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Diffstat (limited to 'include/math-emu/op-2.h')
| -rw-r--r-- | include/math-emu/op-2.h | 613 |
1 files changed, 613 insertions, 0 deletions
diff --git a/include/math-emu/op-2.h b/include/math-emu/op-2.h new file mode 100644 index 000000000..4f26ecc14 --- /dev/null +++ b/include/math-emu/op-2.h @@ -0,0 +1,613 @@ +/* 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) \ + do { \ + if ((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); \ + } \ + } \ + else \ + { \ + X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \ + X##_f0 = 0; \ + } \ + } while (0) + +#define _FP_FRAC_SRL_2(X,N) \ + do { \ + if ((N) < _FP_W_TYPE_SIZE) \ + { \ + X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \ + X##_f1 >>= (N); \ + } \ + else \ + { \ + X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \ + X##_f1 = 0; \ + } \ + } while (0) + +/* Right shift with sticky-lsb. */ +#define _FP_FRAC_SRS_2(X,N,sz) \ + do { \ + if ((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); \ + } \ + else \ + { \ + X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) | \ + (((X##_f1 << (2*_FP_W_TYPE_SIZE - (N))) | X##_f0) != 0)); \ + X##_f1 = 0; \ + } \ + } while (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 |