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|	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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