1/* $NetBSD: n_cabs.S,v 1.6 2008/03/20 16:41:26 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 * @(#)cabs.s 8.1 (Berkeley) 6/4/93 31 */ 32 33#include <machine/asm.h> 34 35 .globl _C_LABEL(__libm_dsqrt_r5) 36/* 37 * double precision complex absolute value 38 * CABS by W. Kahan, 9/7/80. 39 * Revised for reserved operands by E. LeBlanc, 8/18/82 40 * argument for complex absolute value by reference, *4(%ap) 41 * argument for cabs and hypot (C fcns) by value, 4(%ap) 42 * output is in %r0:%r1 (error less than 0.86 ulps) 43 */ 44 45/* entry for c functions cabs and hypot */ 46#ifdef WEAK_ALIAS 47WEAK_ALIAS(hypotf, _hypotf) 48#endif 49 50ENTRY(_hypotf, 0) 51 cvtfd 4(%ap),-(%sp) 52 calls $2,_C_LABEL(_hypot) 53 cvtdf %r0,%r0 54 ret 55 56#ifdef WEAK_ALIAS 57WEAK_ALIAS(hypot, _hypot) 58#endif 59 60ALTENTRY(cabs) 61ENTRY(_hypot, 0x8040) # save %r6, enable floating overflow 62 movq 4(%ap),%r0 # %r0:1 = x 63 movq 12(%ap),%r2 # %r2:3 = y 64 jbr cabs2 65 66/* entry for Fortran use, call by: d = abs(z) */ 67ENTRY(z_abs, 0x8040) # save %r6, enable floating overflow 68 movl 4(%ap),%r2 # indirect addressing is necessary here 69 movq (%r2)+,%r0 # %r0:1 = x 70 movq (%r2),%r2 # %r2:3 = y 71 72cabs2: 73 bicw3 $0x7f,%r0,%r4 # %r4 has signed biased exp of x 74 cmpw $0x8000,%r4 75 jeql return # x is a reserved operand, so return it 76 bicw3 $0x7f,%r2,%r5 # %r5 has signed biased exp of y 77 cmpw $0x8000,%r5 78 jneq cont /* y isn't a reserved operand */ 79 movq %r2,%r0 /* return y if it's reserved */ 80 ret 81 82cont: 83 bsbb regs_set # %r0:1 = dsqrt(x^2+y^2)/2^%r6 84 addw2 %r6,%r0 # unscaled cdabs in %r0:1 85 jvc return # unless it overflows 86 subw2 $0x80,%r0 # halve %r0 to get meaningful overflow 87 addd2 %r0,%r0 # overflow; %r0 is half of true abs value 88return: 89 ret 90 91ENTRY(__libm_cdabs_r6,0) # ENTRY POINT for cdsqrt 92 # calculates a scaled (factor in %r6) 93 # complex absolute value 94 95 movq (%r4)+,%r0 # %r0:%r1 = x via indirect addressing 96 movq (%r4),%r2 # %r2:%r3 = y via indirect addressing 97 98 bicw3 $0x7f,%r0,%r5 # %r5 has signed biased exp of x 99 cmpw $0x8000,%r5 100 jeql cdreserved # x is a reserved operand 101 bicw3 $0x7f,%r2,%r5 # %r5 has signed biased exp of y 102 cmpw $0x8000,%r5 103 jneq regs_set /* y isn't a reserved operand either? */ 104 105cdreserved: 106 movl *4(%ap),%r4 # %r4 -> (u,v), if x or y is reserved 107 movq %r0,(%r4)+ # copy u and v as is and return 108 movq %r2,(%r4) # (again addressing is indirect) 109 ret 110 111regs_set: 112 bicw2 $0x8000,%r0 # %r0:%r1 = dabs(x) 113 bicw2 $0x8000,%r2 # %r2:%r3 = dabs(y) 114 cmpw %r0,%r2 115 jgeq ordered 116 movq %r0,%r4 117 movq %r2,%r0 118 movq %r4,%r2 # force y's exp <= x's exp 119ordered: 120 bicw3 $0x7f,%r0,%r6 # %r6 = exponent(x) + bias(129) 121 jeql retsb # if x = y = 0 then cdabs(x,y) = 0 122 subw2 $0x4780,%r6 # %r6 = exponent(x) - 14 123 subw2 %r6,%r0 # 2^14 <= scaled x < 2^15 124 bitw $0xff80,%r2 125 jeql retsb # if y = 0 return dabs(x) 126 subw2 %r6,%r2 127 cmpw $0x3780,%r2 # if scaled y < 2^-18 128 jgtr retsb # return dabs(x) 129 emodd %r0,$0,%r0,%r4,%r0 # %r4 + %r0:1 = scaled x^2 130 emodd %r2,$0,%r2,%r5,%r2 # %r5 + %r2:3 = scaled y^2 131 addd2 %r2,%r0 132 addl2 %r5,%r4 133 cvtld %r4,%r2 134 addd2 %r2,%r0 # %r0:1 = scaled x^2 + y^2 135 jmp _C_LABEL(__libm_dsqrt_r5)+2 136 # %r0:1 = dsqrt(x^2+y^2)/2^%r6 137retsb: 138 rsb # error < 0.86 ulp 139