mirror of
https://git.kernel.org/pub/scm/linux/kernel/git/stable/linux.git
synced 2024-08-25 18:30:06 +00:00
![Thomas Gleixner](/assets/img/avatar_default.png)
Based on 1 normalized pattern(s): 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 extracted by the scancode license scanner the SPDX license identifier GPL-2.0-only has been chosen to replace the boilerplate/reference in 33 file(s). Signed-off-by: Thomas Gleixner <tglx@linutronix.de> Reviewed-by: Allison Randal <allison@lohutok.net> Reviewed-by: Richard Fontana <rfontana@redhat.com> Reviewed-by: Kate Stewart <kstewart@linuxfoundation.org> Cc: linux-spdx@vger.kernel.org Link: https://lkml.kernel.org/r/20190531081038.563233189@linutronix.de Signed-off-by: Greg Kroah-Hartman <gregkh@linuxfoundation.org>
153 lines
3.4 KiB
C
153 lines
3.4 KiB
C
// SPDX-License-Identifier: GPL-2.0-only
|
|
/* IEEE754 floating point arithmetic
|
|
* double precision square root
|
|
*/
|
|
/*
|
|
* MIPS floating point support
|
|
* Copyright (C) 1994-2000 Algorithmics Ltd.
|
|
*/
|
|
|
|
#include "ieee754dp.h"
|
|
|
|
static const unsigned int 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 int 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;
|
|
}
|
|
|
|
x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
|
|
y = x;
|
|
|
|
/* 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; */
|
|
t = ieee754dp_mul(y, y);
|
|
z = t;
|
|
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;
|
|
/* fall 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;
|
|
}
|