| /* Software floating-point emulation. |
| Basic two-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_2_H__ |
| #define __MATH_EMU_OP_2_H__ |
| |
| #define _FP_FRAC_DECL_2(X) _FP_W_TYPE X##_f0 = 0, X##_f1 = 0 |
| #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_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_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 _t = xl; \ |
| xh -= yh + ((xl -= yl) > _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 _flo; _flo.flt = (val); \ |
| \ |
| X##_f0 = _flo.bits.frac0; \ |
| X##_f1 = _flo.bits.frac1; \ |
| X##_e = _flo.bits.exp; \ |
| X##_s = _flo.bits.sign; \ |
| } while (0) |
| |
| #define _FP_UNPACK_RAW_2_P(fs, X, val) \ |
| do { \ |
| union _FP_UNION_##fs *_flo = \ |
| (union _FP_UNION_##fs *)(val); \ |
| \ |
| X##_f0 = _flo->bits.frac0; \ |
| X##_f1 = _flo->bits.frac1; \ |
| X##_e = _flo->bits.exp; \ |
| X##_s = _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 _flo; \ |
| \ |
| _flo.bits.frac0 = X##_f0; \ |
| _flo.bits.frac1 = X##_f1; \ |
| _flo.bits.exp = X##_e; \ |
| _flo.bits.sign = X##_s; \ |
| \ |
| (val) = _flo.flt; \ |
| } while (0) |
| |
| #define _FP_PACK_RAW_2_P(fs, val, X) \ |
| do { \ |
| union _FP_UNION_##fs *_flo = \ |
| (union _FP_UNION_##fs *)(val); \ |
| \ |
| _flo->bits.frac0 = X##_f0; \ |
| _flo->bits.frac1 = X##_f1; \ |
| _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_2_wide(wfracbits, R, X, Y, doit) \ |
| do { \ |
| _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ |
| \ |
| doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \ |
| doit(_b_f1, _b_f0, X##_f0, Y##_f1); \ |
| doit(_c_f1, _c_f0, X##_f1, Y##_f0); \ |
| doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \ |
| \ |
| __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
| _FP_FRAC_WORD_4(_z,1), 0, _b_f1, _b_f0, \ |
| _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
| _FP_FRAC_WORD_4(_z,1)); \ |
| __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
| _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0, \ |
| _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
| _FP_FRAC_WORD_4(_z,1)); \ |
| \ |
| /* 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(_z, wfracbits-1, 2*wfracbits); \ |
| R##_f0 = _FP_FRAC_WORD_4(_z,0); \ |
| R##_f1 = _FP_FRAC_WORD_4(_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_2_wide_3mul(wfracbits, R, X, Y, doit) \ |
| do { \ |
| _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ |
| _FP_W_TYPE _d; \ |
| int _c1, _c2; \ |
| \ |
| _b_f0 = X##_f0 + X##_f1; \ |
| _c1 = _b_f0 < X##_f0; \ |
| _b_f1 = Y##_f0 + Y##_f1; \ |
| _c2 = _b_f1 < Y##_f0; \ |
| doit(_d, _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \ |
| doit(_FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1), _b_f0, _b_f1); \ |
| doit(_c_f1, _c_f0, X##_f1, Y##_f1); \ |
| \ |
| _b_f0 &= -_c2; \ |
| _b_f1 &= -_c1; \ |
| __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
| _FP_FRAC_WORD_4(_z,1), (_c1 & _c2), 0, _d, \ |
| 0, _FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1)); \ |
| __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
| _b_f0); \ |
| __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
| _b_f1); \ |
| __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
| _FP_FRAC_WORD_4(_z,1), \ |
| 0, _d, _FP_FRAC_WORD_4(_z,0)); \ |
| __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
| _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0); \ |
| __FP_FRAC_ADD_2(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), \ |
| _c_f1, _c_f0, \ |
| _FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2)); \ |
| \ |
| /* 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(_z, wfracbits-1, 2*wfracbits); \ |
| R##_f0 = _FP_FRAC_WORD_4(_z,0); \ |
| R##_f1 = _FP_FRAC_WORD_4(_z,1); \ |
| } while (0) |
| |
| #define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y) \ |
| do { \ |
| _FP_FRAC_DECL_4(_z); \ |
| _FP_W_TYPE _x[2], _y[2]; \ |
| _x[0] = X##_f0; _x[1] = X##_f1; \ |
| _y[0] = Y##_f0; _y[1] = Y##_f1; \ |
| \ |
| mpn_mul_n(_z_f, _x, _y, 2); \ |
| \ |
| /* 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(_z, wfracbits-1, 2*wfracbits); \ |
| R##_f0 = _z_f[0]; \ |
| R##_f1 = _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; \ |
| \ |
| if (wfracbits < 106 || wfracbits > 120) \ |
| abort(); \ |
| \ |
| 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 _n_f2, _n_f1, _n_f0, _r_f1, _r_f0, _m_f1, _m_f0; \ |
| if (_FP_FRAC_GT_2(X, Y)) \ |
| { \ |
| _n_f2 = X##_f1 >> 1; \ |
| _n_f1 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \ |
| _n_f0 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \ |
| } \ |
| else \ |
| { \ |
| R##_e--; \ |
| _n_f2 = X##_f1; \ |
| _n_f1 = X##_f0; \ |
| _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, _r_f1, _n_f2, _n_f1, Y##_f1); \ |
| umul_ppmm(_m_f1, _m_f0, R##_f1, Y##_f0); \ |
| _r_f0 = _n_f0; \ |
| if (_FP_FRAC_GT_2(_m, _r)) \ |
| { \ |
| R##_f1--; \ |
| _FP_FRAC_ADD_2(_r, Y, _r); \ |
| if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ |
| { \ |
| R##_f1--; \ |
| _FP_FRAC_ADD_2(_r, Y, _r); \ |
| } \ |
| } \ |
| _FP_FRAC_DEC_2(_r, _m); \ |
| \ |
| if (_r_f1 == Y##_f1) \ |
| { \ |
| /* This is a special case, not an optimization \ |
| (_r/Y##_f1 would not fit into UWtype). \ |
| As _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, _r_f1, _r_f1, _r_f0, Y##_f1); \ |
| umul_ppmm(_m_f1, _m_f0, R##_f0, Y##_f0); \ |
| _r_f0 = 0; \ |
| if (_FP_FRAC_GT_2(_m, _r)) \ |
| { \ |
| R##_f0--; \ |
| _FP_FRAC_ADD_2(_r, Y, _r); \ |
| if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ |
| { \ |
| R##_f0--; \ |
| _FP_FRAC_ADD_2(_r, Y, _r); \ |
| } \ |
| } \ |
| if (!_FP_FRAC_EQ_2(_r, _m)) \ |
| R##_f0 |= _FP_WORK_STICKY; \ |
| } \ |
| } while (0) |
| |
| |
| #define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \ |
| do { \ |
| _FP_W_TYPE _x[4], _y[2], _z[4]; \ |
| _y[0] = Y##_f0; _y[1] = Y##_f1; \ |
| _x[0] = _x[3] = 0; \ |
| if (_FP_FRAC_GT_2(X, Y)) \ |
| { \ |
| R##_e++; \ |
| _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE) | \ |
| X##_f1 >> (_FP_W_TYPE_SIZE - \ |
| (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE))); \ |
| _x[2] = X##_f1 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE); \ |
| } \ |
| else \ |
| { \ |
| _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE) | \ |
| X##_f1 >> (_FP_W_TYPE_SIZE - \ |
| (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE))); \ |
| _x[2] = X##_f1 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE); \ |
| } \ |
| \ |
| (void) mpn_divrem (_z, 0, _x, 4, _y, 2); \ |
| R##_f1 = _z[1]; \ |
| R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0); \ |
| } 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) \ |
| do { \ |
| if (rsize <= _FP_W_TYPE_SIZE) \ |
| r = X##_f0; \ |
| else \ |
| { \ |
| r = X##_f1; \ |
| r <<= _FP_W_TYPE_SIZE; \ |
| r += X##_f0; \ |
| } \ |
| } while (0) |
| |
| #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_CONV_1_2(dfs, sfs, D, S) \ |
| do { \ |
| if (S##_c != FP_CLS_NAN) \ |
| _FP_FRAC_SRS_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \ |
| _FP_WFRACBITS_##sfs); \ |
| else \ |
| _FP_FRAC_SRL_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs)); \ |
| D##_f = S##_f0; \ |
| } while (0) |
| |
| #define _FP_FRAC_CONV_2_1(dfs, sfs, D, S) \ |
| do { \ |
| D##_f0 = S##_f; \ |
| D##_f1 = 0; \ |
| _FP_FRAC_SLL_2(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \ |
| } while (0) |
| |
| #endif |
