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awilliam
GitHub Repository: awilliam/linux-vfio
 Path: blob/master/arch/m68k/fpsp040/satanh.S
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|	satanh.sa 3.3 12/19/90

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|

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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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|

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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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|

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|	Output: The value arctanh(X) returned in floating-point register Fp0.

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|

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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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|

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|	Speed: The program satanh takes approximately 270 cycles.

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|

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|	Algorithm:

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|

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|	ATANH

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|	1. If |X| >= 1, go to 3.

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|

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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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|

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|	3. If |X| > 1, go to 5.

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|

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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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|

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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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|

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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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|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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