| Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 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 | | |
| Matt Waddel | e00d82d | 2006-02-11 17:55:48 -0800 | [diff] [blame] | 41 | | For details on the license for this file, please see the |
| 42 | | file, README, in this same directory. |
| Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 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 |