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      1 *	$NetBSD: sasin.sa,v 1.2 1994/10/26 07:49:29 cgd Exp $
      2 
      3 *	MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
      4 *	M68000 Hi-Performance Microprocessor Division
      5 *	M68040 Software Package 
      6 *
      7 *	M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
      8 *	All rights reserved.
      9 *
     10 *	THE SOFTWARE is provided on an "AS IS" basis and without warranty.
     11 *	To the maximum extent permitted by applicable law,
     12 *	MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
     13 *	INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
     14 *	PARTICULAR PURPOSE and any warranty against infringement with
     15 *	regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
     16 *	and any accompanying written materials. 
     17 *
     18 *	To the maximum extent permitted by applicable law,
     19 *	IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
     20 *	(INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
     21 *	PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
     22 *	OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
     23 *	SOFTWARE.  Motorola assumes no responsibility for the maintenance
     24 *	and support of the SOFTWARE.  
     25 *
     26 *	You are hereby granted a copyright license to use, modify, and
     27 *	distribute the SOFTWARE so long as this entire notice is retained
     28 *	without alteration in any modified and/or redistributed versions,
     29 *	and that such modified versions are clearly identified as such.
     30 *	No licenses are granted by implication, estoppel or otherwise
     31 *	under any patents or trademarks of Motorola, Inc.
     32 
     33 *
     34 *	sasin.sa 3.3 12/19/90
     35 *
     36 *	Description: The entry point sAsin computes the inverse sine of
     37 *		an input argument; sAsind does the same except for denormalized
     38 *		input.
     39 *
     40 *	Input: Double-extended number X in location pointed to
     41 *		by address register a0.
     42 *
     43 *	Output: The value arcsin(X) returned in floating-point register Fp0.
     44 *
     45 *	Accuracy and Monotonicity: The returned result is within 3 ulps in
     46 *		64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
     47 *		result is subsequently rounded to double precision. The 
     48 *		result is provably monotonic in double precision.
     49 *
     50 *	Speed: The program sASIN takes approximately 310 cycles.
     51 *
     52 *	Algorithm:
     53 *
     54 *	ASIN
     55 *	1. If |X| >= 1, go to 3.
     56 *
     57 *	2. (|X| < 1) Calculate asin(X) by
     58 *		z := sqrt( [1-X][1+X] )
     59 *		asin(X) = atan( x / z ).
     60 *		Exit.
     61 *
     62 *	3. If |X| > 1, go to 5.
     63 *
     64 *	4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. Exit.
     65 *
     66 *	5. (|X| > 1) Generate an invalid operation by 0 * infinity.
     67 *		Exit.
     68 *
     69 
     70 SASIN	IDNT	2,1 Motorola 040 Floating Point Software Package
     71 
     72 	section	8
     73 
     74 PIBY2	DC.L $3FFF0000,$C90FDAA2,$2168C235,$00000000
     75 
     76 	xref	t_operr
     77 	xref	t_frcinx
     78 	xref	t_extdnrm
     79 	xref	satan
     80 
     81 	xdef	sasind
     82 sasind:
     83 *--ASIN(X) = X FOR DENORMALIZED X
     84 
     85 	bra		t_extdnrm
     86 
     87 	xdef	sasin
     88 sasin:
     89 	FMOVE.X		(a0),FP0	...LOAD INPUT
     90 
     91 	move.l		(a0),d0
     92 	move.w		4(a0),d0
     93 	ANDI.L		#$7FFFFFFF,D0
     94 	CMPI.L		#$3FFF8000,D0
     95 	BGE.B		asinbig
     96 
     97 *--THIS IS THE USUAL CASE, |X| < 1
     98 *--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
     99 
    100 	FMOVE.S		#:3F800000,FP1
    101 	FSUB.X		FP0,FP1		...1-X
    102 	fmovem.x	fp2,-(a7)
    103 	FMOVE.S		#:3F800000,FP2
    104 	FADD.X		FP0,FP2		...1+X
    105 	FMUL.X		FP2,FP1		...(1+X)(1-X)
    106 	fmovem.x	(a7)+,fp2
    107 	FSQRT.X		FP1		...SQRT([1-X][1+X])
    108 	FDIV.X		FP1,FP0	 	...X/SQRT([1-X][1+X])
    109 	fmovem.x	fp0,(a0)
    110 	bsr		satan
    111 	bra		t_frcinx
    112 
    113 asinbig:
    114 	FABS.X		FP0	 ...|X|
    115 	FCMP.S		#:3F800000,FP0
    116 	fbgt		t_operr		;cause an operr exception
    117 
    118 *--|X| = 1, ASIN(X) = +- PI/2.
    119 
    120 	FMOVE.X		PIBY2,FP0
    121 	move.l		(a0),d0
    122 	ANDI.L		#$80000000,D0	...SIGN BIT OF X
    123 	ORI.L		#$3F800000,D0	...+-1 IN SGL FORMAT
    124 	MOVE.L		D0,-(sp)	...push SIGN(X) IN SGL-FMT
    125 	FMOVE.L		d1,FPCR		
    126 	FMUL.S		(sp)+,FP0
    127 	bra		t_frcinx
    128 
    129 	end
    130