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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+|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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