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sqrt.s
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1993-09-23
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# Copyright (c) 1985 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.
#
# @(#)sqrt.s 5.4 (Berkeley) 10/9/90
#
.data
.align 2
_sccsid:
.asciz "@(#)sqrt.s 1.1 (Berkeley) 8/21/85; 5.4 (ucb.elefunt) 10/9/90"
/*
* 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
*
* entry points:_d_sqrt address of double arg is on the stack
* _sqrt double arg is on the stack
*/
.text
.align 1
.globl _sqrt
.globl _d_sqrt
.globl libm$dsqrt_r5
.set EDOM,33
_d_sqrt:
.word 0x003c # save r5,r4,r3,r2
movq *4(ap),r0
jmp dsqrt2
_sqrt:
.word 0x003c # save r5,r4,r3,r2
movq 4(ap),r0
dsqrt2: bicw3 $0x807f,r0,r2 # check exponent of input
jeql noexp # biased exponent is zero -> 0.0 or reserved
bsbb libm$dsqrt_r5
noexp: ret
/* **************************** internal procedure */
libm$dsqrt_r5: # ENTRY POINT FOR cdabs and cdsqrt
# returns double square root scaled by
# 2^r6
movd r0,r4
jleq nonpos # argument is not positive
movzwl r4,r2
ashl $-1,r2,r0
addw2 $0x203c,r0 # r0 has magic initial approximation
/*
* Do two steps of Heron's rule
* ((arg/guess) + guess) / 2 = better guess
*/
divf3 r0,r4,r2
addf2 r2,r0
subw2 $0x80,r0 # divide by two
divf3 r0,r4,r2
addf2 r2,r0
subw2 $0x80,r0 # divide by two
/* Scale argument and approximation to prevent over/underflow */
bicw3 $0x807f,r4,r1
subw2 $0x4080,r1 # r1 contains scaling factor
subw2 r1,r4
movl r0,r2
subw2 r1,r2
/* 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.
* (let s be scale factor in the following comments)
*/
clrl r1
clrl r3
muld2 r0,r2 # r2:r3 = a*a/s
subd2 r2,r4 # r4:r5 = n/s - a*a/s
addw2 $0x100,r2 # r2:r3 = 4*a*a/s
addd2 r4,r2 # r2:r3 = n/s + 3*a*a/s
muld2 r0,r4 # r4:r5 = a*n/s - a*a*a/s
divd2 r2,r4 # r4:r5 = a*(n-a*a)/(n+3*a*a)
addw2 $0x80,r4 # r4:r5 = 2*a*(n-a*a)/(n+3*a*a)
addd2 r4,r0 # r0:r1 = a + 2*a*(n-a*a)/(n+3*a*a)
rsb # DONE!
nonpos:
jneq negarg
ret # argument and root are zero
negarg:
pushl $EDOM
calls $1,_infnan # generate the reserved op fault
ret