1/* $NetBSD: n_sqrt.S,v 1.11 2014/10/11 06:59:29 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) 37WEAK_ALIAS(sqrtl, sqrt) 38#endif 39 40/* 41 * double sqrt(arg) revised August 15,1982 42 * double arg; 43 * if(arg<0.0) { _errno = EDOM; return(<a reserved operand>); } 44 * if arg is a reserved operand it is returned as it is 45 * W. Kahan's magic square root 46 * coded by Heidi Stettner and revised by Emile LeBlanc 8/18/82 47 * 48 * entry points:_d_sqrt address of double arg is on the stack 49 * _sqrt double arg is on the stack 50 */ 51 .set EDOM,33 52 53ENTRY(d_sqrt, 0x003c) # save %r5,%r4,%r3,%r2 54 movq *4(%ap),%r0 55 jbr dsqrt2 56 57ENTRY(sqrt, 0x003c) # save %r5,%r4,%r3,%r2 58 movq 4(%ap),%r0 59 60dsqrt2: bicw3 $0x807f,%r0,%r2 # check exponent of input 61 jeql noexp # biased exponent is zero -> 0.0 or reserved 62 bsbb __libm_dsqrt_r5_lcl 63noexp: ret 64 65/* **************************** internal procedure */ 66 67 .hidden __libm_dsqrt_r5 68ALTENTRY(__libm_dsqrt_r5) 69 halt 70 halt 71__libm_dsqrt_r5_lcl: 72 /* ENTRY POINT FOR cdabs and cdsqrt */ 73 /* returns double square root scaled by */ 74 /* 2^%r6 */ 75 76 movd %r0,%r4 77 jleq nonpos # argument is not positive 78 movzwl %r4,%r2 79 ashl $-1,%r2,%r0 80 addw2 $0x203c,%r0 # %r0 has magic initial approximation 81/* 82 * Do two steps of Heron's rule 83 * ((arg/guess) + guess) / 2 = better guess 84 */ 85 divf3 %r0,%r4,%r2 86 addf2 %r2,%r0 87 subw2 $0x80,%r0 # divide by two 88 89 divf3 %r0,%r4,%r2 90 addf2 %r2,%r0 91 subw2 $0x80,%r0 # divide by two 92 93/* Scale argument and approximation to prevent over/underflow */ 94 95 bicw3 $0x807f,%r4,%r1 96 subw2 $0x4080,%r1 # %r1 contains scaling factor 97 subw2 %r1,%r4 98 movl %r0,%r2 99 subw2 %r1,%r2 100 101/* Cubic step 102 * 103 * b = a + 2*a*(n-a*a)/(n+3*a*a) where b is better approximation, 104 * a is approximation, and n is the original argument. 105 * (let s be scale factor in the following comments) 106 */ 107 clrl %r1 108 clrl %r3 109 muld2 %r0,%r2 # %r2:%r3 = a*a/s 110 subd2 %r2,%r4 # %r4:%r5 = n/s - a*a/s 111 addw2 $0x100,%r2 # %r2:%r3 = 4*a*a/s 112 addd2 %r4,%r2 # %r2:%r3 = n/s + 3*a*a/s 113 muld2 %r0,%r4 # %r4:%r5 = a*n/s - a*a*a/s 114 divd2 %r2,%r4 # %r4:%r5 = a*(n-a*a)/(n+3*a*a) 115 addw2 $0x80,%r4 # %r4:%r5 = 2*a*(n-a*a)/(n+3*a*a) 116 addd2 %r4,%r0 # %r0:%r1 = a + 2*a*(n-a*a)/(n+3*a*a) 117 rsb # DONE! 118nonpos: 119 jneq negarg 120 ret # argument and root are zero 121negarg: 122 pushl $EDOM 123 calls $1,_C_LABEL(infnan) # generate the reserved op fault 124 ret 125 126ENTRY(sqrtf, 0) 127 cvtfd 4(%ap),-(%sp) 128 calls $2,_C_LABEL(sqrt) 129 cvtdf %r0,%r0 130 ret 131