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 | | 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