1/* $NetBSD: n_sqrt.S,v 1.7 2004/05/13 20:35:40 mhitch 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 48ENTRY(d_sqrt, 0x003c) # save %r5,%r4,%r3,%r2 49 movq *4(%ap),%r0 50 jbr dsqrt2 51 52ENTRY(sqrt, 0x003c) # save %r5,%r4,%r3,%r2 53 movq 4(%ap),%r0 54 55dsqrt2: 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+2 58noexp: ret 59 60/* **************************** internal procedure */ 61 62__libm_dsqrt_r5_lcl: 63ALTENTRY(__libm_dsqrt_r5) 64 nop 65 nop 66 /* ENTRY POINT FOR cdabs and cdsqrt */ 67 /* returns double square root scaled by */ 68 /* 2^%r6 */ 69 70 movd %r0,%r4 71 jleq nonpos # argument is not positive 72 movzwl %r4,%r2 73 ashl $-1,%r2,%r0 74 addw2 $0x203c,%r0 # %r0 has magic initial approximation 75/* 76 * Do two steps of Heron's rule 77 * ((arg/guess) + guess) / 2 = better guess 78 */ 79 divf3 %r0,%r4,%r2 80 addf2 %r2,%r0 81 subw2 $0x80,%r0 # divide by two 82 83 divf3 %r0,%r4,%r2 84 addf2 %r2,%r0 85 subw2 $0x80,%r0 # divide by two 86 87/* Scale argument and approximation to prevent over/underflow */ 88 89 bicw3 $0x807f,%r4,%r1 90 subw2 $0x4080,%r1 # %r1 contains scaling factor 91 subw2 %r1,%r4 92 movl %r0,%r2 93 subw2 %r1,%r2 94 95/* Cubic step 96 * 97 * b = a + 2*a*(n-a*a)/(n+3*a*a) where b is better approximation, 98 * a is approximation, and n is the original argument. 99 * (let s be scale factor in the following comments) 100 */ 101 clrl %r1 102 clrl %r3 103 muld2 %r0,%r2 # %r2:%r3 = a*a/s 104 subd2 %r2,%r4 # %r4:%r5 = n/s - a*a/s 105 addw2 $0x100,%r2 # %r2:%r3 = 4*a*a/s 106 addd2 %r4,%r2 # %r2:%r3 = n/s + 3*a*a/s 107 muld2 %r0,%r4 # %r4:%r5 = a*n/s - a*a*a/s 108 divd2 %r2,%r4 # %r4:%r5 = a*(n-a*a)/(n+3*a*a) 109 addw2 $0x80,%r4 # %r4:%r5 = 2*a*(n-a*a)/(n+3*a*a) 110 addd2 %r4,%r0 # %r0:%r1 = a + 2*a*(n-a*a)/(n+3*a*a) 111 rsb # DONE! 112nonpos: 113 jneq negarg 114 ret # argument and root are zero 115negarg: 116 pushl $EDOM 117 calls $1,_C_LABEL(infnan) # generate the reserved op fault 118 ret 119 120ENTRY(sqrtf, 0) 121 cvtfd 4(%ap),-(%sp) 122 calls $2,_C_LABEL(sqrt) 123 cvtdf %r0,%r0 124 ret 125