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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|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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