1/* $NetBSD: n_cbrt.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. 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 * @(#)cbrt.s 8.1 (Berkeley) 6/4/93 31 */ 32 33#include <machine/asm.h> 34 35/* 36 * double cbrt(double arg) 37 * W. Kahan, 10/13/80. revised 1/13/84 for keeping sign symmetry 38 * error check by E LeBlanc, 8/18/82 39 * Revised and tested by K.C. Ng, 5/2/85 40 * Max error less than 0.667 ulps (unit in the last places) 41 */ 42 43ALTENTRY(cbrt) 44ENTRY(d_cbrt, 0x00c0) # save %r6 & %r7 45 movq 4(%ap),%r0 # %r0 = argument x 46 jbr dcbrt2 47 48ENTRY(dcbrt_, 0x00c0) # save %r6 & %r7 49 movq *4(%ap),%r0 # %r0 = argument x 50 51dcbrt2: bicw3 $0x807f,%r0,%r2 # biased exponent of x 52 jeql return # dcbrt(0)=0 dcbrt(res)=res. operand 53 bicw3 $0x7fff,%r0,%ap # ap has sign(x) 54 xorw2 %ap,%r0 # %r0 is abs(x) 55 movl %r0,%r2 # %r2 has abs(x) 56 rotl $16,%r2,%r2 # %r2 = |x| with bits unscrambled 57 divl2 $3,%r2 # rough dcbrt with bias/3 58 addl2 B,%r2 # restore bias, diminish fraction 59 rotl $16,%r2,%r2 # %r2=|q|=|dcbrt| to 5 bits 60 mulf3 %r2,%r2,%r3 # %r3 =qq 61 divf2 %r0,%r3 # %r3 = qq/x 62 mulf2 %r2,%r3 63 addf2 C,%r3 # %r3 = s = C + qqq/x 64 divf3 %r3,D,%r4 # %r4 = D/s 65 addf2 E,%r4 66 addf2 %r4,%r3 # %r3 = s + E + D/s 67 divf3 %r3,F,%r3 # %r3 = F / (s + E + D/s) 68 addf2 G,%r3 # %r3 = G + F / (s + E + D/s) 69 mulf2 %r3,%r2 # %r2 = q%r3 = new q to 23 bits 70 clrl %r3 # %r2:%r3 = q as double float 71 muld3 %r2,%r2,%r4 # %r4:%r5 = qq exactly 72 divd2 %r4,%r0 # %r0:%r1 = x/(q*q) rounded 73 subd3 %r2,%r0,%r6 # %r6:%r7 = x/(q*q) - q exactly 74 movq %r2,%r4 # %r4:%r5 = q 75 addw2 $0x80,%r4 # %r4:%r5 = 2 * q 76 addd2 %r0,%r4 # %r4:%r5 = 2*q + x/(q*q) 77 divd2 %r4,%r6 # %r6:%r7 = (x/(q*q)-q)/(2*q+x/(q*q)) 78 muld2 %r2,%r6 # %r6:%r7 = q*(x/(q*q)-q)/(2*q+x/(q*q)) 79 addd3 %r6,%r2,%r0 # %r0:%r1 = q + %r6:%r7 80 bisw2 %ap,%r0 # restore the sign bit 81return: 82 ret # error less than 0.667 ulps 83 84 _ALIGN_TEXT 85B : .long 721142941 # (86-0.03306235651)*(2^23) 86C : .float 0f0.5428571429 # 19/35 87D : .float 0f-0.7053061224 # -864/1225 88E : .float 0f1.414285714 # 99/70 89F : .float 0f1.607142857 # 45/28 90G : .float 0f0.3571428571 # 5/14 91