| 1 | |
| 2 | Basic four-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_4_H__
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| 26 | #define __MATH_EMU_OP_4_H__
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| 27 |
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| 28 | #define _FP_FRAC_DECL_4(X) _FP_W_TYPE X##_f[4]
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| 29 | #define _FP_FRAC_COPY_4(D,S) \
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| 30 | (D##_f[0] = S##_f[0], D##_f[1] = S##_f[1], \
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| 31 | D##_f[2] = S##_f[2], D##_f[3] = S##_f[3])
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| 32 | #define _FP_FRAC_SET_4(X,I) __FP_FRAC_SET_4(X, I)
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| 33 | #define _FP_FRAC_HIGH_4(X) (X##_f[3])
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| 34 | #define _FP_FRAC_LOW_4(X) (X##_f[0])
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| 35 | #define _FP_FRAC_WORD_4(X,w) (X##_f[w])
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| 36 |
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| 37 | #define _FP_FRAC_SLL_4(X,N) \
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| 38 | do { \
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| 39 | _FP_I_TYPE _up, _down, _skip, _i; \
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| 40 | _skip = (N) / _FP_W_TYPE_SIZE; \
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| 41 | _up = (N) % _FP_W_TYPE_SIZE; \
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| 42 | _down = _FP_W_TYPE_SIZE - _up; \
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| 43 | if (!_up) \
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| 44 | for (_i = 3; _i >= _skip; --_i) \
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| 45 | X##_f[_i] = X##_f[_i-_skip]; \
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| 46 | else \
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| 47 | { \
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| 48 | for (_i = 3; _i > _skip; --_i) \
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| 49 | X##_f[_i] = X##_f[_i-_skip] << _up \
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| 50 | | X##_f[_i-_skip-1] >> _down; \
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| 51 | X##_f[_i--] = X##_f[0] << _up; \
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| 52 | } \
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| 53 | for (; _i >= 0; --_i) \
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| 54 | X##_f[_i] = 0; \
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| 55 | } while (0)
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| 56 |
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| 57 |
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| 58 | #define _FP_FRAC_SRL_4(X,N) \
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| 59 | do { \
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| 60 | _FP_I_TYPE _up, _down, _skip, _i; \
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| 61 | _skip = (N) / _FP_W_TYPE_SIZE; \
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| 62 | _down = (N) % _FP_W_TYPE_SIZE; \
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| 63 | _up = _FP_W_TYPE_SIZE - _down; \
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| 64 | if (!_down) \
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| 65 | for (_i = 0; _i <= 3-_skip; ++_i) \
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| 66 | X##_f[_i] = X##_f[_i+_skip]; \
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| 67 | else \
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| 68 | { \
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| 69 | for (_i = 0; _i < 3-_skip; ++_i) \
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| 70 | X##_f[_i] = X##_f[_i+_skip] >> _down \
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| 71 | | X##_f[_i+_skip+1] << _up; \
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| 72 | X##_f[_i++] = X##_f[3] >> _down; \
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| 73 | } \
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| 74 | for (; _i < 4; ++_i) \
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| 75 | X##_f[_i] = 0; \
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| 76 | } while (0)
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| 77 |
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| 78 |
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| 79 | |
| 80 | * What this actually means is that we do a standard right-shift,
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| 81 | * but that if any of the bits that fall off the right hand side
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| 82 | * were one then we always set the LSbit.
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| 83 |
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| 84 | #define _FP_FRAC_SRS_4(X,N,size) \
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| 85 | do { \
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| 86 | _FP_I_TYPE _up, _down, _skip, _i; \
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| 87 | _FP_W_TYPE _s; \
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| 88 | _skip = (N) / _FP_W_TYPE_SIZE; \
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| 89 | _down = (N) % _FP_W_TYPE_SIZE; \
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| 90 | _up = _FP_W_TYPE_SIZE - _down; \
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| 91 | for (_s = _i = 0; _i < _skip; ++_i) \
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| 92 | _s |= X##_f[_i]; \
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| 93 | _s |= X##_f[_i] << _up; \
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| 94 | \
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| 95 | if (!_down) \
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| 96 | for (_i = 0; _i <= 3-_skip; ++_i) \
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| 97 | X##_f[_i] = X##_f[_i+_skip]; \
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| 98 | else \
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| 99 | { \
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| 100 | for (_i = 0; _i < 3-_skip; ++_i) \
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| 101 | X##_f[_i] = X##_f[_i+_skip] >> _down \
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| 102 | | X##_f[_i+_skip+1] << _up; \
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| 103 | X##_f[_i++] = X##_f[3] >> _down; \
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| 104 | } \
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| 105 | for (; _i < 4; ++_i) \
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| 106 | X##_f[_i] = 0; \
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| 107 | \
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| 108 | X##_f[0] |= (_s != 0); \
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| 109 | } while (0)
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| 110 |
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| 111 | #define _FP_FRAC_ADD_4(R,X,Y) \
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| 112 | __FP_FRAC_ADD_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0], \
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| 113 | X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
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| 114 | Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
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| 115 |
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| 116 | #define _FP_FRAC_SUB_4(R,X,Y) \
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| 117 | __FP_FRAC_SUB_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0], \
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| 118 | X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
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| 119 | Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
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| 120 |
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| 121 | #define _FP_FRAC_DEC_4(X,Y) \
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| 122 | __FP_FRAC_DEC_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
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| 123 | Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
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| 124 |
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| 125 | #define _FP_FRAC_ADDI_4(X,I) \
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| 126 | __FP_FRAC_ADDI_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], I)
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| 127 |
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| 128 | #define _FP_ZEROFRAC_4 0,0,0,0
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| 129 | #define _FP_MINFRAC_4 0,0,0,1
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| 130 | #define _FP_MAXFRAC_4 (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0)
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| 131 |
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| 132 | #define _FP_FRAC_ZEROP_4(X) ((X##_f[0] | X##_f[1] | X##_f[2] | X##_f[3]) == 0)
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| 133 | #define _FP_FRAC_NEGP_4(X) ((_FP_WS_TYPE)X##_f[3] < 0)
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| 134 | #define _FP_FRAC_OVERP_4(fs,X) (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs)
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| 135 | #define _FP_FRAC_CLEAR_OVERP_4(fs,X) (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs)
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| 136 |
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| 137 | #define _FP_FRAC_EQ_4(X,Y) \
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| 138 | (X##_f[0] == Y##_f[0] && X##_f[1] == Y##_f[1] \
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| 139 | && X##_f[2] == Y##_f[2] && X##_f[3] == Y##_f[3])
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| 140 |
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| 141 | #define _FP_FRAC_GT_4(X,Y) \
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| 142 | (X##_f[3] > Y##_f[3] || \
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| 143 | (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] || \
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| 144 | (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] || \
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| 145 | (X##_f[1] == Y##_f[1] && X##_f[0] > Y##_f[0]) \
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| 146 | )) \
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| 147 | )) \
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| 148 | )
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| 149 |
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| 150 | #define _FP_FRAC_GE_4(X,Y) \
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| 151 | (X##_f[3] > Y##_f[3] || \
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| 152 | (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] || \
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| 153 | (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] || \
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| 154 | (X##_f[1] == Y##_f[1] && X##_f[0] >= Y##_f[0]) \
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| 155 | )) \
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| 156 | )) \
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| 157 | )
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| 158 |
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| 159 |
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| 160 | #define _FP_FRAC_CLZ_4(R,X) \
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| 161 | do { \
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| 162 | if (X##_f[3]) \
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| 163 | { \
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| 164 | __FP_CLZ(R,X##_f[3]); \
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| 165 | } \
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| 166 | else if (X##_f[2]) \
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| 167 | { \
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| 168 | __FP_CLZ(R,X##_f[2]); \
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| 169 | R += _FP_W_TYPE_SIZE; \
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| 170 | } \
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| 171 | else if (X##_f[1]) \
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| 172 | { \
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| 173 | __FP_CLZ(R,X##_f[2]); \
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| 174 | R += _FP_W_TYPE_SIZE*2; \
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| 175 | } \
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| 176 | else \
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| 177 | { \
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| 178 | __FP_CLZ(R,X##_f[0]); \
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| 179 | R += _FP_W_TYPE_SIZE*3; \
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| 180 | } \
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| 181 | } while(0)
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| 182 |
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| 183 |
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| 184 | #define _FP_UNPACK_RAW_4(fs, X, val) \
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| 185 | do { \
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| 186 | union _FP_UNION_##fs _flo; _flo.flt = (val); \
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| 187 | X##_f[0] = _flo.bits.frac0; \
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| 188 | X##_f[1] = _flo.bits.frac1; \
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| 189 | X##_f[2] = _flo.bits.frac2; \
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| 190 | X##_f[3] = _flo.bits.frac3; \
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| 191 | X##_e = _flo.bits.exp; \
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| 192 | X##_s = _flo.bits.sign; \
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| 193 | } while (0)
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| 194 |
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| 195 | #define _FP_UNPACK_RAW_4_P(fs, X, val) \
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| 196 | do { \
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| 197 | union _FP_UNION_##fs *_flo = \
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| 198 | (union _FP_UNION_##fs *)(val); \
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| 199 | \
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| 200 | X##_f[0] = _flo->bits.frac0; \
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| 201 | X##_f[1] = _flo->bits.frac1; \
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| 202 | X##_f[2] = _flo->bits.frac2; \
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| 203 | X##_f[3] = _flo->bits.frac3; \
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| 204 | X##_e = _flo->bits.exp; \
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| 205 | X##_s = _flo->bits.sign; \
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| 206 | } while (0)
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| 207 |
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| 208 | #define _FP_PACK_RAW_4(fs, val, X) \
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| 209 | do { \
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| 210 | union _FP_UNION_##fs _flo; \
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| 211 | _flo.bits.frac0 = X##_f[0]; \
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| 212 | _flo.bits.frac1 = X##_f[1]; \
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| 213 | _flo.bits.frac2 = X##_f[2]; \
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| 214 | _flo.bits.frac3 = X##_f[3]; \
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| 215 | _flo.bits.exp = X##_e; \
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| 216 | _flo.bits.sign = X##_s; \
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| 217 | (val) = _flo.flt; \
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| 218 | } while (0)
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| 219 |
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| 220 | #define _FP_PACK_RAW_4_P(fs, val, X) \
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| 221 | do { \
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| 222 | union _FP_UNION_##fs *_flo = \
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| 223 | (union _FP_UNION_##fs *)(val); \
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| 224 | \
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| 225 | _flo->bits.frac0 = X##_f[0]; \
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| 226 | _flo->bits.frac1 = X##_f[1]; \
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| 227 | _flo->bits.frac2 = X##_f[2]; \
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| 228 | _flo->bits.frac3 = X##_f[3]; \
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| 229 | _flo->bits.exp = X##_e; \
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| 230 | _flo->bits.sign = X##_s; \
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| 231 | } while (0)
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| 232 |
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| 233 | |
| 234 | * Multiplication algorithms:
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| 235 |
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| 236 |
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| 237 |
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| 238 |
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| 239 | #define _FP_MUL_MEAT_4_wide(wfracbits, R, X, Y, doit) \
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| 240 | do { \
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| 241 | _FP_FRAC_DECL_8(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \
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| 242 | _FP_FRAC_DECL_2(_d); _FP_FRAC_DECL_2(_e); _FP_FRAC_DECL_2(_f); \
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| 243 | \
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| 244 | doit(_FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0), X##_f[0], Y##_f[0]); \
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| 245 | doit(_b_f1, _b_f0, X##_f[0], Y##_f[1]); \
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| 246 | doit(_c_f1, _c_f0, X##_f[1], Y##_f[0]); \
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| 247 | doit(_d_f1, _d_f0, X##_f[1], Y##_f[1]); \
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| 248 | doit(_e_f1, _e_f0, X##_f[0], Y##_f[2]); \
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| 249 | doit(_f_f1, _f_f0, X##_f[2], Y##_f[0]); \
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| 250 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \
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| 251 | _FP_FRAC_WORD_8(_z,1), 0,_b_f1,_b_f0, \
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| 252 | 0,0,_FP_FRAC_WORD_8(_z,1)); \
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| 253 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \
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| 254 | _FP_FRAC_WORD_8(_z,1), 0,_c_f1,_c_f0, \
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| 255 | _FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \
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| 256 | _FP_FRAC_WORD_8(_z,1)); \
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| 257 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
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| 258 | _FP_FRAC_WORD_8(_z,2), 0,_d_f1,_d_f0, \
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| 259 | 0,_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2)); \
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| 260 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
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| 261 | _FP_FRAC_WORD_8(_z,2), 0,_e_f1,_e_f0, \
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| 262 | _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
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| 263 | _FP_FRAC_WORD_8(_z,2)); \
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| 264 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
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| 265 | _FP_FRAC_WORD_8(_z,2), 0,_f_f1,_f_f0, \
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| 266 | _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
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| 267 | _FP_FRAC_WORD_8(_z,2)); \
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| 268 | doit(_b_f1, _b_f0, X##_f[0], Y##_f[3]); \
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| 269 | doit(_c_f1, _c_f0, X##_f[3], Y##_f[0]); \
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| 270 | doit(_d_f1, _d_f0, X##_f[1], Y##_f[2]); \
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| 271 | doit(_e_f1, _e_f0, X##_f[2], Y##_f[1]); \
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| 272 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
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| 273 | _FP_FRAC_WORD_8(_z,3), 0,_b_f1,_b_f0, \
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| 274 | 0,_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3)); \
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| 275 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
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| 276 | _FP_FRAC_WORD_8(_z,3), 0,_c_f1,_c_f0, \
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| 277 | _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
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| 278 | _FP_FRAC_WORD_8(_z,3)); \
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| 279 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
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| 280 | _FP_FRAC_WORD_8(_z,3), 0,_d_f1,_d_f0, \
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| 281 | _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
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| 282 | _FP_FRAC_WORD_8(_z,3)); \
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| 283 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
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| 284 | _FP_FRAC_WORD_8(_z,3), 0,_e_f1,_e_f0, \
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| 285 | _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
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| 286 | _FP_FRAC_WORD_8(_z,3)); \
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| 287 | doit(_b_f1, _b_f0, X##_f[2], Y##_f[2]); \
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| 288 | doit(_c_f1, _c_f0, X##_f[1], Y##_f[3]); \
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| 289 | doit(_d_f1, _d_f0, X##_f[3], Y##_f[1]); \
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| 290 | doit(_e_f1, _e_f0, X##_f[2], Y##_f[3]); \
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| 291 | doit(_f_f1, _f_f0, X##_f[3], Y##_f[2]); \
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| 292 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
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| 293 | _FP_FRAC_WORD_8(_z,4), 0,_b_f1,_b_f0, \
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| 294 | 0,_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4)); \
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| 295 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
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| 296 | _FP_FRAC_WORD_8(_z,4), 0,_c_f1,_c_f0, \
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| 297 | _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
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| 298 | _FP_FRAC_WORD_8(_z,4)); \
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| 299 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
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| 300 | _FP_FRAC_WORD_8(_z,4), 0,_d_f1,_d_f0, \
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| 301 | _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
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| 302 | _FP_FRAC_WORD_8(_z,4)); \
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| 303 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \
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| 304 | _FP_FRAC_WORD_8(_z,5), 0,_e_f1,_e_f0, \
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| 305 | 0,_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5)); \
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| 306 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \
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| 307 | _FP_FRAC_WORD_8(_z,5), 0,_f_f1,_f_f0, \
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| 308 | _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \
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| 309 | _FP_FRAC_WORD_8(_z,5)); \
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| 310 | doit(_b_f1, _b_f0, X##_f[3], Y##_f[3]); \
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| 311 | __FP_FRAC_ADD_2(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \
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| 312 | _b_f1,_b_f0, \
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| 313 | _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6)); \
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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_8(_z, wfracbits-1, 2*wfracbits); \
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| 319 | __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2), \
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| 320 | _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0)); \
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| 321 | } while (0)
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| 322 |
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| 323 | #define _FP_MUL_MEAT_4_gmp(wfracbits, R, X, Y) \
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| 324 | do { \
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| 325 | _FP_FRAC_DECL_8(_z); \
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| 326 | \
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| 327 | mpn_mul_n(_z_f, _x_f, _y_f, 4); \
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| 328 | \
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| 329 | |
| 330 | were (bit B), we know that the msb of the of the product is \
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| 331 | at either 2B or 2B-1. \
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| 332 | _FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits); \
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| 333 | __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2), \
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| 334 | _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0)); \
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| 335 | } while (0)
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| 336 |
|
| 337 | |
| 338 | * Helper utility for _FP_DIV_MEAT_4_udiv:
|
| 339 | * pppp = m * nnn
|
| 340 |
|
| 341 | #define umul_ppppmnnn(p3,p2,p1,p0,m,n2,n1,n0) \
|
| 342 | do { \
|
| 343 | UWtype _t; \
|
| 344 | umul_ppmm(p1,p0,m,n0); \
|
| 345 | umul_ppmm(p2,_t,m,n1); \
|
| 346 | __FP_FRAC_ADDI_2(p2,p1,_t); \
|
| 347 | umul_ppmm(p3,_t,m,n2); \
|
| 348 | __FP_FRAC_ADDI_2(p3,p2,_t); \
|
| 349 | } while (0)
|
| 350 |
|
| 351 | |
| 352 | * Division algorithms:
|
| 353 |
|
| 354 |
|
| 355 | #define _FP_DIV_MEAT_4_udiv(fs, R, X, Y) \
|
| 356 | do { \
|
| 357 | int _i; \
|
| 358 | _FP_FRAC_DECL_4(_n); _FP_FRAC_DECL_4(_m); \
|
| 359 | _FP_FRAC_SET_4(_n, _FP_ZEROFRAC_4); \
|
| 360 | if (_FP_FRAC_GT_4(X, Y)) \
|
| 361 | { \
|
| 362 | _n_f[3] = X##_f[0] << (_FP_W_TYPE_SIZE - 1); \
|
| 363 | _FP_FRAC_SRL_4(X, 1); \
|
| 364 | } \
|
| 365 | else \
|
| 366 | R##_e--; \
|
| 367 | \
|
| 368 | |
| 369 | denominator set. \
|
| 370 | _FP_FRAC_SLL_4(Y, _FP_WFRACXBITS_##fs); \
|
| 371 | \
|
| 372 | for (_i = 3; ; _i--) \
|
| 373 | { \
|
| 374 | if (X##_f[3] == Y##_f[3]) \
|
| 375 | { \
|
| 376 | |
| 377 | (X##_f[3]/Y##_f[3] would not fit into UWtype). \
|
| 378 | As X## is guaranteed to be < Y, R##_f[_i] can be either \
|
| 379 | (UWtype)-1 or (UWtype)-2. \
|
| 380 | R##_f[_i] = -1; \
|
| 381 | if (!_i) \
|
| 382 | break; \
|
| 383 | __FP_FRAC_SUB_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
|
| 384 | Y##_f[2], Y##_f[1], Y##_f[0], 0, \
|
| 385 | X##_f[2], X##_f[1], X##_f[0], _n_f[_i]); \
|
| 386 | _FP_FRAC_SUB_4(X, Y, X); \
|
| 387 | if (X##_f[3] > Y##_f[3]) \
|
| 388 | { \
|
| 389 | R##_f[_i] = -2; \
|
| 390 | _FP_FRAC_ADD_4(X, Y, X); \
|
| 391 | } \
|
| 392 | } \
|
| 393 | else \
|
| 394 | { \
|
| 395 | udiv_qrnnd(R##_f[_i], X##_f[3], X##_f[3], X##_f[2], Y##_f[3]); \
|
| 396 | umul_ppppmnnn(_m_f[3], _m_f[2], _m_f[1], _m_f[0], \
|
| 397 | R##_f[_i], Y##_f[2], Y##_f[1], Y##_f[0]); \
|
| 398 | X##_f[2] = X##_f[1]; \
|
| 399 | X##_f[1] = X##_f[0]; \
|
| 400 | X##_f[0] = _n_f[_i]; \
|
| 401 | if (_FP_FRAC_GT_4(_m, X)) \
|
| 402 | { \
|
| 403 | R##_f[_i]--; \
|
| 404 | _FP_FRAC_ADD_4(X, Y, X); \
|
| 405 | if (_FP_FRAC_GE_4(X, Y) && _FP_FRAC_GT_4(_m, X)) \
|
| 406 | { \
|
| 407 | R##_f[_i]--; \
|
| 408 | _FP_FRAC_ADD_4(X, Y, X); \
|
| 409 | } \
|
| 410 | } \
|
| 411 | _FP_FRAC_DEC_4(X, _m); \
|
| 412 | if (!_i) \
|
| 413 | { \
|
| 414 | if (!_FP_FRAC_EQ_4(X, _m)) \
|
| 415 | R##_f[0] |= _FP_WORK_STICKY; \
|
| 416 | break; \
|
| 417 | } \
|
| 418 | } \
|
| 419 | } \
|
| 420 | } while (0)
|
| 421 |
|
| 422 |
|
| 423 | |
| 424 | * Square root algorithms:
|
| 425 | * We have just one right now, maybe Newton approximation
|
| 426 | * should be added for those machines where division is fast.
|
| 427 |
|
| 428 |
|
| 429 | #define _FP_SQRT_MEAT_4(R, S, T, X, q) \
|
| 430 | do { \
|
| 431 | while (q) \
|
| 432 | { \
|
| 433 | T##_f[3] = S##_f[3] + q; \
|
| 434 | if (T##_f[3] <= X##_f[3]) \
|
| 435 | { \
|
| 436 | S##_f[3] = T##_f[3] + q; \
|
| 437 | X##_f[3] -= T##_f[3]; \
|
| 438 | R##_f[3] += q; \
|
| 439 | } \
|
| 440 | _FP_FRAC_SLL_4(X, 1); \
|
| 441 | q >>= 1; \
|
| 442 | } \
|
| 443 | q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
|
| 444 | while (q) \
|
| 445 | { \
|
| 446 | T##_f[2] = S##_f[2] + q; \
|
| 447 | T##_f[3] = S##_f[3]; \
|
| 448 | if (T##_f[3] < X##_f[3] || \
|
| 449 | (T##_f[3] == X##_f[3] && T##_f[2] <= X##_f[2])) \
|
| 450 | { \
|
| 451 | S##_f[2] = T##_f[2] + q; \
|
| 452 | S##_f[3] += (T##_f[2] > S##_f[2]); \
|
| 453 | __FP_FRAC_DEC_2(X##_f[3], X##_f[2], \
|
| 454 | T##_f[3], T##_f[2]); \
|
| 455 | R##_f[2] += q; \
|
| 456 | } \
|
| 457 | _FP_FRAC_SLL_4(X, 1); \
|
| 458 | q >>= 1; \
|
| 459 | } \
|
| 460 | q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
|
| 461 | while (q) \
|
| 462 | { \
|
| 463 | T##_f[1] = S##_f[1] + q; \
|
| 464 | T##_f[2] = S##_f[2]; \
|
| 465 | T##_f[3] = S##_f[3]; \
|
| 466 | if (T##_f[3] < X##_f[3] || \
|
| 467 | (T##_f[3] == X##_f[3] && (T##_f[2] < X##_f[2] || \
|
| 468 | (T##_f[2] == X##_f[2] && T##_f[1] <= X##_f[1])))) \
|
| 469 | { \
|
| 470 | S##_f[1] = T##_f[1] + q; \
|
| 471 | S##_f[2] += (T##_f[1] > S##_f[1]); \
|
| 472 | S##_f[3] += (T##_f[2] > S##_f[2]); \
|
| 473 | __FP_FRAC_DEC_3(X##_f[3], X##_f[2], X##_f[1], \
|
| 474 | T##_f[3], T##_f[2], T##_f[1]); \
|
| 475 | R##_f[1] += q; \
|
| 476 | } \
|
| 477 | _FP_FRAC_SLL_4(X, 1); \
|
| 478 | q >>= 1; \
|
| 479 | } \
|
| 480 | q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
|
| 481 | while (q != _FP_WORK_ROUND) \
|
| 482 | { \
|
| 483 | T##_f[0] = S##_f[0] + q; \
|
| 484 | T##_f[1] = S##_f[1]; \
|
| 485 | T##_f[2] = S##_f[2]; \
|
| 486 | T##_f[3] = S##_f[3]; \
|
| 487 | if (_FP_FRAC_GE_4(X,T)) \
|
| 488 | { \
|
| 489 | S##_f[0] = T##_f[0] + q; \
|
| 490 | S##_f[1] += (T##_f[0] > S##_f[0]); \
|
| 491 | S##_f[2] += (T##_f[1] > S##_f[1]); \
|
| 492 | S##_f[3] += (T##_f[2] > S##_f[2]); \
|
| 493 | _FP_FRAC_DEC_4(X, T); \
|
| 494 | R##_f[0] += q; \
|
| 495 | } \
|
| 496 | _FP_FRAC_SLL_4(X, 1); \
|
| 497 | q >>= 1; \
|
| 498 | } \
|
| 499 | if (!_FP_FRAC_ZEROP_4(X)) \
|
| 500 | { \
|
| 501 | if (_FP_FRAC_GT_4(X,S)) \
|
| 502 | R##_f[0] |= _FP_WORK_ROUND; \
|
| 503 | R##_f[0] |= _FP_WORK_STICKY; \
|
| 504 | } \
|
| 505 | } while (0)
|
| 506 |
|
| 507 |
|
| 508 | |
| 509 | * Internals
|
| 510 |
|
| 511 |
|
| 512 | #define __FP_FRAC_SET_4(X,I3,I2,I1,I0) \
|
| 513 | (X##_f[3] = I3, X##_f[2] = I2, X##_f[1] = I1, X##_f[0] = I0)
|
| 514 |
|
| 515 | #ifndef __FP_FRAC_ADD_3
|
| 516 | #define __FP_FRAC_ADD_3(r2,r1,r0,x2,x1,x0,y2,y1,y0) \
|
| 517 | do { \
|
| 518 | int _c1, _c2; \
|
| 519 | r0 = x0 + y0; \
|
| 520 | _c1 = r0 < x0; \
|
| 521 | r1 = x1 + y1; \
|
| 522 | _c2 = r1 < x1; \
|
| 523 | r1 += _c1; \
|
| 524 | _c2 |= r1 < _c1; \
|
| 525 | r2 = x2 + y2 + _c2; \
|
| 526 | } while (0)
|
| 527 | #endif
|
| 528 |
|
| 529 | #ifndef __FP_FRAC_ADD_4
|
| 530 | #define __FP_FRAC_ADD_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0) \
|
| 531 | do { \
|
| 532 | int _c1, _c2, _c3; \
|
| 533 | r0 = x0 + y0; \
|
| 534 | _c1 = r0 < x0; \
|
| 535 | r1 = x1 + y1; \
|
| 536 | _c2 = r1 < x1; \
|
| 537 | r1 += _c1; \
|
| 538 | _c2 |= r1 < _c1; \
|
| 539 | r2 = x2 + y2; \
|
| 540 | _c3 = r2 < x2; \
|
| 541 | r2 += _c2; \
|
| 542 | _c3 |= r2 < _c2; \
|
| 543 | r3 = x3 + y3 + _c3; \
|
| 544 | } while (0)
|
| 545 | #endif
|
| 546 |
|
| 547 | #ifndef __FP_FRAC_SUB_3
|
| 548 | #define __FP_FRAC_SUB_3(r2,r1,r0,x2,x1,x0,y2,y1,y0) \
|
| 549 | do { \
|
| 550 | int _c1, _c2; \
|
| 551 | r0 = x0 - y0; \
|
| 552 | _c1 = r0 > x0; \
|
| 553 | r1 = x1 - y1; \
|
| 554 | _c2 = r1 > x1; \
|
| 555 | r1 -= _c1; \
|
| 556 | _c2 |= r1 > _c1; \
|
| 557 | r2 = x2 - y2 - _c2; \
|
| 558 | } while (0)
|
| 559 | #endif
|
| 560 |
|
| 561 | #ifndef __FP_FRAC_SUB_4
|
| 562 | #define __FP_FRAC_SUB_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0) \
|
| 563 | do { \
|
| 564 | int _c1, _c2, _c3; \
|
| 565 | r0 = x0 - y0; \
|
| 566 | _c1 = r0 > x0; \
|
| 567 | r1 = x1 - y1; \
|
| 568 | _c2 = r1 > x1; \
|
| 569 | r1 -= _c1; \
|
| 570 | _c2 |= r1 > _c1; \
|
| 571 | r2 = x2 - y2; \
|
| 572 | _c3 = r2 > x2; \
|
| 573 | r2 -= _c2; \
|
| 574 | _c3 |= r2 > _c2; \
|
| 575 | r3 = x3 - y3 - _c3; \
|
| 576 | } while (0)
|
| 577 | #endif
|
| 578 |
|
| 579 | #ifndef __FP_FRAC_DEC_3
|
| 580 | #define __FP_FRAC_DEC_3(x2,x1,x0,y2,y1,y0) \
|
| 581 | do { \
|
| 582 | UWtype _t0, _t1, _t2; \
|
| 583 | _t0 = x0, _t1 = x1, _t2 = x2; \
|
| 584 | __FP_FRAC_SUB_3 (x2, x1, x0, _t2, _t1, _t0, y2, y1, y0); \
|
| 585 | } while (0)
|
| 586 | #endif
|
| 587 |
|
| 588 | #ifndef __FP_FRAC_DEC_4
|
| 589 | #define __FP_FRAC_DEC_4(x3,x2,x1,x0,y3,y2,y1,y0) \
|
| 590 | do { \
|
| 591 | UWtype _t0, _t1, _t2, _t3; \
|
| 592 | _t0 = x0, _t1 = x1, _t2 = x2, _t3 = x3; \
|
| 593 | __FP_FRAC_SUB_4 (x3,x2,x1,x0,_t3,_t2,_t1,_t0, y3,y2,y1,y0); \
|
| 594 | } while (0)
|
| 595 | #endif
|
| 596 |
|
| 597 | #ifndef __FP_FRAC_ADDI_4
|
| 598 | #define __FP_FRAC_ADDI_4(x3,x2,x1,x0,i) \
|
| 599 | do { \
|
| 600 | UWtype _t; \
|
| 601 | _t = ((x0 += i) < i); \
|
| 602 | x1 += _t; _t = (x1 < _t); \
|
| 603 | x2 += _t; _t = (x2 < _t); \
|
| 604 | x3 += _t; \
|
| 605 | } while (0)
|
| 606 | #endif
|
| 607 |
|
| 608 | |
| 609 | * complicated than I'd have expected it to be, so these might be
|
| 610 | * wrong... These macros are in any case somewhat bogus because they
|
| 611 | * use information about what various FRAC_n variables look like
|
| 612 | * internally [eg, that 2 word vars are X_f0 and x_f1]. But so do
|
| 613 | * the ones in op-2.h and op-1.h.
|
| 614 |
|
| 615 | #define _FP_FRAC_CONV_1_4(dfs, sfs, D, S) \
|
| 616 | do { \
|
| 617 | if (S##_c != FP_CLS_NAN) \
|
| 618 | _FP_FRAC_SRS_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \
|
| 619 | _FP_WFRACBITS_##sfs); \
|
| 620 | else \
|
| 621 | _FP_FRAC_SRL_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs)); \
|
| 622 | D##_f = S##_f[0]; \
|
| 623 | } while (0)
|
| 624 |
|
| 625 | #define _FP_FRAC_CONV_2_4(dfs, sfs, D, S) \
|
| 626 | do { \
|
| 627 | if (S##_c != FP_CLS_NAN) \
|
| 628 | _FP_FRAC_SRS_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \
|
| 629 | _FP_WFRACBITS_##sfs); \
|
| 630 | else \
|
| 631 | _FP_FRAC_SRL_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs)); \
|
| 632 | D##_f0 = S##_f[0]; \
|
| 633 | D##_f1 = S##_f[1]; \
|
| 634 | } while (0)
|
| 635 |
|
| 636 | |
| 637 | * No shifting or overflow handled here.
|
| 638 |
|
| 639 |
|
| 640 | #define _FP_FRAC_ASSEMBLE_4(r, X, rsize) \
|
| 641 | do { \
|
| 642 | if (rsize <= _FP_W_TYPE_SIZE) \
|
| 643 | r = X##_f[0]; \
|
| 644 | else if (rsize <= 2*_FP_W_TYPE_SIZE) \
|
| 645 | { \
|
| 646 | r = X##_f[1]; \
|
| 647 | r <<= _FP_W_TYPE_SIZE; \
|
| 648 | r += X##_f[0]; \
|
| 649 | } \
|
| 650 | else \
|
| 651 | { \
|
| 652 | \
|
| 653 | \
|
| 654 | r = X##_f[3]; \
|
| 655 | r <<= _FP_W_TYPE_SIZE; \
|
| 656 | r += X##_f[2]; \
|
| 657 | r <<= _FP_W_TYPE_SIZE; \
|
| 658 | r += X##_f[1]; \
|
| 659 | r <<= _FP_W_TYPE_SIZE; \
|
| 660 | r += X##_f[0]; \
|
| 661 | } \
|
| 662 | } while (0)
|
| 663 |
|
| 664 |
|
| 665 | |
| 666 | * the _f[] array consisting of words of size _FP_W_TYPE_SIZE to avoid
|
| 667 | * having to mask the values we store into it.
|
| 668 |
|
| 669 | #define _FP_FRAC_DISASSEMBLE_4(X, r, rsize) \
|
| 670 | do { \
|
| 671 | X##_f[0] = r; \
|
| 672 | X##_f[1] = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \
|
| 673 | X##_f[2] = (rsize <= 2*_FP_W_TYPE_SIZE ? 0 : r >> 2*_FP_W_TYPE_SIZE); \
|
| 674 | X##_f[3] = (rsize <= 3*_FP_W_TYPE_SIZE ? 0 : r >> 3*_FP_W_TYPE_SIZE); \
|
| 675 | } while (0)
|
| 676 |
|
| 677 | #define _FP_FRAC_CONV_4_1(dfs, sfs, D, S) \
|
| 678 | do { \
|
| 679 | D##_f[0] = S##_f; \
|
| 680 | D##_f[1] = D##_f[2] = D##_f[3] = 0; \
|
| 681 | _FP_FRAC_SLL_4(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \
|
| 682 | } while (0)
|
| 683 |
|
| 684 | #define _FP_FRAC_CONV_4_2(dfs, sfs, D, S) \
|
| 685 | do { \
|
| 686 | D##_f[0] = S##_f0; \
|
| 687 | D##_f[1] = S##_f1; \
|
| 688 | D##_f[2] = D##_f[3] = 0; \
|
| 689 | _FP_FRAC_SLL_4(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \
|
| 690 | } while (0)
|
| 691 |
|
| 692 | #endif
|