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      1 *	$NetBSD: sacos.sa,v 1.3 1994/10/26 07:49:27 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 *	sacos.sa 3.3 12/19/90
     35 *
     36 *	Description: The entry point sAcos computes the inverse cosine of
     37 *		an input argument; sAcosd 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 arccos(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 sCOS takes approximately 310 cycles.
     51 *
     52 *	Algorithm:
     53 *
     54 *	ACOS
     55 *	1. If |X| >= 1, go to 3.
     56 *
     57 *	2. (|X| < 1) Calculate acos(X) by
     58 *		z := (1-X) / (1+X)
     59 *		acos(X) = 2 * atan( sqrt(z) ).
     60 *		Exit.
     61 *
     62 *	3. If |X| > 1, go to 5.
     63 *
     64 *	4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. Exit.
     65 *
     66 *	5. (|X| > 1) Generate an invalid operation by 0 * infinity.
     67 *		Exit.
     68 *
     69 
     70 SACOS	IDNT	2,1 Motorola 040 Floating Point Software Package
     71 
     72 	section	8
     73 
     74 PI	DC.L $40000000,$C90FDAA2,$2168C235,$00000000
     75 PIBY2	DC.L $3FFF0000,$C90FDAA2,$2168C235,$00000000
     76 
     77 	xref	t_operr
     78 	xref	t_frcinx
     79 	xref	satan
     80 
     81 	xdef	sacosd
     82 sacosd:
     83 *--ACOS(X) = PI/2 FOR DENORMALIZED X
     84 	fmove.l		d1,fpcr		...load user's rounding mode/precision
     85 	FMOVE.X		PIBY2,FP0
     86 	bra		t_frcinx
     87 
     88 	xdef	sacos
     89 sacos:
     90 	FMOVE.X		(a0),FP0	...LOAD INPUT
     91 
     92 	move.l		(a0),d0		...pack exponent with upper 16 fraction
     93 	move.w		4(a0),d0
     94 	ANDI.L		#$7FFFFFFF,D0
     95 	CMPI.L		#$3FFF8000,D0
     96 	BGE.B		ACOSBIG
     97 
     98 *--THIS IS THE USUAL CASE, |X| < 1
     99 *--ACOS(X) = 2 * ATAN(	SQRT( (1-X)/(1+X) )	)
    100 
    101 	FMOVE.S		#:3F800000,FP1
    102 	FADD.X		FP0,FP1	 	...1+X
    103 	FNEG.X		FP0	 	... -X
    104 	FADD.S		#:3F800000,FP0	...1-X
    105 	FDIV.X		FP1,FP0	 	...(1-X)/(1+X)
    106 	FSQRT.X		FP0		...SQRT((1-X)/(1+X))
    107 	fmovem.x	fp0,(a0)	...overwrite input
    108 	move.l		d1,-(sp)	;save original users fpcr
    109 	clr.l		d1
    110 	bsr		satan		...ATAN(SQRT([1-X]/[1+X]))
    111 	fMOVE.L		(sp)+,fpcr	;restore users exceptions
    112 	FADD.X		FP0,FP0	 	...2 * ATAN( STUFF )
    113 	bra		t_frcinx
    114 
    115 ACOSBIG:
    116 	FABS.X		FP0
    117 	FCMP.S		#:3F800000,FP0
    118 	fbgt		t_operr		;cause an operr exception
    119 
    120 *--|X| = 1, ACOS(X) = 0 OR PI
    121 	move.l		(a0),d0		...pack exponent with upper 16 fraction
    122 	move.w		4(a0),d0
    123 	TST.L		D0		;D0 has original exponent+fraction
    124 	BGT.B		ACOSP1
    125 
    126 *--X = -1
    127 *Returns PI and inexact exception
    128 	FMOVE.X		PI,FP0
    129 	FMOVE.L		d1,FPCR
    130 	FADD.S		#:00800000,FP0	;cause an inexact exception to be put
    131 *					;into the 040 - will not trap until next
    132 *					;fp inst.
    133 	bra		t_frcinx
    134 
    135 ACOSP1:
    136 	FMOVE.L		d1,FPCR
    137 	FMOVE.S		#:00000000,FP0
    138 	rts				;Facos of +1 is exact	
    139 
    140 	end
    141