Subversion Repositories or1k

|
|       sasin.sa 3.3 12/19/90
|
|       Description: The entry point sAsin computes the inverse sine of
|               an input argument; sAsind does the same except for denormalized
|               input.
|
|       Input: Double-extended number X in location pointed to
|               by address register a0.
|
|       Output: The value arcsin(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 sASIN takes approximately 310 cycles.
|
|       Algorithm:
|
|       ASIN
|       1. If |X| >= 1, go to 3.
|
|       2. (|X| < 1) Calculate asin(X) by
|               z := sqrt( [1-X][1+X] )
|               asin(X) = atan( x / z ).
|               Exit.
|
|       3. If |X| > 1, go to 5.
|
|       4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. 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|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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.

|SASIN  idnt    2,1 | Motorola 040 Floating Point Software Package

        |section        8

PIBY2:  .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000

        |xref   t_operr
        |xref   t_frcinx
        |xref   t_extdnrm
        |xref   satan

        .global sasind
sasind:
|--ASIN(X) = X FOR DENORMALIZED X

        bra             t_extdnrm

        .global sasin
sasin:
        fmovex          (%a0),%fp0      | ...LOAD INPUT

        movel           (%a0),%d0
        movew           4(%a0),%d0
        andil           #0x7FFFFFFF,%d0
        cmpil           #0x3FFF8000,%d0
        bges            asinbig

|--THIS IS THE USUAL CASE, |X| < 1
|--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )

        fmoves          #0x3F800000,%fp1
        fsubx           %fp0,%fp1               | ...1-X
        fmovemx %fp2-%fp2,-(%a7)
        fmoves          #0x3F800000,%fp2
        faddx           %fp0,%fp2               | ...1+X
        fmulx           %fp2,%fp1               | ...(1+X)(1-X)
        fmovemx (%a7)+,%fp2-%fp2
        fsqrtx          %fp1            | ...SQRT([1-X][1+X])
        fdivx           %fp1,%fp0               | ...X/SQRT([1-X][1+X])
        fmovemx %fp0-%fp0,(%a0)
        bsr             satan
        bra             t_frcinx

asinbig:
        fabsx           %fp0     | ...|X|
        fcmps           #0x3F800000,%fp0
        fbgt            t_operr         |cause an operr exception

|--|X| = 1, ASIN(X) = +- PI/2.

        fmovex          PIBY2,%fp0
        movel           (%a0),%d0
        andil           #0x80000000,%d0 | ...SIGN BIT OF X
        oril            #0x3F800000,%d0 | ...+-1 IN SGL FORMAT
        movel           %d0,-(%sp)      | ...push SIGN(X) IN SGL-FMT
        fmovel          %d1,%FPCR               
        fmuls           (%sp)+,%fp0
        bra             t_frcinx

        |end