2005-04-17 06:20:36 +08:00
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| satanh.sa 3.3 12/19/90
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| The entry point satanh computes the inverse
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| hyperbolic tangent of
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| an input argument; satanhd does the same except for denormalized
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| input.
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| Input: Double-extended number X in location pointed to
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| by address register a0.
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| Output: The value arctanh(X) returned in floating-point register Fp0.
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| Accuracy and Monotonicity: The returned result is within 3 ulps in
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| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
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| result is subsequently rounded to double precision. The
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| result is provably monotonic in double precision.
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| Speed: The program satanh takes approximately 270 cycles.
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| Algorithm:
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| ATANH
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| 1. If |X| >= 1, go to 3.
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| 2. (|X| < 1) Calculate atanh(X) by
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| sgn := sign(X)
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| y := |X|
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| z := 2y/(1-y)
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| atanh(X) := sgn * (1/2) * logp1(z)
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| Exit.
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| 3. If |X| > 1, go to 5.
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| 4. (|X| = 1) Generate infinity with an appropriate sign and
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| divide-by-zero by
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| sgn := sign(X)
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| atan(X) := sgn / (+0).
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| Exit.
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| 5. (|X| > 1) Generate an invalid operation by 0 * infinity.
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| Exit.
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| Copyright (C) Motorola, Inc. 1990
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| All Rights Reserved
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2006-02-12 09:55:48 +08:00
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| For details on the license for this file, please see the
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| file, README, in this same directory.
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2005-04-17 06:20:36 +08:00
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|satanh idnt 2,1 | Motorola 040 Floating Point Software Package
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|section 8
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|xref t_dz
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|xref t_operr
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|xref t_frcinx
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|xref t_extdnrm
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|xref slognp1
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.global satanhd
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satanhd:
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|--ATANH(X) = X FOR DENORMALIZED X
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bra t_extdnrm
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.global satanh
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satanh:
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movel (%a0),%d0
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movew 4(%a0),%d0
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andil #0x7FFFFFFF,%d0
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cmpil #0x3FFF8000,%d0
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bges ATANHBIG
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|--THIS IS THE USUAL CASE, |X| < 1
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|--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).
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fabsx (%a0),%fp0 | ...Y = |X|
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fmovex %fp0,%fp1
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fnegx %fp1 | ...-Y
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faddx %fp0,%fp0 | ...2Y
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fadds #0x3F800000,%fp1 | ...1-Y
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fdivx %fp1,%fp0 | ...2Y/(1-Y)
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movel (%a0),%d0
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andil #0x80000000,%d0
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oril #0x3F000000,%d0 | ...SIGN(X)*HALF
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movel %d0,-(%sp)
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fmovemx %fp0-%fp0,(%a0) | ...overwrite input
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movel %d1,-(%sp)
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clrl %d1
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bsr slognp1 | ...LOG1P(Z)
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fmovel (%sp)+,%fpcr
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fmuls (%sp)+,%fp0
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bra t_frcinx
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ATANHBIG:
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fabsx (%a0),%fp0 | ...|X|
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fcmps #0x3F800000,%fp0
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fbgt t_operr
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bra t_dz
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|end
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