16, 1e32, 1e64, 1e128, 1e256}; |
---|
| 959 | |
---|
| 960 | const double tinytens[] = |
---|
| 961 | {1e-16, 1e-32, 1e-64, 1e-128, 1e-256}; |
---|
| 962 | #else |
---|
| 963 | const double bigtens[] = |
---|
| 964 | {1e16, 1e32}; |
---|
| 965 | |
---|
| 966 | const double tinytens[] = |
---|
| 967 | {1e-16, 1e-32}; |
---|
| 968 | #endif |
---|
| 969 | |
---|
| 970 | |
---|
| 971 | double |
---|
| 972 | _mprec_log10 (int dig) |
---|
| 973 | { |
---|
| 974 | double v = 1.0; |
---|
| 975 | if (dig < 24) |
---|
| 976 | return tens[dig]; |
---|
| 977 | while (dig > 0) |
---|
| 978 | { |
---|
| 979 | v *= 10; |
---|
| 980 | dig--; |
---|
| 981 | } |
---|
| 982 | return v; |
---|
| 983 | } |
---|
| 984 | |
---|
| 985 | void |
---|
| 986 | copybits (__ULong *c, |
---|
| 987 | int n, |
---|
| 988 | _Bigint *b) |
---|
| 989 | { |
---|
| 990 | __ULong *ce, *x, *xe; |
---|
| 991 | #ifdef Pack_16 |
---|
| 992 | int nw, nw1; |
---|
| 993 | #endif |
---|
| 994 | |
---|
| 995 | ce = c + ((n-1) >> kshift) + 1; |
---|
| 996 | x = b->_x; |
---|
| 997 | #ifdef Pack_32 |
---|
| 998 | xe = x + b->_wds; |
---|
| 999 | while(x < xe) |
---|
| 1000 | *c++ = *x++; |
---|
| 1001 | #else |
---|
| 1002 | nw = b->_wds; |
---|
| 1003 | nw1 = nw & 1; |
---|
| 1004 | for(xe = x + (nw - nw1); x < xe; x += 2) |
---|
| 1005 | Storeinc(c, x[1], x[0]); |
---|
| 1006 | if (nw1) |
---|
| 1007 | *c++ = *x; |
---|
| 1008 | #endif |
---|
| 1009 | while(c < ce) |
---|
| 1010 | *c++ = 0; |
---|
| 1011 | } |
---|
| 1012 | |
---|
| 1013 | __ULong |
---|
| 1014 | any_on (_Bigint *b, |
---|
| 1015 | int k) |
---|
| 1016 | { |
---|
| 1017 | int n, nwds; |
---|
| 1018 | __ULong *x, *x0, x1, x2; |
---|
| 1019 | |
---|
| 1020 | x = b->_x; |
---|
| 1021 | nwds = b->_wds; |
---|
| 1022 | n = k >> kshift; |
---|
| 1023 | if (n > nwds) |
---|
| 1024 | n = nwds; |
---|
| 1025 | else if (n < nwds && (k &= kmask)) { |
---|
| 1026 | x1 = x2 = x[n]; |
---|
| 1027 | x1 >>= k; |
---|
| 1028 | x1 <<= k; |
---|
| 1029 | if (x1 != x2) |
---|
| 1030 | return 1; |
---|
| 1031 | } |
---|
| 1032 | x0 = x; |
---|
| 1033 | x += n; |
---|
| 1034 | while(x > x0) |
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| 1035 | if (*--x) |
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| 1036 | return 1; |
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| 1037 | return 0; |
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| 1038 | } |
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| 1039 | |
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