![Ralf Baechle](/assets/img/avatar_default.png)
Previously math-emu was using the IEEE-754 constants internally. These were differing by having the constants for rounding to +/- infinity switched, so a conversion was necessary. This would be entirely avoidable if the MIPS constants were used throughout, so get rid of the bloat. Signed-off-by: Ralf Baechle <ralf@linux-mips.org>
165 lines
4.1 KiB
C
165 lines
4.1 KiB
C
/* 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_QNAN:
|
|
/* sqrt(Nan) = Nan */
|
|
return ieee754dp_nanxcpt(x);
|
|
|
|
case IEEE754_CLASS_SNAN:
|
|
ieee754_setcx(IEEE754_INVALID_OPERATION);
|
|
return ieee754dp_nanxcpt(ieee754dp_indef());
|
|
|
|
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_nanxcpt(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_nanxcpt(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;
|
|
}
|