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glibc/ports/sysdeps/alpha/fpu/e_sqrt.c
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/* Copyright (C) 1996,1997,1998,2002,2003 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 Lesser General Public | |
License as published by the Free Software Foundation; either | |
version 2.1 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 | |
Lesser General Public License for more details. | |
You should have received a copy of the GNU Lesser General Public | |
License along with the GNU C Library. If not, see | |
<http://www.gnu.org/licenses/>. */ | |
#include <math.h> | |
#include <math_private.h> | |
#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 __attribute__((used)) = { | |
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. */ \n\ | |
$DN = 0*8 \n\ | |
$UP = 1*8 \n\ | |
$HALF = 2*8 \n\ | |
$ALMOST_THREE_HALF = 3*8 \n\ | |
$NAN = 7*8 \n\ | |
$T2 = 8*8 \n\ | |
\n\ | |
/* Stack variables. */ \n\ | |
$K = 0 \n\ | |
$Y = 8 \n\ | |
\n\ | |
.text \n\ | |
.align 5 \n\ | |
.globl __ieee754_sqrt \n\ | |
.ent __ieee754_sqrt \n\ | |
__ieee754_sqrt: \n\ | |
ldgp $29, 0($27) \n\ | |
subq $sp, 16, $sp \n\ | |
.frame $sp, 16, $26, 0\n" | |
#ifdef PROF | |
" lda $28, _mcount \n\ | |
jsr $28, ($28), _mcount\n" | |
#endif | |
" .prologue 1 \n\ | |
\n\ | |
.align 4 \n\ | |
stt $f16, $K($sp) # e0 : \n\ | |
mult $f31, $f31, $f31 # .. fm : \n\ | |
lda $4, sqrt_data # e0 : \n\ | |
fblt $f16, $fixup # .. fa : \n\ | |
\n\ | |
ldah $2, 0x5fe8 # e0 : \n\ | |
ldq $3, $K($sp) # .. e1 : \n\ | |
ldt $f12, $HALF($4) # e0 : \n\ | |
ldt $f18, $ALMOST_THREE_HALF($4) # .. e1 : \n\ | |
\n\ | |
sll $3, 52, $5 # e0 : \n\ | |
lda $6, 0x7fd # .. e1 : \n\ | |
fnop # .. fa : \n\ | |
fnop # .. fm : \n\ | |
\n\ | |
subq $5, 1, $5 # e1 : \n\ | |
srl $3, 33, $1 # .. e0 : \n\ | |
cmpule $5, $6, $5 # e0 : \n\ | |
beq $5, $fixup # .. e1 : \n\ | |
\n\ | |
mult $f16, $f12, $f11 # fm : $f11 = x * 0.5 \n\ | |
subl $2, $1, $2 # .. e0 : \n\ | |
addt $f12, $f12, $f17 # .. fa : $f17 = 1.0 \n\ | |
srl $2, 12, $1 # e0 : \n\ | |
\n\ | |
and $1, 0xfc, $1 # e0 : \n\ | |
addq $1, $4, $1 # e1 : \n\ | |
ldl $1, $T2($1) # e0 : \n\ | |
addt $f12, $f17, $f15 # .. fa : $f15 = 1.5 \n\ | |
\n\ | |
subl $2, $1, $2 # e0 : \n\ | |
ldt $f14, $DN($4) # .. e1 : \n\ | |
sll $2, 32, $2 # e0 : \n\ | |
stq $2, $Y($sp) # e0 : \n\ | |
\n\ | |
ldt $f13, $Y($sp) # e0 : \n\ | |
mult/su $f11, $f13, $f10 # fm 2: $f10 = (x * 0.5) * y \n\ | |
mult $f10, $f13, $f10 # fm 4: $f10 = ((x*0.5)*y)*y \n\ | |
subt $f15, $f10, $f1 # fa 4: $f1 = (1.5-0.5*x*y*y) \n\ | |
\n\ | |
mult $f13, $f1, $f13 # fm 4: yp = y*(1.5-0.5*x*y^2)\n\ | |
mult/su $f11, $f13, $f1 # fm 4: $f11 = x * 0.5 * yp \n\ | |
mult $f1, $f13, $f11 # fm 4: $f11 = (x*0.5*yp)*yp \n\ | |
subt $f18, $f11, $f1 # fa 4: $f1=(1.5-2^-30)-x/2*yp^2\n\ | |
\n\ | |
mult $f13, $f1, $f13 # fm 4: ypp = $f13 = yp*$f1 \n\ | |
subt $f15, $f12, $f1 # .. fa : $f1 = (1.5 - 0.5) \n\ | |
ldt $f15, $UP($4) # .. e0 : \n\ | |
mult/su $f16, $f13, $f10 # fm 4: z = $f10 = x * ypp \n\ | |
\n\ | |
mult $f10, $f13, $f11 # fm 4: $f11 = z*ypp \n\ | |
mult $f10, $f12, $f12 # fm : $f12 = z*0.5 \n\ | |
subt $f1, $f11, $f1 # fa 4: $f1 = 1 - z*ypp \n\ | |
mult $f12, $f1, $f12 # fm 4: $f12 = z/2*(1 - z*ypp)\n\ | |
\n\ | |
addt $f10, $f12, $f0 # fa 4: zp=res= z+z/2*(1-z*ypp)\n\ | |
mult/c $f0, $f14, $f12 # fm 4: zmi = zp * DN \n\ | |
mult/c $f0, $f15, $f11 # fm : zpl = zp * UP \n\ | |
mult/c $f0, $f12, $f1 # fm : $f1 = zp * zmi \n\ | |
\n\ | |
mult/c $f0, $f11, $f15 # fm : $f15 = zp * zpl \n\ | |
subt/su $f1, $f16, $f13 # .. fa : y1 = zp*zmi - x \n\ | |
subt/su $f15, $f16, $f14 # fa 4: y2 = zp*zpl - x \n\ | |
fcmovge $f13, $f12, $f0 # fa 3: res = (y1>=0)?zmi:res \n\ | |
\n\ | |
fcmovlt $f14, $f11, $f0 # fa 4: res = (y2<0)?zpl:res \n\ | |
addq $sp, 16, $sp # .. e0 : \n\ | |
ret # .. e1 : \n\ | |
\n\ | |
.align 4 \n\ | |
$fixup: \n\ | |
addq $sp, 16, $sp \n\ | |
br __full_ieee754_sqrt !samegp \n\ | |
\n\ | |
.end __ieee754_sqrt"); | |
static double __full_ieee754_sqrt(double) __attribute_used__; | |
#define __ieee754_sqrt __full_ieee754_sqrt | |
#endif /* _IEEE_FP_INEXACT */ | |
#include <sysdeps/ieee754/dbl-64/e_sqrt.c> |