| 1 | |
| 2 | Basic two-word fraction declaration and manipulation.
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| 3 | Copyright (C) 1997,1998,1999 Free Software Foundation, Inc.
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| 4 | This file is part of the GNU C Library.
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| 5 | Contributed by Richard Henderson ([email protected]),
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| 6 | Jakub Jelinek ([email protected]),
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| 7 | David S. Miller ([email protected]) and
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| 8 | Peter Maydell ([email protected]).
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| 9 |
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| 10 | The GNU C Library is free software; you can redistribute it and/or
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| 11 | modify it under the terms of the GNU Library General Public License as
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| 12 | published by the Free Software Foundation; either version 2 of the
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| 13 | License, or (at your option) any later version.
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| 14 |
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| 15 | The GNU C Library is distributed in the hope that it will be useful,
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| 16 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 17 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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| 18 | Library General Public License for more details.
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| 19 |
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| 20 | You should have received a copy of the GNU Library General Public
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| 21 | License along with the GNU C Library; see the file COPYING.LIB. If
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| 22 | not, write to the Free Software Foundation, Inc.,
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| 23 | 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
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| 24 |
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| 25 | #ifndef __MATH_EMU_OP_2_H__
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| 26 | #define __MATH_EMU_OP_2_H__
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| 27 |
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| 28 | #define _FP_FRAC_DECL_2(X) _FP_W_TYPE X##_f0 = 0, X##_f1 = 0
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| 29 | #define _FP_FRAC_COPY_2(D,S) (D##_f0 = S##_f0, D##_f1 = S##_f1)
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| 30 | #define _FP_FRAC_SET_2(X,I) __FP_FRAC_SET_2(X, I)
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| 31 | #define _FP_FRAC_HIGH_2(X) (X##_f1)
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| 32 | #define _FP_FRAC_LOW_2(X) (X##_f0)
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| 33 | #define _FP_FRAC_WORD_2(X,w) (X##_f##w)
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| 34 | #define _FP_FRAC_SLL_2(X, N) ( \
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| 35 | (void) (((N) < _FP_W_TYPE_SIZE) \
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| 36 | ? ({ \
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| 37 | if (__builtin_constant_p(N) && (N) == 1) { \
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| 38 | X##_f1 = X##_f1 + X##_f1 + \
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| 39 | (((_FP_WS_TYPE) (X##_f0)) < 0); \
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| 40 | X##_f0 += X##_f0; \
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| 41 | } else { \
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| 42 | X##_f1 = X##_f1 << (N) | X##_f0 >> \
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| 43 | (_FP_W_TYPE_SIZE - (N)); \
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| 44 | X##_f0 <<= (N); \
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| 45 | } \
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| 46 | 0; \
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| 47 | }) \
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| 48 | : ({ \
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| 49 | X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \
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| 50 | X##_f0 = 0; \
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| 51 | })))
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| 52 |
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| 53 |
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| 54 | #define _FP_FRAC_SRL_2(X, N) ( \
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| 55 | (void) (((N) < _FP_W_TYPE_SIZE) \
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| 56 | ? ({ \
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| 57 | X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \
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| 58 | X##_f1 >>= (N); \
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| 59 | }) \
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| 60 | : ({ \
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| 61 | X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \
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| 62 | X##_f1 = 0; \
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| 63 | })))
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| 64 |
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| 65 |
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| 66 |
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| 67 | #define _FP_FRAC_SRS_2(X, N, sz) ( \
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| 68 | (void) (((N) < _FP_W_TYPE_SIZE) \
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| 69 | ? ({ \
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| 70 | X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) \
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| 71 | | (__builtin_constant_p(N) && (N) == 1 \
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| 72 | ? X##_f0 & 1 \
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| 73 | : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \
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| 74 | X##_f1 >>= (N); \
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| 75 | }) \
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| 76 | : ({ \
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| 77 | X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) \
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| 78 | | ((((N) == _FP_W_TYPE_SIZE \
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| 79 | ? 0 \
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| 80 | : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \
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| 81 | | X##_f0) != 0)); \
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| 82 | X##_f1 = 0; \
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| 83 | })))
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| 84 |
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| 85 | #define _FP_FRAC_ADDI_2(X,I) \
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| 86 | __FP_FRAC_ADDI_2(X##_f1, X##_f0, I)
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| 87 |
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| 88 | #define _FP_FRAC_ADD_2(R,X,Y) \
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| 89 | __FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
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| 90 |
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| 91 | #define _FP_FRAC_SUB_2(R,X,Y) \
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| 92 | __FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
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| 93 |
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| 94 | #define _FP_FRAC_DEC_2(X,Y) \
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| 95 | __FP_FRAC_DEC_2(X##_f1, X##_f0, Y##_f1, Y##_f0)
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| 96 |
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| 97 | #define _FP_FRAC_CLZ_2(R,X) \
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| 98 | do { \
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| 99 | if (X##_f1) \
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| 100 | __FP_CLZ(R,X##_f1); \
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| 101 | else \
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| 102 | { \
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| 103 | __FP_CLZ(R,X##_f0); \
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| 104 | R += _FP_W_TYPE_SIZE; \
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| 105 | } \
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| 106 | } while(0)
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| 107 |
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| 108 |
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| 109 | #define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE)X##_f1 < 0)
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| 110 | #define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0)
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| 111 | #define _FP_FRAC_OVERP_2(fs,X) (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs)
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| 112 | #define _FP_FRAC_CLEAR_OVERP_2(fs,X) (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs)
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| 113 | #define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0)
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| 114 | #define _FP_FRAC_GT_2(X, Y) \
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| 115 | (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0))
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| 116 | #define _FP_FRAC_GE_2(X, Y) \
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| 117 | (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0))
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| 118 |
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| 119 | #define _FP_ZEROFRAC_2 0, 0
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| 120 | #define _FP_MINFRAC_2 0, 1
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| 121 | #define _FP_MAXFRAC_2 (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0)
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| 122 |
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| 123 | |
| 124 | * Internals
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| 125 |
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| 126 |
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| 127 | #define __FP_FRAC_SET_2(X,I1,I0) (X##_f0 = I0, X##_f1 = I1)
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| 128 |
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| 129 | #define __FP_CLZ_2(R, xh, xl) \
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| 130 | do { \
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| 131 | if (xh) \
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| 132 | __FP_CLZ(R,xh); \
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| 133 | else \
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| 134 | { \
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| 135 | __FP_CLZ(R,xl); \
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| 136 | R += _FP_W_TYPE_SIZE; \
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| 137 | } \
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| 138 | } while(0)
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| 139 |
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| 140 | #if 0 |
| 141 |
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| 142 | #ifndef __FP_FRAC_ADDI_2
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| 143 | #define __FP_FRAC_ADDI_2(xh, xl, i) \
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| 144 | (xh += ((xl += i) < i))
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| 145 | #endif
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| 146 | #ifndef __FP_FRAC_ADD_2
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| 147 | #define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \
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| 148 | (rh = xh + yh + ((rl = xl + yl) < xl))
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| 149 | #endif
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| 150 | #ifndef __FP_FRAC_SUB_2
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| 151 | #define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \
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| 152 | (rh = xh - yh - ((rl = xl - yl) > xl))
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| 153 | #endif
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| 154 | #ifndef __FP_FRAC_DEC_2
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| 155 | #define __FP_FRAC_DEC_2(xh, xl, yh, yl) \
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| 156 | do { \
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| 157 | UWtype _t = xl; \
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| 158 | xh -= yh + ((xl -= yl) > _t); \
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| 159 | } while (0)
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| 160 | #endif
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| 161 |
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| 162 | #else
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| 163 |
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| 164 | #undef __FP_FRAC_ADDI_2
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| 165 | #define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa(xh, xl, xh, xl, 0, i)
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| 166 | #undef __FP_FRAC_ADD_2
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| 167 | #define __FP_FRAC_ADD_2 add_ssaaaa
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| 168 | #undef __FP_FRAC_SUB_2
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| 169 | #define __FP_FRAC_SUB_2 sub_ddmmss
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| 170 | #undef __FP_FRAC_DEC_2
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| 171 | #define __FP_FRAC_DEC_2(xh, xl, yh, yl) sub_ddmmss(xh, xl, xh, xl, yh, yl)
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| 172 |
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| 173 | #endif
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| 174 |
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| 175 | |
| 176 | * Unpack the raw bits of a native fp value. Do not classify or
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| 177 | * normalize the data.
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| 178 |
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| 179 |
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| 180 | #define _FP_UNPACK_RAW_2(fs, X, val) \
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| 181 | do { \
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| 182 | union _FP_UNION_##fs _flo; _flo.flt = (val); \
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| 183 | \
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| 184 | X##_f0 = _flo.bits.frac0; \
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| 185 | X##_f1 = _flo.bits.frac1; \
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| 186 | X##_e = _flo.bits.exp; \
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| 187 | X##_s = _flo.bits.sign; \
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| 188 | } while (0)
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| 189 |
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| 190 | #define _FP_UNPACK_RAW_2_P(fs, X, val) \
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| 191 | do { \
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| 192 | union _FP_UNION_##fs *_flo = \
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| 193 | (union _FP_UNION_##fs *)(val); \
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| 194 | \
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| 195 | X##_f0 = _flo->bits.frac0; \
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| 196 | X##_f1 = _flo->bits.frac1; \
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| 197 | X##_e = _flo->bits.exp; \
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| 198 | X##_s = _flo->bits.sign; \
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| 199 | } while (0)
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| 200 |
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| 201 |
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| 202 | |
| 203 | * Repack the raw bits of a native fp value.
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| 204 |
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| 205 |
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| 206 | #define _FP_PACK_RAW_2(fs, val, X) \
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| 207 | do { \
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| 208 | union _FP_UNION_##fs _flo; \
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| 209 | \
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| 210 | _flo.bits.frac0 = X##_f0; \
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| 211 | _flo.bits.frac1 = X##_f1; \
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| 212 | _flo.bits.exp = X##_e; \
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| 213 | _flo.bits.sign = X##_s; \
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| 214 | \
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| 215 | (val) = _flo.flt; \
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| 216 | } while (0)
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| 217 |
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| 218 | #define _FP_PACK_RAW_2_P(fs, val, X) \
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| 219 | do { \
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| 220 | union _FP_UNION_##fs *_flo = \
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| 221 | (union _FP_UNION_##fs *)(val); \
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| 222 | \
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| 223 | _flo->bits.frac0 = X##_f0; \
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| 224 | _flo->bits.frac1 = X##_f1; \
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| 225 | _flo->bits.exp = X##_e; \
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| 226 | _flo->bits.sign = X##_s; \
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| 227 | } while (0)
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| 228 |
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| 229 |
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| 230 | |
| 231 | * Multiplication algorithms:
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| 232 |
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| 233 |
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| 234 |
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| 235 |
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| 236 | #define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit) \
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| 237 | do { \
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| 238 | _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \
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| 239 | \
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| 240 | doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \
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| 241 | doit(_b_f1, _b_f0, X##_f0, Y##_f1); \
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| 242 | doit(_c_f1, _c_f0, X##_f1, Y##_f0); \
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| 243 | doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \
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| 244 | \
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| 245 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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| 246 | _FP_FRAC_WORD_4(_z,1), 0, _b_f1, _b_f0, \
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| 247 | _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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| 248 | _FP_FRAC_WORD_4(_z,1)); \
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| 249 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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| 250 | _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0, \
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| 251 | _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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| 252 | _FP_FRAC_WORD_4(_z,1)); \
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| 253 | \
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| 254 | |
| 255 | were (bit B), we know that the msb of the of the product is \
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| 256 | at either 2B or 2B-1. \
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| 257 | _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \
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| 258 | R##_f0 = _FP_FRAC_WORD_4(_z,0); \
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| 259 | R##_f1 = _FP_FRAC_WORD_4(_z,1); \
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| 260 | } while (0)
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| 261 |
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| 262 | |
| 263 | Do only 3 multiplications instead of four. This one is for machines
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| 264 | where multiplication is much more expensive than subtraction.
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| 265 |
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| 266 | #define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit) \
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| 267 | do { \
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| 268 | _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \
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| 269 | _FP_W_TYPE _d; \
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| 270 | int _c1, _c2; \
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| 271 | \
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| 272 | _b_f0 = X##_f0 + X##_f1; \
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| 273 | _c1 = _b_f0 < X##_f0; \
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| 274 | _b_f1 = Y##_f0 + Y##_f1; \
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| 275 | _c2 = _b_f1 < Y##_f0; \
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| 276 | doit(_d, _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \
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| 277 | doit(_FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1), _b_f0, _b_f1); \
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| 278 | doit(_c_f1, _c_f0, X##_f1, Y##_f1); \
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| 279 | \
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| 280 | _b_f0 &= -_c2; \
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| 281 | _b_f1 &= -_c1; \
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| 282 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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| 283 | _FP_FRAC_WORD_4(_z,1), (_c1 & _c2), 0, _d, \
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| 284 | 0, _FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1)); \
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| 285 | __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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| 286 | _b_f0); \
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| 287 | __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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| 288 | _b_f1); \
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| 289 | __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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| 290 | _FP_FRAC_WORD_4(_z,1), \
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| 291 | 0, _d, _FP_FRAC_WORD_4(_z,0)); \
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| 292 | __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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| 293 | _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0); \
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| 294 | __FP_FRAC_ADD_2(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), \
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| 295 | _c_f1, _c_f0, \
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| 296 | _FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2)); \
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| 297 | \
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| 298 | |
| 299 | were (bit B), we know that the msb of the of the product is \
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| 300 | at either 2B or 2B-1. \
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| 301 | _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \
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| 302 | R##_f0 = _FP_FRAC_WORD_4(_z,0); \
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| 303 | R##_f1 = _FP_FRAC_WORD_4(_z,1); \
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| 304 | } while (0)
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| 305 |
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| 306 | #define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y) \
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| 307 | do { \
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| 308 | _FP_FRAC_DECL_4(_z); \
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| 309 | _FP_W_TYPE _x[2], _y[2]; \
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| 310 | _x[0] = X##_f0; _x[1] = X##_f1; \
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| 311 | _y[0] = Y##_f0; _y[1] = Y##_f1; \
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| 312 | \
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| 313 | mpn_mul_n(_z_f, _x, _y, 2); \
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| 314 | \
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| 315 | |
| 316 | were (bit B), we know that the msb of the of the product is \
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| 317 | at either 2B or 2B-1. \
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| 318 | _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \
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| 319 | R##_f0 = _z_f[0]; \
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| 320 | R##_f1 = _z_f[1]; \
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| 321 | } while (0)
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| 322 |
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| 323 | |
| 324 | point multiplication. This is useful if floating point
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| 325 | multiplication has much bigger throughput than integer multiply.
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| 326 | It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits
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| 327 | between 106 and 120 only.
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| 328 | Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set.
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| 329 | SETFETZ is a macro which will disable all FPU exceptions and set rounding
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| 330 | towards zero, RESETFE should optionally reset it back.
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| 331 |
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| 332 | #define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe) \
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| 333 | do { \
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| 334 | static const double _const[] = { \
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| 335 | 5.9604644775390625e-08, \
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| 336 | 3.5527136788005009e-15, \
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| 337 | 2.1175823681357508e-22, \
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| 338 | 1.2621774483536189e-29, \
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| 339 | 2.68435456e+08, \
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| 340 | 1.600000e+01, \
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| 341 | 9.5367431640625e-07, \
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| 342 | 5.6843418860808015e-14, \
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| 343 | 3.3881317890172014e-21, \
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| 344 | 2.0194839173657902e-28, \
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| 345 | 1.2037062152420224e-35}; \
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| 346 | double _a240, _b240, _c240, _d240, _e240, _f240, \
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| 347 | _g240, _h240, _i240, _j240, _k240; \
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| 348 | union { double d; UDItype i; } _l240, _m240, _n240, _o240, \
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| 349 | _p240, _q240, _r240, _s240; \
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| 350 | UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0; \
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| 351 | \
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| 352 | if (wfracbits < 106 || wfracbits > 120) \
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| 353 | abort(); \
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| 354 | \
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| 355 | setfetz; \
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| 356 | \
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| 357 | _e240 = (double)(long)(X##_f0 & 0xffffff); \
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| 358 | _j240 = (double)(long)(Y##_f0 & 0xffffff); \
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| 359 | _d240 = (double)(long)((X##_f0 >> 24) & 0xffffff); \
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| 360 | _i240 = (double)(long)((Y##_f0 >> 24) & 0xffffff); \
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| 361 | _c240 = (double)(long)(((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48)); \
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| 362 | _h240 = (double)(long)(((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48)); \
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| 363 | _b240 = (double)(long)((X##_f1 >> 8) & 0xffffff); \
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| 364 | _g240 = (double)(long)((Y##_f1 >> 8) & 0xffffff); \
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| 365 | _a240 = (double)(long)(X##_f1 >> 32); \
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| 366 | _f240 = (double)(long)(Y##_f1 >> 32); \
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| 367 | _e240 *= _const[3]; \
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| 368 | _j240 *= _const[3]; \
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| 369 | _d240 *= _const[2]; \
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| 370 | _i240 *= _const[2]; \
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| 371 | _c240 *= _const[1]; \
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| 372 | _h240 *= _const[1]; \
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| 373 | _b240 *= _const[0]; \
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| 374 | _g240 *= _const[0]; \
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| 375 | _s240.d = _e240*_j240;\
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| 376 | _r240.d = _d240*_j240 + _e240*_i240;\
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| 377 | _q240.d = _c240*_j240 + _d240*_i240 + _e240*_h240;\
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| 378 | _p240.d = _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240;\
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| 379 | _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240;\
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| 380 | _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240; \
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| 381 | _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240; \
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| 382 | _l240.d = _a240*_g240 + _b240*_f240; \
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| 383 | _k240 = _a240*_f240; \
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| 384 | _r240.d += _s240.d; \
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| 385 | _q240.d += _r240.d; \
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| 386 | _p240.d += _q240.d; \
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| 387 | _o240.d += _p240.d; \
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| 388 | _n240.d += _o240.d; \
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| 389 | _m240.d += _n240.d; \
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| 390 | _l240.d += _m240.d; \
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| 391 | _k240 += _l240.d; \
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| 392 | _s240.d -= ((_const[10]+_s240.d)-_const[10]); \
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| 393 | _r240.d -= ((_const[9]+_r240.d)-_const[9]); \
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| 394 | _q240.d -= ((_const[8]+_q240.d)-_const[8]); \
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| 395 | _p240.d -= ((_const[7]+_p240.d)-_const[7]); \
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| 396 | _o240.d += _const[7]; \
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| 397 | _n240.d += _const[6]; \
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| 398 | _m240.d += _const[5]; \
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| 399 | _l240.d += _const[4]; \
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| 400 | if (_s240.d != 0.0) _y240 = 1; \
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| 401 | if (_r240.d != 0.0) _y240 = 1; \
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| 402 | if (_q240.d != 0.0) _y240 = 1; \
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| 403 | if (_p240.d != 0.0) _y240 = 1; \
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| 404 | _t240 = (DItype)_k240; \
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| 405 | _u240 = _l240.i; \
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| 406 | _v240 = _m240.i; \
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| 407 | _w240 = _n240.i; \
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| 408 | _x240 = _o240.i; \
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| 409 | R##_f1 = (_t240 << (128 - (wfracbits - 1))) \
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| 410 | | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104)); \
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| 411 | R##_f0 = ((_u240 & 0xffffff) << (168 - (wfracbits - 1))) \
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| 412 | | ((_v240 & 0xffffff) << (144 - (wfracbits - 1))) \
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| 413 | | ((_w240 & 0xffffff) << (120 - (wfracbits - 1))) \
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| 414 | | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96)) \
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| 415 | | _y240; \
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| 416 | resetfe; \
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| 417 | } while (0)
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| 418 |
|
| 419 | |
| 420 | * Division algorithms:
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| 421 |
|
| 422 |
|
| 423 | #define _FP_DIV_MEAT_2_udiv(fs, R, X, Y) \
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| 424 | do { \
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| 425 | _FP_W_TYPE _n_f2, _n_f1, _n_f0, _r_f1, _r_f0, _m_f1, _m_f0; \
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| 426 | if (_FP_FRAC_GT_2(X, Y)) \
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| 427 | { \
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| 428 | _n_f2 = X##_f1 >> 1; \
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| 429 | _n_f1 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \
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| 430 | _n_f0 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \
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| 431 | } \
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| 432 | else \
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| 433 | { \
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| 434 | R##_e--; \
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| 435 | _n_f2 = X##_f1; \
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| 436 | _n_f1 = X##_f0; \
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| 437 | _n_f0 = 0; \
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| 438 | } \
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| 439 | \
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| 440 | |
| 441 | denominator set. \
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| 442 | _FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs); \
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| 443 | \
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| 444 | udiv_qrnnd(R##_f1, _r_f1, _n_f2, _n_f1, Y##_f1); \
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| 445 | umul_ppmm(_m_f1, _m_f0, R##_f1, Y##_f0); \
|
| 446 | _r_f0 = _n_f0; \
|
| 447 | if (_FP_FRAC_GT_2(_m, _r)) \
|
| 448 | { \
|
| 449 | R##_f1--; \
|
| 450 | _FP_FRAC_ADD_2(_r, Y, _r); \
|
| 451 | if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \
|
| 452 | { \
|
| 453 | R##_f1--; \
|
| 454 | _FP_FRAC_ADD_2(_r, Y, _r); \
|
| 455 | } \
|
| 456 | } \
|
| 457 | _FP_FRAC_DEC_2(_r, _m); \
|
| 458 | \
|
| 459 | if (_r_f1 == Y##_f1) \
|
| 460 | { \
|
| 461 | |
| 462 | (_r/Y##_f1 would not fit into UWtype). \
|
| 463 | As _r is guaranteed to be < Y, R##_f0 can be either \
|
| 464 | (UWtype)-1 or (UWtype)-2. But as we know what kind \
|
| 465 | of bits it is (sticky, guard, round), we don't care. \
|
| 466 | We also don't care what the reminder is, because the \
|
| 467 | guard bit will be set anyway. -jj \
|
| 468 | R##_f0 = -1; \
|
| 469 | } \
|
| 470 | else \
|
| 471 | { \
|
| 472 | udiv_qrnnd(R##_f0, _r_f1, _r_f1, _r_f0, Y##_f1); \
|
| 473 | umul_ppmm(_m_f1, _m_f0, R##_f0, Y##_f0); \
|
| 474 | _r_f0 = 0; \
|
| 475 | if (_FP_FRAC_GT_2(_m, _r)) \
|
| 476 | { \
|
| 477 | R##_f0--; \
|
| 478 | _FP_FRAC_ADD_2(_r, Y, _r); \
|
| 479 | if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \
|
| 480 | { \
|
| 481 | R##_f0--; \
|
| 482 | _FP_FRAC_ADD_2(_r, Y, _r); \
|
| 483 | } \
|
| 484 | } \
|
| 485 | if (!_FP_FRAC_EQ_2(_r, _m)) \
|
| 486 | R##_f0 |= _FP_WORK_STICKY; \
|
| 487 | } \
|
| 488 | } while (0)
|
| 489 |
|
| 490 |
|
| 491 | #define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \
|
| 492 | do { \
|
| 493 | _FP_W_TYPE _x[4], _y[2], _z[4]; \
|
| 494 | _y[0] = Y##_f0; _y[1] = Y##_f1; \
|
| 495 | _x[0] = _x[3] = 0; \
|
| 496 | if (_FP_FRAC_GT_2(X, Y)) \
|
| 497 | { \
|
| 498 | R##_e++; \
|
| 499 | _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE) | \
|
| 500 | X##_f1 >> (_FP_W_TYPE_SIZE - \
|
| 501 | (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE))); \
|
| 502 | _x[2] = X##_f1 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE); \
|
| 503 | } \
|
| 504 | else \
|
| 505 | { \
|
| 506 | _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE) | \
|
| 507 | X##_f1 >> (_FP_W_TYPE_SIZE - \
|
| 508 | (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE))); \
|
| 509 | _x[2] = X##_f1 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE); \
|
| 510 | } \
|
| 511 | \
|
| 512 | (void) mpn_divrem (_z, 0, _x, 4, _y, 2); \
|
| 513 | R##_f1 = _z[1]; \
|
| 514 | R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0); \
|
| 515 | } while (0)
|
| 516 |
|
| 517 |
|
| 518 | |
| 519 | * Square root algorithms:
|
| 520 | * We have just one right now, maybe Newton approximation
|
| 521 | * should be added for those machines where division is fast.
|
| 522 |
|
| 523 |
|
| 524 | #define _FP_SQRT_MEAT_2(R, S, T, X, q) \
|
| 525 | do { \
|
| 526 | while (q) \
|
| 527 | { \
|
| 528 | T##_f1 = S##_f1 + q; \
|
| 529 | if (T##_f1 <= X##_f1) \
|
| 530 | { \
|
| 531 | S##_f1 = T##_f1 + q; \
|
| 532 | X##_f1 -= T##_f1; \
|
| 533 | R##_f1 += q; \
|
| 534 | } \
|
| 535 | _FP_FRAC_SLL_2(X, 1); \
|
| 536 | q >>= 1; \
|
| 537 | } \
|
| 538 | q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
|
| 539 | while (q != _FP_WORK_ROUND) \
|
| 540 | { \
|
| 541 | T##_f0 = S##_f0 + q; \
|
| 542 | T##_f1 = S##_f1; \
|
| 543 | if (T##_f1 < X##_f1 || \
|
| 544 | (T##_f1 == X##_f1 && T##_f0 <= X##_f0)) \
|
| 545 | { \
|
| 546 | S##_f0 = T##_f0 + q; \
|
| 547 | S##_f1 += (T##_f0 > S##_f0); \
|
| 548 | _FP_FRAC_DEC_2(X, T); \
|
| 549 | R##_f0 += q; \
|
| 550 | } \
|
| 551 | _FP_FRAC_SLL_2(X, 1); \
|
| 552 | q >>= 1; \
|
| 553 | } \
|
| 554 | if (X##_f0 | X##_f1) \
|
| 555 | { \
|
| 556 | if (S##_f1 < X##_f1 || \
|
| 557 | (S##_f1 == X##_f1 && S##_f0 < X##_f0)) \
|
| 558 | R##_f0 |= _FP_WORK_ROUND; \
|
| 559 | R##_f0 |= _FP_WORK_STICKY; \
|
| 560 | } \
|
| 561 | } while (0)
|
| 562 |
|
| 563 |
|
| 564 | |
| 565 | * Assembly/disassembly for converting to/from integral types.
|
| 566 | * No shifting or overflow handled here.
|
| 567 |
|
| 568 |
|
| 569 | #define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \
|
| 570 | (void) (((rsize) <= _FP_W_TYPE_SIZE) \
|
| 571 | ? ({ (r) = X##_f0; }) \
|
| 572 | : ({ \
|
| 573 | (r) = X##_f1; \
|
| 574 | (r) <<= _FP_W_TYPE_SIZE; \
|
| 575 | (r) += X##_f0; \
|
| 576 | }))
|
| 577 |
|
| 578 | #define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \
|
| 579 | do { \
|
| 580 | X##_f0 = r; \
|
| 581 | X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \
|
| 582 | } while (0)
|
| 583 |
|
| 584 | |
| 585 | * Convert FP values between word sizes
|
| 586 |
|
| 587 |
|
| 588 | #define _FP_FRAC_CONV_1_2(dfs, sfs, D, S) \
|
| 589 | do { \
|
| 590 | if (S##_c != FP_CLS_NAN) \
|
| 591 | _FP_FRAC_SRS_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \
|
| 592 | _FP_WFRACBITS_##sfs); \
|
| 593 | else \
|
| 594 | _FP_FRAC_SRL_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs)); \
|
| 595 | D##_f = S##_f0; \
|
| 596 | } while (0)
|
| 597 |
|
| 598 | #define _FP_FRAC_CONV_2_1(dfs, sfs, D, S) \
|
| 599 | do { \
|
| 600 | D##_f0 = S##_f; \
|
| 601 | D##_f1 = 0; \
|
| 602 | _FP_FRAC_SLL_2(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \
|
| 603 | } while (0)
|
| 604 |
|
| 605 | #endif
|