|
| 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
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