# double atan(arg1); -pi/2 < atan < pi/2 #double atan2(arg1,arg2); -pi< atan2<pi #double arg1,arg2 #method: range reduction to [sqrt(2)-1,sqrt(2)+1] # followed by Hart&Cheney ARCTN 5076 D=17.55 # J. F. Jarvis August 8, 1978 .globl _atan .globl _atan2 .text .align 1 _atan: .word 0x03c0 movd 4(ap),r0 jgtr a1 mnegd r0,r0 # atan(arg1), arg1<0 bsbb satan mnegd r0,r0 ret a1: bsbb satan # atan(arg1), arg1>=0 ret # .align 1 _atan2: .word 0x03c0 movd 4(ap),r0 # atan(arg1/arg2) movd 12(ap),r2 addd3 r0,r2,r4 cmpd r0,r4 jneq b1 tstd r0 jgeq b2 mnegd pio2,r0 ret b2: movd pio2,r0 ret # b1: tstd r2 jgeq b3 divd2 r2,r0 jleq b4 bsbb satan # arg1<0, arg2<0 subd2 pi,r0 ret b4: mnegd r0,r0 # arg1>0, arg2<0 bsbb satan subd3 r0,pi,r0 ret # b3: divd2 r2,r0 jleq b5 bsbb satan # arg1>0, arg2>0 ret b5: mnegd r0,r0 # arg1<0, arg2>0 bsbb satan mnegd r0,r0 ret # .globl satan satan: # range reduction on positive arg(r0) cmpd r0,sq2m1 jgeq c1 bsbb xatan rsb c1: cmpd r0,sq2p1 jleq c2 divd3 r0,$0d1.0e+0,r0 bsbb xatan subd3 r0,pio2,r0 rsb c2: addd3 $0d1.0e+0,r0,r2 subd2 $0d1.0e+0,r0 divd2 r2,r0 bsbb xatan addd2 pio4,r0 rsb # xatan: # compute arctan(r0) for:sqrt(2)-1<r0<sqrt(2)+1 # Hart&Cheney ARCTN 5076 is evaluated movd r0,r8 muld3 r0,r0,r6 polyd r6,$4,pcoef muld2 r0,r8 polyd r6,$4,qcoef divd3 r0,r8,r0 rsb .data .align 2 pcoef: .double 0d0.1589740288482307048e+0 .double 0d0.66605790170092626575e+1 .double 0d0.40969264832102256374e+2 .double 0d0.77477687719204208616e+2 .double 0d0.44541340059290680319e+2 qcoef: .double 0d1.0e+0 .double 0d0.15503977551421987525e+2 .double 0d0.62835930511032376833e+2 .double 0d0.92324801072300974840e+2 .double 0d0.44541340059290680444e+2 pio4: .double 0d0.78539816339744830961e+0 pio2: .double 0d1.57079632679489661923e+0 sq2p1: .double 0d2.41421356237309504880e+0 sq2m1: .double 0d0.41421356237309504880e+0 pi: .double 0d3.14159265358979323846e+0