NetBSD/lib/libm/tahoe/sqrt.s

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