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