123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163 |
- /* IEEE754 floating point arithmetic
- * double precision square root
- */
- /*
- * MIPS floating point support
- * Copyright (C) 1994-2000 Algorithmics Ltd.
- *
- * 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.,
- * 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
- */
- #include "ieee754dp.h"
- static const unsigned table[] = {
- 0, 1204, 3062, 5746, 9193, 13348, 18162, 23592,
- 29598, 36145, 43202, 50740, 58733, 67158, 75992,
- 85215, 83599, 71378, 60428, 50647, 41945, 34246,
- 27478, 21581, 16499, 12183, 8588, 5674, 3403,
- 1742, 661, 130
- };
- union ieee754dp ieee754dp_sqrt(union ieee754dp x)
- {
- struct _ieee754_csr oldcsr;
- union ieee754dp y, z, t;
- unsigned scalx, yh;
- COMPXDP;
- EXPLODEXDP;
- ieee754_clearcx();
- FLUSHXDP;
- /* x == INF or NAN? */
- switch (xc) {
- case IEEE754_CLASS_SNAN:
- return ieee754dp_nanxcpt(x);
- case IEEE754_CLASS_QNAN:
- /* sqrt(Nan) = Nan */
- return x;
- case IEEE754_CLASS_ZERO:
- /* sqrt(0) = 0 */
- return x;
- case IEEE754_CLASS_INF:
- if (xs) {
- /* sqrt(-Inf) = Nan */
- ieee754_setcx(IEEE754_INVALID_OPERATION);
- return ieee754dp_indef();
- }
- /* sqrt(+Inf) = Inf */
- return x;
- case IEEE754_CLASS_DNORM:
- DPDNORMX;
- /* fall through */
- case IEEE754_CLASS_NORM:
- if (xs) {
- /* sqrt(-x) = Nan */
- ieee754_setcx(IEEE754_INVALID_OPERATION);
- return ieee754dp_indef();
- }
- break;
- }
- /* save old csr; switch off INX enable & flag; set RN rounding */
- oldcsr = ieee754_csr;
- ieee754_csr.mx &= ~IEEE754_INEXACT;
- ieee754_csr.sx &= ~IEEE754_INEXACT;
- ieee754_csr.rm = FPU_CSR_RN;
- /* adjust exponent to prevent overflow */
- scalx = 0;
- if (xe > 512) { /* x > 2**-512? */
- xe -= 512; /* x = x / 2**512 */
- scalx += 256;
- } else if (xe < -512) { /* x < 2**-512? */
- xe += 512; /* x = x * 2**512 */
- scalx -= 256;
- }
- y = x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
- /* magic initial approximation to almost 8 sig. bits */
- yh = y.bits >> 32;
- yh = (yh >> 1) + 0x1ff80000;
- yh = yh - table[(yh >> 15) & 31];
- y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff);
- /* Heron's rule once with correction to improve to ~18 sig. bits */
- /* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */
- t = ieee754dp_div(x, y);
- y = ieee754dp_add(y, t);
- y.bits -= 0x0010000600000000LL;
- y.bits &= 0xffffffff00000000LL;
- /* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */
- /* t=y*y; z=t; pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */
- z = t = ieee754dp_mul(y, y);
- t.bexp += 0x001;
- t = ieee754dp_add(t, z);
- z = ieee754dp_mul(ieee754dp_sub(x, z), y);
- /* t=z/(t+x) ; pt[n0]+=0x00100000; y+=t; */
- t = ieee754dp_div(z, ieee754dp_add(t, x));
- t.bexp += 0x001;
- y = ieee754dp_add(y, t);
- /* twiddle last bit to force y correctly rounded */
- /* set RZ, clear INEX flag */
- ieee754_csr.rm = FPU_CSR_RZ;
- ieee754_csr.sx &= ~IEEE754_INEXACT;
- /* t=x/y; ...chopped quotient, possibly inexact */
- t = ieee754dp_div(x, y);
- if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) {
- if (!(ieee754_csr.sx & IEEE754_INEXACT))
- /* t = t-ulp */
- t.bits -= 1;
- /* add inexact to result status */
- oldcsr.cx |= IEEE754_INEXACT;
- oldcsr.sx |= IEEE754_INEXACT;
- switch (oldcsr.rm) {
- case FPU_CSR_RU:
- y.bits += 1;
- /* drop through */
- case FPU_CSR_RN:
- t.bits += 1;
- break;
- }
- /* y=y+t; ...chopped sum */
- y = ieee754dp_add(y, t);
- /* adjust scalx for correctly rounded sqrt(x) */
- scalx -= 1;
- }
- /* py[n0]=py[n0]+scalx; ...scale back y */
- y.bexp += scalx;
- /* restore rounding mode, possibly set inexact */
- ieee754_csr = oldcsr;
- return y;
- }
|