/* IEEE754 floating point arithmetic * double precision: common utilities */ /* * MIPS floating point support * Copyright (C) 1994-2000 Algorithmics Ltd. * http://www.algor.co.uk * * ######################################################################## * * This program is free software; you can distribute it and/or modify it * under the terms of the GNU General Public License (Version 2) as * published by the Free Software Foundation. * * This program is distributed in the hope it will be useful, but WITHOUT * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License * for more details. * * You should have received a copy of the GNU General Public License along * with this program; if not, write to the Free Software Foundation, Inc., * 59 Temple Place - Suite 330, Boston MA 02111-1307, USA. * * ######################################################################## */ #include "ieee754dp.h" ieee754dp ieee754dp_mul(ieee754dp x, ieee754dp y) { COMPXDP; COMPYDP; EXPLODEXDP; EXPLODEYDP; CLEARCX; FLUSHXDP; FLUSHYDP; switch (CLPAIR(xc, yc)) { case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF): SETCX(IEEE754_INVALID_OPERATION); return ieee754dp_nanxcpt(ieee754dp_indef(), "mul", x, y); case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN): return y; case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF): return x; /* Infinity handling */ case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF): SETCX(IEEE754_INVALID_OPERATION); return ieee754dp_xcpt(ieee754dp_indef(), "mul", x, y); case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF): return ieee754dp_inf(xs ^ ys); case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM): case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO): return ieee754dp_zero(xs ^ ys); case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM): DPDNORMX; case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM): DPDNORMY; break; case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM): DPDNORMX; break; case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_NORM): break; } /* rm = xm * ym, re = xe+ye basicly */ assert(xm & DP_HIDDEN_BIT); assert(ym & DP_HIDDEN_BIT); { int re = xe + ye; int rs = xs ^ ys; u64 rm; /* shunt to top of word */ xm <<= 64 - (DP_MBITS + 1); ym <<= 64 - (DP_MBITS + 1); /* multiply 32bits xm,ym to give high 32bits rm with stickness */ /* 32 * 32 => 64 */ #define DPXMULT(x,y) ((u64)(x) * (u64)y) { unsigned lxm = xm; unsigned hxm = xm >> 32; unsigned lym = ym; unsigned hym = ym >> 32; u64 lrm; u64 hrm; lrm = DPXMULT(lxm, lym); hrm = DPXMULT(hxm, hym); { u64 t = DPXMULT(lxm, hym); { u64 at = lrm + (t << 32); hrm += at < lrm; lrm = at; } hrm = hrm + (t >> 32); } { u64 t = DPXMULT(hxm, lym); { u64 at = lrm + (t << 32); hrm += at < lrm; lrm = at; } hrm = hrm + (t >> 32); } rm = hrm | (lrm != 0); } /* * sticky shift down to normal rounding precision */ if ((s64) rm < 0) { rm = (rm >> (64 - (DP_MBITS + 1 + 3))) | ((rm << (DP_MBITS + 1 + 3)) != 0); re++; } else { rm = (rm >> (64 - (DP_MBITS + 1 + 3 + 1))) | ((rm << (DP_MBITS + 1 + 3 + 1)) != 0); } assert(rm & (DP_HIDDEN_BIT << 3)); DPNORMRET2(rs, re, rm, "mul", x, y); } }