| 1 | /* Software floating-point emulation. |
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| 2 | Basic two-word fraction declaration and manipulation. |
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| 3 | Copyright (C) 1997-2022 Free Software Foundation, Inc. |
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| 4 | This file is part of the GNU C Library. |
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| 5 | |
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| 6 | The GNU C Library is free software; you can redistribute it and/or |
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| 7 | modify it under the terms of the GNU Lesser General Public |
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| 8 | License as published by the Free Software Foundation; either |
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| 9 | version 2.1 of the License, or (at your option) any later version. |
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| 10 | |
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| 11 | In addition to the permissions in the GNU Lesser General Public |
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| 12 | License, the Free Software Foundation gives you unlimited |
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| 13 | permission to link the compiled version of this file into |
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| 14 | combinations with other programs, and to distribute those |
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| 15 | combinations without any restriction coming from the use of this |
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| 16 | file. (The Lesser General Public License restrictions do apply in |
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| 17 | other respects; for example, they cover modification of the file, |
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| 18 | and distribution when not linked into a combine executable.) |
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| 19 | |
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| 20 | The GNU C Library is distributed in the hope that it will be useful, |
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| 21 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 22 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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| 23 | Lesser General Public License for more details. |
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| 24 | |
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| 25 | You should have received a copy of the GNU Lesser General Public |
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| 26 | License along with the GNU C Library; if not, see |
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| 27 | <https://www.gnu.org/licenses/>. */ |
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| 28 | |
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| 29 | #ifndef SOFT_FP_OP_2_H |
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| 30 | #define SOFT_FP_OP_2_H 1 |
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| 31 | |
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| 32 | #define _FP_FRAC_DECL_2(X) \ |
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| 33 | _FP_W_TYPE X##_f0 _FP_ZERO_INIT, X##_f1 _FP_ZERO_INIT |
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| 34 | #define _FP_FRAC_COPY_2(D, S) (D##_f0 = S##_f0, D##_f1 = S##_f1) |
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| 35 | #define _FP_FRAC_SET_2(X, I) __FP_FRAC_SET_2 (X, I) |
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| 36 | #define _FP_FRAC_HIGH_2(X) (X##_f1) |
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| 37 | #define _FP_FRAC_LOW_2(X) (X##_f0) |
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| 38 | #define _FP_FRAC_WORD_2(X, w) (X##_f##w) |
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| 39 | |
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| 40 | #define _FP_FRAC_SLL_2(X, N) \ |
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| 41 | (void) (((N) < _FP_W_TYPE_SIZE) \ |
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| 42 | ? ({ \ |
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| 43 | if (__builtin_constant_p (N) && (N) == 1) \ |
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| 44 | { \ |
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| 45 | X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE) (X##_f0)) < 0); \ |
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| 46 | X##_f0 += X##_f0; \ |
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| 47 | } \ |
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| 48 | else \ |
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| 49 | { \ |
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| 50 | X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \ |
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| 51 | X##_f0 <<= (N); \ |
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| 52 | } \ |
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| 53 | 0; \ |
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| 54 | }) \ |
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| 55 | : ({ \ |
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| 56 | X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \ |
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| 57 | X##_f0 = 0; \ |
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| 58 | })) |
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| 59 | |
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| 60 | |
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| 61 | #define _FP_FRAC_SRL_2(X, N) \ |
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| 62 | (void) (((N) < _FP_W_TYPE_SIZE) \ |
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| 63 | ? ({ \ |
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| 64 | X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \ |
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| 65 | X##_f1 >>= (N); \ |
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| 66 | }) \ |
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| 67 | : ({ \ |
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| 68 | X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \ |
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| 69 | X##_f1 = 0; \ |
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| 70 | })) |
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| 71 | |
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| 72 | /* Right shift with sticky-lsb. */ |
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| 73 | #define _FP_FRAC_SRST_2(X, S, N, sz) \ |
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| 74 | (void) (((N) < _FP_W_TYPE_SIZE) \ |
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| 75 | ? ({ \ |
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| 76 | S = (__builtin_constant_p (N) && (N) == 1 \ |
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| 77 | ? X##_f0 & 1 \ |
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| 78 | : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0); \ |
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| 79 | X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N)); \ |
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| 80 | X##_f1 >>= (N); \ |
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| 81 | }) \ |
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| 82 | : ({ \ |
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| 83 | S = ((((N) == _FP_W_TYPE_SIZE \ |
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| 84 | ? 0 \ |
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| 85 | : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \ |
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| 86 | | X##_f0) != 0); \ |
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| 87 | X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE)); \ |
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| 88 | X##_f1 = 0; \ |
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| 89 | })) |
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| 90 | |
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| 91 | #define _FP_FRAC_SRS_2(X, N, sz) \ |
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| 92 | (void) (((N) < _FP_W_TYPE_SIZE) \ |
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| 93 | ? ({ \ |
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| 94 | X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) \ |
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| 95 | | (__builtin_constant_p (N) && (N) == 1 \ |
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| 96 | ? X##_f0 & 1 \ |
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| 97 | : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \ |
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| 98 | X##_f1 >>= (N); \ |
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| 99 | }) \ |
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| 100 | : ({ \ |
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| 101 | X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) \ |
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| 102 | | ((((N) == _FP_W_TYPE_SIZE \ |
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| 103 | ? 0 \ |
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| 104 | : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \ |
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| 105 | | X##_f0) != 0)); \ |
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| 106 | X##_f1 = 0; \ |
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| 107 | })) |
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| 108 | |
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| 109 | #define _FP_FRAC_ADDI_2(X, I) \ |
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| 110 | __FP_FRAC_ADDI_2 (X##_f1, X##_f0, I) |
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| 111 | |
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| 112 | #define _FP_FRAC_ADD_2(R, X, Y) \ |
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| 113 | __FP_FRAC_ADD_2 (R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) |
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| 114 | |
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| 115 | #define _FP_FRAC_SUB_2(R, X, Y) \ |
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| 116 | __FP_FRAC_SUB_2 (R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) |
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| 117 | |
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| 118 | #define _FP_FRAC_DEC_2(X, Y) \ |
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| 119 | __FP_FRAC_DEC_2 (X##_f1, X##_f0, Y##_f1, Y##_f0) |
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| 120 | |
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| 121 | #define _FP_FRAC_CLZ_2(R, X) \ |
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| 122 | do \ |
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| 123 | { \ |
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| 124 | if (X##_f1) \ |
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| 125 | __FP_CLZ ((R), X##_f1); \ |
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| 126 | else \ |
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| 127 | { \ |
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| 128 | __FP_CLZ ((R), X##_f0); \ |
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| 129 | (R) += _FP_W_TYPE_SIZE; \ |
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| 130 | } \ |
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| 131 | } \ |
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| 132 | while (0) |
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| 133 | |
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| 134 | /* Predicates. */ |
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| 135 | #define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE) X##_f1 < 0) |
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| 136 | #define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0) |
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| 137 | #define _FP_FRAC_OVERP_2(fs, X) (_FP_FRAC_HIGH_##fs (X) & _FP_OVERFLOW_##fs) |
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| 138 | #define _FP_FRAC_CLEAR_OVERP_2(fs, X) (_FP_FRAC_HIGH_##fs (X) &= ~_FP_OVERFLOW_##fs) |
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| 139 | #define _FP_FRAC_HIGHBIT_DW_2(fs, X) \ |
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| 140 | (_FP_FRAC_HIGH_DW_##fs (X) & _FP_HIGHBIT_DW_##fs) |
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| 141 | #define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0) |
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| 142 | #define _FP_FRAC_GT_2(X, Y) \ |
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| 143 | (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0)) |
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| 144 | #define _FP_FRAC_GE_2(X, Y) \ |
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| 145 | (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0)) |
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| 146 | |
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| 147 | #define _FP_ZEROFRAC_2 0, 0 |
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| 148 | #define _FP_MINFRAC_2 0, 1 |
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| 149 | #define _FP_MAXFRAC_2 (~(_FP_WS_TYPE) 0), (~(_FP_WS_TYPE) 0) |
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| 150 | |
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| 151 | /* Internals. */ |
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| 152 | |
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| 153 | #define __FP_FRAC_SET_2(X, I1, I0) (X##_f0 = I0, X##_f1 = I1) |
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| 154 | |
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| 155 | #define __FP_CLZ_2(R, xh, xl) \ |
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| 156 | do \ |
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| 157 | { \ |
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| 158 | if (xh) \ |
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| 159 | __FP_CLZ ((R), xh); \ |
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| 160 | else \ |
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| 161 | { \ |
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| 162 | __FP_CLZ ((R), xl); \ |
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| 163 | (R) += _FP_W_TYPE_SIZE; \ |
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| 164 | } \ |
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| 165 | } \ |
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| 166 | while (0) |
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| 167 | |
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| 168 | #if 0 |
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| 169 | |
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| 170 | # ifndef __FP_FRAC_ADDI_2 |
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| 171 | # define __FP_FRAC_ADDI_2(xh, xl, i) \ |
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| 172 | (xh += ((xl += i) < i)) |
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| 173 | # endif |
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| 174 | # ifndef __FP_FRAC_ADD_2 |
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| 175 | # define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \ |
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| 176 | (rh = xh + yh + ((rl = xl + yl) < xl)) |
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| 177 | # endif |
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| 178 | # ifndef __FP_FRAC_SUB_2 |
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| 179 | # define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \ |
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| 180 | (rh = xh - yh - ((rl = xl - yl) > xl)) |
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| 181 | # endif |
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| 182 | # ifndef __FP_FRAC_DEC_2 |
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| 183 | # define __FP_FRAC_DEC_2(xh, xl, yh, yl) \ |
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| 184 | do \ |
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| 185 | { \ |
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| 186 | UWtype __FP_FRAC_DEC_2_t = xl; \ |
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| 187 | xh -= yh + ((xl -= yl) > __FP_FRAC_DEC_2_t); \ |
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| 188 | } \ |
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| 189 | while (0) |
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| 190 | # endif |
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| 191 | |
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| 192 | #else |
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| 193 | |
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| 194 | # undef __FP_FRAC_ADDI_2 |
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| 195 | # define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa (xh, xl, xh, xl, 0, i) |
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| 196 | # undef __FP_FRAC_ADD_2 |
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| 197 | # define __FP_FRAC_ADD_2 add_ssaaaa |
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| 198 | # undef __FP_FRAC_SUB_2 |
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| 199 | # define __FP_FRAC_SUB_2 sub_ddmmss |
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| 200 | # undef __FP_FRAC_DEC_2 |
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| 201 | # define __FP_FRAC_DEC_2(xh, xl, yh, yl) \ |
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| 202 | sub_ddmmss (xh, xl, xh, xl, yh, yl) |
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| 203 | |
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| 204 | #endif |
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| 205 | |
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| 206 | /* Unpack the raw bits of a native fp value. Do not classify or |
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| 207 | normalize the data. */ |
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| 208 | |
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| 209 | #define _FP_UNPACK_RAW_2(fs, X, val) \ |
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| 210 | do \ |
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| 211 | { \ |
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| 212 | union _FP_UNION_##fs _FP_UNPACK_RAW_2_flo; \ |
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| 213 | _FP_UNPACK_RAW_2_flo.flt = (val); \ |
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| 214 | \ |
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| 215 | X##_f0 = _FP_UNPACK_RAW_2_flo.bits.frac0; \ |
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| 216 | X##_f1 = _FP_UNPACK_RAW_2_flo.bits.frac1; \ |
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| 217 | X##_e = _FP_UNPACK_RAW_2_flo.bits.exp; \ |
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| 218 | X##_s = _FP_UNPACK_RAW_2_flo.bits.sign; \ |
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| 219 | } \ |
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| 220 | while (0) |
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| 221 | |
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| 222 | #define _FP_UNPACK_RAW_2_P(fs, X, val) \ |
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| 223 | do \ |
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| 224 | { \ |
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| 225 | union _FP_UNION_##fs *_FP_UNPACK_RAW_2_P_flo \ |
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| 226 | = (union _FP_UNION_##fs *) (val); \ |
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| 227 | \ |
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| 228 | X##_f0 = _FP_UNPACK_RAW_2_P_flo->bits.frac0; \ |
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| 229 | X##_f1 = _FP_UNPACK_RAW_2_P_flo->bits.frac1; \ |
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| 230 | X##_e = _FP_UNPACK_RAW_2_P_flo->bits.exp; \ |
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| 231 | X##_s = _FP_UNPACK_RAW_2_P_flo->bits.sign; \ |
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| 232 | } \ |
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| 233 | while (0) |
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| 234 | |
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| 235 | |
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| 236 | /* Repack the raw bits of a native fp value. */ |
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| 237 | |
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| 238 | #define _FP_PACK_RAW_2(fs, val, X) \ |
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| 239 | do \ |
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| 240 | { \ |
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| 241 | union _FP_UNION_##fs _FP_PACK_RAW_2_flo; \ |
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| 242 | \ |
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| 243 | _FP_PACK_RAW_2_flo.bits.frac0 = X##_f0; \ |
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| 244 | _FP_PACK_RAW_2_flo.bits.frac1 = X##_f1; \ |
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| 245 | _FP_PACK_RAW_2_flo.bits.exp = X##_e; \ |
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| 246 | _FP_PACK_RAW_2_flo.bits.sign = X##_s; \ |
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| 247 | \ |
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| 248 | (val) = _FP_PACK_RAW_2_flo.flt; \ |
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| 249 | } \ |
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| 250 | while (0) |
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| 251 | |
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| 252 | #define _FP_PACK_RAW_2_P(fs, val, X) \ |
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| 253 | do \ |
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| 254 | { \ |
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| 255 | union _FP_UNION_##fs *_FP_PACK_RAW_2_P_flo \ |
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| 256 | = (union _FP_UNION_##fs *) (val); \ |
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| 257 | \ |
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| 258 | _FP_PACK_RAW_2_P_flo->bits.frac0 = X##_f0; \ |
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| 259 | _FP_PACK_RAW_2_P_flo->bits.frac1 = X##_f1; \ |
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| 260 | _FP_PACK_RAW_2_P_flo->bits.exp = X##_e; \ |
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| 261 | _FP_PACK_RAW_2_P_flo->bits.sign = X##_s; \ |
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| 262 | } \ |
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| 263 | while (0) |
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| 264 | |
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| 265 | |
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| 266 | /* Multiplication algorithms: */ |
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| 267 | |
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| 268 | /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ |
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| 269 | |
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| 270 | #define _FP_MUL_MEAT_DW_2_wide(wfracbits, R, X, Y, doit) \ |
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| 271 | do \ |
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| 272 | { \ |
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| 273 | _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_b); \ |
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| 274 | _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_c); \ |
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| 275 | \ |
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| 276 | doit (_FP_FRAC_WORD_4 (R, 1), _FP_FRAC_WORD_4 (R, 0), \ |
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| 277 | X##_f0, Y##_f0); \ |
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| 278 | doit (_FP_MUL_MEAT_DW_2_wide_b_f1, _FP_MUL_MEAT_DW_2_wide_b_f0, \ |
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| 279 | X##_f0, Y##_f1); \ |
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| 280 | doit (_FP_MUL_MEAT_DW_2_wide_c_f1, _FP_MUL_MEAT_DW_2_wide_c_f0, \ |
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| 281 | X##_f1, Y##_f0); \ |
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| 282 | doit (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
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| 283 | X##_f1, Y##_f1); \ |
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| 284 | \ |
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| 285 | __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
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| 286 | _FP_FRAC_WORD_4 (R, 1), 0, \ |
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| 287 | _FP_MUL_MEAT_DW_2_wide_b_f1, \ |
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| 288 | _FP_MUL_MEAT_DW_2_wide_b_f0, \ |
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| 289 | _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
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| 290 | _FP_FRAC_WORD_4 (R, 1)); \ |
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| 291 | __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
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| 292 | _FP_FRAC_WORD_4 (R, 1), 0, \ |
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| 293 | _FP_MUL_MEAT_DW_2_wide_c_f1, \ |
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| 294 | _FP_MUL_MEAT_DW_2_wide_c_f0, \ |
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| 295 | _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
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| 296 | _FP_FRAC_WORD_4 (R, 1)); \ |
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| 297 | } \ |
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| 298 | while (0) |
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| 299 | |
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| 300 | #define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit) \ |
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| 301 | do \ |
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| 302 | { \ |
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| 303 | _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_wide_z); \ |
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| 304 | \ |
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| 305 | _FP_MUL_MEAT_DW_2_wide ((wfracbits), _FP_MUL_MEAT_2_wide_z, \ |
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| 306 | X, Y, doit); \ |
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| 307 | \ |
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| 308 | /* Normalize since we know where the msb of the multiplicands \ |
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| 309 | were (bit B), we know that the msb of the of the product is \ |
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| 310 | at either 2B or 2B-1. */ \ |
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| 311 | _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_wide_z, (wfracbits)-1, \ |
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| 312 | 2*(wfracbits)); \ |
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| 313 | R##_f0 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_z, 0); \ |
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| 314 | R##_f1 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_z, 1); \ |
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| 315 | } \ |
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| 316 | while (0) |
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| 317 | |
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| 318 | /* Given a 1W * 1W => 2W primitive, do the extended multiplication. |
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| 319 | Do only 3 multiplications instead of four. This one is for machines |
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| 320 | where multiplication is much more expensive than subtraction. */ |
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| 321 | |
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| 322 | #define _FP_MUL_MEAT_DW_2_wide_3mul(wfracbits, R, X, Y, doit) \ |
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| 323 | do \ |
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| 324 | { \ |
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| 325 | _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_3mul_b); \ |
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| 326 | _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_3mul_c); \ |
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| 327 | _FP_W_TYPE _FP_MUL_MEAT_DW_2_wide_3mul_d; \ |
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| 328 | int _FP_MUL_MEAT_DW_2_wide_3mul_c1; \ |
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| 329 | int _FP_MUL_MEAT_DW_2_wide_3mul_c2; \ |
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| 330 | \ |
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| 331 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f0 = X##_f0 + X##_f1; \ |
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| 332 | _FP_MUL_MEAT_DW_2_wide_3mul_c1 \ |
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| 333 | = _FP_MUL_MEAT_DW_2_wide_3mul_b_f0 < X##_f0; \ |
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| 334 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f1 = Y##_f0 + Y##_f1; \ |
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| 335 | _FP_MUL_MEAT_DW_2_wide_3mul_c2 \ |
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| 336 | = _FP_MUL_MEAT_DW_2_wide_3mul_b_f1 < Y##_f0; \ |
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| 337 | doit (_FP_MUL_MEAT_DW_2_wide_3mul_d, _FP_FRAC_WORD_4 (R, 0), \ |
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| 338 | X##_f0, Y##_f0); \ |
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| 339 | doit (_FP_FRAC_WORD_4 (R, 2), _FP_FRAC_WORD_4 (R, 1), \ |
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| 340 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f0, \ |
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| 341 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f1); \ |
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| 342 | doit (_FP_MUL_MEAT_DW_2_wide_3mul_c_f1, \ |
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| 343 | _FP_MUL_MEAT_DW_2_wide_3mul_c_f0, X##_f1, Y##_f1); \ |
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| 344 | \ |
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| 345 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f0 \ |
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| 346 | &= -_FP_MUL_MEAT_DW_2_wide_3mul_c2; \ |
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| 347 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f1 \ |
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| 348 | &= -_FP_MUL_MEAT_DW_2_wide_3mul_c1; \ |
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| 349 | __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
|---|
| 350 | _FP_FRAC_WORD_4 (R, 1), \ |
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| 351 | (_FP_MUL_MEAT_DW_2_wide_3mul_c1 \ |
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| 352 | & _FP_MUL_MEAT_DW_2_wide_3mul_c2), 0, \ |
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| 353 | _FP_MUL_MEAT_DW_2_wide_3mul_d, \ |
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| 354 | 0, _FP_FRAC_WORD_4 (R, 2), _FP_FRAC_WORD_4 (R, 1)); \ |
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| 355 | __FP_FRAC_ADDI_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
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| 356 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f0); \ |
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| 357 | __FP_FRAC_ADDI_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
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| 358 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f1); \ |
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| 359 | __FP_FRAC_DEC_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
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| 360 | _FP_FRAC_WORD_4 (R, 1), \ |
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| 361 | 0, _FP_MUL_MEAT_DW_2_wide_3mul_d, \ |
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| 362 | _FP_FRAC_WORD_4 (R, 0)); \ |
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| 363 | __FP_FRAC_DEC_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
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| 364 | _FP_FRAC_WORD_4 (R, 1), 0, \ |
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| 365 | _FP_MUL_MEAT_DW_2_wide_3mul_c_f1, \ |
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| 366 | _FP_MUL_MEAT_DW_2_wide_3mul_c_f0); \ |
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| 367 | __FP_FRAC_ADD_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
|---|
| 368 | _FP_MUL_MEAT_DW_2_wide_3mul_c_f1, \ |
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| 369 | _FP_MUL_MEAT_DW_2_wide_3mul_c_f0, \ |
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| 370 | _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2)); \ |
|---|
| 371 | } \ |
|---|
| 372 | while (0) |
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| 373 | |
|---|
| 374 | #define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit) \ |
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| 375 | do \ |
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| 376 | { \ |
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| 377 | _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_wide_3mul_z); \ |
|---|
| 378 | \ |
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| 379 | _FP_MUL_MEAT_DW_2_wide_3mul ((wfracbits), \ |
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| 380 | _FP_MUL_MEAT_2_wide_3mul_z, \ |
|---|
| 381 | X, Y, doit); \ |
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| 382 | \ |
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| 383 | /* Normalize since we know where the msb of the multiplicands \ |
|---|
| 384 | were (bit B), we know that the msb of the of the product is \ |
|---|
| 385 | at either 2B or 2B-1. */ \ |
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| 386 | _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_wide_3mul_z, \ |
|---|
| 387 | (wfracbits)-1, 2*(wfracbits)); \ |
|---|
| 388 | R##_f0 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_3mul_z, 0); \ |
|---|
| 389 | R##_f1 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_3mul_z, 1); \ |
|---|
| 390 | } \ |
|---|
| 391 | while (0) |
|---|
| 392 | |
|---|
| 393 | #define _FP_MUL_MEAT_DW_2_gmp(wfracbits, R, X, Y) \ |
|---|
| 394 | do \ |
|---|
| 395 | { \ |
|---|
| 396 | _FP_W_TYPE _FP_MUL_MEAT_DW_2_gmp_x[2]; \ |
|---|
| 397 | _FP_W_TYPE _FP_MUL_MEAT_DW_2_gmp_y[2]; \ |
|---|
| 398 | _FP_MUL_MEAT_DW_2_gmp_x[0] = X##_f0; \ |
|---|
| 399 | _FP_MUL_MEAT_DW_2_gmp_x[1] = X##_f1; \ |
|---|
| 400 | _FP_MUL_MEAT_DW_2_gmp_y[0] = Y##_f0; \ |
|---|
| 401 | _FP_MUL_MEAT_DW_2_gmp_y[1] = Y##_f1; \ |
|---|
| 402 | \ |
|---|
| 403 | mpn_mul_n (R##_f, _FP_MUL_MEAT_DW_2_gmp_x, \ |
|---|
| 404 | _FP_MUL_MEAT_DW_2_gmp_y, 2); \ |
|---|
| 405 | } \ |
|---|
| 406 | while (0) |
|---|
| 407 | |
|---|
| 408 | #define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y) \ |
|---|
| 409 | do \ |
|---|
| 410 | { \ |
|---|
| 411 | _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_gmp_z); \ |
|---|
| 412 | \ |
|---|
| 413 | _FP_MUL_MEAT_DW_2_gmp ((wfracbits), _FP_MUL_MEAT_2_gmp_z, X, Y); \ |
|---|
| 414 | \ |
|---|
| 415 | /* Normalize since we know where the msb of the multiplicands \ |
|---|
| 416 | were (bit B), we know that the msb of the of the product is \ |
|---|
| 417 | at either 2B or 2B-1. */ \ |
|---|
| 418 | _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_gmp_z, (wfracbits)-1, \ |
|---|
| 419 | 2*(wfracbits)); \ |
|---|
| 420 | R##_f0 = _FP_MUL_MEAT_2_gmp_z_f[0]; \ |
|---|
| 421 | R##_f1 = _FP_MUL_MEAT_2_gmp_z_f[1]; \ |
|---|
| 422 | } \ |
|---|
| 423 | while (0) |
|---|
| 424 | |
|---|
| 425 | /* Do at most 120x120=240 bits multiplication using double floating |
|---|
| 426 | point multiplication. This is useful if floating point |
|---|
| 427 | multiplication has much bigger throughput than integer multiply. |
|---|
| 428 | It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits |
|---|
| 429 | between 106 and 120 only. |
|---|
| 430 | Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set. |
|---|
| 431 | SETFETZ is a macro which will disable all FPU exceptions and set rounding |
|---|
| 432 | towards zero, RESETFE should optionally reset it back. */ |
|---|
| 433 | |
|---|
| 434 | #define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe) \ |
|---|
| 435 | do \ |
|---|
| 436 | { \ |
|---|
| 437 | static const double _const[] = \ |
|---|
| 438 | { \ |
|---|
| 439 | /* 2^-24 */ 5.9604644775390625e-08, \ |
|---|
| 440 | /* 2^-48 */ 3.5527136788005009e-15, \ |
|---|
| 441 | /* 2^-72 */ 2.1175823681357508e-22, \ |
|---|
| 442 | /* 2^-96 */ 1.2621774483536189e-29, \ |
|---|
| 443 | /* 2^28 */ 2.68435456e+08, \ |
|---|
| 444 | /* 2^4 */ 1.600000e+01, \ |
|---|
| 445 | /* 2^-20 */ 9.5367431640625e-07, \ |
|---|
| 446 | /* 2^-44 */ 5.6843418860808015e-14, \ |
|---|
| 447 | /* 2^-68 */ 3.3881317890172014e-21, \ |
|---|
| 448 | /* 2^-92 */ 2.0194839173657902e-28, \ |
|---|
| 449 | /* 2^-116 */ 1.2037062152420224e-35 \ |
|---|
| 450 | }; \ |
|---|
| 451 | double _a240, _b240, _c240, _d240, _e240, _f240, \ |
|---|
| 452 | _g240, _h240, _i240, _j240, _k240; \ |
|---|
| 453 | union { double d; UDItype i; } _l240, _m240, _n240, _o240, \ |
|---|
| 454 | _p240, _q240, _r240, _s240; \ |
|---|
| 455 | UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0; \ |
|---|
| 456 | \ |
|---|
| 457 | _FP_STATIC_ASSERT ((wfracbits) >= 106 && (wfracbits) <= 120, \ |
|---|
| 458 | "wfracbits out of range"); \ |
|---|
| 459 | \ |
|---|
| 460 | setfetz; \ |
|---|
| 461 | \ |
|---|
| 462 | _e240 = (double) (long) (X##_f0 & 0xffffff); \ |
|---|
| 463 | _j240 = (double) (long) (Y##_f0 & 0xffffff); \ |
|---|
| 464 | _d240 = (double) (long) ((X##_f0 >> 24) & 0xffffff); \ |
|---|
| 465 | _i240 = (double) (long) ((Y##_f0 >> 24) & 0xffffff); \ |
|---|
| 466 | _c240 = (double) (long) (((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48)); \ |
|---|
| 467 | _h240 = (double) (long) (((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48)); \ |
|---|
| 468 | _b240 = (double) (long) ((X##_f1 >> 8) & 0xffffff); \ |
|---|
| 469 | _g240 = (double) (long) ((Y##_f1 >> 8) & 0xffffff); \ |
|---|
| 470 | _a240 = (double) (long) (X##_f1 >> 32); \ |
|---|
| 471 | _f240 = (double) (long) (Y##_f1 >> 32); \ |
|---|
| 472 | _e240 *= _const[3]; \ |
|---|
| 473 | _j240 *= _const[3]; \ |
|---|
| 474 | _d240 *= _const[2]; \ |
|---|
| 475 | _i240 *= _const[2]; \ |
|---|
| 476 | _c240 *= _const[1]; \ |
|---|
| 477 | _h240 *= _const[1]; \ |
|---|
| 478 | _b240 *= _const[0]; \ |
|---|
| 479 | _g240 *= _const[0]; \ |
|---|
| 480 | _s240.d = _e240*_j240; \ |
|---|
| 481 | _r240.d = _d240*_j240 + _e240*_i240; \ |
|---|
| 482 | _q240.d = _c240*_j240 + _d240*_i240 + _e240*_h240; \ |
|---|
| 483 | _p240.d = _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240; \ |
|---|
| 484 | _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240; \ |
|---|
| 485 | _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240; \ |
|---|
| 486 | _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240; \ |
|---|
| 487 | _l240.d = _a240*_g240 + _b240*_f240; \ |
|---|
| 488 | _k240 = _a240*_f240; \ |
|---|
| 489 | _r240.d += _s240.d; \ |
|---|
| 490 | _q240.d += _r240.d; \ |
|---|
| 491 | _p240.d += _q240.d; \ |
|---|
| 492 | _o240.d += _p240.d; \ |
|---|
| 493 | _n240.d += _o240.d; \ |
|---|
| 494 | _m240.d += _n240.d; \ |
|---|
| 495 | _l240.d += _m240.d; \ |
|---|
| 496 | _k240 += _l240.d; \ |
|---|
| 497 | _s240.d -= ((_const[10]+_s240.d)-_const[10]); \ |
|---|
| 498 | _r240.d -= ((_const[9]+_r240.d)-_const[9]); \ |
|---|
| 499 | _q240.d -= ((_const[8]+_q240.d)-_const[8]); \ |
|---|
| 500 | _p240.d -= ((_const[7]+_p240.d)-_const[7]); \ |
|---|
| 501 | _o240.d += _const[7]; \ |
|---|
| 502 | _n240.d += _const[6]; \ |
|---|
| 503 | _m240.d += _const[5]; \ |
|---|
| 504 | _l240.d += _const[4]; \ |
|---|
| 505 | if (_s240.d != 0.0) \ |
|---|
| 506 | _y240 = 1; \ |
|---|
| 507 | if (_r240.d != 0.0) \ |
|---|
| 508 | _y240 = 1; \ |
|---|
| 509 | if (_q240.d != 0.0) \ |
|---|
| 510 | _y240 = 1; \ |
|---|
| 511 | if (_p240.d != 0.0) \ |
|---|
| 512 | _y240 = 1; \ |
|---|
| 513 | _t240 = (DItype) _k240; \ |
|---|
| 514 | _u240 = _l240.i; \ |
|---|
| 515 | _v240 = _m240.i; \ |
|---|
| 516 | _w240 = _n240.i; \ |
|---|
| 517 | _x240 = _o240.i; \ |
|---|
| 518 | R##_f1 = ((_t240 << (128 - (wfracbits - 1))) \ |
|---|
| 519 | | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104))); \ |
|---|
| 520 | R##_f0 = (((_u240 & 0xffffff) << (168 - (wfracbits - 1))) \ |
|---|
| 521 | | ((_v240 & 0xffffff) << (144 - (wfracbits - 1))) \ |
|---|
| 522 | | ((_w240 & 0xffffff) << (120 - (wfracbits - 1))) \ |
|---|
| 523 | | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96)) \ |
|---|
| 524 | | _y240); \ |
|---|
| 525 | resetfe; \ |
|---|
| 526 | } \ |
|---|
| 527 | while (0) |
|---|
| 528 | |
|---|
| 529 | /* Division algorithms: */ |
|---|
| 530 | |
|---|
| 531 | #define _FP_DIV_MEAT_2_udiv(fs, R, X, Y) \ |
|---|
| 532 | do \ |
|---|
| 533 | { \ |
|---|
| 534 | _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f2; \ |
|---|
| 535 | _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f1; \ |
|---|
| 536 | _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f0; \ |
|---|
| 537 | _FP_W_TYPE _FP_DIV_MEAT_2_udiv_r_f1; \ |
|---|
| 538 | _FP_W_TYPE _FP_DIV_MEAT_2_udiv_r_f0; \ |
|---|
| 539 | _FP_W_TYPE _FP_DIV_MEAT_2_udiv_m_f1; \ |
|---|
| 540 | _FP_W_TYPE _FP_DIV_MEAT_2_udiv_m_f0; \ |
|---|
| 541 | if (_FP_FRAC_GE_2 (X, Y)) \ |
|---|
| 542 | { \ |
|---|
| 543 | _FP_DIV_MEAT_2_udiv_n_f2 = X##_f1 >> 1; \ |
|---|
| 544 | _FP_DIV_MEAT_2_udiv_n_f1 \ |
|---|
| 545 | = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \ |
|---|
| 546 | _FP_DIV_MEAT_2_udiv_n_f0 \ |
|---|
| 547 | = X##_f0 << (_FP_W_TYPE_SIZE - 1); \ |
|---|
| 548 | } \ |
|---|
| 549 | else \ |
|---|
| 550 | { \ |
|---|
| 551 | R##_e--; \ |
|---|
| 552 | _FP_DIV_MEAT_2_udiv_n_f2 = X##_f1; \ |
|---|
| 553 | _FP_DIV_MEAT_2_udiv_n_f1 = X##_f0; \ |
|---|
| 554 | _FP_DIV_MEAT_2_udiv_n_f0 = 0; \ |
|---|
| 555 | } \ |
|---|
| 556 | \ |
|---|
| 557 | /* Normalize, i.e. make the most significant bit of the \ |
|---|
| 558 | denominator set. */ \ |
|---|
| 559 | _FP_FRAC_SLL_2 (Y, _FP_WFRACXBITS_##fs); \ |
|---|
| 560 | \ |
|---|
| 561 | udiv_qrnnd (R##_f1, _FP_DIV_MEAT_2_udiv_r_f1, \ |
|---|
| 562 | _FP_DIV_MEAT_2_udiv_n_f2, _FP_DIV_MEAT_2_udiv_n_f1, \ |
|---|
| 563 | Y##_f1); \ |
|---|
| 564 | umul_ppmm (_FP_DIV_MEAT_2_udiv_m_f1, _FP_DIV_MEAT_2_udiv_m_f0, \ |
|---|
| 565 | R##_f1, Y##_f0); \ |
|---|
| 566 | _FP_DIV_MEAT_2_udiv_r_f0 = _FP_DIV_MEAT_2_udiv_n_f0; \ |
|---|
| 567 | if (_FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, _FP_DIV_MEAT_2_udiv_r)) \ |
|---|
| 568 | { \ |
|---|
| 569 | R##_f1--; \ |
|---|
| 570 | _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \ |
|---|
| 571 | _FP_DIV_MEAT_2_udiv_r); \ |
|---|
| 572 | if (_FP_FRAC_GE_2 (_FP_DIV_MEAT_2_udiv_r, Y) \ |
|---|
| 573 | && _FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, \ |
|---|
| 574 | _FP_DIV_MEAT_2_udiv_r)) \ |
|---|
| 575 | { \ |
|---|
| 576 | R##_f1--; \ |
|---|
| 577 | _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \ |
|---|
| 578 | _FP_DIV_MEAT_2_udiv_r); \ |
|---|
| 579 | } \ |
|---|
| 580 | } \ |
|---|
| 581 | _FP_FRAC_DEC_2 (_FP_DIV_MEAT_2_udiv_r, _FP_DIV_MEAT_2_udiv_m); \ |
|---|
| 582 | \ |
|---|
| 583 | if (_FP_DIV_MEAT_2_udiv_r_f1 == Y##_f1) \ |
|---|
| 584 | { \ |
|---|
| 585 | /* This is a special case, not an optimization \ |
|---|
| 586 | (_FP_DIV_MEAT_2_udiv_r/Y##_f1 would not fit into UWtype). \ |
|---|
| 587 | As _FP_DIV_MEAT_2_udiv_r is guaranteed to be < Y, \ |
|---|
| 588 | R##_f0 can be either (UWtype)-1 or (UWtype)-2. But as we \ |
|---|
| 589 | know what kind of bits it is (sticky, guard, round), \ |
|---|
| 590 | we don't care. We also don't care what the reminder is, \ |
|---|
| 591 | because the guard bit will be set anyway. -jj */ \ |
|---|
| 592 | R##_f0 = -1; \ |
|---|
| 593 | } \ |
|---|
| 594 | else \ |
|---|
| 595 | { \ |
|---|
| 596 | udiv_qrnnd (R##_f0, _FP_DIV_MEAT_2_udiv_r_f1, \ |
|---|
| 597 | _FP_DIV_MEAT_2_udiv_r_f1, \ |
|---|
| 598 | _FP_DIV_MEAT_2_udiv_r_f0, Y##_f1); \ |
|---|
| 599 | umul_ppmm (_FP_DIV_MEAT_2_udiv_m_f1, \ |
|---|
| 600 | _FP_DIV_MEAT_2_udiv_m_f0, R##_f0, Y##_f0); \ |
|---|
| 601 | _FP_DIV_MEAT_2_udiv_r_f0 = 0; \ |
|---|
| 602 | if (_FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, \ |
|---|
| 603 | _FP_DIV_MEAT_2_udiv_r)) \ |
|---|
| 604 | { \ |
|---|
| 605 | R##_f0--; \ |
|---|
| 606 | _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \ |
|---|
| 607 | _FP_DIV_MEAT_2_udiv_r); \ |
|---|
| 608 | if (_FP_FRAC_GE_2 (_FP_DIV_MEAT_2_udiv_r, Y) \ |
|---|
| 609 | && _FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, \ |
|---|
| 610 | _FP_DIV_MEAT_2_udiv_r)) \ |
|---|
| 611 | { \ |
|---|
| 612 | R##_f0--; \ |
|---|
| 613 | _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \ |
|---|
| 614 | _FP_DIV_MEAT_2_udiv_r); \ |
|---|
| 615 | } \ |
|---|
| 616 | } \ |
|---|
| 617 | if (!_FP_FRAC_EQ_2 (_FP_DIV_MEAT_2_udiv_r, \ |
|---|
| 618 | _FP_DIV_MEAT_2_udiv_m)) \ |
|---|
| 619 | R##_f0 |= _FP_WORK_STICKY; \ |
|---|
| 620 | } \ |
|---|
| 621 | } \ |
|---|
| 622 | while (0) |
|---|
| 623 | |
|---|
| 624 | |
|---|
| 625 | /* Square root algorithms: |
|---|
| 626 | We have just one right now, maybe Newton approximation |
|---|
| 627 | should be added for those machines where division is fast. */ |
|---|
| 628 | |
|---|
| 629 | #define _FP_SQRT_MEAT_2(R, S, T, X, q) \ |
|---|
| 630 | do \ |
|---|
| 631 | { \ |
|---|
| 632 | while (q) \ |
|---|
| 633 | { \ |
|---|
| 634 | T##_f1 = S##_f1 + (q); \ |
|---|
| 635 | if (T##_f1 <= X##_f1) \ |
|---|
| 636 | { \ |
|---|
| 637 | S##_f1 = T##_f1 + (q); \ |
|---|
| 638 | X##_f1 -= T##_f1; \ |
|---|
| 639 | R##_f1 += (q); \ |
|---|
| 640 | } \ |
|---|
| 641 | _FP_FRAC_SLL_2 (X, 1); \ |
|---|
| 642 | (q) >>= 1; \ |
|---|
| 643 | } \ |
|---|
| 644 | (q) = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \ |
|---|
| 645 | while ((q) != _FP_WORK_ROUND) \ |
|---|
| 646 | { \ |
|---|
| 647 | T##_f0 = S##_f0 + (q); \ |
|---|
| 648 | T##_f1 = S##_f1; \ |
|---|
| 649 | if (T##_f1 < X##_f1 \ |
|---|
| 650 | || (T##_f1 == X##_f1 && T##_f0 <= X##_f0)) \ |
|---|
| 651 | { \ |
|---|
| 652 | S##_f0 = T##_f0 + (q); \ |
|---|
| 653 | S##_f1 += (T##_f0 > S##_f0); \ |
|---|
| 654 | _FP_FRAC_DEC_2 (X, T); \ |
|---|
| 655 | R##_f0 += (q); \ |
|---|
| 656 | } \ |
|---|
| 657 | _FP_FRAC_SLL_2 (X, 1); \ |
|---|
| 658 | (q) >>= 1; \ |
|---|
| 659 | } \ |
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| 660 | if (X##_f0 | X##_f1) \ |
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| 661 | { \ |
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| 662 | if (S##_f1 < X##_f1 \ |
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| 663 | || (S##_f1 == X##_f1 && S##_f0 < X##_f0)) \ |
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| 664 | R##_f0 |= _FP_WORK_ROUND; \ |
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| 665 | R##_f0 |= _FP_WORK_STICKY; \ |
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| 666 | } \ |
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| 667 | } \ |
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| 668 | while (0) |
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| 669 | |
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| 670 | |
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| 671 | /* Assembly/disassembly for converting to/from integral types. |
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| 672 | No shifting or overflow handled here. */ |
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| 673 | |
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| 674 | #define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \ |
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| 675 | (void) (((rsize) <= _FP_W_TYPE_SIZE) \ |
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| 676 | ? ({ (r) = X##_f0; }) \ |
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| 677 | : ({ \ |
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| 678 | (r) = X##_f1; \ |
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| 679 | (r) <<= _FP_W_TYPE_SIZE; \ |
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| 680 | (r) += X##_f0; \ |
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| 681 | })) |
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| 682 | |
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| 683 | #define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \ |
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| 684 | do \ |
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| 685 | { \ |
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| 686 | X##_f0 = (r); \ |
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| 687 | X##_f1 = ((rsize) <= _FP_W_TYPE_SIZE \ |
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| 688 | ? 0 \ |
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| 689 | : (r) >> _FP_W_TYPE_SIZE); \ |
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| 690 | } \ |
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| 691 | while (0) |
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| 692 | |
|---|
| 693 | /* Convert FP values between word sizes. */ |
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| 694 | |
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| 695 | #define _FP_FRAC_COPY_1_2(D, S) (D##_f = S##_f0) |
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| 696 | |
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| 697 | #define _FP_FRAC_COPY_2_1(D, S) ((D##_f0 = S##_f), (D##_f1 = 0)) |
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| 698 | |
|---|
| 699 | #define _FP_FRAC_COPY_2_2(D, S) _FP_FRAC_COPY_2 (D, S) |
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| 700 | |
|---|
| 701 | #endif /* !SOFT_FP_OP_2_H */ |
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| 702 | |
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