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/* Software floating-point emulation. |
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Basic one-word fraction declaration and manipulation. |
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Copyright (C) 1997-2014 Free Software Foundation, Inc. |
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This file is part of the GNU C Library. |
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Contributed by Richard Henderson (rth@cygnus.com), |
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Jakub Jelinek (jj@ultra.linux.cz), |
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David S. Miller (davem@redhat.com) and |
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Peter Maydell (pmaydell@chiark.greenend.org.uk). |
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The GNU C Library is free software; you can redistribute it and/or |
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modify it under the terms of the GNU Lesser General Public |
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License as published by the Free Software Foundation; either |
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version 2.1 of the License, or (at your option) any later version. |
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In addition to the permissions in the GNU Lesser General Public |
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License, the Free Software Foundation gives you unlimited |
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permission to link the compiled version of this file into |
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combinations with other programs, and to distribute those |
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combinations without any restriction coming from the use of this |
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file. (The Lesser General Public License restrictions do apply in |
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other respects; for example, they cover modification of the file, |
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and distribution when not linked into a combine executable.) |
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The GNU C Library is distributed in the hope that it will be useful, |
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but WITHOUT ANY WARRANTY; without even the implied warranty of |
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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Lesser General Public License for more details. |
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You should have received a copy of the GNU Lesser General Public |
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License along with the GNU C Library; if not, see |
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. */ |
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#define _FP_FRAC_DECL_1(X) _FP_W_TYPE X##_f |
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#define _FP_FRAC_COPY_1(D, S) (D##_f = S##_f) |
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#define _FP_FRAC_SET_1(X, I) (X##_f = I) |
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#define _FP_FRAC_HIGH_1(X) (X##_f) |
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#define _FP_FRAC_LOW_1(X) (X##_f) |
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#define _FP_FRAC_WORD_1(X, w) (X##_f) |
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#define _FP_FRAC_ADDI_1(X, I) (X##_f += I) |
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#define _FP_FRAC_SLL_1(X, N) \ |
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do \ |
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{ \ |
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if (__builtin_constant_p (N) && (N) == 1) \ |
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X##_f += X##_f; \ |
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else \ |
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X##_f <<= (N); \ |
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} \ |
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while (0) |
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#define _FP_FRAC_SRL_1(X, N) (X##_f >>= N) |
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/* Right shift with sticky-lsb. */ |
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#define _FP_FRAC_SRST_1(X, S, N, sz) __FP_FRAC_SRST_1 (X##_f, S, (N), (sz)) |
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#define _FP_FRAC_SRS_1(X, N, sz) __FP_FRAC_SRS_1 (X##_f, (N), (sz)) |
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#define __FP_FRAC_SRST_1(X, S, N, sz) \ |
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do \ |
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{ \ |
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S = (__builtin_constant_p (N) && (N) == 1 \ |
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? X & 1 \ |
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: (X << (_FP_W_TYPE_SIZE - (N))) != 0); \ |
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X = X >> (N); \ |
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} \ |
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while (0) |
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#define __FP_FRAC_SRS_1(X, N, sz) \ |
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(X = (X >> (N) | (__builtin_constant_p (N) && (N) == 1 \ |
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? X & 1 \ |
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: (X << (_FP_W_TYPE_SIZE - (N))) != 0))) |
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#define _FP_FRAC_ADD_1(R, X, Y) (R##_f = X##_f + Y##_f) |
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#define _FP_FRAC_SUB_1(R, X, Y) (R##_f = X##_f - Y##_f) |
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#define _FP_FRAC_DEC_1(X, Y) (X##_f -= Y##_f) |
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#define _FP_FRAC_CLZ_1(z, X) __FP_CLZ ((z), X##_f) |
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/* Predicates. */ |
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#define _FP_FRAC_NEGP_1(X) ((_FP_WS_TYPE) X##_f < 0) |
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#define _FP_FRAC_ZEROP_1(X) (X##_f == 0) |
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#define _FP_FRAC_OVERP_1(fs, X) (X##_f & _FP_OVERFLOW_##fs) |
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#define _FP_FRAC_CLEAR_OVERP_1(fs, X) (X##_f &= ~_FP_OVERFLOW_##fs) |
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#define _FP_FRAC_HIGHBIT_DW_1(fs, X) (X##_f & _FP_HIGHBIT_DW_##fs) |
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#define _FP_FRAC_EQ_1(X, Y) (X##_f == Y##_f) |
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#define _FP_FRAC_GE_1(X, Y) (X##_f >= Y##_f) |
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#define _FP_FRAC_GT_1(X, Y) (X##_f > Y##_f) |
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#define _FP_ZEROFRAC_1 0 |
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#define _FP_MINFRAC_1 1 |
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#define _FP_MAXFRAC_1 (~(_FP_WS_TYPE) 0) |
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/* Unpack the raw bits of a native fp value. Do not classify or |
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normalize the data. */ |
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#define _FP_UNPACK_RAW_1(fs, X, val) \ |
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do \ |
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{ \ |
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union _FP_UNION_##fs _FP_UNPACK_RAW_1_flo; \ |
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_FP_UNPACK_RAW_1_flo.flt = (val); \ |
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\ |
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X##_f = _FP_UNPACK_RAW_1_flo.bits.frac; \ |
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X##_e = _FP_UNPACK_RAW_1_flo.bits.exp; \ |
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X##_s = _FP_UNPACK_RAW_1_flo.bits.sign; \ |
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} \ |
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while (0) |
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#define _FP_UNPACK_RAW_1_P(fs, X, val) \ |
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do \ |
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{ \ |
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union _FP_UNION_##fs *_FP_UNPACK_RAW_1_P_flo \ |
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= (union _FP_UNION_##fs *) (val); \ |
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\ |
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X##_f = _FP_UNPACK_RAW_1_P_flo->bits.frac; \ |
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X##_e = _FP_UNPACK_RAW_1_P_flo->bits.exp; \ |
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X##_s = _FP_UNPACK_RAW_1_P_flo->bits.sign; \ |
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} \ |
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while (0) |
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/* Repack the raw bits of a native fp value. */ |
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#define _FP_PACK_RAW_1(fs, val, X) \ |
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do \ |
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{ \ |
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union _FP_UNION_##fs _FP_PACK_RAW_1_flo; \ |
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\ |
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_FP_PACK_RAW_1_flo.bits.frac = X##_f; \ |
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_FP_PACK_RAW_1_flo.bits.exp = X##_e; \ |
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_FP_PACK_RAW_1_flo.bits.sign = X##_s; \ |
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\ |
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(val) = _FP_PACK_RAW_1_flo.flt; \ |
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} \ |
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while (0) |
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#define _FP_PACK_RAW_1_P(fs, val, X) \ |
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do \ |
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{ \ |
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union _FP_UNION_##fs *_FP_PACK_RAW_1_P_flo \ |
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= (union _FP_UNION_##fs *) (val); \ |
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\ |
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_FP_PACK_RAW_1_P_flo->bits.frac = X##_f; \ |
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_FP_PACK_RAW_1_P_flo->bits.exp = X##_e; \ |
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_FP_PACK_RAW_1_P_flo->bits.sign = X##_s; \ |
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} \ |
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while (0) |
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/* Multiplication algorithms: */ |
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/* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the |
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multiplication immediately. */ |
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#define _FP_MUL_MEAT_DW_1_imm(wfracbits, R, X, Y) \ |
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do \ |
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{ \ |
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R##_f = X##_f * Y##_f; \ |
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} \ |
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while (0) |
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#define _FP_MUL_MEAT_1_imm(wfracbits, R, X, Y) \ |
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do \ |
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{ \ |
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_FP_MUL_MEAT_DW_1_imm ((wfracbits), R, X, Y); \ |
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/* Normalize since we know where the msb of the multiplicands \ |
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were (bit B), we know that the msb of the of the product is \ |
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at either 2B or 2B-1. */ \ |
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_FP_FRAC_SRS_1 (R, (wfracbits)-1, 2*(wfracbits)); \ |
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} \ |
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while (0) |
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/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ |
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#define _FP_MUL_MEAT_DW_1_wide(wfracbits, R, X, Y, doit) \ |
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do \ |
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{ \ |
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doit (R##_f1, R##_f0, X##_f, Y##_f); \ |
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} \ |
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while (0) |
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#define _FP_MUL_MEAT_1_wide(wfracbits, R, X, Y, doit) \ |
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do \ |
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{ \ |
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_FP_FRAC_DECL_2 (_FP_MUL_MEAT_1_wide_Z); \ |
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_FP_MUL_MEAT_DW_1_wide ((wfracbits), _FP_MUL_MEAT_1_wide_Z, \ |
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X, Y, doit); \ |
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/* Normalize since we know where the msb of the multiplicands \ |
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were (bit B), we know that the msb of the of the product is \ |
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at either 2B or 2B-1. */ \ |
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_FP_FRAC_SRS_2 (_FP_MUL_MEAT_1_wide_Z, (wfracbits)-1, \ |
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2*(wfracbits)); \ |
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R##_f = _FP_MUL_MEAT_1_wide_Z_f0; \ |
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} \ |
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while (0) |
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/* Finally, a simple widening multiply algorithm. What fun! */ |
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#define _FP_MUL_MEAT_DW_1_hard(wfracbits, R, X, Y) \ |
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do \ |
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{ \ |
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_FP_W_TYPE _FP_MUL_MEAT_DW_1_hard_xh, _FP_MUL_MEAT_DW_1_hard_xl; \ |
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_FP_W_TYPE _FP_MUL_MEAT_DW_1_hard_yh, _FP_MUL_MEAT_DW_1_hard_yl; \ |
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_FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_1_hard_a); \ |
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\ |
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/* Split the words in half. */ \ |
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_FP_MUL_MEAT_DW_1_hard_xh = X##_f >> (_FP_W_TYPE_SIZE/2); \ |
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_FP_MUL_MEAT_DW_1_hard_xl \ |
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= X##_f & (((_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2)) - 1); \ |
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_FP_MUL_MEAT_DW_1_hard_yh = Y##_f >> (_FP_W_TYPE_SIZE/2); \ |
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_FP_MUL_MEAT_DW_1_hard_yl \ |
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= Y##_f & (((_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2)) - 1); \ |
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\ |
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/* Multiply the pieces. */ \ |
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R##_f0 = _FP_MUL_MEAT_DW_1_hard_xl * _FP_MUL_MEAT_DW_1_hard_yl; \ |
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_FP_MUL_MEAT_DW_1_hard_a_f0 \ |
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= _FP_MUL_MEAT_DW_1_hard_xh * _FP_MUL_MEAT_DW_1_hard_yl; \ |
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_FP_MUL_MEAT_DW_1_hard_a_f1 \ |
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= _FP_MUL_MEAT_DW_1_hard_xl * _FP_MUL_MEAT_DW_1_hard_yh; \ |
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R##_f1 = _FP_MUL_MEAT_DW_1_hard_xh * _FP_MUL_MEAT_DW_1_hard_yh; \ |
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\ |
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/* Reassemble into two full words. */ \ |
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if ((_FP_MUL_MEAT_DW_1_hard_a_f0 += _FP_MUL_MEAT_DW_1_hard_a_f1) \ |
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< _FP_MUL_MEAT_DW_1_hard_a_f1) \ |
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R##_f1 += (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2); \ |
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_FP_MUL_MEAT_DW_1_hard_a_f1 \ |
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= _FP_MUL_MEAT_DW_1_hard_a_f0 >> (_FP_W_TYPE_SIZE/2); \ |
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_FP_MUL_MEAT_DW_1_hard_a_f0 \ |
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= _FP_MUL_MEAT_DW_1_hard_a_f0 << (_FP_W_TYPE_SIZE/2); \ |
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_FP_FRAC_ADD_2 (R, R, _FP_MUL_MEAT_DW_1_hard_a); \ |
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} \ |
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while (0) |
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#define _FP_MUL_MEAT_1_hard(wfracbits, R, X, Y) \ |
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do \ |
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{ \ |
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_FP_FRAC_DECL_2 (_FP_MUL_MEAT_1_hard_z); \ |
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_FP_MUL_MEAT_DW_1_hard ((wfracbits), \ |
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_FP_MUL_MEAT_1_hard_z, X, Y); \ |
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\ |
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/* Normalize. */ \ |
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_FP_FRAC_SRS_2 (_FP_MUL_MEAT_1_hard_z, \ |
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(wfracbits) - 1, 2*(wfracbits)); \ |
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R##_f = _FP_MUL_MEAT_1_hard_z_f0; \ |
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} \ |
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while (0) |
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/* Division algorithms: */ |
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/* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the |
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division immediately. Give this macro either _FP_DIV_HELP_imm for |
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C primitives or _FP_DIV_HELP_ldiv for the ISO function. Which you |
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choose will depend on what the compiler does with divrem4. */ |
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#define _FP_DIV_MEAT_1_imm(fs, R, X, Y, doit) \ |
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do \ |
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{ \ |
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_FP_W_TYPE _FP_DIV_MEAT_1_imm_q, _FP_DIV_MEAT_1_imm_r; \ |
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X##_f <<= (X##_f < Y##_f \ |
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? R##_e--, _FP_WFRACBITS_##fs \ |
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: _FP_WFRACBITS_##fs - 1); \ |
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doit (_FP_DIV_MEAT_1_imm_q, _FP_DIV_MEAT_1_imm_r, X##_f, Y##_f); \ |
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R##_f = _FP_DIV_MEAT_1_imm_q | (_FP_DIV_MEAT_1_imm_r != 0); \ |
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} \ |
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while (0) |
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/* GCC's longlong.h defines a 2W / 1W => (1W,1W) primitive udiv_qrnnd |
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that may be useful in this situation. This first is for a primitive |
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that requires normalization, the second for one that does not. Look |
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for UDIV_NEEDS_NORMALIZATION to tell which your machine needs. */ |
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#define _FP_DIV_MEAT_1_udiv_norm(fs, R, X, Y) \ |
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do \ |
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{ \ |
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_FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_nh; \ |
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_FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_nl; \ |
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_FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_q; \ |
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_FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_r; \ |
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_FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_y; \ |
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\ |
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/* Normalize Y -- i.e. make the most significant bit set. */ \ |
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_FP_DIV_MEAT_1_udiv_norm_y = Y##_f << _FP_WFRACXBITS_##fs; \ |
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\ |
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/* Shift X op correspondingly high, that is, up one full word. */ \ |
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if (X##_f < Y##_f) \ |
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{ \ |
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R##_e--; \ |
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_FP_DIV_MEAT_1_udiv_norm_nl = 0; \ |
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_FP_DIV_MEAT_1_udiv_norm_nh = X##_f; \ |
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} \ |
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else \ |
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{ \ |
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_FP_DIV_MEAT_1_udiv_norm_nl = X##_f << (_FP_W_TYPE_SIZE - 1); \ |
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_FP_DIV_MEAT_1_udiv_norm_nh = X##_f >> 1; \ |
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} \ |
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\ |
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udiv_qrnnd (_FP_DIV_MEAT_1_udiv_norm_q, \ |
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_FP_DIV_MEAT_1_udiv_norm_r, \ |
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_FP_DIV_MEAT_1_udiv_norm_nh, \ |
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_FP_DIV_MEAT_1_udiv_norm_nl, \ |
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_FP_DIV_MEAT_1_udiv_norm_y); \ |
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R##_f = (_FP_DIV_MEAT_1_udiv_norm_q \ |
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| (_FP_DIV_MEAT_1_udiv_norm_r != 0)); \ |
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} \ |
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while (0) |
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#define _FP_DIV_MEAT_1_udiv(fs, R, X, Y) \ |
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do \ |
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{ \ |
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_FP_W_TYPE _FP_DIV_MEAT_1_udiv_nh, _FP_DIV_MEAT_1_udiv_nl; \ |
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307 |
_FP_W_TYPE _FP_DIV_MEAT_1_udiv_q, _FP_DIV_MEAT_1_udiv_r; \ |
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308 |
if (X##_f < Y##_f) \ |
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309 |
{ \ |
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310 |
R##_e--; \ |
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311 |
_FP_DIV_MEAT_1_udiv_nl = X##_f << _FP_WFRACBITS_##fs; \ |
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312 |
_FP_DIV_MEAT_1_udiv_nh = X##_f >> _FP_WFRACXBITS_##fs; \ |
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313 |
} \ |
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314 |
else \ |
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315 |
{ \ |
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316 |
_FP_DIV_MEAT_1_udiv_nl = X##_f << (_FP_WFRACBITS_##fs - 1); \ |
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317 |
_FP_DIV_MEAT_1_udiv_nh = X##_f >> (_FP_WFRACXBITS_##fs + 1); \ |
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318 |
} \ |
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319 |
udiv_qrnnd (_FP_DIV_MEAT_1_udiv_q, _FP_DIV_MEAT_1_udiv_r, \ |
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320 |
_FP_DIV_MEAT_1_udiv_nh, _FP_DIV_MEAT_1_udiv_nl, \ |
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321 |
Y##_f); \ |
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322 |
R##_f = _FP_DIV_MEAT_1_udiv_q | (_FP_DIV_MEAT_1_udiv_r != 0); \ |
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323 |
} \ |
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324 |
while (0) |
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325 |
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326 |
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327 |
/* Square root algorithms: |
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328 |
We have just one right now, maybe Newton approximation |
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329 |
should be added for those machines where division is fast. */ |
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330 |
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331 |
#define _FP_SQRT_MEAT_1(R, S, T, X, q) \ |
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332 |
do \ |
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|
333 |
{ \ |
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334 |
while ((q) != _FP_WORK_ROUND) \ |
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|
335 |
{ \ |
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|
336 |
T##_f = S##_f + (q); \ |
|
|
337 |
if (T##_f <= X##_f) \ |
|
|
338 |
{ \ |
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|
339 |
S##_f = T##_f + (q); \ |
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|
340 |
X##_f -= T##_f; \ |
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|
341 |
R##_f += (q); \ |
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|
342 |
} \ |
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|
343 |
_FP_FRAC_SLL_1 (X, 1); \ |
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|
344 |
(q) >>= 1; \ |
|
|
345 |
} \ |
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|
346 |
if (X##_f) \ |
|
|
347 |
{ \ |
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|
348 |
if (S##_f < X##_f) \ |
|
|
349 |
R##_f |= _FP_WORK_ROUND; \ |
|
|
350 |
R##_f |= _FP_WORK_STICKY; \ |
|
|
351 |
} \ |
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|
352 |
} \ |
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|
353 |
while (0) |
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|
354 |
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|
355 |
/* Assembly/disassembly for converting to/from integral types. |
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|
356 |
No shifting or overflow handled here. */ |
|
|
357 |
|
|
|
358 |
#define _FP_FRAC_ASSEMBLE_1(r, X, rsize) ((r) = X##_f) |
|
|
359 |
#define _FP_FRAC_DISASSEMBLE_1(X, r, rsize) (X##_f = (r)) |
|
|
360 |
|
|
|
361 |
|
|
|
362 |
/* Convert FP values between word sizes. */ |
|
|
363 |
|
|
|
364 |
#define _FP_FRAC_COPY_1_1(D, S) (D##_f = S##_f) |