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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
-|
-| For details on the license for this file, please see the
-| file, README, in this same directory.
-
-|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