1# Copyright (c) 1987 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 5.4 (Berkeley) 06/30/88 22# 23 .data 24 .align 2 25_sccsid: 26.asciz "@(#)cbrt.s 5.4 (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# Re-coded in tahoe assembly language by Z. Alex Liu (7/13/87) 31# Max error less than 0.667 ULPs _if_ +,-,*,/ were all correctly rounded... 32 .globl _cbrt 33 .globl _d_cbrt 34 .globl _dcbrt_ 35 .text 36 .align 2 37_cbrt: 38_d_cbrt: 39 .word 0x01fc # save r2-r8 40 movl 4(fp),r0 # r0:r1 = x 41 movl 8(fp),r1 42 brb 1f 43_dcbrt_: 44 .word 0x01fc # save r2-r8 45 movl 4(fp),r8 46 movl (r8),r0 47 movl 4(r8),r1 # r0:r1 = x 48 491: andl3 $0x7f800000,r0,r2 # biased exponent of x 50 beql return # dcbrt(0)=0 dcbrt(res)=res. operand 51 andl3 $0x80000000,r0,r8 # r8 has sign(x) 52 xorl2 r8,r0 # r0 is abs(x) 53 movl r0,r2 # r2 has abs(x) 54 divl2 $3,r2 # rough dcbrt with bias/3 55 addl2 B,r2 # restore bias, diminish fraction 56 ldf r2 # acc = |q|=|dcbrt| to 5 bits 57 mulf r2 # acc = qq 58 divf r0 # acc = qq/|x| 59 mulf r2 # acc = qqq/|x| 60 addf C # acc = C+qqq/|x| 61 stf r3 # r3 = s = C+qqq/|x| 62 ldf D # acc = D 63 divf r3 # acc = D/s 64 addf E # acc = E+D/s 65 addf r3 # acc = s+E+D/s 66 stf r3 # r3 = s+E+D/s 67 ldf F # acc = F 68 divf r3 # acc = F/(s+E+D/s) 69 addf G # acc = G+F/(s+E+D/s) 70 mulf r2 # acc = q*(G+F/(s+E+D/s)) = new q to 23 bits 71 stf r2 # r2 = q*(G+F/(s+E+D/s)) = new q to 23 bits 72 clrl r3 # r2:r3 = q as double float 73 ldd r2 # acc = q as double float 74 muld r2 # acc = qq exactly 75 std r4 # r4:r5 = qq exactly 76 ldd r0 # acc = |x| 77 divd r4 # acc = |x|/(q*q) rounded 78 std r0 # r0:r1 = |x|/(q*q) rounded 79 subd r2 # acc = |x|/(q*q)-q exactly 80 std r6 # r6:r7 = |x|/(q*q)-q exactly 81 movl r2,r4 82 clrl r5 # r4:r5 = q as double float 83 addl2 $0x800000,r4 # r4:r5 = 2*q 84 ldd r4 # acc = 2*q 85 addd r0 # acc = 2*q+|x|/(q*q) 86 std r4 # r4:r5 = 2*q+|x|/(q*q) 87 ldd r6 # acc = |x|/(q*q)-q 88 divd r4 # acc = (|x|/(q*q)-q)/(2*q+|x|/(q*q)) 89 muld r2 # acc = q*(|x|/(q*q)-q)/(2*q+|x|/(q*q)) 90 addd r2 # acc = q+q*(|x|/(q*q)-q)/(2*q+|x|/(q*q)) 91 std r0 # r0:r1 = |result| 92 orl2 r8,r0 # restore the sign bit 93return: ret # error less than 0.667ULPs? 94 95 .data 96 .align 2 97B : .long 721142941 #(86-0.03306235651)*(2^23) 98 .align 2 99C: .long 0x400af8b0 #.float 0f0.5428571429 # 19/35 100 .align 2 101D: .long 0xc0348ef1 #.float 0f-0.7053061224 # -864/1225 102 .align 2 103E: .long 0x40b50750 #.float 0f1.414285714 # 99/70 104 .align 2 105F: .long 0x40cdb6db #.float 0f1.607142857 # 45/28 106 .align 2 107G: .long 0x3fb6db6e #.float 0f0.3571428571 # 5/14 108