1# Copyright (c) 1985, 1993 2# The Regents of the University of California. All rights reserved. 3# 4# %sccs.include.redist.sh% 5# 6# @(#)cbrt.s 8.1 (Berkeley) 06/04/93 7# 8 .data 9 .align 2 10_sccsid: 11.asciz "@(#)cbrt.s 1.1 (Berkeley) 5/23/85; 8.1 (ucb.elefunt) 06/04/93" 12 13# double cbrt(double arg) 14# W. Kahan, 10/13/80. revised 1/13/84 for keeping sign symmetry 15# error check by E LeBlanc, 8/18/82 16# Revised and tested by K.C. Ng, 5/2/85 17# Max error less than 0.667 ulps (unit in the last places) 18 .globl _cbrt 19 .globl _d_cbrt 20 .globl _dcbrt_ 21 .text 22 .align 1 23 24_cbrt: 25_d_cbrt: 26 .word 0x00fc # save r2 to r7 27 movq 4(ap),r0 # r0 = argument x 28 jmp dcbrt2 29_dcbrt_: 30 .word 0x00fc # save r2 to r7 31 movq *4(ap),r0 # r0 = argument x 32 33dcbrt2: bicw3 $0x807f,r0,r2 # biased exponent of x 34 jeql return # dcbrt(0)=0 dcbrt(res)=res. operand 35 bicw3 $0x7fff,r0,ap # ap has sign(x) 36 xorw2 ap,r0 # r0 is abs(x) 37 movl r0,r2 # r2 has abs(x) 38 rotl $16,r2,r2 # r2 = |x| with bits unscrambled 39 divl2 $3,r2 # rough dcbrt with bias/3 40 addl2 B,r2 # restore bias, diminish fraction 41 rotl $16,r2,r2 # r2=|q|=|dcbrt| to 5 bits 42 mulf3 r2,r2,r3 # r3 =qq 43 divf2 r0,r3 # r3 = qq/x 44 mulf2 r2,r3 45 addf2 C,r3 # r3 = s = C + qqq/x 46 divf3 r3,D,r4 # r4 = D/s 47 addf2 E,r4 48 addf2 r4,r3 # r3 = s + E + D/s 49 divf3 r3,F,r3 # r3 = F / (s + E + D/s) 50 addf2 G,r3 # r3 = G + F / (s + E + D/s) 51 mulf2 r3,r2 # r2 = qr3 = new q to 23 bits 52 clrl r3 # r2:r3 = q as double float 53 muld3 r2,r2,r4 # r4:r5 = qq exactly 54 divd2 r4,r0 # r0:r1 = x/(q*q) rounded 55 subd3 r2,r0,r6 # r6:r7 = x/(q*q) - q exactly 56 movq r2,r4 # r4:r5 = q 57 addw2 $0x80,r4 # r4:r5 = 2 * q 58 addd2 r0,r4 # r4:r5 = 2*q + x/(q*q) 59 divd2 r4,r6 # r6:r7 = (x/(q*q)-q)/(2*q+x/(q*q)) 60 muld2 r2,r6 # r6:r7 = q*(x/(q*q)-q)/(2*q+x/(q*q)) 61 addd3 r6,r2,r0 # r0:r1 = q + r6:r7 62 bisw2 ap,r0 # restore the sign bit 63return: 64 ret # error less than 0.667 ulps 65 66.data 67.align 2 68B : .long 721142941 # (86-0.03306235651)*(2^23) 69C : .float 0f0.5428571429 # 19/35 70D : .float 0f-0.7053061224 # -864/1225 71E : .float 0f1.414285714 # 99/70 72F : .float 0f1.607142857 # 45/28 73G : .float 0f0.3571428571 # 5/14 74 75