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# @(#)cabs.s 1.2 (Berkeley) 08/21/85 15 16# double precision complex absolute value 17# CABS by W. Kahan, 9/7/80. 18# Revised for reserved operands by E. LeBlanc, 8/18/82 19# argument for complex absolute value by reference, *4(ap) 20# argument for cabs and hypot (C fcns) by value, 4(ap) 21# output is in r0:r1 (error less than 0.86 ulps) 22 23 .text 24 .align 1 25 .globl _cabs 26 .globl _hypot 27 .globl _z_abs 28 .globl libm$cdabs_r6 29 .globl libm$dsqrt_r5 30 31# entry for c functions cabs and hypot 32_cabs: 33_hypot: 34 .word 0x807c # save r2-r6, enable floating overflow 35 movq 4(ap),r0 # r0:1 = x 36 movq 12(ap),r2 # r2:3 = y 37 jmp cabs2 38# entry for Fortran use, call by: d = abs(z) 39_z_abs: 40 .word 0x807c # save r2-r6, enable floating overflow 41 movl 4(ap),r2 # indirect addressing is necessary here 42 movq (r2)+,r0 # r0:1 = x 43 movq (r2),r2 # r2:3 = y 44 45cabs2: 46 bicw3 $0x7f,r0,r4 # r4 has signed biased exp of x 47 cmpw $0x8000,r4 48 jeql return # x is a reserved operand, so return it 49 bicw3 $0x7f,r2,r5 # r5 has signed biased exp of y 50 cmpw $0x8000,r5 51 jneq cont # y isn't a reserved operand 52 movq r2,r0 # return y if it's reserved 53 ret 54 55cont: 56 bsbb regs_set # r0:1 = dsqrt(x^2+y^2)/2^r6 57 addw2 r6,r0 # unscaled cdabs in r0:1 58 jvc return # unless it overflows 59 subw2 $0x80,r0 # halve r0 to get meaningful overflow 60 addd2 r0,r0 # overflow; r0 is half of true abs value 61return: 62 ret 63 64libm$cdabs_r6: # ENTRY POINT for cdsqrt 65 # calculates a scaled (factor in r6) 66 # complex absolute value 67 68 movq (r4)+,r0 # r0:r1 = x via indirect addressing 69 movq (r4),r2 # r2:r3 = y via indirect addressing 70 71 bicw3 $0x7f,r0,r5 # r5 has signed biased exp of x 72 cmpw $0x8000,r5 73 jeql cdreserved # x is a reserved operand 74 bicw3 $0x7f,r2,r5 # r5 has signed biased exp of y 75 cmpw $0x8000,r5 76 jneq regs_set # y isn't a reserved operand either? 77 78cdreserved: 79 movl *4(ap),r4 # r4 -> (u,v), if x or y is reserved 80 movq r0,(r4)+ # copy u and v as is and return 81 movq r2,(r4) # (again addressing is indirect) 82 ret 83 84regs_set: 85 bicw2 $0x8000,r0 # r0:r1 = dabs(x) 86 bicw2 $0x8000,r2 # r2:r3 = dabs(y) 87 cmpw r0,r2 88 jgeq ordered 89 movq r0,r4 90 movq r2,r0 91 movq r4,r2 # force y's exp <= x's exp 92ordered: 93 bicw3 $0x7f,r0,r6 # r6 = exponent(x) + bias(129) 94 jeql retsb # if x = y = 0 then cdabs(x,y) = 0 95 subw2 $0x4780,r6 # r6 = exponent(x) - 14 96 subw2 r6,r0 # 2^14 <= scaled x < 2^15 97 bitw $0xff80,r2 98 jeql retsb # if y = 0 return dabs(x) 99 subw2 r6,r2 100 cmpw $0x3780,r2 # if scaled y < 2^-18 101 jgtr retsb # return dabs(x) 102 emodd r0,$0,r0,r4,r0 # r4 + r0:1 = scaled x^2 103 emodd r2,$0,r2,r5,r2 # r5 + r2:3 = scaled y^2 104 addd2 r2,r0 105 addl2 r5,r4 106 cvtld r4,r2 107 addd2 r2,r0 # r0:1 = scaled x^2 + y^2 108 jmp libm$dsqrt_r5 # r0:1 = dsqrt(x^2+y^2)/2^r6 109retsb: 110 rsb # error < 0.86 ulp 111