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/* Copyright (C) 1996, 1997 Free Software Foundation, Inc.
Contributed by David Mosberger (davidm@cs.arizona.edu).
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 of the
License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If not,
write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA. */
/*
* We have three versions, depending on how exact we need the results.
*/
#if defined(_IEEE_FP) && defined(_IEEE_FP_INEXACT)
/* Most demanding: go to the original source. */
#include <libm-ieee754/e_sqrt.c>
#else
/* Careful with rearranging this without consulting the assembly below. */
const static struct sqrt_data_struct {
unsigned long dn, up, half, almost_three_half;
unsigned long one_and_a_half, two_to_minus_30, one, nan;
const int T2[64];
} sqrt_data = {
0x3fefffffffffffff, /* __dn = nextafter(1,-Inf) */
0x3ff0000000000001, /* __up = nextafter(1,+Inf) */
0x3fe0000000000000, /* half */
0x3ff7ffffffc00000, /* almost_three_half = 1.5-2^-30 */
0x3ff8000000000000, /* one_and_a_half */
0x3e10000000000000, /* two_to_minus_30 */
0x3ff0000000000000, /* one */
0xffffffffffffffff, /* nan */
{ 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd }
};
#ifdef _IEEE_FP
/*
* This version is much faster than the standard one included above,
* but it doesn't maintain the inexact flag.
*/
#define lobits(x) (((unsigned int *)&x)[0])
#define hibits(x) (((unsigned int *)&x)[1])
static inline double initial_guess(double x, unsigned int k,
const struct sqrt_data_struct * const ptr)
{
double ret = 0.0;
k = 0x5fe80000 - (k >> 1);
k = k - ptr->T2[63&(k>>14)];
hibits(ret) = k;
return ret;
}
/* up = nextafter(1,+Inf), dn = nextafter(1,-Inf) */
#define __half (ptr->half)
#define __one_and_a_half (ptr->one_and_a_half)
#define __two_to_minus_30 (ptr->two_to_minus_30)
#define __one (ptr->one)
#define __up (ptr->up)
#define __dn (ptr->dn)
#define __Nan (ptr->nan)
#define Double(x) (*(double *)&x)
/* Multiply with chopping rounding.. */
#define choppedmul(a,b,c) \
__asm__("multc %1,%2,%0":"=&f" (c):"f" (a), "f" (b))
double
__ieee754_sqrt(double x)
{
const struct sqrt_data_struct * const ptr = &sqrt_data;
unsigned long k, bits;
double y, z, zp, zn;
double dn, up, low, high;
double half, one_and_a_half, one, two_to_minus_30;
*(double *)&bits = x;
k = bits;
/* Negative or NaN or Inf */
if ((k >> 52) >= 0x7ff)
goto special;
y = initial_guess(x, k >> 32, ptr);
half = Double(__half);
one_and_a_half = Double(__one_and_a_half);
y = y*(one_and_a_half - half*x*y*y);
dn = Double(__dn);
two_to_minus_30 = Double(__two_to_minus_30);
y = y*((one_and_a_half - two_to_minus_30) - half*x*y*y);
up = Double(__up);
z = x*y;
one = Double(__one);
z = z + half*z*(one-z*y);
choppedmul(z,dn,zp);
choppedmul(z,up,zn);
choppedmul(z,zp,low);
low = low - x;
choppedmul(z,zn,high);
high = high - x;
/* I can't get gcc to use fcmov's.. */
__asm__("fcmovge %2,%3,%0"
:"=f" (z)
:"0" (z), "f" (low), "f" (zp));
__asm__("fcmovlt %2,%3,%0"
:"=f" (z)
:"0" (z), "f" (high), "f" (zn));
return z; /* Argh! gcc jumps to end here */
special:
/* throw away sign bit */
k <<= 1;
/* -0 */
if (!k)
return x;
/* special? */
if ((k >> 53) == 0x7ff) {
/* NaN? */
if (k << 11)
return x;
/* sqrt(+Inf) = +Inf */
if (x > 0)
return x;
}
x = Double(__Nan);
return x;
}
#else
/*
* This version is much faster than generic sqrt implementation, but
* it doesn't handle exceptional values or the inexact flag.
*/
asm ("\
/* Define offsets into the structure defined in C above. */
$DN = 0*8
$UP = 1*8
$HALF = 2*8
$ALMOST_THREE_HALF = 3*8
$NAN = 7*8
$T2 = 8*8
/* Stack variables. */
$K = 0
$Y = 8
.text
.align 3
.globl __ieee754_sqrt
.ent __ieee754_sqrt
__ieee754_sqrt:
ldgp $29, 0($27)
subq $sp, 16, $sp
.frame $sp, 16, $26, 0\n"
#ifdef PROF
" lda $28, _mcount
jsr $28, ($28), _mcount\n"
#endif
" .prologue 1
stt $f16, $K($sp)
lda $4, sqrt_data # load base address into t3
fblt $f16, $negative
/* Compute initial guess. */
.align 3
ldah $2, 0x5fe8 # e0 :
ldq $3, $K($sp) # .. e1 :
ldt $f12, $HALF($4) # e0 :
ldt $f18, $ALMOST_THREE_HALF($4) # .. e1 :
srl $3, 33, $1 # e0 :
mult $f16, $f12, $f11 # .. fm : $f11 = x * 0.5
subl $2, $1, $2 # e0 :
addt $f12, $f12, $f17 # .. fa : $f17 = 1.0
srl $2, 12, $1 # e0 :
and $1, 0xfc, $1 # .. e1 :
addq $1, $4, $1 # e0 :
ldl $1, $T2($1) # .. e1 :
addt $f12, $f17, $f15 # fa : $f15 = 1.5
subl $2, $1, $2 # .. e1 :
sll $2, 32, $2 # e0 :
ldt $f14, $DN($4) # .. e1 :
stq $2, $Y($sp) # e0 :
nop # .. e1 : avoid pipe flash
nop # e0 :
ldt $f13, $Y($sp) # .. e1 :
mult/su $f11, $f13, $f10 # fm : $f10 = (x * 0.5) * y
mult $f10, $f13, $f10 # fm : $f10 = ((x * 0.5) * y) * y
subt $f15, $f10, $f1 # fa : $f1 = (1.5 - 0.5*x*y*y)
mult $f13, $f1, $f13 # fm : yp = y*(1.5 - 0.5*x*y*y)
mult/su $f11, $f13, $f1 # fm : $f11 = x * 0.5 * yp
mult $f1, $f13, $f11 # fm : $f11 = (x * 0.5 * yp) * yp
subt $f18, $f11, $f1 # fa : $f1= (1.5-2^-30) - 0.5*x*yp*yp
mult $f13, $f1, $f13 # fm : ypp = $f13 = yp*$f1
subt $f15, $f12, $f1 # fa : $f1 = (1.5 - 0.5)
ldt $f15, $UP($4) # .. e1 :
mult/su $f16, $f13, $f10 # fm : z = $f10 = x * ypp
mult $f10, $f13, $f11 # fm : $f11 = z*ypp
mult $f10, $f12, $f12 # fm : $f12 = z*0.5
subt $f1, $f11, $f1 # .. fa : $f1 = 1 - z*ypp
mult $f12, $f1, $f12 # fm : $f12 = z*0.5*(1 - z*ypp)
addt $f10, $f12, $f0 # fa : zp=res=$f0= z + z*0.5*(1 - z*ypp)
mult/c $f0, $f14, $f12 # fm : zmi = zp * DN
mult/c $f0, $f15, $f11 # fm : zpl = zp * UP
mult/c $f0, $f12, $f1 # fm : $f1 = zp * zmi
mult/c $f0, $f11, $f15 # fm : $f15 = zp * zpl
subt/su $f1, $f16, $f13 # fa : y1 = zp*zmi - x
subt/su $f15, $f16, $f14 # fa : y2 = zp*zpl - x
fcmovge $f13, $f12, $f0 # res = (y1 >= 0) ? zmi : res
fcmovlt $f14, $f11, $f0 # res = (y2 < 0) ? zpl : res
addq $sp, 16, $sp # e0 :
ret # .. e1 :
$negative:
ldt $f0, $NAN($4)
addq $sp, 16, $sp
ret
.end __ieee754_sqrt");
#endif /* _IEEE_FP */
#endif /* _IEEE_FP && _IEEE_FP_INEXACT */
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