```|
|	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
|
|	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
|
|       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
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
```