1# Copyright (c) 1985 Regents of the University of California. 2# All rights reserved. 3# 4# Redistribution and use in source and binary forms are permitted 5# provided that the above copyright notice and this paragraph are 6# duplicated in all such forms and that any documentation, 7# advertising materials, and other materials related to such 8# distribution and use acknowledge that the software was developed 9# by the University of California, Berkeley. The name of the 10# University may not be used to endorse or promote products derived 11# from this software without specific prior written permission. 12# THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR 13# IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED 14# WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE. 15# 16# All recipients should regard themselves as participants in an ongoing 17# research project and hence should feel obligated to report their 18# experiences (good or bad) with these elementary function codes, using 19# the sendbug(8) program, to the authors. 20# 21# @(#)cbrt.s 5.3 (Berkeley) 06/30/88 22# 23 .data 24 .align 2 25_sccsid: 26.asciz "@(#)cbrt.s 1.1 (Berkeley) 5/23/85; 5.3 (ucb.elefunt) 06/30/88" 27 28# double cbrt(double arg) 29# W. Kahan, 10/13/80. revised 1/13/84 for keeping sign symmetry 30# error check by E LeBlanc, 8/18/82 31# Revised and tested by K.C. Ng, 5/2/85 32# Max error less than 0.667 ulps (unit in the last places) 33 .globl _cbrt 34 .globl _d_cbrt 35 .globl _dcbrt_ 36 .text 37 .align 1 38 39_cbrt: 40_d_cbrt: 41 .word 0x00fc # save r2 to r7 42 movq 4(ap),r0 # r0 = argument x 43 jmp dcbrt2 44_dcbrt_: 45 .word 0x00fc # save r2 to r7 46 movq *4(ap),r0 # r0 = argument x 47 48dcbrt2: bicw3 $0x807f,r0,r2 # biased exponent of x 49 jeql return # dcbrt(0)=0 dcbrt(res)=res. operand 50 bicw3 $0x7fff,r0,ap # ap has sign(x) 51 xorw2 ap,r0 # r0 is abs(x) 52 movl r0,r2 # r2 has abs(x) 53 rotl $16,r2,r2 # r2 = |x| with bits unscrambled 54 divl2 $3,r2 # rough dcbrt with bias/3 55 addl2 B,r2 # restore bias, diminish fraction 56 rotl $16,r2,r2 # r2=|q|=|dcbrt| to 5 bits 57 mulf3 r2,r2,r3 # r3 =qq 58 divf2 r0,r3 # r3 = qq/x 59 mulf2 r2,r3 60 addf2 C,r3 # r3 = s = C + qqq/x 61 divf3 r3,D,r4 # r4 = D/s 62 addf2 E,r4 63 addf2 r4,r3 # r3 = s + E + D/s 64 divf3 r3,F,r3 # r3 = F / (s + E + D/s) 65 addf2 G,r3 # r3 = G + F / (s + E + D/s) 66 mulf2 r3,r2 # r2 = qr3 = new q to 23 bits 67 clrl r3 # r2:r3 = q as double float 68 muld3 r2,r2,r4 # r4:r5 = qq exactly 69 divd2 r4,r0 # r0:r1 = x/(q*q) rounded 70 subd3 r2,r0,r6 # r6:r7 = x/(q*q) - q exactly 71 movq r2,r4 # r4:r5 = q 72 addw2 $0x80,r4 # r4:r5 = 2 * q 73 addd2 r0,r4 # r4:r5 = 2*q + x/(q*q) 74 divd2 r4,r6 # r6:r7 = (x/(q*q)-q)/(2*q+x/(q*q)) 75 muld2 r2,r6 # r6:r7 = q*(x/(q*q)-q)/(2*q+x/(q*q)) 76 addd3 r6,r2,r0 # r0:r1 = q + r6:r7 77 bisw2 ap,r0 # restore the sign bit 78return: 79 ret # error less than 0.667 ulps 80 81.data 82.align 2 83B : .long 721142941 # (86-0.03306235651)*(2^23) 84C : .float 0f0.5428571429 # 19/35 85D : .float 0f-0.7053061224 # -864/1225 86E : .float 0f1.414285714 # 99/70 87F : .float 0f1.607142857 # 45/28 88G : .float 0f0.3571428571 # 5/14 89 90