| /* Software floating-point emulation. |
| Basic four-word fraction declaration and manipulation. |
| Copyright (C) 1997-2014 Free Software Foundation, Inc. |
| This file is part of the GNU C Library. |
| Contributed by Richard Henderson (rth@cygnus.com), |
| Jakub Jelinek (jj@ultra.linux.cz), |
| David S. Miller (davem@redhat.com) and |
| Peter Maydell (pmaydell@chiark.greenend.org.uk). |
| |
| 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 |
| <http://www.gnu.org/licenses/>. */ |
| |
| #define _FP_FRAC_DECL_4(X) _FP_W_TYPE X##_f[4] |
| #define _FP_FRAC_COPY_4(D, S) \ |
| (D##_f[0] = S##_f[0], D##_f[1] = S##_f[1], \ |
| D##_f[2] = S##_f[2], D##_f[3] = S##_f[3]) |
| #define _FP_FRAC_SET_4(X, I) __FP_FRAC_SET_4 (X, I) |
| #define _FP_FRAC_HIGH_4(X) (X##_f[3]) |
| #define _FP_FRAC_LOW_4(X) (X##_f[0]) |
| #define _FP_FRAC_WORD_4(X, w) (X##_f[w]) |
| |
| #define _FP_FRAC_SLL_4(X, N) \ |
| do \ |
| { \ |
| _FP_I_TYPE _up, _down, _skip, _i; \ |
| _skip = (N) / _FP_W_TYPE_SIZE; \ |
| _up = (N) % _FP_W_TYPE_SIZE; \ |
| _down = _FP_W_TYPE_SIZE - _up; \ |
| if (!_up) \ |
| for (_i = 3; _i >= _skip; --_i) \ |
| X##_f[_i] = X##_f[_i-_skip]; \ |
| else \ |
| { \ |
| for (_i = 3; _i > _skip; --_i) \ |
| X##_f[_i] = (X##_f[_i-_skip] << _up \ |
| | X##_f[_i-_skip-1] >> _down); \ |
| X##_f[_i--] = X##_f[0] << _up; \ |
| } \ |
| for (; _i >= 0; --_i) \ |
| X##_f[_i] = 0; \ |
| } \ |
| while (0) |
| |
| /* This one was broken too */ |
| #define _FP_FRAC_SRL_4(X, N) \ |
| do \ |
| { \ |
| _FP_I_TYPE _up, _down, _skip, _i; \ |
| _skip = (N) / _FP_W_TYPE_SIZE; \ |
| _down = (N) % _FP_W_TYPE_SIZE; \ |
| _up = _FP_W_TYPE_SIZE - _down; \ |
| if (!_down) \ |
| for (_i = 0; _i <= 3-_skip; ++_i) \ |
| X##_f[_i] = X##_f[_i+_skip]; \ |
| else \ |
| { \ |
| for (_i = 0; _i < 3-_skip; ++_i) \ |
| X##_f[_i] = (X##_f[_i+_skip] >> _down \ |
| | X##_f[_i+_skip+1] << _up); \ |
| X##_f[_i++] = X##_f[3] >> _down; \ |
| } \ |
| for (; _i < 4; ++_i) \ |
| X##_f[_i] = 0; \ |
| } \ |
| while (0) |
| |
| |
| /* Right shift with sticky-lsb. |
| * What this actually means is that we do a standard right-shift, |
| * but that if any of the bits that fall off the right hand side |
| * were one then we always set the LSbit. |
| */ |
| #define _FP_FRAC_SRST_4(X, S, N, size) \ |
| do \ |
| { \ |
| _FP_I_TYPE _up, _down, _skip, _i; \ |
| _FP_W_TYPE _s; \ |
| _skip = (N) / _FP_W_TYPE_SIZE; \ |
| _down = (N) % _FP_W_TYPE_SIZE; \ |
| _up = _FP_W_TYPE_SIZE - _down; \ |
| for (_s = _i = 0; _i < _skip; ++_i) \ |
| _s |= X##_f[_i]; \ |
| if (!_down) \ |
| for (_i = 0; _i <= 3-_skip; ++_i) \ |
| X##_f[_i] = X##_f[_i+_skip]; \ |
| else \ |
| { \ |
| _s |= X##_f[_i] << _up; \ |
| for (_i = 0; _i < 3-_skip; ++_i) \ |
| X##_f[_i] = (X##_f[_i+_skip] >> _down \ |
| | X##_f[_i+_skip+1] << _up); \ |
| X##_f[_i++] = X##_f[3] >> _down; \ |
| } \ |
| for (; _i < 4; ++_i) \ |
| X##_f[_i] = 0; \ |
| S = (_s != 0); \ |
| } \ |
| while (0) |
| |
| #define _FP_FRAC_SRS_4(X, N, size) \ |
| do \ |
| { \ |
| int _sticky; \ |
| _FP_FRAC_SRST_4 (X, _sticky, N, size); \ |
| X##_f[0] |= _sticky; \ |
| } \ |
| while (0) |
| |
| #define _FP_FRAC_ADD_4(R, X, Y) \ |
| __FP_FRAC_ADD_4 (R##_f[3], R##_f[2], R##_f[1], R##_f[0], \ |
| X##_f[3], X##_f[2], X##_f[1], X##_f[0], \ |
| Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0]) |
| |
| #define _FP_FRAC_SUB_4(R, X, Y) \ |
| __FP_FRAC_SUB_4 (R##_f[3], R##_f[2], R##_f[1], R##_f[0], \ |
| X##_f[3], X##_f[2], X##_f[1], X##_f[0], \ |
| Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0]) |
| |
| #define _FP_FRAC_DEC_4(X, Y) \ |
| __FP_FRAC_DEC_4 (X##_f[3], X##_f[2], X##_f[1], X##_f[0], \ |
| Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0]) |
| |
| #define _FP_FRAC_ADDI_4(X, I) \ |
| __FP_FRAC_ADDI_4 (X##_f[3], X##_f[2], X##_f[1], X##_f[0], I) |
| |
| #define _FP_ZEROFRAC_4 0, 0, 0, 0 |
| #define _FP_MINFRAC_4 0, 0, 0, 1 |
| #define _FP_MAXFRAC_4 (~(_FP_WS_TYPE) 0), (~(_FP_WS_TYPE) 0), (~(_FP_WS_TYPE) 0), (~(_FP_WS_TYPE) 0) |
| |
| #define _FP_FRAC_ZEROP_4(X) ((X##_f[0] | X##_f[1] | X##_f[2] | X##_f[3]) == 0) |
| #define _FP_FRAC_NEGP_4(X) ((_FP_WS_TYPE) X##_f[3] < 0) |
| #define _FP_FRAC_OVERP_4(fs, X) (_FP_FRAC_HIGH_##fs (X) & _FP_OVERFLOW_##fs) |
| #define _FP_FRAC_HIGHBIT_DW_4(fs, X) \ |
| (_FP_FRAC_HIGH_DW_##fs (X) & _FP_HIGHBIT_DW_##fs) |
| #define _FP_FRAC_CLEAR_OVERP_4(fs, X) (_FP_FRAC_HIGH_##fs (X) &= ~_FP_OVERFLOW_##fs) |
| |
| #define _FP_FRAC_EQ_4(X, Y) \ |
| (X##_f[0] == Y##_f[0] && X##_f[1] == Y##_f[1] \ |
| && X##_f[2] == Y##_f[2] && X##_f[3] == Y##_f[3]) |
| |
| #define _FP_FRAC_GT_4(X, Y) \ |
| (X##_f[3] > Y##_f[3] \ |
| || (X##_f[3] == Y##_f[3] \ |
| && (X##_f[2] > Y##_f[2] \ |
| || (X##_f[2] == Y##_f[2] \ |
| && (X##_f[1] > Y##_f[1] \ |
| || (X##_f[1] == Y##_f[1] \ |
| && X##_f[0] > Y##_f[0])))))) |
| |
| #define _FP_FRAC_GE_4(X, Y) \ |
| (X##_f[3] > Y##_f[3] \ |
| || (X##_f[3] == Y##_f[3] \ |
| && (X##_f[2] > Y##_f[2] \ |
| || (X##_f[2] == Y##_f[2] \ |
| && (X##_f[1] > Y##_f[1] \ |
| || (X##_f[1] == Y##_f[1] \ |
| && X##_f[0] >= Y##_f[0])))))) |
| |
| |
| #define _FP_FRAC_CLZ_4(R, X) \ |
| do \ |
| { \ |
| if (X##_f[3]) \ |
| __FP_CLZ (R, X##_f[3]); \ |
| else if (X##_f[2]) \ |
| { \ |
| __FP_CLZ (R, X##_f[2]); \ |
| R += _FP_W_TYPE_SIZE; \ |
| } \ |
| else if (X##_f[1]) \ |
| { \ |
| __FP_CLZ (R, X##_f[1]); \ |
| R += _FP_W_TYPE_SIZE*2; \ |
| } \ |
| else \ |
| { \ |
| __FP_CLZ (R, X##_f[0]); \ |
| R += _FP_W_TYPE_SIZE*3; \ |
| } \ |
| } \ |
| while (0) |
| |
| |
| #define _FP_UNPACK_RAW_4(fs, X, val) \ |
| do \ |
| { \ |
| union _FP_UNION_##fs _flo; \ |
| _flo.flt = (val); \ |
| X##_f[0] = _flo.bits.frac0; \ |
| X##_f[1] = _flo.bits.frac1; \ |
| X##_f[2] = _flo.bits.frac2; \ |
| X##_f[3] = _flo.bits.frac3; \ |
| X##_e = _flo.bits.exp; \ |
| X##_s = _flo.bits.sign; \ |
| } \ |
| while (0) |
| |
| #define _FP_UNPACK_RAW_4_P(fs, X, val) \ |
| do \ |
| { \ |
| union _FP_UNION_##fs *_flo = (union _FP_UNION_##fs *) (val); \ |
| \ |
| X##_f[0] = _flo->bits.frac0; \ |
| X##_f[1] = _flo->bits.frac1; \ |
| X##_f[2] = _flo->bits.frac2; \ |
| X##_f[3] = _flo->bits.frac3; \ |
| X##_e = _flo->bits.exp; \ |
| X##_s = _flo->bits.sign; \ |
| } \ |
| while (0) |
| |
| #define _FP_PACK_RAW_4(fs, val, X) \ |
| do \ |
| { \ |
| union _FP_UNION_##fs _flo; \ |
| _flo.bits.frac0 = X##_f[0]; \ |
| _flo.bits.frac1 = X##_f[1]; \ |
| _flo.bits.frac2 = X##_f[2]; \ |
| _flo.bits.frac3 = X##_f[3]; \ |
| _flo.bits.exp = X##_e; \ |
| _flo.bits.sign = X##_s; \ |
| (val) = _flo.flt; \ |
| } \ |
| while (0) |
| |
| #define _FP_PACK_RAW_4_P(fs, val, X) \ |
| do \ |
| { \ |
| union _FP_UNION_##fs *_flo = (union _FP_UNION_##fs *) (val); \ |
| \ |
| _flo->bits.frac0 = X##_f[0]; \ |
| _flo->bits.frac1 = X##_f[1]; \ |
| _flo->bits.frac2 = X##_f[2]; \ |
| _flo->bits.frac3 = X##_f[3]; \ |
| _flo->bits.exp = X##_e; \ |
| _flo->bits.sign = X##_s; \ |
| } \ |
| while (0) |
| |
| /* |
| * Multiplication algorithms: |
| */ |
| |
| /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ |
| |
| #define _FP_MUL_MEAT_DW_4_wide(wfracbits, R, X, Y, doit) \ |
| do \ |
| { \ |
| _FP_FRAC_DECL_2 (_b); \ |
| _FP_FRAC_DECL_2 (_c); \ |
| _FP_FRAC_DECL_2 (_d); \ |
| _FP_FRAC_DECL_2 (_e); \ |
| _FP_FRAC_DECL_2 (_f); \ |
| \ |
| doit (_FP_FRAC_WORD_8 (R, 1), _FP_FRAC_WORD_8 (R, 0), X##_f[0], Y##_f[0]); \ |
| doit (_b_f1, _b_f0, X##_f[0], Y##_f[1]); \ |
| doit (_c_f1, _c_f0, X##_f[1], Y##_f[0]); \ |
| doit (_d_f1, _d_f0, X##_f[1], Y##_f[1]); \ |
| doit (_e_f1, _e_f0, X##_f[0], Y##_f[2]); \ |
| doit (_f_f1, _f_f0, X##_f[2], Y##_f[0]); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 3), _FP_FRAC_WORD_8 (R, 2), \ |
| _FP_FRAC_WORD_8 (R, 1), 0, _b_f1, _b_f0, \ |
| 0, 0, _FP_FRAC_WORD_8 (R, 1)); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 3), _FP_FRAC_WORD_8 (R, 2), \ |
| _FP_FRAC_WORD_8 (R, 1), 0, _c_f1, _c_f0, \ |
| _FP_FRAC_WORD_8 (R, 3), _FP_FRAC_WORD_8 (R, 2), \ |
| _FP_FRAC_WORD_8 (R, 1)); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 4), _FP_FRAC_WORD_8 (R, 3), \ |
| _FP_FRAC_WORD_8 (R, 2), 0, _d_f1, _d_f0, \ |
| 0, _FP_FRAC_WORD_8 (R, 3), _FP_FRAC_WORD_8 (R, 2)); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 4), _FP_FRAC_WORD_8 (R, 3), \ |
| _FP_FRAC_WORD_8 (R, 2), 0, _e_f1, _e_f0, \ |
| _FP_FRAC_WORD_8 (R, 4), _FP_FRAC_WORD_8 (R, 3), \ |
| _FP_FRAC_WORD_8 (R, 2)); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 4), _FP_FRAC_WORD_8 (R, 3), \ |
| _FP_FRAC_WORD_8 (R, 2), 0, _f_f1, _f_f0, \ |
| _FP_FRAC_WORD_8 (R, 4), _FP_FRAC_WORD_8 (R, 3), \ |
| _FP_FRAC_WORD_8 (R, 2)); \ |
| doit (_b_f1, _b_f0, X##_f[0], Y##_f[3]); \ |
| doit (_c_f1, _c_f0, X##_f[3], Y##_f[0]); \ |
| doit (_d_f1, _d_f0, X##_f[1], Y##_f[2]); \ |
| doit (_e_f1, _e_f0, X##_f[2], Y##_f[1]); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4), \ |
| _FP_FRAC_WORD_8 (R, 3), 0, _b_f1, _b_f0, \ |
| 0, _FP_FRAC_WORD_8 (R, 4), _FP_FRAC_WORD_8 (R, 3)); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4), \ |
| _FP_FRAC_WORD_8 (R, 3), 0, _c_f1, _c_f0, \ |
| _FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4), \ |
| _FP_FRAC_WORD_8 (R, 3)); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4), \ |
| _FP_FRAC_WORD_8 (R, 3), 0, _d_f1, _d_f0, \ |
| _FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4), \ |
| _FP_FRAC_WORD_8 (R, 3)); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4), \ |
| _FP_FRAC_WORD_8 (R, 3), 0, _e_f1, _e_f0, \ |
| _FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4), \ |
| _FP_FRAC_WORD_8 (R, 3)); \ |
| doit (_b_f1, _b_f0, X##_f[2], Y##_f[2]); \ |
| doit (_c_f1, _c_f0, X##_f[1], Y##_f[3]); \ |
| doit (_d_f1, _d_f0, X##_f[3], Y##_f[1]); \ |
| doit (_e_f1, _e_f0, X##_f[2], Y##_f[3]); \ |
| doit (_f_f1, _f_f0, X##_f[3], Y##_f[2]); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 6), _FP_FRAC_WORD_8 (R, 5), \ |
| _FP_FRAC_WORD_8 (R, 4), 0, _b_f1, _b_f0, \ |
| 0, _FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4)); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 6), _FP_FRAC_WORD_8 (R, 5), \ |
| _FP_FRAC_WORD_8 (R, 4), 0, _c_f1, _c_f0, \ |
| _FP_FRAC_WORD_8 (R, 6), _FP_FRAC_WORD_8 (R, 5), \ |
| _FP_FRAC_WORD_8 (R, 4)); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 6), _FP_FRAC_WORD_8 (R, 5), \ |
| _FP_FRAC_WORD_8 (R, 4), 0, _d_f1, _d_f0, \ |
| _FP_FRAC_WORD_8 (R, 6), _FP_FRAC_WORD_8 (R, 5), \ |
| _FP_FRAC_WORD_8 (R, 4)); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 7), _FP_FRAC_WORD_8 (R, 6), \ |
| _FP_FRAC_WORD_8 (R, 5), 0, _e_f1, _e_f0, \ |
| 0, _FP_FRAC_WORD_8 (R, 6), _FP_FRAC_WORD_8 (R, 5)); \ |
| __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 7), _FP_FRAC_WORD_8 (R, 6), \ |
| _FP_FRAC_WORD_8 (R, 5), 0, _f_f1, _f_f0, \ |
| _FP_FRAC_WORD_8 (R, 7), _FP_FRAC_WORD_8 (R, 6), \ |
| _FP_FRAC_WORD_8 (R, 5)); \ |
| doit (_b_f1, _b_f0, X##_f[3], Y##_f[3]); \ |
| __FP_FRAC_ADD_2 (_FP_FRAC_WORD_8 (R, 7), _FP_FRAC_WORD_8 (R, 6), \ |
| _b_f1, _b_f0, \ |
| _FP_FRAC_WORD_8 (R, 7), _FP_FRAC_WORD_8 (R, 6)); \ |
| } \ |
| while (0) |
| |
| #define _FP_MUL_MEAT_4_wide(wfracbits, R, X, Y, doit) \ |
| do \ |
| { \ |
| _FP_FRAC_DECL_8 (_z); \ |
| \ |
| _FP_MUL_MEAT_DW_4_wide (wfracbits, _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_8 (_z, wfracbits-1, 2*wfracbits); \ |
| __FP_FRAC_SET_4 (R, _FP_FRAC_WORD_8 (_z, 3), _FP_FRAC_WORD_8 (_z, 2), \ |
| _FP_FRAC_WORD_8 (_z, 1), _FP_FRAC_WORD_8 (_z, 0)); \ |
| } \ |
| while (0) |
| |
| #define _FP_MUL_MEAT_DW_4_gmp(wfracbits, R, X, Y) \ |
| do \ |
| { \ |
| mpn_mul_n (R##_f, _x_f, _y_f, 4); \ |
| } \ |
| while (0) |
| |
| #define _FP_MUL_MEAT_4_gmp(wfracbits, R, X, Y) \ |
| do \ |
| { \ |
| _FP_FRAC_DECL_8 (_z); \ |
| \ |
| _FP_MUL_MEAT_DW_4_gmp (wfracbits, _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_8 (_z, wfracbits-1, 2*wfracbits); \ |
| __FP_FRAC_SET_4 (R, _FP_FRAC_WORD_8 (_z, 3), _FP_FRAC_WORD_8 (_z, 2), \ |
| _FP_FRAC_WORD_8 (_z, 1), _FP_FRAC_WORD_8 (_z, 0)); \ |
| } \ |
| while (0) |
| |
| /* |
| * Helper utility for _FP_DIV_MEAT_4_udiv: |
| * pppp = m * nnn |
| */ |
| #define umul_ppppmnnn(p3, p2, p1, p0, m, n2, n1, n0) \ |
| do \ |
| { \ |
| UWtype _t; \ |
| umul_ppmm (p1, p0, m, n0); \ |
| umul_ppmm (p2, _t, m, n1); \ |
| __FP_FRAC_ADDI_2 (p2, p1, _t); \ |
| umul_ppmm (p3, _t, m, n2); \ |
| __FP_FRAC_ADDI_2 (p3, p2, _t); \ |
| } \ |
| while (0) |
| |
| /* |
| * Division algorithms: |
| */ |
| |
| #define _FP_DIV_MEAT_4_udiv(fs, R, X, Y) \ |
| do \ |
| { \ |
| int _i; \ |
| _FP_FRAC_DECL_4 (_n); \ |
| _FP_FRAC_DECL_4 (_m); \ |
| _FP_FRAC_SET_4 (_n, _FP_ZEROFRAC_4); \ |
| if (_FP_FRAC_GE_4 (X, Y)) \ |
| { \ |
| _n_f[3] = X##_f[0] << (_FP_W_TYPE_SIZE - 1); \ |
| _FP_FRAC_SRL_4 (X, 1); \ |
| } \ |
| else \ |
| R##_e--; \ |
| \ |
| /* Normalize, i.e. make the most significant bit of the \ |
| denominator set. */ \ |
| _FP_FRAC_SLL_4 (Y, _FP_WFRACXBITS_##fs); \ |
| \ |
| for (_i = 3; ; _i--) \ |
| { \ |
| if (X##_f[3] == Y##_f[3]) \ |
| { \ |
| /* This is a special case, not an optimization \ |
| (X##_f[3]/Y##_f[3] would not fit into UWtype). \ |
| As X## is guaranteed to be < Y, R##_f[_i] can be either \ |
| (UWtype)-1 or (UWtype)-2. */ \ |
| R##_f[_i] = -1; \ |
| if (!_i) \ |
| break; \ |
| __FP_FRAC_SUB_4 (X##_f[3], X##_f[2], X##_f[1], X##_f[0], \ |
| Y##_f[2], Y##_f[1], Y##_f[0], 0, \ |
| X##_f[2], X##_f[1], X##_f[0], _n_f[_i]); \ |
| _FP_FRAC_SUB_4 (X, Y, X); \ |
| if (X##_f[3] > Y##_f[3]) \ |
| { \ |
| R##_f[_i] = -2; \ |
| _FP_FRAC_ADD_4 (X, Y, X); \ |
| } \ |
| } \ |
| else \ |
| { \ |
| udiv_qrnnd (R##_f[_i], X##_f[3], X##_f[3], X##_f[2], Y##_f[3]); \ |
| umul_ppppmnnn (_m_f[3], _m_f[2], _m_f[1], _m_f[0], \ |
| R##_f[_i], Y##_f[2], Y##_f[1], Y##_f[0]); \ |
| X##_f[2] = X##_f[1]; \ |
| X##_f[1] = X##_f[0]; \ |
| X##_f[0] = _n_f[_i]; \ |
| if (_FP_FRAC_GT_4 (_m, X)) \ |
| { \ |
| R##_f[_i]--; \ |
| _FP_FRAC_ADD_4 (X, Y, X); \ |
| if (_FP_FRAC_GE_4 (X, Y) && _FP_FRAC_GT_4 (_m, X)) \ |
| { \ |
| R##_f[_i]--; \ |
| _FP_FRAC_ADD_4 (X, Y, X); \ |
| } \ |
| } \ |
| _FP_FRAC_DEC_4 (X, _m); \ |
| if (!_i) \ |
| { \ |
| if (!_FP_FRAC_EQ_4 (X, _m)) \ |
| R##_f[0] |= _FP_WORK_STICKY; \ |
| break; \ |
| } \ |
| } \ |
| } \ |
| } \ |
| 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_4(R, S, T, X, q) \ |
| do \ |
| { \ |
| while (q) \ |
| { \ |
| T##_f[3] = S##_f[3] + q; \ |
| if (T##_f[3] <= X##_f[3]) \ |
| { \ |
| S##_f[3] = T##_f[3] + q; \ |
| X##_f[3] -= T##_f[3]; \ |
| R##_f[3] += q; \ |
| } \ |
| _FP_FRAC_SLL_4 (X, 1); \ |
| q >>= 1; \ |
| } \ |
| q = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \ |
| while (q) \ |
| { \ |
| T##_f[2] = S##_f[2] + q; \ |
| T##_f[3] = S##_f[3]; \ |
| if (T##_f[3] < X##_f[3] \ |
| || (T##_f[3] == X##_f[3] && T##_f[2] <= X##_f[2])) \ |
| { \ |
| S##_f[2] = T##_f[2] + q; \ |
| S##_f[3] += (T##_f[2] > S##_f[2]); \ |
| __FP_FRAC_DEC_2 (X##_f[3], X##_f[2], \ |
| T##_f[3], T##_f[2]); \ |
| R##_f[2] += q; \ |
| } \ |
| _FP_FRAC_SLL_4 (X, 1); \ |
| q >>= 1; \ |
| } \ |
| q = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \ |
| while (q) \ |
| { \ |
| T##_f[1] = S##_f[1] + q; \ |
| T##_f[2] = S##_f[2]; \ |
| T##_f[3] = S##_f[3]; \ |
| if (T##_f[3] < X##_f[3] \ |
| || (T##_f[3] == X##_f[3] \ |
| && (T##_f[2] < X##_f[2] \ |
| || (T##_f[2] == X##_f[2] \ |
| && T##_f[1] <= X##_f[1])))) \ |
| { \ |
| S##_f[1] = T##_f[1] + q; \ |
| S##_f[2] += (T##_f[1] > S##_f[1]); \ |
| S##_f[3] += (T##_f[2] > S##_f[2]); \ |
| __FP_FRAC_DEC_3 (X##_f[3], X##_f[2], X##_f[1], \ |
| T##_f[3], T##_f[2], T##_f[1]); \ |
| R##_f[1] += q; \ |
| } \ |
| _FP_FRAC_SLL_4 (X, 1); \ |
| q >>= 1; \ |
| } \ |
| q = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \ |
| while (q != _FP_WORK_ROUND) \ |
| { \ |
| T##_f[0] = S##_f[0] + q; \ |
| T##_f[1] = S##_f[1]; \ |
| T##_f[2] = S##_f[2]; \ |
| T##_f[3] = S##_f[3]; \ |
| if (_FP_FRAC_GE_4 (X, T)) \ |
| { \ |
| S##_f[0] = T##_f[0] + q; \ |
| S##_f[1] += (T##_f[0] > S##_f[0]); \ |
| S##_f[2] += (T##_f[1] > S##_f[1]); \ |
| S##_f[3] += (T##_f[2] > S##_f[2]); \ |
| _FP_FRAC_DEC_4 (X, T); \ |
| R##_f[0] += q; \ |
| } \ |
| _FP_FRAC_SLL_4 (X, 1); \ |
| q >>= 1; \ |
| } \ |
| if (!_FP_FRAC_ZEROP_4 (X)) \ |
| { \ |
| if (_FP_FRAC_GT_4 (X, S)) \ |
| R##_f[0] |= _FP_WORK_ROUND; \ |
| R##_f[0] |= _FP_WORK_STICKY; \ |
| } \ |
| } \ |
| while (0) |
| |
| |
| /* |
| * Internals |
| */ |
| |
| #define __FP_FRAC_SET_4(X, I3, I2, I1, I0) \ |
| (X##_f[3] = I3, X##_f[2] = I2, X##_f[1] = I1, X##_f[0] = I0) |
| |
| #ifndef __FP_FRAC_ADD_3 |
| # define __FP_FRAC_ADD_3(r2, r1, r0, x2, x1, x0, y2, y1, y0) \ |
| do \ |
| { \ |
| _FP_W_TYPE __FP_FRAC_ADD_3_c1, __FP_FRAC_ADD_3_c2; \ |
| r0 = x0 + y0; \ |
| __FP_FRAC_ADD_3_c1 = r0 < x0; \ |
| r1 = x1 + y1; \ |
| __FP_FRAC_ADD_3_c2 = r1 < x1; \ |
| r1 += __FP_FRAC_ADD_3_c1; \ |
| __FP_FRAC_ADD_3_c2 |= r1 < __FP_FRAC_ADD_3_c1; \ |
| r2 = x2 + y2 + __FP_FRAC_ADD_3_c2; \ |
| } \ |
| while (0) |
| #endif |
| |
| #ifndef __FP_FRAC_ADD_4 |
| # define __FP_FRAC_ADD_4(r3, r2, r1, r0, x3, x2, x1, x0, y3, y2, y1, y0) \ |
| do \ |
| { \ |
| _FP_W_TYPE _c1, _c2, _c3; \ |
| r0 = x0 + y0; \ |
| _c1 = r0 < x0; \ |
| r1 = x1 + y1; \ |
| _c2 = r1 < x1; \ |
| r1 += _c1; \ |
| _c2 |= r1 < _c1; \ |
| r2 = x2 + y2; \ |
| _c3 = r2 < x2; \ |
| r2 += _c2; \ |
| _c3 |= r2 < _c2; \ |
| r3 = x3 + y3 + _c3; \ |
| } \ |
| while (0) |
| #endif |
| |
| #ifndef __FP_FRAC_SUB_3 |
| # define __FP_FRAC_SUB_3(r2, r1, r0, x2, x1, x0, y2, y1, y0) \ |
| do \ |
| { \ |
| _FP_W_TYPE _c1, _c2; \ |
| r0 = x0 - y0; \ |
| _c1 = r0 > x0; \ |
| r1 = x1 - y1; \ |
| _c2 = r1 > x1; \ |
| r1 -= _c1; \ |
| _c2 |= _c1 && (y1 == x1); \ |
| r2 = x2 - y2 - _c2; \ |
| } \ |
| while (0) |
| #endif |
| |
| #ifndef __FP_FRAC_SUB_4 |
| # define __FP_FRAC_SUB_4(r3, r2, r1, r0, x3, x2, x1, x0, y3, y2, y1, y0) \ |
| do \ |
| { \ |
| _FP_W_TYPE _c1, _c2, _c3; \ |
| r0 = x0 - y0; \ |
| _c1 = r0 > x0; \ |
| r1 = x1 - y1; \ |
| _c2 = r1 > x1; \ |
| r1 -= _c1; \ |
| _c2 |= _c1 && (y1 == x1); \ |
| r2 = x2 - y2; \ |
| _c3 = r2 > x2; \ |
| r2 -= _c2; \ |
| _c3 |= _c2 && (y2 == x2); \ |
| r3 = x3 - y3 - _c3; \ |
| } \ |
| while (0) |
| #endif |
| |
| #ifndef __FP_FRAC_DEC_3 |
| # define __FP_FRAC_DEC_3(x2, x1, x0, y2, y1, y0) \ |
| do \ |
| { \ |
| UWtype _t0, _t1, _t2; \ |
| _t0 = x0, _t1 = x1, _t2 = x2; \ |
| __FP_FRAC_SUB_3 (x2, x1, x0, _t2, _t1, _t0, y2, y1, y0); \ |
| } \ |
| while (0) |
| #endif |
| |
| #ifndef __FP_FRAC_DEC_4 |
| # define __FP_FRAC_DEC_4(x3, x2, x1, x0, y3, y2, y1, y0) \ |
| do \ |
| { \ |
| UWtype _t0, _t1, _t2, _t3; \ |
| _t0 = x0, _t1 = x1, _t2 = x2, _t3 = x3; \ |
| __FP_FRAC_SUB_4 (x3, x2, x1, x0, _t3, _t2, _t1, _t0, y3, y2, y1, y0); \ |
| } \ |
| while (0) |
| #endif |
| |
| #ifndef __FP_FRAC_ADDI_4 |
| # define __FP_FRAC_ADDI_4(x3, x2, x1, x0, i) \ |
| do \ |
| { \ |
| UWtype _t; \ |
| _t = ((x0 += i) < i); \ |
| x1 += _t; \ |
| _t = (x1 < _t); \ |
| x2 += _t; \ |
| _t = (x2 < _t); \ |
| x3 += _t; \ |
| } \ |
| while (0) |
| #endif |
| |
| /* Convert FP values between word sizes. This appears to be more |
| * complicated than I'd have expected it to be, so these might be |
| * wrong... These macros are in any case somewhat bogus because they |
| * use information about what various FRAC_n variables look like |
| * internally [eg, that 2 word vars are X_f0 and x_f1]. But so do |
| * the ones in op-2.h and op-1.h. |
| */ |
| #define _FP_FRAC_COPY_1_4(D, S) (D##_f = S##_f[0]) |
| |
| #define _FP_FRAC_COPY_2_4(D, S) \ |
| do \ |
| { \ |
| D##_f0 = S##_f[0]; \ |
| D##_f1 = S##_f[1]; \ |
| } \ |
| while (0) |
| |
| /* Assembly/disassembly for converting to/from integral types. |
| * No shifting or overflow handled here. |
| */ |
| /* Put the FP value X into r, which is an integer of size rsize. */ |
| #define _FP_FRAC_ASSEMBLE_4(r, X, rsize) \ |
| do \ |
| { \ |
| if (rsize <= _FP_W_TYPE_SIZE) \ |
| r = X##_f[0]; \ |
| else if (rsize <= 2*_FP_W_TYPE_SIZE) \ |
| { \ |
| r = X##_f[1]; \ |
| r = (rsize <= _FP_W_TYPE_SIZE ? 0 : r << _FP_W_TYPE_SIZE); \ |
| r += X##_f[0]; \ |
| } \ |
| else \ |
| { \ |
| /* I'm feeling lazy so we deal with int == 3words (implausible)*/ \ |
| /* and int == 4words as a single case. */ \ |
| r = X##_f[3]; \ |
| r = (rsize <= _FP_W_TYPE_SIZE ? 0 : r << _FP_W_TYPE_SIZE); \ |
| r += X##_f[2]; \ |
| r = (rsize <= _FP_W_TYPE_SIZE ? 0 : r << _FP_W_TYPE_SIZE); \ |
| r += X##_f[1]; \ |
| r = (rsize <= _FP_W_TYPE_SIZE ? 0 : r << _FP_W_TYPE_SIZE); \ |
| r += X##_f[0]; \ |
| } \ |
| } \ |
| while (0) |
| |
| /* "No disassemble Number Five!" */ |
| /* move an integer of size rsize into X's fractional part. We rely on |
| * the _f[] array consisting of words of size _FP_W_TYPE_SIZE to avoid |
| * having to mask the values we store into it. |
| */ |
| #define _FP_FRAC_DISASSEMBLE_4(X, r, rsize) \ |
| do \ |
| { \ |
| X##_f[0] = r; \ |
| X##_f[1] = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \ |
| X##_f[2] = (rsize <= 2*_FP_W_TYPE_SIZE ? 0 : r >> 2*_FP_W_TYPE_SIZE); \ |
| X##_f[3] = (rsize <= 3*_FP_W_TYPE_SIZE ? 0 : r >> 3*_FP_W_TYPE_SIZE); \ |
| } \ |
| while (0) |
| |
| #define _FP_FRAC_COPY_4_1(D, S) \ |
| do \ |
| { \ |
| D##_f[0] = S##_f; \ |
| D##_f[1] = D##_f[2] = D##_f[3] = 0; \ |
| } \ |
| while (0) |
| |
| #define _FP_FRAC_COPY_4_2(D, S) \ |
| do \ |
| { \ |
| D##_f[0] = S##_f0; \ |
| D##_f[1] = S##_f1; \ |
| D##_f[2] = D##_f[3] = 0; \ |
| } \ |
| while (0) |
| |
| #define _FP_FRAC_COPY_4_4(D, S) _FP_FRAC_COPY_4 (D, S) |