satanh.S
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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- | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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