|	MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
|	M68000 Hi-Performance Microprocessor Division
|	M68040 Software Package 
|
|	M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
|	All rights reserved.
|
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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.
|

|satanh	IDNT	2,1 Motorola 040 Floating Point Software Package

	.text

|	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	a0@(4),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