1# Copyright (c) 1987 Regents of the University of California. 2# All rights reserved. 3# 4# %sccs.include.redist.sh% 5# 6# @(#)cbrt.s 5.5 (Berkeley) 10/09/90 7# 8 .data 9 .align 2 10_sccsid: 11.asciz "@(#)cbrt.s 5.5 (ucb.elefunt) 10/09/90" 12 13# double cbrt(double arg) 14# W. Kahan, 10/13/80. revised 1/13/84 for keeping sign symmetry 15# Re-coded in tahoe assembly language by Z. Alex Liu (7/13/87) 16# Max error less than 0.667 ULPs _if_ +,-,*,/ were all correctly rounded... 17 .globl _cbrt 18 .globl _d_cbrt 19 .globl _dcbrt_ 20 .text 21 .align 2 22_cbrt: 23_d_cbrt: 24 .word 0x01fc # save r2-r8 25 movl 4(fp),r0 # r0:r1 = x 26 movl 8(fp),r1 27 brb 1f 28_dcbrt_: 29 .word 0x01fc # save r2-r8 30 movl 4(fp),r8 31 movl (r8),r0 32 movl 4(r8),r1 # r0:r1 = x 33 341: andl3 $0x7f800000,r0,r2 # biased exponent of x 35 beql return # dcbrt(0)=0 dcbrt(res)=res. operand 36 andl3 $0x80000000,r0,r8 # r8 has sign(x) 37 xorl2 r8,r0 # r0 is abs(x) 38 movl r0,r2 # r2 has abs(x) 39 divl2 $3,r2 # rough dcbrt with bias/3 40 addl2 B,r2 # restore bias, diminish fraction 41 ldf r2 # acc = |q|=|dcbrt| to 5 bits 42 mulf r2 # acc = qq 43 divf r0 # acc = qq/|x| 44 mulf r2 # acc = qqq/|x| 45 addf C # acc = C+qqq/|x| 46 stf r3 # r3 = s = C+qqq/|x| 47 ldf D # acc = D 48 divf r3 # acc = D/s 49 addf E # acc = E+D/s 50 addf r3 # acc = s+E+D/s 51 stf r3 # r3 = s+E+D/s 52 ldf F # acc = F 53 divf r3 # acc = F/(s+E+D/s) 54 addf G # acc = G+F/(s+E+D/s) 55 mulf r2 # acc = q*(G+F/(s+E+D/s)) = new q to 23 bits 56 stf r2 # r2 = q*(G+F/(s+E+D/s)) = new q to 23 bits 57 clrl r3 # r2:r3 = q as double float 58 ldd r2 # acc = q as double float 59 muld r2 # acc = qq exactly 60 std r4 # r4:r5 = qq exactly 61 ldd r0 # acc = |x| 62 divd r4 # acc = |x|/(q*q) rounded 63 std r0 # r0:r1 = |x|/(q*q) rounded 64 subd r2 # acc = |x|/(q*q)-q exactly 65 std r6 # r6:r7 = |x|/(q*q)-q exactly 66 movl r2,r4 67 clrl r5 # r4:r5 = q as double float 68 addl2 $0x800000,r4 # r4:r5 = 2*q 69 ldd r4 # acc = 2*q 70 addd r0 # acc = 2*q+|x|/(q*q) 71 std r4 # r4:r5 = 2*q+|x|/(q*q) 72 ldd r6 # acc = |x|/(q*q)-q 73 divd r4 # acc = (|x|/(q*q)-q)/(2*q+|x|/(q*q)) 74 muld r2 # acc = q*(|x|/(q*q)-q)/(2*q+|x|/(q*q)) 75 addd r2 # acc = q+q*(|x|/(q*q)-q)/(2*q+|x|/(q*q)) 76 std r0 # r0:r1 = |result| 77 orl2 r8,r0 # restore the sign bit 78return: ret # error less than 0.667ULPs? 79 80 .data 81 .align 2 82B : .long 721142941 #(86-0.03306235651)*(2^23) 83 .align 2 84C: .long 0x400af8b0 #.float 0f0.5428571429 # 19/35 85 .align 2 86D: .long 0xc0348ef1 #.float 0f-0.7053061224 # -864/1225 87 .align 2 88E: .long 0x40b50750 #.float 0f1.414285714 # 99/70 89 .align 2 90F: .long 0x40cdb6db #.float 0f1.607142857 # 45/28 91 .align 2 92G: .long 0x3fb6db6e #.float 0f0.3571428571 # 5/14 93