142 lines
4.4 KiB
ArmAsm
142 lines
4.4 KiB
ArmAsm
/*
|
|
* Copyright (c) 1987 Regents of the University of California.
|
|
* All rights reserved.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
* 1. Redistributions of source code must retain the above copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in the
|
|
* documentation and/or other materials provided with the distribution.
|
|
* 3. All advertising materials mentioning features or use of this software
|
|
* must display the following acknowledgement:
|
|
* This product includes software developed by the University of
|
|
* California, Berkeley and its contributors.
|
|
* 4. Neither the name of the University nor the names of its contributors
|
|
* may be used to endorse or promote products derived from this software
|
|
* without specific prior written permission.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
|
|
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
|
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
|
|
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
|
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
|
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
|
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
|
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
|
* SUCH DAMAGE.
|
|
*/
|
|
.data
|
|
.align 2
|
|
;_sccsid:
|
|
;.asciz "from: @(#)sqrt.s 5.6 (ucb.elefunt) 10/9/90"
|
|
_rcsid:
|
|
.asciz "$Id: sqrt.S,v 1.1 1993/08/14 13:44:01 mycroft Exp $"
|
|
|
|
/*
|
|
* double sqrt(arg) revised August 15,1982
|
|
* double arg;
|
|
* if(arg<0.0) { _errno = EDOM; return(<a reserved operand>); }
|
|
* if arg is a reserved operand it is returned as it is
|
|
* W. Kahan's magic square root
|
|
* Coded by Heidi Stettner and revised by Emile LeBlanc 8/18/82.
|
|
* Re-coded in tahoe assembly language by Z. Alex Liu 7/13/87.
|
|
*
|
|
* entry points:_d_sqrt address of double arg is on the stack
|
|
* _sqrt double arg is on the stack
|
|
*/
|
|
.text
|
|
.align 2
|
|
.globl _sqrt
|
|
.globl _d_sqrt
|
|
.globl libm$dsqrt_r5
|
|
.set EDOM,33
|
|
|
|
_d_sqrt:
|
|
.word 0x003c # save r2-r5
|
|
movl 4(fp),r2
|
|
movl (r2),r0
|
|
movl 4(r2),r1 # r0:r1 = x
|
|
brb 1f
|
|
_sqrt:
|
|
.word 0x003c # save r2-r5
|
|
movl 4(fp),r0
|
|
movl 8(fp),r1 # r0:r1 = x
|
|
1: andl3 $0x7f800000,r0,r2 # r2 = biased exponent
|
|
bneq 2f
|
|
ret # biased exponent is zero -> 0 or reserved op.
|
|
/*
|
|
* # internal procedure
|
|
* # ENTRY POINT FOR cdabs and cdsqrt
|
|
*/
|
|
libm$dsqrt_r5: # returns double square root scaled by 2^r6
|
|
.word 0x0000 # save nothing
|
|
2: ldd r0
|
|
std r4
|
|
bleq nonpos # argument is not positive
|
|
andl3 $0xfffe0000,r4,r2
|
|
shar $1,r2,r0
|
|
addl2 $0x203c0000,r0 # r0 has magic initial approximation
|
|
/*
|
|
* # Do two steps of Heron's rule
|
|
* # ((arg/guess)+guess)/2 = better guess
|
|
*/
|
|
ldf r4
|
|
divf r0
|
|
addf r0
|
|
stf r0
|
|
subl2 $0x800000,r0 # divide by two
|
|
ldf r4
|
|
divf r0
|
|
addf r0
|
|
stf r0
|
|
subl2 $0x800000,r0 # divide by two
|
|
/*
|
|
* # Scale argument and approximation
|
|
* # to prevent over/underflow
|
|
*/
|
|
andl3 $0x7f800000,r4,r1
|
|
subl2 $0x40800000,r1 # r1 contains scaling factor
|
|
subl2 r1,r4 # r4:r5 = n/s
|
|
movl r0,r2
|
|
subl2 r1,r2 # r2 = a/s
|
|
/*
|
|
* # Cubic step
|
|
* # b = a+2*a*(n-a*a)/(n+3*a*a) where
|
|
* # b is better approximation, a is approximation
|
|
* # and n is the original argument.
|
|
* # s := scale factor.
|
|
*/
|
|
clrl r1 # r0:r1 = a
|
|
clrl r3 # r2:r3 = a/s
|
|
ldd r0 # acc = a
|
|
muld r2 # acc = a*a/s
|
|
std r2 # r2:r3 = a*a/s
|
|
negd # acc = -a*a/s
|
|
addd r4 # acc = n/s-a*a/s
|
|
std r4 # r4:r5 = n/s-a*a/s
|
|
addl2 $0x1000000,r2 # r2:r3 = 4*a*a/s
|
|
ldd r2 # acc = 4*a*a/s
|
|
addd r4 # acc = n/s+3*a*a/s
|
|
std r2 # r2:r3 = n/s+3*a*a/s
|
|
ldd r0 # acc = a
|
|
muld r4 # acc = a*n/s-a*a*a/s
|
|
divd r2 # acc = a*(n-a*a)/(n+3*a*a)
|
|
std r4 # r4:r5 = a*(n-a*a)/(n+3*a*a)
|
|
addl2 $0x800000,r4 # r4:r5 = 2*a*(n-a*a)/(n+3*a*a)
|
|
ldd r4 # acc = 2*a*(n-a*a)/(n+3*a*a)
|
|
addd r0 # acc = a+2*a*(n-a*a)/(n+3*a*a)
|
|
std r0 # r0:r1 = a+2*a*(n-a*a)/(n+3*a*a)
|
|
ret # rsb
|
|
nonpos:
|
|
bneq negarg
|
|
ret # argument and root are zero
|
|
negarg:
|
|
pushl $EDOM
|
|
callf $8,_infnan # generate the reserved op fault
|
|
ret
|