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1.1 ! root 1: # double cbrt(arg) ! 2: # double arg ! 3: # no error exits ! 4: #method: range reduction to [1/8,1], poly appox, newtons method ! 5: # J F Jarvis, August 10,1978 ! 6: .globl _cbrt ! 7: .text ! 8: .align 1 ! 9: _cbrt: ! 10: .word 0x00c0 ! 11: bispsw $0xe0 ! 12: clrl r3 ! 13: movd 4(ap),r4 ! 14: jgtr range ! 15: jeql retz ! 16: mnegd r4,r4 # |arg| in r0,r1 ! 17: movl $0x100,r3 # sign bit of result ! 18: range: ! 19: extzv $7,$8,r4,r6 ! 20: insv $128,$7,$8,r4 # 0.5<= frac: r4,r5 <1.0 ! 21: clrl r7 ! 22: ediv $3,r6,r6,r7 # r6= expnt/3; r7= expnt%3 ! 23: addb2 $86,r6 ! 24: bisl2 r3,r6 # sign,exponent of result ! 25: polyf r4,$3,pcoef # initial estimate is Hart&Cheney CBRT 0642 ! 26: # D=4.1 ! 27: muld3 r0,r0,r2 # Newtons method, iteration 1, H&C 6.1.10 ! 28: divd3 r2,r4,r2 ! 29: subd3 r2,r0,r2 ! 30: muld2 third,r2 ! 31: subd2 r2,r0 # D=8.2 ! 32: muld3 r0,r0,r2 # iteration 2 ! 33: divd3 r2,r4,r2 ! 34: subd3 r2,r0,r2 ! 35: muld2 third,r2 ! 36: subd2 r2,r0 ! 37: muld2 hc[r7],r0 # set range ! 38: insv r6,$7,$9,r0 # set sign,exponent ! 39: ret ! 40: retz: ! 41: clrd r0 ! 42: ret ! 43: .data ! 44: .align 2 ! 45: third: .double 0d0.33333333333333333333e+0 ! 46: hc: ! 47: .double 0d1.25992104989487316476e+0 ! 48: .double 0d1.58740105196819947475e+0 ! 49: .double 0d1.0e+0 ! 50: pcoef: ! 51: .float 0f0.1467073818e+0 ! 52: .float 0f-0.5173964673e+0 ! 53: .float 0f0.9319858515e+0 ! 54: .float 0f0.4387762363e+0
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