n_cbrt.S revision 1.2
1/* $NetBSD: n_cbrt.S,v 1.2 1998/10/31 02:06:02 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. All advertising materials mentioning features or use of this software 15 * must display the following acknowledgement: 16 * This product includes software developed by the University of 17 * California, Berkeley and its contributors. 18 * 4. Neither the name of the University nor the names of its contributors 19 * may be used to endorse or promote products derived from this software 20 * without specific prior written permission. 21 * 22 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 23 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 24 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 25 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 26 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 27 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 28 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 29 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 30 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 31 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 32 * SUCH DAMAGE. 33 * 34 * @(#)cbrt.s 8.1 (Berkeley) 6/4/93 35 */ 36 37/* 38 * double cbrt(double arg) 39 * W. Kahan, 10/13/80. revised 1/13/84 for keeping sign symmetry 40 * error check by E LeBlanc, 8/18/82 41 * Revised and tested by K.C. Ng, 5/2/85 42 * Max error less than 0.667 ulps (unit in the last places) 43 */ 44 45 .globl _cbrt 46 .type _cbrt,@function 47 .globl _d_cbrt 48 .type _d_cbrt,@function 49 .globl _dcbrt_ 50 .type _dcbrt_,@function 51 .text 52 .align 1 53 54_cbrt: 55_d_cbrt: 56 .word 0x00fc # save r2 to r7 57 movq 4(ap),r0 # r0 = argument x 58 jmp dcbrt2 59_dcbrt_: 60 .word 0x00fc # save r2 to r7 61 movq *4(ap),r0 # r0 = argument x 62 63dcbrt2: bicw3 $0x807f,r0,r2 # biased exponent of x 64 jeql return # dcbrt(0)=0 dcbrt(res)=res. operand 65 bicw3 $0x7fff,r0,ap # ap has sign(x) 66 xorw2 ap,r0 # r0 is abs(x) 67 movl r0,r2 # r2 has abs(x) 68 rotl $16,r2,r2 # r2 = |x| with bits unscrambled 69 divl2 $3,r2 # rough dcbrt with bias/3 70 addl2 B,r2 # restore bias, diminish fraction 71 rotl $16,r2,r2 # r2=|q|=|dcbrt| to 5 bits 72 mulf3 r2,r2,r3 # r3 =qq 73 divf2 r0,r3 # r3 = qq/x 74 mulf2 r2,r3 75 addf2 C,r3 # r3 = s = C + qqq/x 76 divf3 r3,D,r4 # r4 = D/s 77 addf2 E,r4 78 addf2 r4,r3 # r3 = s + E + D/s 79 divf3 r3,F,r3 # r3 = F / (s + E + D/s) 80 addf2 G,r3 # r3 = G + F / (s + E + D/s) 81 mulf2 r3,r2 # r2 = qr3 = new q to 23 bits 82 clrl r3 # r2:r3 = q as double float 83 muld3 r2,r2,r4 # r4:r5 = qq exactly 84 divd2 r4,r0 # r0:r1 = x/(q*q) rounded 85 subd3 r2,r0,r6 # r6:r7 = x/(q*q) - q exactly 86 movq r2,r4 # r4:r5 = q 87 addw2 $0x80,r4 # r4:r5 = 2 * q 88 addd2 r0,r4 # r4:r5 = 2*q + x/(q*q) 89 divd2 r4,r6 # r6:r7 = (x/(q*q)-q)/(2*q+x/(q*q)) 90 muld2 r2,r6 # r6:r7 = q*(x/(q*q)-q)/(2*q+x/(q*q)) 91 addd3 r6,r2,r0 # r0:r1 = q + r6:r7 92 bisw2 ap,r0 # restore the sign bit 93return: 94 ret # error less than 0.667 ulps 95 96.data 97.align 2 98B : .long 721142941 # (86-0.03306235651)*(2^23) 99C : .float 0f0.5428571429 # 19/35 100D : .float 0f-0.7053061224 # -864/1225 101E : .float 0f1.414285714 # 99/70 102F : .float 0f1.607142857 # 45/28 103G : .float 0f0.3571428571 # 5/14 104 105