166 lines
4 KiB
C
166 lines
4 KiB
C
/* IEEE754 floating point arithmetic
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* double precision square root
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*/
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/*
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* MIPS floating point support
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* Copyright (C) 1994-2000 Algorithmics Ltd.
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*
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* This program is free software; you can distribute it and/or modify it
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* under the terms of the GNU General Public License (Version 2) as
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* published by the Free Software Foundation.
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*
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* This program is distributed in the hope it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*/
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#include "ieee754dp.h"
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static const unsigned int table[] = {
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0, 1204, 3062, 5746, 9193, 13348, 18162, 23592,
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29598, 36145, 43202, 50740, 58733, 67158, 75992,
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85215, 83599, 71378, 60428, 50647, 41945, 34246,
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27478, 21581, 16499, 12183, 8588, 5674, 3403,
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1742, 661, 130
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};
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union ieee754dp ieee754dp_sqrt(union ieee754dp x)
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{
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struct _ieee754_csr oldcsr;
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union ieee754dp y, z, t;
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unsigned int scalx, yh;
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COMPXDP;
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EXPLODEXDP;
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ieee754_clearcx();
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FLUSHXDP;
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/* x == INF or NAN? */
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switch (xc) {
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case IEEE754_CLASS_SNAN:
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return ieee754dp_nanxcpt(x);
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case IEEE754_CLASS_QNAN:
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/* sqrt(Nan) = Nan */
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return x;
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case IEEE754_CLASS_ZERO:
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/* sqrt(0) = 0 */
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return x;
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case IEEE754_CLASS_INF:
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if (xs) {
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/* sqrt(-Inf) = Nan */
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ieee754_setcx(IEEE754_INVALID_OPERATION);
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return ieee754dp_indef();
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}
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/* sqrt(+Inf) = Inf */
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return x;
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case IEEE754_CLASS_DNORM:
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DPDNORMX;
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/* fall through */
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case IEEE754_CLASS_NORM:
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if (xs) {
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/* sqrt(-x) = Nan */
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ieee754_setcx(IEEE754_INVALID_OPERATION);
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return ieee754dp_indef();
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}
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break;
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}
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/* save old csr; switch off INX enable & flag; set RN rounding */
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oldcsr = ieee754_csr;
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ieee754_csr.mx &= ~IEEE754_INEXACT;
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ieee754_csr.sx &= ~IEEE754_INEXACT;
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ieee754_csr.rm = FPU_CSR_RN;
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/* adjust exponent to prevent overflow */
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scalx = 0;
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if (xe > 512) { /* x > 2**-512? */
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xe -= 512; /* x = x / 2**512 */
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scalx += 256;
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} else if (xe < -512) { /* x < 2**-512? */
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xe += 512; /* x = x * 2**512 */
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scalx -= 256;
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}
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x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
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y = x;
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/* magic initial approximation to almost 8 sig. bits */
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yh = y.bits >> 32;
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yh = (yh >> 1) + 0x1ff80000;
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yh = yh - table[(yh >> 15) & 31];
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y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff);
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/* Heron's rule once with correction to improve to ~18 sig. bits */
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/* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */
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t = ieee754dp_div(x, y);
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y = ieee754dp_add(y, t);
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y.bits -= 0x0010000600000000LL;
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y.bits &= 0xffffffff00000000LL;
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/* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */
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/* t=y*y; z=t; pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */
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t = ieee754dp_mul(y, y);
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z = t;
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t.bexp += 0x001;
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t = ieee754dp_add(t, z);
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z = ieee754dp_mul(ieee754dp_sub(x, z), y);
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/* t=z/(t+x) ; pt[n0]+=0x00100000; y+=t; */
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t = ieee754dp_div(z, ieee754dp_add(t, x));
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t.bexp += 0x001;
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y = ieee754dp_add(y, t);
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/* twiddle last bit to force y correctly rounded */
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/* set RZ, clear INEX flag */
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ieee754_csr.rm = FPU_CSR_RZ;
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ieee754_csr.sx &= ~IEEE754_INEXACT;
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/* t=x/y; ...chopped quotient, possibly inexact */
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t = ieee754dp_div(x, y);
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if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) {
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if (!(ieee754_csr.sx & IEEE754_INEXACT))
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/* t = t-ulp */
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t.bits -= 1;
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/* add inexact to result status */
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oldcsr.cx |= IEEE754_INEXACT;
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oldcsr.sx |= IEEE754_INEXACT;
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switch (oldcsr.rm) {
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case FPU_CSR_RU:
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y.bits += 1;
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/* fall through */
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case FPU_CSR_RN:
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t.bits += 1;
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break;
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}
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/* y=y+t; ...chopped sum */
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y = ieee754dp_add(y, t);
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/* adjust scalx for correctly rounded sqrt(x) */
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scalx -= 1;
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}
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/* py[n0]=py[n0]+scalx; ...scale back y */
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y.bexp += scalx;
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/* restore rounding mode, possibly set inexact */
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ieee754_csr = oldcsr;
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return y;
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}
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