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sasin.sa revision 1.1
      1  1.1  mycroft *	MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
      2  1.1  mycroft *	M68000 Hi-Performance Microprocessor Division
      3  1.1  mycroft *	M68040 Software Package 
      4  1.1  mycroft *
      5  1.1  mycroft *	M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
      6  1.1  mycroft *	All rights reserved.
      7  1.1  mycroft *
      8  1.1  mycroft *	THE SOFTWARE is provided on an "AS IS" basis and without warranty.
      9  1.1  mycroft *	To the maximum extent permitted by applicable law,
     10  1.1  mycroft *	MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
     11  1.1  mycroft *	INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
     12  1.1  mycroft *	PARTICULAR PURPOSE and any warranty against infringement with
     13  1.1  mycroft *	regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
     14  1.1  mycroft *	and any accompanying written materials. 
     15  1.1  mycroft *
     16  1.1  mycroft *	To the maximum extent permitted by applicable law,
     17  1.1  mycroft *	IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
     18  1.1  mycroft *	(INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
     19  1.1  mycroft *	PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
     20  1.1  mycroft *	OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
     21  1.1  mycroft *	SOFTWARE.  Motorola assumes no responsibility for the maintenance
     22  1.1  mycroft *	and support of the SOFTWARE.  
     23  1.1  mycroft *
     24  1.1  mycroft *	You are hereby granted a copyright license to use, modify, and
     25  1.1  mycroft *	distribute the SOFTWARE so long as this entire notice is retained
     26  1.1  mycroft *	without alteration in any modified and/or redistributed versions,
     27  1.1  mycroft *	and that such modified versions are clearly identified as such.
     28  1.1  mycroft *	No licenses are granted by implication, estoppel or otherwise
     29  1.1  mycroft *	under any patents or trademarks of Motorola, Inc.
     30  1.1  mycroft 
     31  1.1  mycroft *
     32  1.1  mycroft *	sasin.sa 3.3 12/19/90
     33  1.1  mycroft *
     34  1.1  mycroft *	Description: The entry point sAsin computes the inverse sine of
     35  1.1  mycroft *		an input argument; sAsind does the same except for denormalized
     36  1.1  mycroft *		input.
     37  1.1  mycroft *
     38  1.1  mycroft *	Input: Double-extended number X in location pointed to
     39  1.1  mycroft *		by address register a0.
     40  1.1  mycroft *
     41  1.1  mycroft *	Output: The value arcsin(X) returned in floating-point register Fp0.
     42  1.1  mycroft *
     43  1.1  mycroft *	Accuracy and Monotonicity: The returned result is within 3 ulps in
     44  1.1  mycroft *		64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
     45  1.1  mycroft *		result is subsequently rounded to double precision. The 
     46  1.1  mycroft *		result is provably monotonic in double precision.
     47  1.1  mycroft *
     48  1.1  mycroft *	Speed: The program sASIN takes approximately 310 cycles.
     49  1.1  mycroft *
     50  1.1  mycroft *	Algorithm:
     51  1.1  mycroft *
     52  1.1  mycroft *	ASIN
     53  1.1  mycroft *	1. If |X| >= 1, go to 3.
     54  1.1  mycroft *
     55  1.1  mycroft *	2. (|X| < 1) Calculate asin(X) by
     56  1.1  mycroft *		z := sqrt( [1-X][1+X] )
     57  1.1  mycroft *		asin(X) = atan( x / z ).
     58  1.1  mycroft *		Exit.
     59  1.1  mycroft *
     60  1.1  mycroft *	3. If |X| > 1, go to 5.
     61  1.1  mycroft *
     62  1.1  mycroft *	4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. Exit.
     63  1.1  mycroft *
     64  1.1  mycroft *	5. (|X| > 1) Generate an invalid operation by 0 * infinity.
     65  1.1  mycroft *		Exit.
     66  1.1  mycroft *
     67  1.1  mycroft 
     68  1.1  mycroft SASIN	IDNT	2,1 Motorola 040 Floating Point Software Package
     69  1.1  mycroft 
     70  1.1  mycroft 	section	8
     71  1.1  mycroft 
     72  1.1  mycroft PIBY2	DC.L $3FFF0000,$C90FDAA2,$2168C235,$00000000
     73  1.1  mycroft 
     74  1.1  mycroft 	xref	t_operr
     75  1.1  mycroft 	xref	t_frcinx
     76  1.1  mycroft 	xref	t_extdnrm
     77  1.1  mycroft 	xref	satan
     78  1.1  mycroft 
     79  1.1  mycroft 	xdef	sasind
     80  1.1  mycroft sasind:
     81  1.1  mycroft *--ASIN(X) = X FOR DENORMALIZED X
     82  1.1  mycroft 
     83  1.1  mycroft 	bra		t_extdnrm
     84  1.1  mycroft 
     85  1.1  mycroft 	xdef	sasin
     86  1.1  mycroft sasin:
     87  1.1  mycroft 	FMOVE.X		(a0),FP0	...LOAD INPUT
     88  1.1  mycroft 
     89  1.1  mycroft 	move.l		(a0),d0
     90  1.1  mycroft 	move.w		4(a0),d0
     91  1.1  mycroft 	ANDI.L		#$7FFFFFFF,D0
     92  1.1  mycroft 	CMPI.L		#$3FFF8000,D0
     93  1.1  mycroft 	BGE.B		asinbig
     94  1.1  mycroft 
     95  1.1  mycroft *--THIS IS THE USUAL CASE, |X| < 1
     96  1.1  mycroft *--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
     97  1.1  mycroft 
     98  1.1  mycroft 	FMOVE.S		#:3F800000,FP1
     99  1.1  mycroft 	FSUB.X		FP0,FP1		...1-X
    100  1.1  mycroft 	fmovem.x	fp2,-(a7)
    101  1.1  mycroft 	FMOVE.S		#:3F800000,FP2
    102  1.1  mycroft 	FADD.X		FP0,FP2		...1+X
    103  1.1  mycroft 	FMUL.X		FP2,FP1		...(1+X)(1-X)
    104  1.1  mycroft 	fmovem.x	(a7)+,fp2
    105  1.1  mycroft 	FSQRT.X		FP1		...SQRT([1-X][1+X])
    106  1.1  mycroft 	FDIV.X		FP1,FP0	 	...X/SQRT([1-X][1+X])
    107  1.1  mycroft 	fmovem.x	fp0,(a0)
    108  1.1  mycroft 	bsr		satan
    109  1.1  mycroft 	bra		t_frcinx
    110  1.1  mycroft 
    111  1.1  mycroft asinbig:
    112  1.1  mycroft 	FABS.X		FP0	 ...|X|
    113  1.1  mycroft 	FCMP.S		#:3F800000,FP0
    114  1.1  mycroft 	fbgt		t_operr		;cause an operr exception
    115  1.1  mycroft 
    116  1.1  mycroft *--|X| = 1, ASIN(X) = +- PI/2.
    117  1.1  mycroft 
    118  1.1  mycroft 	FMOVE.X		PIBY2,FP0
    119  1.1  mycroft 	move.l		(a0),d0
    120  1.1  mycroft 	ANDI.L		#$80000000,D0	...SIGN BIT OF X
    121  1.1  mycroft 	ORI.L		#$3F800000,D0	...+-1 IN SGL FORMAT
    122  1.1  mycroft 	MOVE.L		D0,-(sp)	...push SIGN(X) IN SGL-FMT
    123  1.1  mycroft 	FMOVE.L		d1,FPCR		
    124  1.1  mycroft 	FMUL.S		(sp)+,FP0
    125  1.1  mycroft 	bra		t_frcinx
    126  1.1  mycroft 
    127  1.1  mycroft 	end
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