| /* Software floating-point emulation. |
| Basic two-word fraction declaration and manipulation. |
| Copyright (C) 1997-2022 Free Software Foundation, Inc. |
| This file is part of the GNU C Library. |
| |
| The GNU C Library is free software; you can redistribute it and/or |
| modify it under the terms of the GNU Lesser General Public |
| License as published by the Free Software Foundation; either |
| version 2.1 of the License, or (at your option) any later version. |
| |
| In addition to the permissions in the GNU Lesser General Public |
| License, the Free Software Foundation gives you unlimited |
| permission to link the compiled version of this file into |
| combinations with other programs, and to distribute those |
| combinations without any restriction coming from the use of this |
| file. (The Lesser General Public License restrictions do apply in |
| other respects; for example, they cover modification of the file, |
| and distribution when not linked into a combine executable.) |
| |
| The GNU C Library is distributed in the hope that it will be useful, |
| but WITHOUT ANY WARRANTY; without even the implied warranty of |
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| Lesser General Public License for more details. |
| |
| You should have received a copy of the GNU Lesser General Public |
| License along with the GNU C Library; if not, see |
| <https://www.gnu.org/licenses/>. */ |
| |
| #ifndef SOFT_FP_OP_2_H |
| #define SOFT_FP_OP_2_H 1 |
| |
| #define _FP_FRAC_DECL_2(X) \ |
| _FP_W_TYPE X##_f0 _FP_ZERO_INIT, X##_f1 _FP_ZERO_INIT |
| #define _FP_FRAC_COPY_2(D, S) (D##_f0 = S##_f0, D##_f1 = S##_f1) |
| #define _FP_FRAC_SET_2(X, I) __FP_FRAC_SET_2 (X, I) |
| #define _FP_FRAC_HIGH_2(X) (X##_f1) |
| #define _FP_FRAC_LOW_2(X) (X##_f0) |
| #define _FP_FRAC_WORD_2(X, w) (X##_f##w) |
| |
| #define _FP_FRAC_SLL_2(X, N) \ |
| (void) (((N) < _FP_W_TYPE_SIZE) \ |
| ? ({ \ |
| if (__builtin_constant_p (N) && (N) == 1) \ |
| { \ |
| X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE) (X##_f0)) < 0); \ |
| X##_f0 += X##_f0; \ |
| } \ |
| else \ |
| { \ |
| X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \ |
| X##_f0 <<= (N); \ |
| } \ |
| 0; \ |
| }) \ |
| : ({ \ |
| X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \ |
| X##_f0 = 0; \ |
| })) |
| |
| |
| #define _FP_FRAC_SRL_2(X, N) \ |
| (void) (((N) < _FP_W_TYPE_SIZE) \ |
| ? ({ \ |
| X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \ |
| X##_f1 >>= (N); \ |
| }) \ |
| : ({ \ |
| X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \ |
| X##_f1 = 0; \ |
| })) |
| |
| /* Right shift with sticky-lsb. */ |
| #define _FP_FRAC_SRST_2(X, S, N, sz) \ |
| (void) (((N) < _FP_W_TYPE_SIZE) \ |
| ? ({ \ |
| S = (__builtin_constant_p (N) && (N) == 1 \ |
| ? X##_f0 & 1 \ |
| : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0); \ |
| X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N)); \ |
| X##_f1 >>= (N); \ |
| }) \ |
| : ({ \ |
| S = ((((N) == _FP_W_TYPE_SIZE \ |
| ? 0 \ |
| : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \ |
| | X##_f0) != 0); \ |
| X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE)); \ |
| X##_f1 = 0; \ |
| })) |
| |
| #define _FP_FRAC_SRS_2(X, N, sz) \ |
| (void) (((N) < _FP_W_TYPE_SIZE) \ |
| ? ({ \ |
| X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) \ |
| | (__builtin_constant_p (N) && (N) == 1 \ |
| ? X##_f0 & 1 \ |
| : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \ |
| X##_f1 >>= (N); \ |
| }) \ |
| : ({ \ |
| X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) \ |
| | ((((N) == _FP_W_TYPE_SIZE \ |
| ? 0 \ |
| : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \ |
| | X##_f0) != 0)); \ |
| X##_f1 = 0; \ |
| })) |
| |
| #define _FP_FRAC_ADDI_2(X, I) \ |
| __FP_FRAC_ADDI_2 (X##_f1, X##_f0, I) |
| |
| #define _FP_FRAC_ADD_2(R, X, Y) \ |
| __FP_FRAC_ADD_2 (R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) |
| |
| #define _FP_FRAC_SUB_2(R, X, Y) \ |
| __FP_FRAC_SUB_2 (R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) |
| |
| #define _FP_FRAC_DEC_2(X, Y) \ |
| __FP_FRAC_DEC_2 (X##_f1, X##_f0, Y##_f1, Y##_f0) |
| |
| #define _FP_FRAC_CLZ_2(R, X) \ |
| do \ |
| { \ |
| if (X##_f1) \ |
| __FP_CLZ ((R), X##_f1); \ |
| else \ |
| { \ |
| __FP_CLZ ((R), X##_f0); \ |
| (R) += _FP_W_TYPE_SIZE; \ |
| } \ |
| } \ |
| while (0) |
| |
| /* Predicates. */ |
| #define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE) X##_f1 < 0) |
| #define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0) |
| #define _FP_FRAC_OVERP_2(fs, X) (_FP_FRAC_HIGH_##fs (X) & _FP_OVERFLOW_##fs) |
| #define _FP_FRAC_CLEAR_OVERP_2(fs, X) (_FP_FRAC_HIGH_##fs (X) &= ~_FP_OVERFLOW_##fs) |
| #define _FP_FRAC_HIGHBIT_DW_2(fs, X) \ |
| (_FP_FRAC_HIGH_DW_##fs (X) & _FP_HIGHBIT_DW_##fs) |
| #define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0) |
| #define _FP_FRAC_GT_2(X, Y) \ |
| (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0)) |
| #define _FP_FRAC_GE_2(X, Y) \ |
| (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0)) |
| |
| #define _FP_ZEROFRAC_2 0, 0 |
| #define _FP_MINFRAC_2 0, 1 |
| #define _FP_MAXFRAC_2 (~(_FP_WS_TYPE) 0), (~(_FP_WS_TYPE) 0) |
| |
| /* Internals. */ |
| |
| #define __FP_FRAC_SET_2(X, I1, I0) (X##_f0 = I0, X##_f1 = I1) |
| |
| #define __FP_CLZ_2(R, xh, xl) \ |
| do \ |
| { \ |
| if (xh) \ |
| __FP_CLZ ((R), xh); \ |
| else \ |
| { \ |
| __FP_CLZ ((R), xl); \ |
| (R) += _FP_W_TYPE_SIZE; \ |
| } \ |
| } \ |
| while (0) |
| |
| #if 0 |
| |
| # ifndef __FP_FRAC_ADDI_2 |
| # define __FP_FRAC_ADDI_2(xh, xl, i) \ |
| (xh += ((xl += i) < i)) |
| # endif |
| # ifndef __FP_FRAC_ADD_2 |
| # define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \ |
| (rh = xh + yh + ((rl = xl + yl) < xl)) |
| # endif |
| # ifndef __FP_FRAC_SUB_2 |
| # define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \ |
| (rh = xh - yh - ((rl = xl - yl) > xl)) |
| # endif |
| # ifndef __FP_FRAC_DEC_2 |
| # define __FP_FRAC_DEC_2(xh, xl, yh, yl) \ |
| do \ |
| { \ |
| UWtype __FP_FRAC_DEC_2_t = xl; \ |
| xh -= yh + ((xl -= yl) > __FP_FRAC_DEC_2_t); \ |
| } \ |
| while (0) |
| # endif |
| |
| #else |
| |
| # undef __FP_FRAC_ADDI_2 |
| # define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa (xh, xl, xh, xl, 0, i) |
| # undef __FP_FRAC_ADD_2 |
| # define __FP_FRAC_ADD_2 add_ssaaaa |
| # undef __FP_FRAC_SUB_2 |
| # define __FP_FRAC_SUB_2 sub_ddmmss |
| # undef __FP_FRAC_DEC_2 |
| # define __FP_FRAC_DEC_2(xh, xl, yh, yl) \ |
| sub_ddmmss (xh, xl, xh, xl, yh, yl) |
| |
| #endif |
| |
| /* Unpack the raw bits of a native fp value. Do not classify or |
| normalize the data. */ |
| |
| #define _FP_UNPACK_RAW_2(fs, X, val) \ |
| do \ |
| { \ |
| union _FP_UNION_##fs _FP_UNPACK_RAW_2_flo; \ |
| _FP_UNPACK_RAW_2_flo.flt = (val); \ |
| \ |
| X##_f0 = _FP_UNPACK_RAW_2_flo.bits.frac0; \ |
| X##_f1 = _FP_UNPACK_RAW_2_flo.bits.frac1; \ |
| X##_e = _FP_UNPACK_RAW_2_flo.bits.exp; \ |
| X##_s = _FP_UNPACK_RAW_2_flo.bits.sign; \ |
| } \ |
| while (0) |
| |
| #define _FP_UNPACK_RAW_2_P(fs, X, val) \ |
| do \ |
| { \ |
| union _FP_UNION_##fs *_FP_UNPACK_RAW_2_P_flo \ |
| = (union _FP_UNION_##fs *) (val); \ |
| \ |
| X##_f0 = _FP_UNPACK_RAW_2_P_flo->bits.frac0; \ |
| X##_f1 = _FP_UNPACK_RAW_2_P_flo->bits.frac1; \ |
| X##_e = _FP_UNPACK_RAW_2_P_flo->bits.exp; \ |
| X##_s = _FP_UNPACK_RAW_2_P_flo->bits.sign; \ |
| } \ |
| while (0) |
| |
| |
| /* Repack the raw bits of a native fp value. */ |
| |
| #define _FP_PACK_RAW_2(fs, val, X) \ |
| do \ |
| { \ |
| union _FP_UNION_##fs _FP_PACK_RAW_2_flo; \ |
| \ |
| _FP_PACK_RAW_2_flo.bits.frac0 = X##_f0; \ |
| _FP_PACK_RAW_2_flo.bits.frac1 = X##_f1; \ |
| _FP_PACK_RAW_2_flo.bits.exp = X##_e; \ |
| _FP_PACK_RAW_2_flo.bits.sign = X##_s; \ |
| \ |
| (val) = _FP_PACK_RAW_2_flo.flt; \ |
| } \ |
| while (0) |
| |
| #define _FP_PACK_RAW_2_P(fs, val, X) \ |
| do \ |
| { \ |
| union _FP_UNION_##fs *_FP_PACK_RAW_2_P_flo \ |
| = (union _FP_UNION_##fs *) (val); \ |
| \ |
| _FP_PACK_RAW_2_P_flo->bits.frac0 = X##_f0; \ |
| _FP_PACK_RAW_2_P_flo->bits.frac1 = X##_f1; \ |
| _FP_PACK_RAW_2_P_flo->bits.exp = X##_e; \ |
| _FP_PACK_RAW_2_P_flo->bits.sign = X##_s; \ |
| } \ |
| while (0) |
| |
| |
| /* Multiplication algorithms: */ |
| |
| /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ |
| |
| #define _FP_MUL_MEAT_DW_2_wide(wfracbits, R, X, Y, doit) \ |
| do \ |
| { \ |
| _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_b); \ |
| _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_c); \ |
| \ |
| doit (_FP_FRAC_WORD_4 (R, 1), _FP_FRAC_WORD_4 (R, 0), \ |
| X##_f0, Y##_f0); \ |
| doit (_FP_MUL_MEAT_DW_2_wide_b_f1, _FP_MUL_MEAT_DW_2_wide_b_f0, \ |
| X##_f0, Y##_f1); \ |
| doit (_FP_MUL_MEAT_DW_2_wide_c_f1, _FP_MUL_MEAT_DW_2_wide_c_f0, \ |
| X##_f1, Y##_f0); \ |
| doit (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
| X##_f1, Y##_f1); \ |
| \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
| _FP_FRAC_WORD_4 (R, 1), 0, \ |
| _FP_MUL_MEAT_DW_2_wide_b_f1, \ |
| _FP_MUL_MEAT_DW_2_wide_b_f0, \ |
| _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
| _FP_FRAC_WORD_4 (R, 1)); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
| _FP_FRAC_WORD_4 (R, 1), 0, \ |
| _FP_MUL_MEAT_DW_2_wide_c_f1, \ |
| _FP_MUL_MEAT_DW_2_wide_c_f0, \ |
| _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
| _FP_FRAC_WORD_4 (R, 1)); \ |
| } \ |
| while (0) |
| |
| #define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit) \ |
| do \ |
| { \ |
| _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_wide_z); \ |
| \ |
| _FP_MUL_MEAT_DW_2_wide ((wfracbits), _FP_MUL_MEAT_2_wide_z, \ |
| X, Y, doit); \ |
| \ |
| /* Normalize since we know where the msb of the multiplicands \ |
| were (bit B), we know that the msb of the of the product is \ |
| at either 2B or 2B-1. */ \ |
| _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_wide_z, (wfracbits)-1, \ |
| 2*(wfracbits)); \ |
| R##_f0 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_z, 0); \ |
| R##_f1 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_z, 1); \ |
| } \ |
| while (0) |
| |
| /* Given a 1W * 1W => 2W primitive, do the extended multiplication. |
| Do only 3 multiplications instead of four. This one is for machines |
| where multiplication is much more expensive than subtraction. */ |
| |
| #define _FP_MUL_MEAT_DW_2_wide_3mul(wfracbits, R, X, Y, doit) \ |
| do \ |
| { \ |
| _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_3mul_b); \ |
| _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_3mul_c); \ |
| _FP_W_TYPE _FP_MUL_MEAT_DW_2_wide_3mul_d; \ |
| int _FP_MUL_MEAT_DW_2_wide_3mul_c1; \ |
| int _FP_MUL_MEAT_DW_2_wide_3mul_c2; \ |
| \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_b_f0 = X##_f0 + X##_f1; \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_c1 \ |
| = _FP_MUL_MEAT_DW_2_wide_3mul_b_f0 < X##_f0; \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_b_f1 = Y##_f0 + Y##_f1; \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_c2 \ |
| = _FP_MUL_MEAT_DW_2_wide_3mul_b_f1 < Y##_f0; \ |
| doit (_FP_MUL_MEAT_DW_2_wide_3mul_d, _FP_FRAC_WORD_4 (R, 0), \ |
| X##_f0, Y##_f0); \ |
| doit (_FP_FRAC_WORD_4 (R, 2), _FP_FRAC_WORD_4 (R, 1), \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_b_f0, \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_b_f1); \ |
| doit (_FP_MUL_MEAT_DW_2_wide_3mul_c_f1, \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_c_f0, X##_f1, Y##_f1); \ |
| \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_b_f0 \ |
| &= -_FP_MUL_MEAT_DW_2_wide_3mul_c2; \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_b_f1 \ |
| &= -_FP_MUL_MEAT_DW_2_wide_3mul_c1; \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
| _FP_FRAC_WORD_4 (R, 1), \ |
| (_FP_MUL_MEAT_DW_2_wide_3mul_c1 \ |
| & _FP_MUL_MEAT_DW_2_wide_3mul_c2), 0, \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_d, \ |
| 0, _FP_FRAC_WORD_4 (R, 2), _FP_FRAC_WORD_4 (R, 1)); \ |
| __FP_FRAC_ADDI_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_b_f0); \ |
| __FP_FRAC_ADDI_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_b_f1); \ |
| __FP_FRAC_DEC_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
| _FP_FRAC_WORD_4 (R, 1), \ |
| 0, _FP_MUL_MEAT_DW_2_wide_3mul_d, \ |
| _FP_FRAC_WORD_4 (R, 0)); \ |
| __FP_FRAC_DEC_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
| _FP_FRAC_WORD_4 (R, 1), 0, \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_c_f1, \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_c_f0); \ |
| __FP_FRAC_ADD_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_c_f1, \ |
| _FP_MUL_MEAT_DW_2_wide_3mul_c_f0, \ |
| _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2)); \ |
| } \ |
| while (0) |
| |
| #define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit) \ |
| do \ |
| { \ |
| _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_wide_3mul_z); \ |
| \ |
| _FP_MUL_MEAT_DW_2_wide_3mul ((wfracbits), \ |
| _FP_MUL_MEAT_2_wide_3mul_z, \ |
| X, Y, doit); \ |
| \ |
| /* Normalize since we know where the msb of the multiplicands \ |
| were (bit B), we know that the msb of the of the product is \ |
| at either 2B or 2B-1. */ \ |
| _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_wide_3mul_z, \ |
| (wfracbits)-1, 2*(wfracbits)); \ |
| R##_f0 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_3mul_z, 0); \ |
| R##_f1 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_3mul_z, 1); \ |
| } \ |
| while (0) |
| |
| #define _FP_MUL_MEAT_DW_2_gmp(wfracbits, R, X, Y) \ |
| do \ |
| { \ |
| _FP_W_TYPE _FP_MUL_MEAT_DW_2_gmp_x[2]; \ |
| _FP_W_TYPE _FP_MUL_MEAT_DW_2_gmp_y[2]; \ |
| _FP_MUL_MEAT_DW_2_gmp_x[0] = X##_f0; \ |
| _FP_MUL_MEAT_DW_2_gmp_x[1] = X##_f1; \ |
| _FP_MUL_MEAT_DW_2_gmp_y[0] = Y##_f0; \ |
| _FP_MUL_MEAT_DW_2_gmp_y[1] = Y##_f1; \ |
| \ |
| mpn_mul_n (R##_f, _FP_MUL_MEAT_DW_2_gmp_x, \ |
| _FP_MUL_MEAT_DW_2_gmp_y, 2); \ |
| } \ |
| while (0) |
| |
| #define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y) \ |
| do \ |
| { \ |
| _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_gmp_z); \ |
| \ |
| _FP_MUL_MEAT_DW_2_gmp ((wfracbits), _FP_MUL_MEAT_2_gmp_z, X, Y); \ |
| \ |
| /* Normalize since we know where the msb of the multiplicands \ |
| were (bit B), we know that the msb of the of the product is \ |
| at either 2B or 2B-1. */ \ |
| _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_gmp_z, (wfracbits)-1, \ |
| 2*(wfracbits)); \ |
| R##_f0 = _FP_MUL_MEAT_2_gmp_z_f[0]; \ |
| R##_f1 = _FP_MUL_MEAT_2_gmp_z_f[1]; \ |
| } \ |
| while (0) |
| |
| /* Do at most 120x120=240 bits multiplication using double floating |
| point multiplication. This is useful if floating point |
| multiplication has much bigger throughput than integer multiply. |
| It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits |
| between 106 and 120 only. |
| Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set. |
| SETFETZ is a macro which will disable all FPU exceptions and set rounding |
| towards zero, RESETFE should optionally reset it back. */ |
| |
| #define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe) \ |
| do \ |
| { \ |
| static const double _const[] = \ |
| { \ |
| /* 2^-24 */ 5.9604644775390625e-08, \ |
| /* 2^-48 */ 3.5527136788005009e-15, \ |
| /* 2^-72 */ 2.1175823681357508e-22, \ |
| /* 2^-96 */ 1.2621774483536189e-29, \ |
| /* 2^28 */ 2.68435456e+08, \ |
| /* 2^4 */ 1.600000e+01, \ |
| /* 2^-20 */ 9.5367431640625e-07, \ |
| /* 2^-44 */ 5.6843418860808015e-14, \ |
| /* 2^-68 */ 3.3881317890172014e-21, \ |
| /* 2^-92 */ 2.0194839173657902e-28, \ |
| /* 2^-116 */ 1.2037062152420224e-35 \ |
| }; \ |
| double _a240, _b240, _c240, _d240, _e240, _f240, \ |
| _g240, _h240, _i240, _j240, _k240; \ |
| union { double d; UDItype i; } _l240, _m240, _n240, _o240, \ |
| _p240, _q240, _r240, _s240; \ |
| UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0; \ |
| \ |
| _FP_STATIC_ASSERT ((wfracbits) >= 106 && (wfracbits) <= 120, \ |
| "wfracbits out of range"); \ |
| \ |
| setfetz; \ |
| \ |
| _e240 = (double) (long) (X##_f0 & 0xffffff); \ |
| _j240 = (double) (long) (Y##_f0 & 0xffffff); \ |
| _d240 = (double) (long) ((X##_f0 >> 24) & 0xffffff); \ |
| _i240 = (double) (long) ((Y##_f0 >> 24) & 0xffffff); \ |
| _c240 = (double) (long) (((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48)); \ |
| _h240 = (double) (long) (((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48)); \ |
| _b240 = (double) (long) ((X##_f1 >> 8) & 0xffffff); \ |
| _g240 = (double) (long) ((Y##_f1 >> 8) & 0xffffff); \ |
| _a240 = (double) (long) (X##_f1 >> 32); \ |
| _f240 = (double) (long) (Y##_f1 >> 32); \ |
| _e240 *= _const[3]; \ |
| _j240 *= _const[3]; \ |
| _d240 *= _const[2]; \ |
| _i240 *= _const[2]; \ |
| _c240 *= _const[1]; \ |
| _h240 *= _const[1]; \ |
| _b240 *= _const[0]; \ |
| _g240 *= _const[0]; \ |
| _s240.d = _e240*_j240; \ |
| _r240.d = _d240*_j240 + _e240*_i240; \ |
| _q240.d = _c240*_j240 + _d240*_i240 + _e240*_h240; \ |
| _p240.d = _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240; \ |
| _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240; \ |
| _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240; \ |
| _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240; \ |
| _l240.d = _a240*_g240 + _b240*_f240; \ |
| _k240 = _a240*_f240; \ |
| _r240.d += _s240.d; \ |
| _q240.d += _r240.d; \ |
| _p240.d += _q240.d; \ |
| _o240.d += _p240.d; \ |
| _n240.d += _o240.d; \ |
| _m240.d += _n240.d; \ |
| _l240.d += _m240.d; \ |
| _k240 += _l240.d; \ |
| _s240.d -= ((_const[10]+_s240.d)-_const[10]); \ |
| _r240.d -= ((_const[9]+_r240.d)-_const[9]); \ |
| _q240.d -= ((_const[8]+_q240.d)-_const[8]); \ |
| _p240.d -= ((_const[7]+_p240.d)-_const[7]); \ |
| _o240.d += _const[7]; \ |
| _n240.d += _const[6]; \ |
| _m240.d += _const[5]; \ |
| _l240.d += _const[4]; \ |
| if (_s240.d != 0.0) \ |
| _y240 = 1; \ |
| if (_r240.d != 0.0) \ |
| _y240 = 1; \ |
| if (_q240.d != 0.0) \ |
| _y240 = 1; \ |
| if (_p240.d != 0.0) \ |
| _y240 = 1; \ |
| _t240 = (DItype) _k240; \ |
| _u240 = _l240.i; \ |
| _v240 = _m240.i; \ |
| _w240 = _n240.i; \ |
| _x240 = _o240.i; \ |
| R##_f1 = ((_t240 << (128 - (wfracbits - 1))) \ |
| | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104))); \ |
| R##_f0 = (((_u240 & 0xffffff) << (168 - (wfracbits - 1))) \ |
| | ((_v240 & 0xffffff) << (144 - (wfracbits - 1))) \ |
| | ((_w240 & 0xffffff) << (120 - (wfracbits - 1))) \ |
| | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96)) \ |
| | _y240); \ |
| resetfe; \ |
| } \ |
| while (0) |
| |
| /* Division algorithms: */ |
| |
| #define _FP_DIV_MEAT_2_udiv(fs, R, X, Y) \ |
| do \ |
| { \ |
| _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f2; \ |
| _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f1; \ |
| _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f0; \ |
| _FP_W_TYPE _FP_DIV_MEAT_2_udiv_r_f1; \ |
| _FP_W_TYPE _FP_DIV_MEAT_2_udiv_r_f0; \ |
| _FP_W_TYPE _FP_DIV_MEAT_2_udiv_m_f1; \ |
| _FP_W_TYPE _FP_DIV_MEAT_2_udiv_m_f0; \ |
| if (_FP_FRAC_GE_2 (X, Y)) \ |
| { \ |
| _FP_DIV_MEAT_2_udiv_n_f2 = X##_f1 >> 1; \ |
| _FP_DIV_MEAT_2_udiv_n_f1 \ |
| = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \ |
| _FP_DIV_MEAT_2_udiv_n_f0 \ |
| = X##_f0 << (_FP_W_TYPE_SIZE - 1); \ |
| } \ |
| else \ |
| { \ |
| R##_e--; \ |
| _FP_DIV_MEAT_2_udiv_n_f2 = X##_f1; \ |
| _FP_DIV_MEAT_2_udiv_n_f1 = X##_f0; \ |
| _FP_DIV_MEAT_2_udiv_n_f0 = 0; \ |
| } \ |
| \ |
| /* Normalize, i.e. make the most significant bit of the \ |
| denominator set. */ \ |
| _FP_FRAC_SLL_2 (Y, _FP_WFRACXBITS_##fs); \ |
| \ |
| udiv_qrnnd (R##_f1, _FP_DIV_MEAT_2_udiv_r_f1, \ |
| _FP_DIV_MEAT_2_udiv_n_f2, _FP_DIV_MEAT_2_udiv_n_f1, \ |
| Y##_f1); \ |
| umul_ppmm (_FP_DIV_MEAT_2_udiv_m_f1, _FP_DIV_MEAT_2_udiv_m_f0, \ |
| R##_f1, Y##_f0); \ |
| _FP_DIV_MEAT_2_udiv_r_f0 = _FP_DIV_MEAT_2_udiv_n_f0; \ |
| if (_FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, _FP_DIV_MEAT_2_udiv_r)) \ |
| { \ |
| R##_f1--; \ |
| _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \ |
| _FP_DIV_MEAT_2_udiv_r); \ |
| if (_FP_FRAC_GE_2 (_FP_DIV_MEAT_2_udiv_r, Y) \ |
| && _FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, \ |
| _FP_DIV_MEAT_2_udiv_r)) \ |
| { \ |
| R##_f1--; \ |
| _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \ |
| _FP_DIV_MEAT_2_udiv_r); \ |
| } \ |
| } \ |
| _FP_FRAC_DEC_2 (_FP_DIV_MEAT_2_udiv_r, _FP_DIV_MEAT_2_udiv_m); \ |
| \ |
| if (_FP_DIV_MEAT_2_udiv_r_f1 == Y##_f1) \ |
| { \ |
| /* This is a special case, not an optimization \ |
| (_FP_DIV_MEAT_2_udiv_r/Y##_f1 would not fit into UWtype). \ |
| As _FP_DIV_MEAT_2_udiv_r is guaranteed to be < Y, \ |
| R##_f0 can be either (UWtype)-1 or (UWtype)-2. But as we \ |
| know what kind of bits it is (sticky, guard, round), \ |
| we don't care. We also don't care what the reminder is, \ |
| because the guard bit will be set anyway. -jj */ \ |
| R##_f0 = -1; \ |
| } \ |
| else \ |
| { \ |
| udiv_qrnnd (R##_f0, _FP_DIV_MEAT_2_udiv_r_f1, \ |
| _FP_DIV_MEAT_2_udiv_r_f1, \ |
| _FP_DIV_MEAT_2_udiv_r_f0, Y##_f1); \ |
| umul_ppmm (_FP_DIV_MEAT_2_udiv_m_f1, \ |
| _FP_DIV_MEAT_2_udiv_m_f0, R##_f0, Y##_f0); \ |
| _FP_DIV_MEAT_2_udiv_r_f0 = 0; \ |
| if (_FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, \ |
| _FP_DIV_MEAT_2_udiv_r)) \ |
| { \ |
| R##_f0--; \ |
| _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \ |
| _FP_DIV_MEAT_2_udiv_r); \ |
| if (_FP_FRAC_GE_2 (_FP_DIV_MEAT_2_udiv_r, Y) \ |
| && _FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, \ |
| _FP_DIV_MEAT_2_udiv_r)) \ |
| { \ |
| R##_f0--; \ |
| _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \ |
| _FP_DIV_MEAT_2_udiv_r); \ |
| } \ |
| } \ |
| if (!_FP_FRAC_EQ_2 (_FP_DIV_MEAT_2_udiv_r, \ |
| _FP_DIV_MEAT_2_udiv_m)) \ |
| R##_f0 |= _FP_WORK_STICKY; \ |
| } \ |
| } \ |
| while (0) |
| |
| |
| /* Square root algorithms: |
| We have just one right now, maybe Newton approximation |
| should be added for those machines where division is fast. */ |
| |
| #define _FP_SQRT_MEAT_2(R, S, T, X, q) \ |
| do \ |
| { \ |
| while (q) \ |
| { \ |
| T##_f1 = S##_f1 + (q); \ |
| if (T##_f1 <= X##_f1) \ |
| { \ |
| S##_f1 = T##_f1 + (q); \ |
| X##_f1 -= T##_f1; \ |
| R##_f1 += (q); \ |
| } \ |
| _FP_FRAC_SLL_2 (X, 1); \ |
| (q) >>= 1; \ |
| } \ |
| (q) = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \ |
| while ((q) != _FP_WORK_ROUND) \ |
| { \ |
| T##_f0 = S##_f0 + (q); \ |
| T##_f1 = S##_f1; \ |
| if (T##_f1 < X##_f1 \ |
| || (T##_f1 == X##_f1 && T##_f0 <= X##_f0)) \ |
| { \ |
| S##_f0 = T##_f0 + (q); \ |
| S##_f1 += (T##_f0 > S##_f0); \ |
| _FP_FRAC_DEC_2 (X, T); \ |
| R##_f0 += (q); \ |
| } \ |
| _FP_FRAC_SLL_2 (X, 1); \ |
| (q) >>= 1; \ |
| } \ |
| if (X##_f0 | X##_f1) \ |
| { \ |
| if (S##_f1 < X##_f1 \ |
| || (S##_f1 == X##_f1 && S##_f0 < X##_f0)) \ |
| R##_f0 |= _FP_WORK_ROUND; \ |
| R##_f0 |= _FP_WORK_STICKY; \ |
| } \ |
| } \ |
| while (0) |
| |
| |
| /* Assembly/disassembly for converting to/from integral types. |
| No shifting or overflow handled here. */ |
| |
| #define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \ |
| (void) (((rsize) <= _FP_W_TYPE_SIZE) \ |
| ? ({ (r) = X##_f0; }) \ |
| : ({ \ |
| (r) = X##_f1; \ |
| (r) <<= _FP_W_TYPE_SIZE; \ |
| (r) += X##_f0; \ |
| })) |
| |
| #define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \ |
| do \ |
| { \ |
| X##_f0 = (r); \ |
| X##_f1 = ((rsize) <= _FP_W_TYPE_SIZE \ |
| ? 0 \ |
| : (r) >> _FP_W_TYPE_SIZE); \ |
| } \ |
| while (0) |
| |
| /* Convert FP values between word sizes. */ |
| |
| #define _FP_FRAC_COPY_1_2(D, S) (D##_f = S##_f0) |
| |
| #define _FP_FRAC_COPY_2_1(D, S) ((D##_f0 = S##_f), (D##_f1 = 0)) |
| |
| #define _FP_FRAC_COPY_2_2(D, S) _FP_FRAC_COPY_2 (D, S) |
| |
| #endif /* !SOFT_FP_OP_2_H */ |
