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/* Copyright (C) 1996, 1997, 1998 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. */
#if !defined(_IEEE_FP_INEXACT)
/*
* This version is much faster than generic sqrt implementation, but
* it doesn't handle the inexact flag. It doesn't handle exceptional
* values either, but will defer to the full ieee754_sqrt routine which
* can.
*/
/* 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 }
};
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 5
.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
.align 4
stt $f16, $K($sp) # e0 :
mult $f31, $f31, $f31 # .. fm :
lda $4, sqrt_data # e0 :
fblt $f16, $fixup # .. fa :
ldah $2, 0x5fe8 # e0 :
ldq $3, $K($sp) # .. e1 :
ldt $f12, $HALF($4) # e0 :
ldt $f18, $ALMOST_THREE_HALF($4) # .. e1 :
sll $3, 52, $5 # e0 :
lda $6, 0x7fd # .. e1 :
fnop # .. fa :
fnop # .. fm :
subq $5, 1, $5 # e1 :
srl $3, 33, $1 # .. e0 :
cmpule $5, $6, $5 # e0 :
beq $5, $fixup # .. e1 :
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 # e0 :
addq $1, $4, $1 # e1 :
ldl $1, $T2($1) # e0 :
addt $f12, $f17, $f15 # .. fa : $f15 = 1.5
subl $2, $1, $2 # e0 :
ldt $f14, $DN($4) # .. e1 :
sll $2, 32, $2 # e0 :
stq $2, $Y($sp) # e0 :
ldt $f13, $Y($sp) # e0 :
mult/su $f11, $f13, $f10 # fm 2: $f10 = (x * 0.5) * y
mult $f10, $f13, $f10 # fm 4: $f10 = ((x * 0.5) * y) * y
subt $f15, $f10, $f1 # fa 4: $f1 = (1.5 - 0.5*x*y*y)
mult $f13, $f1, $f13 # fm 4: yp = y*(1.5 - 0.5*x*y*y)
mult/su $f11, $f13, $f1 # fm 4: $f11 = x * 0.5 * yp
mult $f1, $f13, $f11 # fm 4: $f11 = (x * 0.5 * yp) * yp
subt $f18, $f11, $f1 # fa 4: $f1= (1.5-2^-30) - 0.5*x*yp*yp
mult $f13, $f1, $f13 # fm 4: ypp = $f13 = yp*$f1
subt $f15, $f12, $f1 # .. fa : $f1 = (1.5 - 0.5)
ldt $f15, $UP($4) # .. e0 :
mult/su $f16, $f13, $f10 # fm 4: z = $f10 = x * ypp
mult $f10, $f13, $f11 # fm 4: $f11 = z*ypp
mult $f10, $f12, $f12 # fm : $f12 = z*0.5
subt $f1, $f11, $f1 # fa 4: $f1 = 1 - z*ypp
mult $f12, $f1, $f12 # fm 4: $f12 = z*0.5*(1 - z*ypp)
addt $f10, $f12, $f0 # fa 4: zp=res= z + z*0.5*(1 - z*ypp)
mult/c $f0, $f14, $f12 # fm 4: 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 4: y2 = zp*zpl - x
fcmovge $f13, $f12, $f0 # fa 3: res = (y1 >= 0) ? zmi : res
fcmovlt $f14, $f11, $f0 # fa 4: res = (y2 < 0) ? zpl : res
addq $sp, 16, $sp # .. e0 :
ret # .. e1 :
.align 4
$fixup:
addq $sp, 16, $sp
br "ASM_ALPHA_NG_SYMBOL_PREFIX"__full_ieee754_sqrt..ng
.end __ieee754_sqrt");
static double __full_ieee754_sqrt(double) __attribute__((unused));
#define __ieee754_sqrt __full_ieee754_sqrt
#endif /* _IEEE_FP_INEXACT */
#include <sysdeps/libm-ieee754/e_sqrt.c>
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