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

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|

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|	Description: The entry point sAsin computes the inverse sine of

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|		an input argument; sAsind 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 arcsin(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 sASIN takes approximately 310 cycles.

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|

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|	Algorithm:

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|	ASIN

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

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|

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|	2. (|X| < 1) Calculate asin(X) by

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|		z := sqrt( [1-X][1+X] )

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|		asin(X) = atan( x / 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) sgn := sign(X), return asin(X) := sgn * Pi/2. 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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|

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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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|SASIN	idnt	2,1 | Motorola 040 Floating Point Software Package

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	|section	8

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PIBY2:	.long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000

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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	satan

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	.global	sasind

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sasind:

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|--ASIN(X) = X FOR DENORMALIZED X

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	bra		t_extdnrm

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	.global	sasin

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sasin:

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	fmovex		(%a0),%fp0	| ...LOAD INPUT

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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		asinbig

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|--THIS IS THE USUAL CASE, |X| < 1

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|--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )

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	fmoves		#0x3F800000,%fp1

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	fsubx		%fp0,%fp1		| ...1-X

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	fmovemx	%fp2-%fp2,-(%a7)

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	fmoves		#0x3F800000,%fp2

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	faddx		%fp0,%fp2		| ...1+X

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	fmulx		%fp2,%fp1		| ...(1+X)(1-X)

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	fmovemx	(%a7)+,%fp2-%fp2

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	fsqrtx		%fp1		| ...SQRT([1-X][1+X])

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	fdivx		%fp1,%fp0		| ...X/SQRT([1-X][1+X])

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	fmovemx	%fp0-%fp0,(%a0)

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	bsr		satan

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	bra		t_frcinx

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asinbig:

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	fabsx		%fp0	 | ...|X|

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	fcmps		#0x3F800000,%fp0

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	fbgt		t_operr		|cause an operr exception

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|--|X| = 1, ASIN(X) = +- PI/2.

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	fmovex		PIBY2,%fp0

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	movel		(%a0),%d0

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	andil		#0x80000000,%d0	| ...SIGN BIT OF X

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	oril		#0x3F800000,%d0	| ...+-1 IN SGL FORMAT

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	movel		%d0,-(%sp)	| ...push SIGN(X) IN SGL-FMT

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	fmovel		%d1,%FPCR

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	fmuls		(%sp)+,%fp0

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	bra		t_frcinx

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	|end

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