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* $OpenBSD: sasin.sa,v 1.2 1996/05/29 21:05:34 niklas Exp $
* $NetBSD: sasin.sa,v 1.2 1994/10/26 07:49:29 cgd Exp $
* MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
* M68000 Hi-Performance Microprocessor Division
* M68040 Software Package
*
* M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
* All rights reserved.
*
* THE SOFTWARE is provided on an "AS IS" basis and without warranty.
* To the maximum extent permitted by applicable law,
* MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
* INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
* PARTICULAR PURPOSE and any warranty against infringement with
* regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
* and any accompanying written materials.
*
* To the maximum extent permitted by applicable law,
* IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
* (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
* PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
* OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
* SOFTWARE. Motorola assumes no responsibility for the maintenance
* and support of the SOFTWARE.
*
* You are hereby granted a copyright license to use, modify, and
* distribute the SOFTWARE so long as this entire notice is retained
* without alteration in any modified and/or redistributed versions,
* and that such modified versions are clearly identified as such.
* No licenses are granted by implication, estoppel or otherwise
* under any patents or trademarks of Motorola, Inc.
*
* sasin.sa 3.3 12/19/90
*
* Description: The entry point sAsin computes the inverse sine of
* an input argument; sAsind does the same except for denormalized
* input.
*
* Input: Double-extended number X in location pointed to
* by address register a0.
*
* Output: The value arcsin(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 sASIN takes approximately 310 cycles.
*
* Algorithm:
*
* ASIN
* 1. If |X| >= 1, go to 3.
*
* 2. (|X| < 1) Calculate asin(X) by
* z := sqrt( [1-X][1+X] )
* asin(X) = atan( x / z ).
* Exit.
*
* 3. If |X| > 1, go to 5.
*
* 4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. Exit.
*
* 5. (|X| > 1) Generate an invalid operation by 0 * infinity.
* Exit.
*
SASIN IDNT 2,1 Motorola 040 Floating Point Software Package
section 8
PIBY2 DC.L $3FFF0000,$C90FDAA2,$2168C235,$00000000
xref t_operr
xref t_frcinx
xref t_extdnrm
xref satan
xdef sasind
sasind:
*--ASIN(X) = X FOR DENORMALIZED X
bra t_extdnrm
xdef sasin
sasin:
FMOVE.X (a0),FP0 ...LOAD INPUT
move.l (a0),d0
move.w 4(a0),d0
ANDI.L #$7FFFFFFF,D0
CMPI.L #$3FFF8000,D0
BGE.B asinbig
*--THIS IS THE USUAL CASE, |X| < 1
*--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
FMOVE.S #:3F800000,FP1
FSUB.X FP0,FP1 ...1-X
fmovem.x fp2,-(a7)
FMOVE.S #:3F800000,FP2
FADD.X FP0,FP2 ...1+X
FMUL.X FP2,FP1 ...(1+X)(1-X)
fmovem.x (a7)+,fp2
FSQRT.X FP1 ...SQRT([1-X][1+X])
FDIV.X FP1,FP0 ...X/SQRT([1-X][1+X])
fmovem.x fp0,(a0)
bsr satan
bra t_frcinx
asinbig:
FABS.X FP0 ...|X|
FCMP.S #:3F800000,FP0
fbgt t_operr ;cause an operr exception
*--|X| = 1, ASIN(X) = +- PI/2.
FMOVE.X PIBY2,FP0
move.l (a0),d0
ANDI.L #$80000000,D0 ...SIGN BIT OF X
ORI.L #$3F800000,D0 ...+-1 IN SGL FORMAT
MOVE.L D0,-(sp) ...push SIGN(X) IN SGL-FMT
FMOVE.L d1,FPCR
FMUL.S (sp)+,FP0
bra t_frcinx
end
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