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//

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

//

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//      THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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