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//

//      $Id: sasin.S,v 1.2 2001-09-27 12:01:22 chris Exp $

//

//      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//      THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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