| | |
| | sacos.sa 3.3 12/19/90 |
| | |
| | Description: The entry point sAcos computes the inverse cosine of |
| | an input argument; sAcosd does the same except for denormalized |
| | input. |
| | |
| | Input: Double-extended number X in location pointed to |
| | by address register a0. |
| | |
| | Output: The value arccos(X) returned in floating-point register Fp0. |
| | |
| | Accuracy and Monotonicity: The returned result is within 3 ulps in |
| | 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the |
| | result is subsequently rounded to double precision. The |
| | result is provably monotonic in double precision. |
| | |
| | Speed: The program sCOS takes approximately 310 cycles. |
| | |
| | Algorithm: |
| | |
| | ACOS |
| | 1. If |X| >= 1, go to 3. |
| | |
| | 2. (|X| < 1) Calculate acos(X) by |
| | z := (1-X) / (1+X) |
| | acos(X) = 2 * atan( sqrt(z) ). |
| | Exit. |
| | |
| | 3. If |X| > 1, go to 5. |
| | |
| | 4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. Exit. |
| | |
| | 5. (|X| > 1) Generate an invalid operation by 0 * infinity. |
| | Exit. |
| | |
| |
| | Copyright (C) Motorola, Inc. 1990 |
| | All Rights Reserved |
| | |
| | For details on the license for this file, please see the |
| | file, README, in this same directory. |
| |
| |SACOS idnt 2,1 | Motorola 040 Floating Point Software Package |
| |
| |section 8 |
| |
| PI: .long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000 |
| PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000 |
| |
| |xref t_operr |
| |xref t_frcinx |
| |xref satan |
| |
| .global sacosd |
| sacosd: |
| |--ACOS(X) = PI/2 FOR DENORMALIZED X |
| fmovel %d1,%fpcr | ...load user's rounding mode/precision |
| fmovex PIBY2,%fp0 |
| bra t_frcinx |
| |
| .global sacos |
| sacos: |
| fmovex (%a0),%fp0 | ...LOAD INPUT |
| |
| movel (%a0),%d0 | ...pack exponent with upper 16 fraction |
| movew 4(%a0),%d0 |
| andil #0x7FFFFFFF,%d0 |
| cmpil #0x3FFF8000,%d0 |
| bges ACOSBIG |
| |
| |--THIS IS THE USUAL CASE, |X| < 1 |
| |--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) ) ) |
| |
| fmoves #0x3F800000,%fp1 |
| faddx %fp0,%fp1 | ...1+X |
| fnegx %fp0 | ... -X |
| fadds #0x3F800000,%fp0 | ...1-X |
| fdivx %fp1,%fp0 | ...(1-X)/(1+X) |
| fsqrtx %fp0 | ...SQRT((1-X)/(1+X)) |
| fmovemx %fp0-%fp0,(%a0) | ...overwrite input |
| movel %d1,-(%sp) |save original users fpcr |
| clrl %d1 |
| bsr satan | ...ATAN(SQRT([1-X]/[1+X])) |
| fmovel (%sp)+,%fpcr |restore users exceptions |
| faddx %fp0,%fp0 | ...2 * ATAN( STUFF ) |
| bra t_frcinx |
| |
| ACOSBIG: |
| fabsx %fp0 |
| fcmps #0x3F800000,%fp0 |
| fbgt t_operr |cause an operr exception |
| |
| |--|X| = 1, ACOS(X) = 0 OR PI |
| movel (%a0),%d0 | ...pack exponent with upper 16 fraction |
| movew 4(%a0),%d0 |
| cmpl #0,%d0 |D0 has original exponent+fraction |
| bgts ACOSP1 |
| |
| |--X = -1 |
| |Returns PI and inexact exception |
| fmovex PI,%fp0 |
| fmovel %d1,%FPCR |
| fadds #0x00800000,%fp0 |cause an inexact exception to be put |
| | ;into the 040 - will not trap until next |
| | ;fp inst. |
| bra t_frcinx |
| |
| ACOSP1: |
| fmovel %d1,%FPCR |
| fmoves #0x00000000,%fp0 |
| rts |Facos ; of +1 is exact |
| |
| |end |
