1# 2# Copyright (c) 1985 Regents of the University of California. 3# 4# Use and reproduction of this software are granted in accordance with 5# the terms and conditions specified in the Berkeley Software License 6# Agreement (in particular, this entails acknowledgement of the programs' 7# source, and inclusion of this notice) with the additional understanding 8# that all recipients should regard themselves as participants in an 9# ongoing research project and hence should feel obligated to report 10# their experiences (good or bad) with these elementary function codes, 11# using "sendbug 4bsd-bugs@BERKELEY", to the authors. 12# 13 14# @(#)cbrt.s 1.1 (Berkeley) 05/23/85 15 16# double cbrt(double arg) 17# W. Kahan, 10/13/80. revised 1/13/84 for keeping sign symmetry 18# error check by E LeBlanc, 8/18/82 19# Revised and tested by K.C. Ng, 5/2/85 20# Max error less than 0.667 ulps (unit in the last places) 21 .globl _cbrt 22 .globl _d_cbrt 23 .globl _dcbrt_ 24 .text 25 .align 1 26 27_cbrt: 28_d_cbrt: 29 .word 0x00fc # save r2 to r7 30 movq 4(ap),r0 # r0 = argument x 31 jmp dcbrt2 32_dcbrt_: 33 .word 0x00fc # save r2 to r7 34 movq *4(ap),r0 # r0 = argument x 35 36dcbrt2: bicw3 $0x807f,r0,r2 # biased exponent of x 37 jeql return # dcbrt(0)=0 dcbrt(res)=res. operand 38 bicw3 $0x7fff,r0,ap # ap has sign(x) 39 xorw2 ap,r0 # r0 is abs(x) 40 movl r0,r2 # r2 has abs(x) 41 rotl $16,r2,r2 # r2 = |x| with bits unscrambled 42 divl2 $3,r2 # rough dcbrt with bias/3 43 addl2 B,r2 # restore bias, diminish fraction 44 rotl $16,r2,r2 # r2=|q|=|dcbrt| to 5 bits 45 mulf3 r2,r2,r3 # r3 =qq 46 divf2 r0,r3 # r3 = qq/x 47 mulf2 r2,r3 48 addf2 C,r3 # r3 = s = C + qqq/x 49 divf3 r3,D,r4 # r4 = D/s 50 addf2 E,r4 51 addf2 r4,r3 # r3 = s + E + D/s 52 divf3 r3,F,r3 # r3 = F / (s + E + D/s) 53 addf2 G,r3 # r3 = G + F / (s + E + D/s) 54 mulf2 r3,r2 # r2 = qr3 = new q to 23 bits 55 clrl r3 # r2:r3 = q as double float 56 muld3 r2,r2,r4 # r4:r5 = qq exactly 57 divd2 r4,r0 # r0:r1 = x/(q*q) rounded 58 subd3 r2,r0,r6 # r6:r7 = x/(q*q) - q exactly 59 movq r2,r4 # r4:r5 = q 60 addw2 $0x80,r4 # r4:r5 = 2 * q 61 addd2 r0,r4 # r4:r5 = 2*q + x/(q*q) 62 divd2 r4,r6 # r6:r7 = (x/(q*q)-q)/(2*q+x/(q*q)) 63 muld2 r2,r6 # r6:r7 = q*(x/(q*q)-q)/(2*q+x/(q*q)) 64 addd3 r6,r2,r0 # r0:r1 = q + r6:r7 65 bisw2 ap,r0 # restore the sign bit 66return: 67 ret # error less than 0.667 ulps 68 69.data 70.align 2 71B : .long 721142941 # (86-0.03306235651)*(2^23) 72C : .float 0f0.5428571429 # 19/35 73D : .float 0f-0.7053061224 # -864/1225 74E : .float 0f1.414285714 # 99/70 75F : .float 0f1.607142857 # 45/28 76G : .float 0f0.3571428571 # 5/14 77 78