1| 2| sacos.sa 3.3 12/19/90 3| 4| Description: The entry point sAcos computes the inverse cosine of 5| an input argument; sAcosd does the same except for denormalized 6| input. 7| 8| Input: Double-extended number X in location pointed to 9| by address register a0. 10| 11| Output: The value arccos(X) returned in floating-point register Fp0. 12| 13| Accuracy and Monotonicity: The returned result is within 3 ulps in 14| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the 15| result is subsequently rounded to double precision. The 16| result is provably monotonic in double precision. 17| 18| Speed: The program sCOS takes approximately 310 cycles. 19| 20| Algorithm: 21| 22| ACOS 23| 1. If |X| >= 1, go to 3. 24| 25| 2. (|X| < 1) Calculate acos(X) by 26| z := (1-X) / (1+X) 27| acos(X) = 2 * atan( sqrt(z) ). 28| Exit. 29| 30| 3. If |X| > 1, go to 5. 31| 32| 4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. Exit. 33| 34| 5. (|X| > 1) Generate an invalid operation by 0 * infinity. 35| Exit. 36| 37 38| Copyright (C) Motorola, Inc. 1990 39| All Rights Reserved 40| 41| For details on the license for this file, please see the 42| file, README, in this same directory. 43 44|SACOS idnt 2,1 | Motorola 040 Floating Point Software Package 45 46 |section 8 47 48PI: .long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000 49PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000 50 51 |xref t_operr 52 |xref t_frcinx 53 |xref satan 54 55 .global sacosd 56sacosd: 57|--ACOS(X) = PI/2 FOR DENORMALIZED X 58 fmovel %d1,%fpcr | ...load user's rounding mode/precision 59 fmovex PIBY2,%fp0 60 bra t_frcinx 61 62 .global sacos 63sacos: 64 fmovex (%a0),%fp0 | ...LOAD INPUT 65 66 movel (%a0),%d0 | ...pack exponent with upper 16 fraction 67 movew 4(%a0),%d0 68 andil #0x7FFFFFFF,%d0 69 cmpil #0x3FFF8000,%d0 70 bges ACOSBIG 71 72|--THIS IS THE USUAL CASE, |X| < 1 73|--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) ) ) 74 75 fmoves #0x3F800000,%fp1 76 faddx %fp0,%fp1 | ...1+X 77 fnegx %fp0 | ... -X 78 fadds #0x3F800000,%fp0 | ...1-X 79 fdivx %fp1,%fp0 | ...(1-X)/(1+X) 80 fsqrtx %fp0 | ...SQRT((1-X)/(1+X)) 81 fmovemx %fp0-%fp0,(%a0) | ...overwrite input 82 movel %d1,-(%sp) |save original users fpcr 83 clrl %d1 84 bsr satan | ...ATAN(SQRT([1-X]/[1+X])) 85 fmovel (%sp)+,%fpcr |restore users exceptions 86 faddx %fp0,%fp0 | ...2 * ATAN( STUFF ) 87 bra t_frcinx 88 89ACOSBIG: 90 fabsx %fp0 91 fcmps #0x3F800000,%fp0 92 fbgt t_operr |cause an operr exception 93 94|--|X| = 1, ACOS(X) = 0 OR PI 95 movel (%a0),%d0 | ...pack exponent with upper 16 fraction 96 movew 4(%a0),%d0 97 cmpl #0,%d0 |D0 has original exponent+fraction 98 bgts ACOSP1 99 100|--X = -1 101|Returns PI and inexact exception 102 fmovex PI,%fp0 103 fmovel %d1,%FPCR 104 fadds #0x00800000,%fp0 |cause an inexact exception to be put 105| ;into the 040 - will not trap until next 106| ;fp inst. 107 bra t_frcinx 108 109ACOSP1: 110 fmovel %d1,%FPCR 111 fmoves #0x00000000,%fp0 112 rts |Facos ; of +1 is exact 113 114 |end 115