source: rtems/c/src/lib/libcpu/m68k/m68040/fpsp/sacos.s @ f9b93da

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//      THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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