1/* $NetBSD: n_sqrt.S,v 1.9 2014/03/06 11:00:17 martin 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#ifdef WEAK_ALIAS 36WEAK_ALIAS(sqrtl, sqrt) 37#endif 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 62noexp: ret 63 64/* **************************** internal procedure */ 65 66 .hidden __libm_dsqrt_r5 67ALTENTRY(__libm_dsqrt_r5) 68 halt 69 halt 70__libm_dsqrt_r5_lcl: 71 /* ENTRY POINT FOR cdabs and cdsqrt */ 72 /* returns double square root scaled by */ 73 /* 2^%r6 */ 74 75 movd %r0,%r4 76 jleq nonpos # argument is not positive 77 movzwl %r4,%r2 78 ashl $-1,%r2,%r0 79 addw2 $0x203c,%r0 # %r0 has magic initial approximation 80/* 81 * Do two steps of Heron's rule 82 * ((arg/guess) + guess) / 2 = better guess 83 */ 84 divf3 %r0,%r4,%r2 85 addf2 %r2,%r0 86 subw2 $0x80,%r0 # divide by two 87 88 divf3 %r0,%r4,%r2 89 addf2 %r2,%r0 90 subw2 $0x80,%r0 # divide by two 91 92/* Scale argument and approximation to prevent over/underflow */ 93 94 bicw3 $0x807f,%r4,%r1 95 subw2 $0x4080,%r1 # %r1 contains scaling factor 96 subw2 %r1,%r4 97 movl %r0,%r2 98 subw2 %r1,%r2 99 100/* Cubic step 101 * 102 * b = a + 2*a*(n-a*a)/(n+3*a*a) where b is better approximation, 103 * a is approximation, and n is the original argument. 104 * (let s be scale factor in the following comments) 105 */ 106 clrl %r1 107 clrl %r3 108 muld2 %r0,%r2 # %r2:%r3 = a*a/s 109 subd2 %r2,%r4 # %r4:%r5 = n/s - a*a/s 110 addw2 $0x100,%r2 # %r2:%r3 = 4*a*a/s 111 addd2 %r4,%r2 # %r2:%r3 = n/s + 3*a*a/s 112 muld2 %r0,%r4 # %r4:%r5 = a*n/s - a*a*a/s 113 divd2 %r2,%r4 # %r4:%r5 = a*(n-a*a)/(n+3*a*a) 114 addw2 $0x80,%r4 # %r4:%r5 = 2*a*(n-a*a)/(n+3*a*a) 115 addd2 %r4,%r0 # %r0:%r1 = a + 2*a*(n-a*a)/(n+3*a*a) 116 rsb # DONE! 117nonpos: 118 jneq negarg 119 ret # argument and root are zero 120negarg: 121 pushl $EDOM 122 calls $1,_C_LABEL(infnan) # generate the reserved op fault 123 ret 124 125ENTRY(sqrtf, 0) 126 cvtfd 4(%ap),-(%sp) 127 calls $2,_C_LABEL(sqrt) 128 cvtdf %r0,%r0 129 ret 130