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|       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|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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