1/* $NetBSD: n_sqrt.S,v 1.5 2002/02/24 01:06:21 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. All advertising materials mentioning features or use of this software 15 * must display the following acknowledgement: 16 * This product includes software developed by the University of 17 * California, Berkeley and its contributors. 18 * 4. Neither the name of the University nor the names of its contributors 19 * may be used to endorse or promote products derived from this software 20 * without specific prior written permission. 21 * 22 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 23 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 24 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 25 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 26 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 27 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 28 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 29 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 30 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 31 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 32 * SUCH DAMAGE. 33 * 34 * @(#)sqrt.s 8.1 (Berkeley) 6/4/93 35 */ 36 37#include <machine/asm.h> 38 39/* 40 * double sqrt(arg) revised August 15,1982 41 * double arg; 42 * if(arg<0.0) { _errno = EDOM; return(<a reserved operand>); } 43 * if arg is a reserved operand it is returned as it is 44 * W. Kahan's magic square root 45 * coded by Heidi Stettner and revised by Emile LeBlanc 8/18/82 46 * 47 * entry points:_d_sqrt address of double arg is on the stack 48 * _sqrt double arg is on the stack 49 */ 50 .set EDOM,33 51 52ENTRY(d_sqrt, 0x003c) # save %r5,%r4,%r3,%r2 53 movq *4(%ap),%r0 54 jbr dsqrt2 55 56ENTRY(sqrt, 0x003c) # save %r5,%r4,%r3,%r2 57 movq 4(%ap),%r0 58 59dsqrt2: bicw3 $0x807f,%r0,%r2 # check exponent of input 60 jeql noexp # biased exponent is zero -> 0.0 or reserved 61 bsbb __libm_dsqrt_r5_lcl+2 62noexp: ret 63 64/* **************************** internal procedure */ 65 66__libm_dsqrt_r5_lcl: 67ALTENTRY(__libm_dsqrt_r5) 68 nop 69 nop 70 /* ENTRY POINT FOR cdabs and cdsqrt */ 71 /* returns double square root scaled by */ 72 /* 2^%r6 */ 73 74 movd %r0,%r4 75 jleq nonpos # argument is not positive 76 movzwl %r4,%r2 77 ashl $-1,%r2,%r0 78 addw2 $0x203c,%r0 # %r0 has magic initial approximation 79/* 80 * Do two steps of Heron's rule 81 * ((arg/guess) + guess) / 2 = better guess 82 */ 83 divf3 %r0,%r4,%r2 84 addf2 %r2,%r0 85 subw2 $0x80,%r0 # divide by two 86 87 divf3 %r0,%r4,%r2 88 addf2 %r2,%r0 89 subw2 $0x80,%r0 # divide by two 90 91/* Scale argument and approximation to prevent over/underflow */ 92 93 bicw3 $0x807f,%r4,%r1 94 subw2 $0x4080,%r1 # %r1 contains scaling factor 95 subw2 %r1,%r4 96 movl %r0,%r2 97 subw2 %r1,%r2 98 99/* Cubic step 100 * 101 * b = a + 2*a*(n-a*a)/(n+3*a*a) where b is better approximation, 102 * a is approximation, and n is the original argument. 103 * (let s be scale factor in the following comments) 104 */ 105 clrl %r1 106 clrl %r3 107 muld2 %r0,%r2 # %r2:%r3 = a*a/s 108 subd2 %r2,%r4 # %r4:%r5 = n/s - a*a/s 109 addw2 $0x100,%r2 # %r2:%r3 = 4*a*a/s 110 addd2 %r4,%r2 # %r2:%r3 = n/s + 3*a*a/s 111 muld2 %r0,%r4 # %r4:%r5 = a*n/s - a*a*a/s 112 divd2 %r2,%r4 # %r4:%r5 = a*(n-a*a)/(n+3*a*a) 113 addw2 $0x80,%r4 # %r4:%r5 = 2*a*(n-a*a)/(n+3*a*a) 114 addd2 %r4,%r0 # %r0:%r1 = a + 2*a*(n-a*a)/(n+3*a*a) 115 rsb # DONE! 116nonpos: 117 jneq negarg 118 ret # argument and root are zero 119negarg: 120 pushl $EDOM 121 calls $1,_C_LABEL(infnan) # generate the reserved op fault 122 ret 123