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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
+|
+| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
+| The copyright notice above does not evidence any
+| actual or intended publication of such source code.
+
+|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