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 48 PI: .long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000 49 PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000 50 51 |xref t_operr 52 |xref t_frcinx 53 |xref satan 54 55 .global sacosd 56 sacosd: 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 63 sacos: 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 89 ACOSBIG: 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 108 109 ACOSP1: 110 fmovel %d1,%FPCR 111 fmoves #0x00000000,%fp0 112 rts |Facos ; of +1 is exact 113 114 |end