| /* Software floating-point emulation. |
| Basic four-word fraction declaration and manipulation. |
| Copyright (C) 1997,1998,1999 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 Library General Public License as |
| published by the Free Software Foundation; either version 2 of the |
| License, or (at your option) any later version. |
| |
| 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 |
| Library General Public License for more details. |
| |
| You should have received a copy of the GNU Library General Public |
| License along with the GNU C Library; see the file COPYING.LIB. If |
| not, write to the Free Software Foundation, Inc., |
| 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ |
| |
| #ifndef __MATH_EMU_OP_4_H__ |
| #define __MATH_EMU_OP_4_H__ |
| |
| #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_SRS_4(X,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]; \ |
| _s |= X##_f[_i] << _up; \ |
| /* s is now != 0 if we want to set the LSbit */ \ |
| 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; \ |
| /* don't fix the LSB until the very end when we're sure f[0] is stable */ \ |
| X##_f[0] |= (_s != 0); \ |
| } 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_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[2]); \ |
| 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_4_wide(wfracbits, R, X, Y, doit) \ |
| do { \ |
| _FP_FRAC_DECL_8(_z); _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(_z,1), _FP_FRAC_WORD_8(_z,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(_z,3),_FP_FRAC_WORD_8(_z,2), \ |
| _FP_FRAC_WORD_8(_z,1), 0,_b_f1,_b_f0, \ |
| 0,0,_FP_FRAC_WORD_8(_z,1)); \ |
| __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \ |
| _FP_FRAC_WORD_8(_z,1), 0,_c_f1,_c_f0, \ |
| _FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \ |
| _FP_FRAC_WORD_8(_z,1)); \ |
| __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ |
| _FP_FRAC_WORD_8(_z,2), 0,_d_f1,_d_f0, \ |
| 0,_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2)); \ |
| __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ |
| _FP_FRAC_WORD_8(_z,2), 0,_e_f1,_e_f0, \ |
| _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ |
| _FP_FRAC_WORD_8(_z,2)); \ |
| __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ |
| _FP_FRAC_WORD_8(_z,2), 0,_f_f1,_f_f0, \ |
| _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ |
| _FP_FRAC_WORD_8(_z,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(_z,5),_FP_FRAC_WORD_8(_z,4), \ |
| _FP_FRAC_WORD_8(_z,3), 0,_b_f1,_b_f0, \ |
| 0,_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3)); \ |
| __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ |
| _FP_FRAC_WORD_8(_z,3), 0,_c_f1,_c_f0, \ |
| _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ |
| _FP_FRAC_WORD_8(_z,3)); \ |
| __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ |
| _FP_FRAC_WORD_8(_z,3), 0,_d_f1,_d_f0, \ |
| _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ |
| _FP_FRAC_WORD_8(_z,3)); \ |
| __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ |
| _FP_FRAC_WORD_8(_z,3), 0,_e_f1,_e_f0, \ |
| _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ |
| _FP_FRAC_WORD_8(_z,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(_z,6),_FP_FRAC_WORD_8(_z,5), \ |
| _FP_FRAC_WORD_8(_z,4), 0,_b_f1,_b_f0, \ |
| 0,_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4)); \ |
| __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \ |
| _FP_FRAC_WORD_8(_z,4), 0,_c_f1,_c_f0, \ |
| _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \ |
| _FP_FRAC_WORD_8(_z,4)); \ |
| __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \ |
| _FP_FRAC_WORD_8(_z,4), 0,_d_f1,_d_f0, \ |
| _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \ |
| _FP_FRAC_WORD_8(_z,4)); \ |
| __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \ |
| _FP_FRAC_WORD_8(_z,5), 0,_e_f1,_e_f0, \ |
| 0,_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5)); \ |
| __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \ |
| _FP_FRAC_WORD_8(_z,5), 0,_f_f1,_f_f0, \ |
| _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \ |
| _FP_FRAC_WORD_8(_z,5)); \ |
| doit(_b_f1, _b_f0, X##_f[3], Y##_f[3]); \ |
| __FP_FRAC_ADD_2(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \ |
| _b_f1,_b_f0, \ |
| _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6)); \ |
| \ |
| /* 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_4_gmp(wfracbits, R, X, Y) \ |
| do { \ |
| _FP_FRAC_DECL_8(_z); \ |
| \ |
| mpn_mul_n(_z_f, _x_f, _y_f, 4); \ |
| \ |
| /* 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_GT_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 { \ |
| int _c1, _c2; \ |
| r0 = x0 + y0; \ |
| _c1 = r0 < x0; \ |
| r1 = x1 + y1; \ |
| _c2 = r1 < x1; \ |
| r1 += _c1; \ |
| _c2 |= r1 < _c1; \ |
| r2 = x2 + y2 + _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 { \ |
| int _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 { \ |
| int _c1, _c2; \ |
| r0 = x0 - y0; \ |
| _c1 = r0 > x0; \ |
| r1 = x1 - y1; \ |
| _c2 = r1 > x1; \ |
| r1 -= _c1; \ |
| _c2 |= r1 > _c1; \ |
| 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 { \ |
| int _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_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_CONV_1_4(dfs, sfs, D, S) \ |
| do { \ |
| if (S##_c != FP_CLS_NAN) \ |
| _FP_FRAC_SRS_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \ |
| _FP_WFRACBITS_##sfs); \ |
| else \ |
| _FP_FRAC_SRL_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs)); \ |
| D##_f = S##_f[0]; \ |
| } while (0) |
| |
| #define _FP_FRAC_CONV_2_4(dfs, sfs, D, S) \ |
| do { \ |
| if (S##_c != FP_CLS_NAN) \ |
| _FP_FRAC_SRS_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \ |
| _FP_WFRACBITS_##sfs); \ |
| else \ |
| _FP_FRAC_SRL_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs)); \ |
| 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 <<= _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 <<= _FP_W_TYPE_SIZE; \ |
| r += X##_f[2]; \ |
| r <<= _FP_W_TYPE_SIZE; \ |
| r += X##_f[1]; \ |
| 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_CONV_4_1(dfs, sfs, D, S) \ |
| do { \ |
| D##_f[0] = S##_f; \ |
| D##_f[1] = D##_f[2] = D##_f[3] = 0; \ |
| _FP_FRAC_SLL_4(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \ |
| } while (0) |
| |
| #define _FP_FRAC_CONV_4_2(dfs, sfs, D, S) \ |
| do { \ |
| D##_f[0] = S##_f0; \ |
| D##_f[1] = S##_f1; \ |
| D##_f[2] = D##_f[3] = 0; \ |
| _FP_FRAC_SLL_4(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \ |
| } while (0) |
| |
| #endif |
