1*1da177e4SLinus Torvalds /* Software floating-point emulation. 2*1da177e4SLinus Torvalds Basic one-word fraction declaration and manipulation. 3*1da177e4SLinus Torvalds Copyright (C) 1997,1998,1999 Free Software Foundation, Inc. 4*1da177e4SLinus Torvalds This file is part of the GNU C Library. 5*1da177e4SLinus Torvalds Contributed by Richard Henderson (rth@cygnus.com), 6*1da177e4SLinus Torvalds Jakub Jelinek (jj@ultra.linux.cz), 7*1da177e4SLinus Torvalds David S. Miller (davem@redhat.com) and 8*1da177e4SLinus Torvalds Peter Maydell (pmaydell@chiark.greenend.org.uk). 9*1da177e4SLinus Torvalds 10*1da177e4SLinus Torvalds The GNU C Library is free software; you can redistribute it and/or 11*1da177e4SLinus Torvalds modify it under the terms of the GNU Library General Public License as 12*1da177e4SLinus Torvalds published by the Free Software Foundation; either version 2 of the 13*1da177e4SLinus Torvalds License, or (at your option) any later version. 14*1da177e4SLinus Torvalds 15*1da177e4SLinus Torvalds The GNU C Library is distributed in the hope that it will be useful, 16*1da177e4SLinus Torvalds but WITHOUT ANY WARRANTY; without even the implied warranty of 17*1da177e4SLinus Torvalds MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 18*1da177e4SLinus Torvalds Library General Public License for more details. 19*1da177e4SLinus Torvalds 20*1da177e4SLinus Torvalds You should have received a copy of the GNU Library General Public 21*1da177e4SLinus Torvalds License along with the GNU C Library; see the file COPYING.LIB. If 22*1da177e4SLinus Torvalds not, write to the Free Software Foundation, Inc., 23*1da177e4SLinus Torvalds 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ 24*1da177e4SLinus Torvalds 25*1da177e4SLinus Torvalds #ifndef __MATH_EMU_OP_1_H__ 26*1da177e4SLinus Torvalds #define __MATH_EMU_OP_1_H__ 27*1da177e4SLinus Torvalds 28*1da177e4SLinus Torvalds #define _FP_FRAC_DECL_1(X) _FP_W_TYPE X##_f=0 29*1da177e4SLinus Torvalds #define _FP_FRAC_COPY_1(D,S) (D##_f = S##_f) 30*1da177e4SLinus Torvalds #define _FP_FRAC_SET_1(X,I) (X##_f = I) 31*1da177e4SLinus Torvalds #define _FP_FRAC_HIGH_1(X) (X##_f) 32*1da177e4SLinus Torvalds #define _FP_FRAC_LOW_1(X) (X##_f) 33*1da177e4SLinus Torvalds #define _FP_FRAC_WORD_1(X,w) (X##_f) 34*1da177e4SLinus Torvalds 35*1da177e4SLinus Torvalds #define _FP_FRAC_ADDI_1(X,I) (X##_f += I) 36*1da177e4SLinus Torvalds #define _FP_FRAC_SLL_1(X,N) \ 37*1da177e4SLinus Torvalds do { \ 38*1da177e4SLinus Torvalds if (__builtin_constant_p(N) && (N) == 1) \ 39*1da177e4SLinus Torvalds X##_f += X##_f; \ 40*1da177e4SLinus Torvalds else \ 41*1da177e4SLinus Torvalds X##_f <<= (N); \ 42*1da177e4SLinus Torvalds } while (0) 43*1da177e4SLinus Torvalds #define _FP_FRAC_SRL_1(X,N) (X##_f >>= N) 44*1da177e4SLinus Torvalds 45*1da177e4SLinus Torvalds /* Right shift with sticky-lsb. */ 46*1da177e4SLinus Torvalds #define _FP_FRAC_SRS_1(X,N,sz) __FP_FRAC_SRS_1(X##_f, N, sz) 47*1da177e4SLinus Torvalds 48*1da177e4SLinus Torvalds #define __FP_FRAC_SRS_1(X,N,sz) \ 49*1da177e4SLinus Torvalds (X = (X >> (N) | (__builtin_constant_p(N) && (N) == 1 \ 50*1da177e4SLinus Torvalds ? X & 1 : (X << (_FP_W_TYPE_SIZE - (N))) != 0))) 51*1da177e4SLinus Torvalds 52*1da177e4SLinus Torvalds #define _FP_FRAC_ADD_1(R,X,Y) (R##_f = X##_f + Y##_f) 53*1da177e4SLinus Torvalds #define _FP_FRAC_SUB_1(R,X,Y) (R##_f = X##_f - Y##_f) 54*1da177e4SLinus Torvalds #define _FP_FRAC_DEC_1(X,Y) (X##_f -= Y##_f) 55*1da177e4SLinus Torvalds #define _FP_FRAC_CLZ_1(z, X) __FP_CLZ(z, X##_f) 56*1da177e4SLinus Torvalds 57*1da177e4SLinus Torvalds /* Predicates */ 58*1da177e4SLinus Torvalds #define _FP_FRAC_NEGP_1(X) ((_FP_WS_TYPE)X##_f < 0) 59*1da177e4SLinus Torvalds #define _FP_FRAC_ZEROP_1(X) (X##_f == 0) 60*1da177e4SLinus Torvalds #define _FP_FRAC_OVERP_1(fs,X) (X##_f & _FP_OVERFLOW_##fs) 61*1da177e4SLinus Torvalds #define _FP_FRAC_CLEAR_OVERP_1(fs,X) (X##_f &= ~_FP_OVERFLOW_##fs) 62*1da177e4SLinus Torvalds #define _FP_FRAC_EQ_1(X, Y) (X##_f == Y##_f) 63*1da177e4SLinus Torvalds #define _FP_FRAC_GE_1(X, Y) (X##_f >= Y##_f) 64*1da177e4SLinus Torvalds #define _FP_FRAC_GT_1(X, Y) (X##_f > Y##_f) 65*1da177e4SLinus Torvalds 66*1da177e4SLinus Torvalds #define _FP_ZEROFRAC_1 0 67*1da177e4SLinus Torvalds #define _FP_MINFRAC_1 1 68*1da177e4SLinus Torvalds #define _FP_MAXFRAC_1 (~(_FP_WS_TYPE)0) 69*1da177e4SLinus Torvalds 70*1da177e4SLinus Torvalds /* 71*1da177e4SLinus Torvalds * Unpack the raw bits of a native fp value. Do not classify or 72*1da177e4SLinus Torvalds * normalize the data. 73*1da177e4SLinus Torvalds */ 74*1da177e4SLinus Torvalds 75*1da177e4SLinus Torvalds #define _FP_UNPACK_RAW_1(fs, X, val) \ 76*1da177e4SLinus Torvalds do { \ 77*1da177e4SLinus Torvalds union _FP_UNION_##fs _flo; _flo.flt = (val); \ 78*1da177e4SLinus Torvalds \ 79*1da177e4SLinus Torvalds X##_f = _flo.bits.frac; \ 80*1da177e4SLinus Torvalds X##_e = _flo.bits.exp; \ 81*1da177e4SLinus Torvalds X##_s = _flo.bits.sign; \ 82*1da177e4SLinus Torvalds } while (0) 83*1da177e4SLinus Torvalds 84*1da177e4SLinus Torvalds #define _FP_UNPACK_RAW_1_P(fs, X, val) \ 85*1da177e4SLinus Torvalds do { \ 86*1da177e4SLinus Torvalds union _FP_UNION_##fs *_flo = \ 87*1da177e4SLinus Torvalds (union _FP_UNION_##fs *)(val); \ 88*1da177e4SLinus Torvalds \ 89*1da177e4SLinus Torvalds X##_f = _flo->bits.frac; \ 90*1da177e4SLinus Torvalds X##_e = _flo->bits.exp; \ 91*1da177e4SLinus Torvalds X##_s = _flo->bits.sign; \ 92*1da177e4SLinus Torvalds } while (0) 93*1da177e4SLinus Torvalds 94*1da177e4SLinus Torvalds /* 95*1da177e4SLinus Torvalds * Repack the raw bits of a native fp value. 96*1da177e4SLinus Torvalds */ 97*1da177e4SLinus Torvalds 98*1da177e4SLinus Torvalds #define _FP_PACK_RAW_1(fs, val, X) \ 99*1da177e4SLinus Torvalds do { \ 100*1da177e4SLinus Torvalds union _FP_UNION_##fs _flo; \ 101*1da177e4SLinus Torvalds \ 102*1da177e4SLinus Torvalds _flo.bits.frac = X##_f; \ 103*1da177e4SLinus Torvalds _flo.bits.exp = X##_e; \ 104*1da177e4SLinus Torvalds _flo.bits.sign = X##_s; \ 105*1da177e4SLinus Torvalds \ 106*1da177e4SLinus Torvalds (val) = _flo.flt; \ 107*1da177e4SLinus Torvalds } while (0) 108*1da177e4SLinus Torvalds 109*1da177e4SLinus Torvalds #define _FP_PACK_RAW_1_P(fs, val, X) \ 110*1da177e4SLinus Torvalds do { \ 111*1da177e4SLinus Torvalds union _FP_UNION_##fs *_flo = \ 112*1da177e4SLinus Torvalds (union _FP_UNION_##fs *)(val); \ 113*1da177e4SLinus Torvalds \ 114*1da177e4SLinus Torvalds _flo->bits.frac = X##_f; \ 115*1da177e4SLinus Torvalds _flo->bits.exp = X##_e; \ 116*1da177e4SLinus Torvalds _flo->bits.sign = X##_s; \ 117*1da177e4SLinus Torvalds } while (0) 118*1da177e4SLinus Torvalds 119*1da177e4SLinus Torvalds 120*1da177e4SLinus Torvalds /* 121*1da177e4SLinus Torvalds * Multiplication algorithms: 122*1da177e4SLinus Torvalds */ 123*1da177e4SLinus Torvalds 124*1da177e4SLinus Torvalds /* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the 125*1da177e4SLinus Torvalds multiplication immediately. */ 126*1da177e4SLinus Torvalds 127*1da177e4SLinus Torvalds #define _FP_MUL_MEAT_1_imm(wfracbits, R, X, Y) \ 128*1da177e4SLinus Torvalds do { \ 129*1da177e4SLinus Torvalds R##_f = X##_f * Y##_f; \ 130*1da177e4SLinus Torvalds /* Normalize since we know where the msb of the multiplicands \ 131*1da177e4SLinus Torvalds were (bit B), we know that the msb of the of the product is \ 132*1da177e4SLinus Torvalds at either 2B or 2B-1. */ \ 133*1da177e4SLinus Torvalds _FP_FRAC_SRS_1(R, wfracbits-1, 2*wfracbits); \ 134*1da177e4SLinus Torvalds } while (0) 135*1da177e4SLinus Torvalds 136*1da177e4SLinus Torvalds /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ 137*1da177e4SLinus Torvalds 138*1da177e4SLinus Torvalds #define _FP_MUL_MEAT_1_wide(wfracbits, R, X, Y, doit) \ 139*1da177e4SLinus Torvalds do { \ 140*1da177e4SLinus Torvalds _FP_W_TYPE _Z_f0, _Z_f1; \ 141*1da177e4SLinus Torvalds doit(_Z_f1, _Z_f0, X##_f, Y##_f); \ 142*1da177e4SLinus Torvalds /* Normalize since we know where the msb of the multiplicands \ 143*1da177e4SLinus Torvalds were (bit B), we know that the msb of the of the product is \ 144*1da177e4SLinus Torvalds at either 2B or 2B-1. */ \ 145*1da177e4SLinus Torvalds _FP_FRAC_SRS_2(_Z, wfracbits-1, 2*wfracbits); \ 146*1da177e4SLinus Torvalds R##_f = _Z_f0; \ 147*1da177e4SLinus Torvalds } while (0) 148*1da177e4SLinus Torvalds 149*1da177e4SLinus Torvalds /* Finally, a simple widening multiply algorithm. What fun! */ 150*1da177e4SLinus Torvalds 151*1da177e4SLinus Torvalds #define _FP_MUL_MEAT_1_hard(wfracbits, R, X, Y) \ 152*1da177e4SLinus Torvalds do { \ 153*1da177e4SLinus Torvalds _FP_W_TYPE _xh, _xl, _yh, _yl, _z_f0, _z_f1, _a_f0, _a_f1; \ 154*1da177e4SLinus Torvalds \ 155*1da177e4SLinus Torvalds /* split the words in half */ \ 156*1da177e4SLinus Torvalds _xh = X##_f >> (_FP_W_TYPE_SIZE/2); \ 157*1da177e4SLinus Torvalds _xl = X##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1); \ 158*1da177e4SLinus Torvalds _yh = Y##_f >> (_FP_W_TYPE_SIZE/2); \ 159*1da177e4SLinus Torvalds _yl = Y##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1); \ 160*1da177e4SLinus Torvalds \ 161*1da177e4SLinus Torvalds /* multiply the pieces */ \ 162*1da177e4SLinus Torvalds _z_f0 = _xl * _yl; \ 163*1da177e4SLinus Torvalds _a_f0 = _xh * _yl; \ 164*1da177e4SLinus Torvalds _a_f1 = _xl * _yh; \ 165*1da177e4SLinus Torvalds _z_f1 = _xh * _yh; \ 166*1da177e4SLinus Torvalds \ 167*1da177e4SLinus Torvalds /* reassemble into two full words */ \ 168*1da177e4SLinus Torvalds if ((_a_f0 += _a_f1) < _a_f1) \ 169*1da177e4SLinus Torvalds _z_f1 += (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2); \ 170*1da177e4SLinus Torvalds _a_f1 = _a_f0 >> (_FP_W_TYPE_SIZE/2); \ 171*1da177e4SLinus Torvalds _a_f0 = _a_f0 << (_FP_W_TYPE_SIZE/2); \ 172*1da177e4SLinus Torvalds _FP_FRAC_ADD_2(_z, _z, _a); \ 173*1da177e4SLinus Torvalds \ 174*1da177e4SLinus Torvalds /* normalize */ \ 175*1da177e4SLinus Torvalds _FP_FRAC_SRS_2(_z, wfracbits - 1, 2*wfracbits); \ 176*1da177e4SLinus Torvalds R##_f = _z_f0; \ 177*1da177e4SLinus Torvalds } while (0) 178*1da177e4SLinus Torvalds 179*1da177e4SLinus Torvalds 180*1da177e4SLinus Torvalds /* 181*1da177e4SLinus Torvalds * Division algorithms: 182*1da177e4SLinus Torvalds */ 183*1da177e4SLinus Torvalds 184*1da177e4SLinus Torvalds /* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the 185*1da177e4SLinus Torvalds division immediately. Give this macro either _FP_DIV_HELP_imm for 186*1da177e4SLinus Torvalds C primitives or _FP_DIV_HELP_ldiv for the ISO function. Which you 187*1da177e4SLinus Torvalds choose will depend on what the compiler does with divrem4. */ 188*1da177e4SLinus Torvalds 189*1da177e4SLinus Torvalds #define _FP_DIV_MEAT_1_imm(fs, R, X, Y, doit) \ 190*1da177e4SLinus Torvalds do { \ 191*1da177e4SLinus Torvalds _FP_W_TYPE _q, _r; \ 192*1da177e4SLinus Torvalds X##_f <<= (X##_f < Y##_f \ 193*1da177e4SLinus Torvalds ? R##_e--, _FP_WFRACBITS_##fs \ 194*1da177e4SLinus Torvalds : _FP_WFRACBITS_##fs - 1); \ 195*1da177e4SLinus Torvalds doit(_q, _r, X##_f, Y##_f); \ 196*1da177e4SLinus Torvalds R##_f = _q | (_r != 0); \ 197*1da177e4SLinus Torvalds } while (0) 198*1da177e4SLinus Torvalds 199*1da177e4SLinus Torvalds /* GCC's longlong.h defines a 2W / 1W => (1W,1W) primitive udiv_qrnnd 200*1da177e4SLinus Torvalds that may be useful in this situation. This first is for a primitive 201*1da177e4SLinus Torvalds that requires normalization, the second for one that does not. Look 202*1da177e4SLinus Torvalds for UDIV_NEEDS_NORMALIZATION to tell which your machine needs. */ 203*1da177e4SLinus Torvalds 204*1da177e4SLinus Torvalds #define _FP_DIV_MEAT_1_udiv_norm(fs, R, X, Y) \ 205*1da177e4SLinus Torvalds do { \ 206*1da177e4SLinus Torvalds _FP_W_TYPE _nh, _nl, _q, _r, _y; \ 207*1da177e4SLinus Torvalds \ 208*1da177e4SLinus Torvalds /* Normalize Y -- i.e. make the most significant bit set. */ \ 209*1da177e4SLinus Torvalds _y = Y##_f << _FP_WFRACXBITS_##fs; \ 210*1da177e4SLinus Torvalds \ 211*1da177e4SLinus Torvalds /* Shift X op correspondingly high, that is, up one full word. */ \ 212*1da177e4SLinus Torvalds if (X##_f < Y##_f) \ 213*1da177e4SLinus Torvalds { \ 214*1da177e4SLinus Torvalds R##_e--; \ 215*1da177e4SLinus Torvalds _nl = 0; \ 216*1da177e4SLinus Torvalds _nh = X##_f; \ 217*1da177e4SLinus Torvalds } \ 218*1da177e4SLinus Torvalds else \ 219*1da177e4SLinus Torvalds { \ 220*1da177e4SLinus Torvalds _nl = X##_f << (_FP_W_TYPE_SIZE - 1); \ 221*1da177e4SLinus Torvalds _nh = X##_f >> 1; \ 222*1da177e4SLinus Torvalds } \ 223*1da177e4SLinus Torvalds \ 224*1da177e4SLinus Torvalds udiv_qrnnd(_q, _r, _nh, _nl, _y); \ 225*1da177e4SLinus Torvalds R##_f = _q | (_r != 0); \ 226*1da177e4SLinus Torvalds } while (0) 227*1da177e4SLinus Torvalds 228*1da177e4SLinus Torvalds #define _FP_DIV_MEAT_1_udiv(fs, R, X, Y) \ 229*1da177e4SLinus Torvalds do { \ 230*1da177e4SLinus Torvalds _FP_W_TYPE _nh, _nl, _q, _r; \ 231*1da177e4SLinus Torvalds if (X##_f < Y##_f) \ 232*1da177e4SLinus Torvalds { \ 233*1da177e4SLinus Torvalds R##_e--; \ 234*1da177e4SLinus Torvalds _nl = X##_f << _FP_WFRACBITS_##fs; \ 235*1da177e4SLinus Torvalds _nh = X##_f >> _FP_WFRACXBITS_##fs; \ 236*1da177e4SLinus Torvalds } \ 237*1da177e4SLinus Torvalds else \ 238*1da177e4SLinus Torvalds { \ 239*1da177e4SLinus Torvalds _nl = X##_f << (_FP_WFRACBITS_##fs - 1); \ 240*1da177e4SLinus Torvalds _nh = X##_f >> (_FP_WFRACXBITS_##fs + 1); \ 241*1da177e4SLinus Torvalds } \ 242*1da177e4SLinus Torvalds udiv_qrnnd(_q, _r, _nh, _nl, Y##_f); \ 243*1da177e4SLinus Torvalds R##_f = _q | (_r != 0); \ 244*1da177e4SLinus Torvalds } while (0) 245*1da177e4SLinus Torvalds 246*1da177e4SLinus Torvalds 247*1da177e4SLinus Torvalds /* 248*1da177e4SLinus Torvalds * Square root algorithms: 249*1da177e4SLinus Torvalds * We have just one right now, maybe Newton approximation 250*1da177e4SLinus Torvalds * should be added for those machines where division is fast. 251*1da177e4SLinus Torvalds */ 252*1da177e4SLinus Torvalds 253*1da177e4SLinus Torvalds #define _FP_SQRT_MEAT_1(R, S, T, X, q) \ 254*1da177e4SLinus Torvalds do { \ 255*1da177e4SLinus Torvalds while (q != _FP_WORK_ROUND) \ 256*1da177e4SLinus Torvalds { \ 257*1da177e4SLinus Torvalds T##_f = S##_f + q; \ 258*1da177e4SLinus Torvalds if (T##_f <= X##_f) \ 259*1da177e4SLinus Torvalds { \ 260*1da177e4SLinus Torvalds S##_f = T##_f + q; \ 261*1da177e4SLinus Torvalds X##_f -= T##_f; \ 262*1da177e4SLinus Torvalds R##_f += q; \ 263*1da177e4SLinus Torvalds } \ 264*1da177e4SLinus Torvalds _FP_FRAC_SLL_1(X, 1); \ 265*1da177e4SLinus Torvalds q >>= 1; \ 266*1da177e4SLinus Torvalds } \ 267*1da177e4SLinus Torvalds if (X##_f) \ 268*1da177e4SLinus Torvalds { \ 269*1da177e4SLinus Torvalds if (S##_f < X##_f) \ 270*1da177e4SLinus Torvalds R##_f |= _FP_WORK_ROUND; \ 271*1da177e4SLinus Torvalds R##_f |= _FP_WORK_STICKY; \ 272*1da177e4SLinus Torvalds } \ 273*1da177e4SLinus Torvalds } while (0) 274*1da177e4SLinus Torvalds 275*1da177e4SLinus Torvalds /* 276*1da177e4SLinus Torvalds * Assembly/disassembly for converting to/from integral types. 277*1da177e4SLinus Torvalds * No shifting or overflow handled here. 278*1da177e4SLinus Torvalds */ 279*1da177e4SLinus Torvalds 280*1da177e4SLinus Torvalds #define _FP_FRAC_ASSEMBLE_1(r, X, rsize) (r = X##_f) 281*1da177e4SLinus Torvalds #define _FP_FRAC_DISASSEMBLE_1(X, r, rsize) (X##_f = r) 282*1da177e4SLinus Torvalds 283*1da177e4SLinus Torvalds 284*1da177e4SLinus Torvalds /* 285*1da177e4SLinus Torvalds * Convert FP values between word sizes 286*1da177e4SLinus Torvalds */ 287*1da177e4SLinus Torvalds 288*1da177e4SLinus Torvalds #define _FP_FRAC_CONV_1_1(dfs, sfs, D, S) \ 289*1da177e4SLinus Torvalds do { \ 290*1da177e4SLinus Torvalds D##_f = S##_f; \ 291*1da177e4SLinus Torvalds if (_FP_WFRACBITS_##sfs > _FP_WFRACBITS_##dfs) \ 292*1da177e4SLinus Torvalds { \ 293*1da177e4SLinus Torvalds if (S##_c != FP_CLS_NAN) \ 294*1da177e4SLinus Torvalds _FP_FRAC_SRS_1(D, (_FP_WFRACBITS_##sfs-_FP_WFRACBITS_##dfs), \ 295*1da177e4SLinus Torvalds _FP_WFRACBITS_##sfs); \ 296*1da177e4SLinus Torvalds else \ 297*1da177e4SLinus Torvalds _FP_FRAC_SRL_1(D, (_FP_WFRACBITS_##sfs-_FP_WFRACBITS_##dfs)); \ 298*1da177e4SLinus Torvalds } \ 299*1da177e4SLinus Torvalds else \ 300*1da177e4SLinus Torvalds D##_f <<= _FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs; \ 301*1da177e4SLinus Torvalds } while (0) 302*1da177e4SLinus Torvalds 303*1da177e4SLinus Torvalds #endif /* __MATH_EMU_OP_1_H__ */ 304