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n_sqrt.S revision 1.8 
      1 /*	$NetBSD: n_sqrt.S,v 1.8 2007/04/18 04:46:13 matt Exp $	*/
      2 /*
      3  * Copyright (c) 1985, 1993
      4  *	The Regents of the University of California.  All rights reserved.
      5  *
      6  * Redistribution and use in source and binary forms, with or without
      7  * modification, are permitted provided that the following conditions
      8  * are met:
      9  * 1. Redistributions of source code must retain the above copyright
     10  *    notice, this list of conditions and the following disclaimer.
     11  * 2. Redistributions in binary form must reproduce the above copyright
     12  *    notice, this list of conditions and the following disclaimer in the
     13  *    documentation and/or other materials provided with the distribution.
     14  * 3. Neither the name of the University nor the names of its contributors
     15  *    may be used to endorse or promote products derived from this software
     16  *    without specific prior written permission.
     17  *
     18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
     19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
     22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
     24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     28  * SUCH DAMAGE.
     29  *
     30  *	@(#)sqrt.s	8.1 (Berkeley) 6/4/93
     31  */
     32 
     33 #include <machine/asm.h>
     34 
     35 /*
     36  * double sqrt(arg)   revised August 15,1982
     37  * double arg;
     38  * if(arg<0.0) { _errno = EDOM; return(<a reserved operand>); }
     39  * if arg is a reserved operand it is returned as it is
     40  * W. Kahan's magic square root
     41  * coded by Heidi Stettner and revised by Emile LeBlanc 8/18/82
     42  *
     43  * entry points:_d_sqrt		address of double arg is on the stack
     44  *		_sqrt		double arg is on the stack
     45  */
     46 	.set	EDOM,33
     47 
     48 ENTRY(d_sqrt, 0x003c)		# save %r5,%r4,%r3,%r2
     49 	movq	*4(%ap),%r0
     50 	jbr  	dsqrt2
     51 
     52 ENTRY(sqrt, 0x003c)		# save %r5,%r4,%r3,%r2
     53 	movq    4(%ap),%r0
     54 
     55 dsqrt2:	bicw3	$0x807f,%r0,%r2	# check exponent of input
     56 	jeql	noexp		# biased exponent is zero -> 0.0 or reserved
     57 	bsbb	__libm_dsqrt_r5_lcl
     58 noexp:	ret
     59 
     60 /* **************************** internal procedure */
     61 
     62 	.hidden __libm_dsqrt_r5
     63 ALTENTRY(__libm_dsqrt_r5)
     64 	halt
     65 	halt
     66 __libm_dsqrt_r5_lcl:
     67 				/* ENTRY POINT FOR cdabs and cdsqrt	*/
     68 				/* returns double square root scaled by	*/
     69 				/* 2^%r6	*/
     70 
     71 	movd	%r0,%r4
     72 	jleq	nonpos		# argument is not positive
     73 	movzwl	%r4,%r2
     74 	ashl	$-1,%r2,%r0
     75 	addw2	$0x203c,%r0	# %r0 has magic initial approximation
     76 /*
     77  * Do two steps of Heron's rule
     78  * ((arg/guess) + guess) / 2 = better guess
     79  */
     80 	divf3	%r0,%r4,%r2
     81 	addf2	%r2,%r0
     82 	subw2	$0x80,%r0	# divide by two
     83 
     84 	divf3	%r0,%r4,%r2
     85 	addf2	%r2,%r0
     86 	subw2	$0x80,%r0	# divide by two
     87 
     88 /* Scale argument and approximation to prevent over/underflow */
     89 
     90 	bicw3	$0x807f,%r4,%r1
     91 	subw2	$0x4080,%r1		# %r1 contains scaling factor
     92 	subw2	%r1,%r4
     93 	movl	%r0,%r2
     94 	subw2	%r1,%r2
     95 
     96 /* Cubic step
     97  *
     98  * b = a + 2*a*(n-a*a)/(n+3*a*a) where b is better approximation,
     99  * a is approximation, and n is the original argument.
    100  * (let s be scale factor in the following comments)
    101  */
    102 	clrl	%r1
    103 	clrl	%r3
    104 	muld2	%r0,%r2			# %r2:%r3 = a*a/s
    105 	subd2	%r2,%r4			# %r4:%r5 = n/s - a*a/s
    106 	addw2	$0x100,%r2		# %r2:%r3 = 4*a*a/s
    107 	addd2	%r4,%r2			# %r2:%r3 = n/s + 3*a*a/s
    108 	muld2	%r0,%r4			# %r4:%r5 = a*n/s - a*a*a/s
    109 	divd2	%r2,%r4			# %r4:%r5 = a*(n-a*a)/(n+3*a*a)
    110 	addw2	$0x80,%r4		# %r4:%r5 = 2*a*(n-a*a)/(n+3*a*a)
    111 	addd2	%r4,%r0			# %r0:%r1 = a + 2*a*(n-a*a)/(n+3*a*a)
    112 	rsb				# DONE!
    113 nonpos:
    114 	jneq	negarg
    115 	ret				# argument and root are zero
    116 negarg:
    117 	pushl	$EDOM
    118 	calls	$1,_C_LABEL(infnan)	# generate the reserved op fault
    119 	ret
    120 
    121 ENTRY(sqrtf, 0)
    122 	cvtfd	4(%ap),-(%sp)
    123 	calls	$2,_C_LABEL(sqrt)
    124 	cvtdf	%r0,%r0
    125 	ret
    126