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//

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

//

//      satanh.sa 3.3 12/19/90

//

//      The entry point satanh computes the inverse

//      hyperbolic tangent of

//      an input argument; satanhd does the same except for denormalized

//      input.

//

//      Input: Double-extended number X in location pointed to

//              by address register a0.

//

//      Output: The value arctanh(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 satanh takes approximately 270 cycles.

//

//      Algorithm:

//

//      ATANH

//      1. If |X| >= 1, go to 3.

//

//      2. (|X| < 1) Calculate atanh(X) by

//              sgn := sign(X)

//              y := |X|

//              z := 2y/(1-y)

//              atanh(X) := sgn * (1/2) * logp1(z)

//              Exit.

//

//      3. If |X| > 1, go to 5.

//

//      4. (|X| = 1) Generate infinity with an appropriate sign and

//              divide-by-zero by

//              sgn := sign(X)

//              atan(X) := sgn / (+0).

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//      THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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

//satanh        idnt    2,1 | Motorola 040 Floating Point Software Package

        |section        8

        |xref   t_dz

        |xref   t_operr

        |xref   t_frcinx

        |xref   t_extdnrm

        |xref   slognp1

        .global satanhd

satanhd:

//--ATANH(X) = X FOR DENORMALIZED X

        bra             t_extdnrm

        .global satanh

satanh:

        movel           (%a0),%d0

        movew           4(%a0),%d0

        andil           #0x7FFFFFFF,%d0

        cmpil           #0x3FFF8000,%d0

        bges            ATANHBIG

//--THIS IS THE USUAL CASE, |X| < 1

//--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).

        fabsx           (%a0),%fp0      // ...Y = |X|

        fmovex          %fp0,%fp1

        fnegx           %fp1            // ...-Y

        faddx           %fp0,%fp0               // ...2Y

        fadds           #0x3F800000,%fp1        // ...1-Y

        fdivx           %fp1,%fp0               // ...2Y/(1-Y)

        movel           (%a0),%d0

        andil           #0x80000000,%d0

        oril            #0x3F000000,%d0 // ...SIGN(X)*HALF

        movel           %d0,-(%sp)

        fmovemx %fp0-%fp0,(%a0) // ...overwrite input

        movel           %d1,-(%sp)

        clrl            %d1

        bsr             slognp1         // ...LOG1P(Z)

        fmovel          (%sp)+,%fpcr

        fmuls           (%sp)+,%fp0

        bra             t_frcinx

ATANHBIG:

        fabsx           (%a0),%fp0      // ...|X|

        fcmps           #0x3F800000,%fp0

        fbgt            t_operr

        bra             t_dz

        |end