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      1 *	$NetBSD: satan.sa,v 1.3 1994/10/26 07:49:31 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 *	satan.sa 3.3 12/19/90
     35 *
     36 *	The entry point satan computes the arctagent of an
     37 *	input value. satand does the same except the input value is a
     38 *	denormalized number.
     39 *
     40 *	Input: Double-extended value in memory location pointed to by address
     41 *		register a0.
     42 *
     43 *	Output:	Arctan(X) returned in floating-point register Fp0.
     44 *
     45 *	Accuracy and Monotonicity: The returned result is within 2 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 satan takes approximately 160 cycles for input
     51 *		argument X such that 1/16 < |X| < 16. For the other arguments,
     52 *		the program will run no worse than 10% slower.
     53 *
     54 *	Algorithm:
     55 *	Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5.
     56 *
     57 *	Step 2. Let X = sgn * 2**k * 1.xxxxxxxx...x. Note that k = -4, -3,..., or 3.
     58 *		Define F = sgn * 2**k * 1.xxxx1, i.e. the first 5 significant bits
     59 *		of X with a bit-1 attached at the 6-th bit position. Define u
     60 *		to be u = (X-F) / (1 + X*F).
     61 *
     62 *	Step 3. Approximate arctan(u) by a polynomial poly.
     63 *
     64 *	Step 4. Return arctan(F) + poly, arctan(F) is fetched from a table of values
     65 *		calculated beforehand. Exit.
     66 *
     67 *	Step 5. If |X| >= 16, go to Step 7.
     68 *
     69 *	Step 6. Approximate arctan(X) by an odd polynomial in X. Exit.
     70 *
     71 *	Step 7. Define X' = -1/X. Approximate arctan(X') by an odd polynomial in X'.
     72 *		Arctan(X) = sign(X)*Pi/2 + arctan(X'). Exit.
     73 *
     74 
     75 satan	IDNT	2,1 Motorola 040 Floating Point Software Package
     76 
     77 	section	8
     78 
     79 	include fpsp.h
     80 	
     81 BOUNDS1	DC.L $3FFB8000,$4002FFFF
     82 
     83 ONE	DC.L $3F800000
     84 
     85 	DC.L $00000000
     86 
     87 ATANA3	DC.L $BFF6687E,$314987D8
     88 ATANA2	DC.L $4002AC69,$34A26DB3
     89 
     90 ATANA1	DC.L $BFC2476F,$4E1DA28E
     91 ATANB6	DC.L $3FB34444,$7F876989
     92 
     93 ATANB5	DC.L $BFB744EE,$7FAF45DB
     94 ATANB4	DC.L $3FBC71C6,$46940220
     95 
     96 ATANB3	DC.L $BFC24924,$921872F9
     97 ATANB2	DC.L $3FC99999,$99998FA9
     98 
     99 ATANB1	DC.L $BFD55555,$55555555
    100 ATANC5	DC.L $BFB70BF3,$98539E6A
    101 
    102 ATANC4	DC.L $3FBC7187,$962D1D7D
    103 ATANC3	DC.L $BFC24924,$827107B8
    104 
    105 ATANC2	DC.L $3FC99999,$9996263E
    106 ATANC1	DC.L $BFD55555,$55555536
    107 
    108 PPIBY2	DC.L $3FFF0000,$C90FDAA2,$2168C235,$00000000
    109 NPIBY2	DC.L $BFFF0000,$C90FDAA2,$2168C235,$00000000
    110 PTINY	DC.L $00010000,$80000000,$00000000,$00000000
    111 NTINY	DC.L $80010000,$80000000,$00000000,$00000000
    112 
    113 ATANTBL:
    114 	DC.L	$3FFB0000,$83D152C5,$060B7A51,$00000000
    115 	DC.L	$3FFB0000,$8BC85445,$65498B8B,$00000000
    116 	DC.L	$3FFB0000,$93BE4060,$17626B0D,$00000000
    117 	DC.L	$3FFB0000,$9BB3078D,$35AEC202,$00000000
    118 	DC.L	$3FFB0000,$A3A69A52,$5DDCE7DE,$00000000
    119 	DC.L	$3FFB0000,$AB98E943,$62765619,$00000000
    120 	DC.L	$3FFB0000,$B389E502,$F9C59862,$00000000
    121 	DC.L	$3FFB0000,$BB797E43,$6B09E6FB,$00000000
    122 	DC.L	$3FFB0000,$C367A5C7,$39E5F446,$00000000
    123 	DC.L	$3FFB0000,$CB544C61,$CFF7D5C6,$00000000
    124 	DC.L	$3FFB0000,$D33F62F8,$2488533E,$00000000
    125 	DC.L	$3FFB0000,$DB28DA81,$62404C77,$00000000
    126 	DC.L	$3FFB0000,$E310A407,$8AD34F18,$00000000
    127 	DC.L	$3FFB0000,$EAF6B0A8,$188EE1EB,$00000000
    128 	DC.L	$3FFB0000,$F2DAF194,$9DBE79D5,$00000000
    129 	DC.L	$3FFB0000,$FABD5813,$61D47E3E,$00000000
    130 	DC.L	$3FFC0000,$8346AC21,$0959ECC4,$00000000
    131 	DC.L	$3FFC0000,$8B232A08,$304282D8,$00000000
    132 	DC.L	$3FFC0000,$92FB70B8,$D29AE2F9,$00000000
    133 	DC.L	$3FFC0000,$9ACF476F,$5CCD1CB4,$00000000
    134 	DC.L	$3FFC0000,$A29E7630,$4954F23F,$00000000
    135 	DC.L	$3FFC0000,$AA68C5D0,$8AB85230,$00000000
    136 	DC.L	$3FFC0000,$B22DFFFD,$9D539F83,$00000000
    137 	DC.L	$3FFC0000,$B9EDEF45,$3E900EA5,$00000000
    138 	DC.L	$3FFC0000,$C1A85F1C,$C75E3EA5,$00000000
    139 	DC.L	$3FFC0000,$C95D1BE8,$28138DE6,$00000000
    140 	DC.L	$3FFC0000,$D10BF300,$840D2DE4,$00000000
    141 	DC.L	$3FFC0000,$D8B4B2BA,$6BC05E7A,$00000000
    142 	DC.L	$3FFC0000,$E0572A6B,$B42335F6,$00000000
    143 	DC.L	$3FFC0000,$E7F32A70,$EA9CAA8F,$00000000
    144 	DC.L	$3FFC0000,$EF888432,$64ECEFAA,$00000000
    145 	DC.L	$3FFC0000,$F7170A28,$ECC06666,$00000000
    146 	DC.L	$3FFD0000,$812FD288,$332DAD32,$00000000
    147 	DC.L	$3FFD0000,$88A8D1B1,$218E4D64,$00000000
    148 	DC.L	$3FFD0000,$9012AB3F,$23E4AEE8,$00000000
    149 	DC.L	$3FFD0000,$976CC3D4,$11E7F1B9,$00000000
    150 	DC.L	$3FFD0000,$9EB68949,$3889A227,$00000000
    151 	DC.L	$3FFD0000,$A5EF72C3,$4487361B,$00000000
    152 	DC.L	$3FFD0000,$AD1700BA,$F07A7227,$00000000
    153 	DC.L	$3FFD0000,$B42CBCFA,$FD37EFB7,$00000000
    154 	DC.L	$3FFD0000,$BB303A94,$0BA80F89,$00000000
    155 	DC.L	$3FFD0000,$C22115C6,$FCAEBBAF,$00000000
    156 	DC.L	$3FFD0000,$C8FEF3E6,$86331221,$00000000
    157 	DC.L	$3FFD0000,$CFC98330,$B4000C70,$00000000
    158 	DC.L	$3FFD0000,$D6807AA1,$102C5BF9,$00000000
    159 	DC.L	$3FFD0000,$DD2399BC,$31252AA3,$00000000
    160 	DC.L	$3FFD0000,$E3B2A855,$6B8FC517,$00000000
    161 	DC.L	$3FFD0000,$EA2D764F,$64315989,$00000000
    162 	DC.L	$3FFD0000,$F3BF5BF8,$BAD1A21D,$00000000
    163 	DC.L	$3FFE0000,$801CE39E,$0D205C9A,$00000000
    164 	DC.L	$3FFE0000,$8630A2DA,$DA1ED066,$00000000
    165 	DC.L	$3FFE0000,$8C1AD445,$F3E09B8C,$00000000
    166 	DC.L	$3FFE0000,$91DB8F16,$64F350E2,$00000000
    167 	DC.L	$3FFE0000,$97731420,$365E538C,$00000000
    168 	DC.L	$3FFE0000,$9CE1C8E6,$A0B8CDBA,$00000000
    169 	DC.L	$3FFE0000,$A22832DB,$CADAAE09,$00000000
    170 	DC.L	$3FFE0000,$A746F2DD,$B7602294,$00000000
    171 	DC.L	$3FFE0000,$AC3EC0FB,$997DD6A2,$00000000
    172 	DC.L	$3FFE0000,$B110688A,$EBDC6F6A,$00000000
    173 	DC.L	$3FFE0000,$B5BCC490,$59ECC4B0,$00000000
    174 	DC.L	$3FFE0000,$BA44BC7D,$D470782F,$00000000
    175 	DC.L	$3FFE0000,$BEA94144,$FD049AAC,$00000000
    176 	DC.L	$3FFE0000,$C2EB4ABB,$661628B6,$00000000
    177 	DC.L	$3FFE0000,$C70BD54C,$E602EE14,$00000000
    178 	DC.L	$3FFE0000,$CD000549,$ADEC7159,$00000000
    179 	DC.L	$3FFE0000,$D48457D2,$D8EA4EA3,$00000000
    180 	DC.L	$3FFE0000,$DB948DA7,$12DECE3B,$00000000
    181 	DC.L	$3FFE0000,$E23855F9,$69E8096A,$00000000
    182 	DC.L	$3FFE0000,$E8771129,$C4353259,$00000000
    183 	DC.L	$3FFE0000,$EE57C16E,$0D379C0D,$00000000
    184 	DC.L	$3FFE0000,$F3E10211,$A87C3779,$00000000
    185 	DC.L	$3FFE0000,$F919039D,$758B8D41,$00000000
    186 	DC.L	$3FFE0000,$FE058B8F,$64935FB3,$00000000
    187 	DC.L	$3FFF0000,$8155FB49,$7B685D04,$00000000
    188 	DC.L	$3FFF0000,$83889E35,$49D108E1,$00000000
    189 	DC.L	$3FFF0000,$859CFA76,$511D724B,$00000000
    190 	DC.L	$3FFF0000,$87952ECF,$FF8131E7,$00000000
    191 	DC.L	$3FFF0000,$89732FD1,$9557641B,$00000000
    192 	DC.L	$3FFF0000,$8B38CAD1,$01932A35,$00000000
    193 	DC.L	$3FFF0000,$8CE7A8D8,$301EE6B5,$00000000
    194 	DC.L	$3FFF0000,$8F46A39E,$2EAE5281,$00000000
    195 	DC.L	$3FFF0000,$922DA7D7,$91888487,$00000000
    196 	DC.L	$3FFF0000,$94D19FCB,$DEDF5241,$00000000
    197 	DC.L	$3FFF0000,$973AB944,$19D2A08B,$00000000
    198 	DC.L	$3FFF0000,$996FF00E,$08E10B96,$00000000
    199 	DC.L	$3FFF0000,$9B773F95,$12321DA7,$00000000
    200 	DC.L	$3FFF0000,$9D55CC32,$0F935624,$00000000
    201 	DC.L	$3FFF0000,$9F100575,$006CC571,$00000000
    202 	DC.L	$3FFF0000,$A0A9C290,$D97CC06C,$00000000
    203 	DC.L	$3FFF0000,$A22659EB,$EBC0630A,$00000000
    204 	DC.L	$3FFF0000,$A388B4AF,$F6EF0EC9,$00000000
    205 	DC.L	$3FFF0000,$A4D35F10,$61D292C4,$00000000
    206 	DC.L	$3FFF0000,$A60895DC,$FBE3187E,$00000000
    207 	DC.L	$3FFF0000,$A72A51DC,$7367BEAC,$00000000
    208 	DC.L	$3FFF0000,$A83A5153,$0956168F,$00000000
    209 	DC.L	$3FFF0000,$A93A2007,$7539546E,$00000000
    210 	DC.L	$3FFF0000,$AA9E7245,$023B2605,$00000000
    211 	DC.L	$3FFF0000,$AC4C84BA,$6FE4D58F,$00000000
    212 	DC.L	$3FFF0000,$ADCE4A4A,$606B9712,$00000000
    213 	DC.L	$3FFF0000,$AF2A2DCD,$8D263C9C,$00000000
    214 	DC.L	$3FFF0000,$B0656F81,$F22265C7,$00000000
    215 	DC.L	$3FFF0000,$B1846515,$0F71496A,$00000000
    216 	DC.L	$3FFF0000,$B28AAA15,$6F9ADA35,$00000000
    217 	DC.L	$3FFF0000,$B37B44FF,$3766B895,$00000000
    218 	DC.L	$3FFF0000,$B458C3DC,$E9630433,$00000000
    219 	DC.L	$3FFF0000,$B525529D,$562246BD,$00000000
    220 	DC.L	$3FFF0000,$B5E2CCA9,$5F9D88CC,$00000000
    221 	DC.L	$3FFF0000,$B692CADA,$7ACA1ADA,$00000000
    222 	DC.L	$3FFF0000,$B736AEA7,$A6925838,$00000000
    223 	DC.L	$3FFF0000,$B7CFAB28,$7E9F7B36,$00000000
    224 	DC.L	$3FFF0000,$B85ECC66,$CB219835,$00000000
    225 	DC.L	$3FFF0000,$B8E4FD5A,$20A593DA,$00000000
    226 	DC.L	$3FFF0000,$B99F41F6,$4AFF9BB5,$00000000
    227 	DC.L	$3FFF0000,$BA7F1E17,$842BBE7B,$00000000
    228 	DC.L	$3FFF0000,$BB471285,$7637E17D,$00000000
    229 	DC.L	$3FFF0000,$BBFABE8A,$4788DF6F,$00000000
    230 	DC.L	$3FFF0000,$BC9D0FAD,$2B689D79,$00000000
    231 	DC.L	$3FFF0000,$BD306A39,$471ECD86,$00000000
    232 	DC.L	$3FFF0000,$BDB6C731,$856AF18A,$00000000
    233 	DC.L	$3FFF0000,$BE31CAC5,$02E80D70,$00000000
    234 	DC.L	$3FFF0000,$BEA2D55C,$E33194E2,$00000000
    235 	DC.L	$3FFF0000,$BF0B10B7,$C03128F0,$00000000
    236 	DC.L	$3FFF0000,$BF6B7A18,$DACB778D,$00000000
    237 	DC.L	$3FFF0000,$BFC4EA46,$63FA18F6,$00000000
    238 	DC.L	$3FFF0000,$C0181BDE,$8B89A454,$00000000
    239 	DC.L	$3FFF0000,$C065B066,$CFBF6439,$00000000
    240 	DC.L	$3FFF0000,$C0AE345F,$56340AE6,$00000000
    241 	DC.L	$3FFF0000,$C0F22291,$9CB9E6A7,$00000000
    242 
    243 X	equ	FP_SCR1
    244 XDCARE	equ	X+2
    245 XFRAC	equ	X+4
    246 XFRACLO	equ	X+8
    247 
    248 ATANF	equ	FP_SCR2
    249 ATANFHI	equ	ATANF+4
    250 ATANFLO	equ	ATANF+8
    251 
    252 
    253 	xref	t_frcinx
    254 	xref	t_extdnrm
    255 
    256 	xdef	satand
    257 satand:
    258 *--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
    259 
    260 	bra		t_extdnrm
    261 
    262 	xdef	satan
    263 satan:
    264 *--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
    265 
    266 	FMOVE.X		(A0),FP0	...LOAD INPUT
    267 
    268 	MOVE.L		(A0),D0
    269 	MOVE.W		4(A0),D0
    270 	FMOVE.X		FP0,X(a6)
    271 	ANDI.L		#$7FFFFFFF,D0
    272 
    273 	CMPI.L		#$3FFB8000,D0		...|X| >= 1/16?
    274 	BGE.B		ATANOK1
    275 	BRA.W		ATANSM
    276 
    277 ATANOK1:
    278 	CMPI.L		#$4002FFFF,D0		...|X| < 16 ?
    279 	BLE.B		ATANMAIN
    280 	BRA.W		ATANBIG
    281 
    282 
    283 *--THE MOST LIKELY CASE, |X| IN [1/16, 16). WE USE TABLE TECHNIQUE
    284 *--THE IDEA IS ATAN(X) = ATAN(F) + ATAN( [X-F] / [1+XF] ).
    285 *--SO IF F IS CHOSEN TO BE CLOSE TO X AND ATAN(F) IS STORED IN
    286 *--A TABLE, ALL WE NEED IS TO APPROXIMATE ATAN(U) WHERE
    287 *--U = (X-F)/(1+XF) IS SMALL (REMEMBER F IS CLOSE TO X). IT IS
    288 *--TRUE THAT A DIVIDE IS NOW NEEDED, BUT THE APPROXIMATION FOR
    289 *--ATAN(U) IS A VERY SHORT POLYNOMIAL AND THE INDEXING TO
    290 *--FETCH F AND SAVING OF REGISTERS CAN BE ALL HIDED UNDER THE
    291 *--DIVIDE. IN THE END THIS METHOD IS MUCH FASTER THAN A TRADITIONAL
    292 *--ONE. NOTE ALSO THAT THE TRADITIONAL SCHEME THAT APPROXIMATE
    293 *--ATAN(X) DIRECTLY WILL NEED TO USE A RATIONAL APPROXIMATION
    294 *--(DIVISION NEEDED) ANYWAY BECAUSE A POLYNOMIAL APPROXIMATION
    295 *--WILL INVOLVE A VERY LONG POLYNOMIAL.
    296 
    297 *--NOW WE SEE X AS +-2^K * 1.BBBBBBB....B <- 1. + 63 BITS
    298 *--WE CHOSE F TO BE +-2^K * 1.BBBB1
    299 *--THAT IS IT MATCHES THE EXPONENT AND FIRST 5 BITS OF X, THE
    300 *--SIXTH BITS IS SET TO BE 1. SINCE K = -4, -3, ..., 3, THERE
    301 *--ARE ONLY 8 TIMES 16 = 2^7 = 128 |F|'S. SINCE ATAN(-|F|) IS
    302 *-- -ATAN(|F|), WE NEED TO STORE ONLY ATAN(|F|).
    303 
    304 ATANMAIN:
    305 
    306 	CLR.W		XDCARE(a6)		...CLEAN UP X JUST IN CASE
    307 	ANDI.L		#$F8000000,XFRAC(a6)	...FIRST 5 BITS
    308 	ORI.L		#$04000000,XFRAC(a6)	...SET 6-TH BIT TO 1
    309 	CLR.L		XFRACLO(a6)		...LOCATION OF X IS NOW F
    310 
    311 	FMOVE.X		FP0,FP1			...FP1 IS X
    312 	FMUL.X		X(a6),FP1		...FP1 IS X*F, NOTE THAT X*F > 0
    313 	FSUB.X		X(a6),FP0		...FP0 IS X-F
    314 	FADD.S		#:3F800000,FP1		...FP1 IS 1 + X*F
    315 	FDIV.X		FP1,FP0			...FP0 IS U = (X-F)/(1+X*F)
    316 
    317 *--WHILE THE DIVISION IS TAKING ITS TIME, WE FETCH ATAN(|F|)
    318 *--CREATE ATAN(F) AND STORE IT IN ATANF, AND
    319 *--SAVE REGISTERS FP2.
    320 
    321 	MOVE.L		d2,-(a7)	...SAVE d2 TEMPORARILY
    322 	MOVE.L		d0,d2		...THE EXPO AND 16 BITS OF X
    323 	ANDI.L		#$00007800,d0	...4 VARYING BITS OF F'S FRACTION
    324 	ANDI.L		#$7FFF0000,d2	...EXPONENT OF F
    325 	SUBI.L		#$3FFB0000,d2	...K+4
    326 	ASR.L		#1,d2
    327 	ADD.L		d2,d0		...THE 7 BITS IDENTIFYING F
    328 	ASR.L		#7,d0		...INDEX INTO TBL OF ATAN(|F|)
    329 	LEA		ATANTBL,a1
    330 	ADDA.L		d0,a1		...ADDRESS OF ATAN(|F|)
    331 	MOVE.L		(a1)+,ATANF(a6)
    332 	MOVE.L		(a1)+,ATANFHI(a6)
    333 	MOVE.L		(a1)+,ATANFLO(a6)	...ATANF IS NOW ATAN(|F|)
    334 	MOVE.L		X(a6),d0		...LOAD SIGN AND EXPO. AGAIN
    335 	ANDI.L		#$80000000,d0	...SIGN(F)
    336 	OR.L		d0,ATANF(a6)	...ATANF IS NOW SIGN(F)*ATAN(|F|)
    337 	MOVE.L		(a7)+,d2	...RESTORE d2
    338 
    339 *--THAT'S ALL I HAVE TO DO FOR NOW,
    340 *--BUT ALAS, THE DIVIDE IS STILL CRANKING!
    341 
    342 *--U IN FP0, WE ARE NOW READY TO COMPUTE ATAN(U) AS
    343 *--U + A1*U*V*(A2 + V*(A3 + V)), V = U*U
    344 *--THE POLYNOMIAL MAY LOOK STRANGE, BUT IS NEVERTHELESS CORRECT.
    345 *--THE NATURAL FORM IS U + U*V*(A1 + V*(A2 + V*A3))
    346 *--WHAT WE HAVE HERE IS MERELY	A1 = A3, A2 = A1/A3, A3 = A2/A3.
    347 *--THE REASON FOR THIS REARRANGEMENT IS TO MAKE THE INDEPENDENT
    348 *--PARTS A1*U*V AND (A2 + ... STUFF) MORE LOAD-BALANCED
    349 
    350 	
    351 	FMOVE.X		FP0,FP1
    352 	FMUL.X		FP1,FP1
    353 	FMOVE.D		ATANA3,FP2
    354 	FADD.X		FP1,FP2		...A3+V
    355 	FMUL.X		FP1,FP2		...V*(A3+V)
    356 	FMUL.X		FP0,FP1		...U*V
    357 	FADD.D		ATANA2,FP2	...A2+V*(A3+V)
    358 	FMUL.D		ATANA1,FP1	...A1*U*V
    359 	FMUL.X		FP2,FP1		...A1*U*V*(A2+V*(A3+V))
    360 	
    361 	FADD.X		FP1,FP0		...ATAN(U), FP1 RELEASED
    362 	FMOVE.L		d1,FPCR		;restore users exceptions
    363 	FADD.X		ATANF(a6),FP0	...ATAN(X)
    364 	bra		t_frcinx
    365 
    366 ATANBORS:
    367 *--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED.
    368 *--FP0 IS X AND |X| <= 1/16 OR |X| >= 16.
    369 	CMPI.L		#$3FFF8000,d0
    370 	BGT.W		ATANBIG	...I.E. |X| >= 16
    371 
    372 ATANSM:
    373 *--|X| <= 1/16
    374 *--IF |X| < 2^(-40), RETURN X AS ANSWER. OTHERWISE, APPROXIMATE
    375 *--ATAN(X) BY X + X*Y*(B1+Y*(B2+Y*(B3+Y*(B4+Y*(B5+Y*B6)))))
    376 *--WHICH IS X + X*Y*( [B1+Z*(B3+Z*B5)] + [Y*(B2+Z*(B4+Z*B6)] )
    377 *--WHERE Y = X*X, AND Z = Y*Y.
    378 
    379 	CMPI.L		#$3FD78000,d0
    380 	BLT.W		ATANTINY
    381 *--COMPUTE POLYNOMIAL
    382 	FMUL.X		FP0,FP0	...FP0 IS Y = X*X
    383 
    384 	
    385 	CLR.W		XDCARE(a6)
    386 
    387 	FMOVE.X		FP0,FP1
    388 	FMUL.X		FP1,FP1		...FP1 IS Z = Y*Y
    389 
    390 	FMOVE.D		ATANB6,FP2
    391 	FMOVE.D		ATANB5,FP3
    392 
    393 	FMUL.X		FP1,FP2		...Z*B6
    394 	FMUL.X		FP1,FP3		...Z*B5
    395 
    396 	FADD.D		ATANB4,FP2	...B4+Z*B6
    397 	FADD.D		ATANB3,FP3	...B3+Z*B5
    398 
    399 	FMUL.X		FP1,FP2		...Z*(B4+Z*B6)
    400 	FMUL.X		FP3,FP1		...Z*(B3+Z*B5)
    401 
    402 	FADD.D		ATANB2,FP2	...B2+Z*(B4+Z*B6)
    403 	FADD.D		ATANB1,FP1	...B1+Z*(B3+Z*B5)
    404 
    405 	FMUL.X		FP0,FP2		...Y*(B2+Z*(B4+Z*B6))
    406 	FMUL.X		X(a6),FP0		...X*Y
    407 
    408 	FADD.X		FP2,FP1		...[B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
    409 	
    410 
    411 	FMUL.X		FP1,FP0	...X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
    412 
    413 	FMOVE.L		d1,FPCR		;restore users exceptions
    414 	FADD.X		X(a6),FP0
    415 
    416 	bra		t_frcinx
    417 
    418 ATANTINY:
    419 *--|X| < 2^(-40), ATAN(X) = X
    420 	CLR.W		XDCARE(a6)
    421 
    422 	FMOVE.L		d1,FPCR		;restore users exceptions
    423 	FMOVE.X		X(a6),FP0	;last inst - possible exception set
    424 
    425 	bra		t_frcinx
    426 
    427 ATANBIG:
    428 *--IF |X| > 2^(100), RETURN	SIGN(X)*(PI/2 - TINY). OTHERWISE,
    429 *--RETURN SIGN(X)*PI/2 + ATAN(-1/X).
    430 	CMPI.L		#$40638000,d0
    431 	BGT.W		ATANHUGE
    432 
    433 *--APPROXIMATE ATAN(-1/X) BY
    434 *--X'+X'*Y*(C1+Y*(C2+Y*(C3+Y*(C4+Y*C5)))), X' = -1/X, Y = X'*X'
    435 *--THIS CAN BE RE-WRITTEN AS
    436 *--X'+X'*Y*( [C1+Z*(C3+Z*C5)] + [Y*(C2+Z*C4)] ), Z = Y*Y.
    437 
    438 	FMOVE.S		#:BF800000,FP1	...LOAD -1
    439 	FDIV.X		FP0,FP1		...FP1 IS -1/X
    440 
    441 	
    442 *--DIVIDE IS STILL CRANKING
    443 
    444 	FMOVE.X		FP1,FP0		...FP0 IS X'
    445 	FMUL.X		FP0,FP0		...FP0 IS Y = X'*X'
    446 	FMOVE.X		FP1,X(a6)		...X IS REALLY X'
    447 
    448 	FMOVE.X		FP0,FP1
    449 	FMUL.X		FP1,FP1		...FP1 IS Z = Y*Y
    450 
    451 	FMOVE.D		ATANC5,FP3
    452 	FMOVE.D		ATANC4,FP2
    453 
    454 	FMUL.X		FP1,FP3		...Z*C5
    455 	FMUL.X		FP1,FP2		...Z*B4
    456 
    457 	FADD.D		ATANC3,FP3	...C3+Z*C5
    458 	FADD.D		ATANC2,FP2	...C2+Z*C4
    459 
    460 	FMUL.X		FP3,FP1		...Z*(C3+Z*C5), FP3 RELEASED
    461 	FMUL.X		FP0,FP2		...Y*(C2+Z*C4)
    462 
    463 	FADD.D		ATANC1,FP1	...C1+Z*(C3+Z*C5)
    464 	FMUL.X		X(a6),FP0		...X'*Y
    465 
    466 	FADD.X		FP2,FP1		...[Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
    467 	
    468 
    469 	FMUL.X		FP1,FP0		...X'*Y*([B1+Z*(B3+Z*B5)]
    470 *					...	+[Y*(B2+Z*(B4+Z*B6))])
    471 	FADD.X		X(a6),FP0
    472 
    473 	FMOVE.L		d1,FPCR		;restore users exceptions
    474 	
    475 	btst.b		#7,(a0)
    476 	beq.b		pos_big
    477 
    478 neg_big:
    479 	FADD.X		NPIBY2,FP0
    480 	bra		t_frcinx
    481 
    482 pos_big:
    483 	FADD.X		PPIBY2,FP0
    484 	bra		t_frcinx
    485 
    486 ATANHUGE:
    487 *--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
    488 	btst.b		#7,(a0)
    489 	beq.b		pos_huge
    490 
    491 neg_huge:
    492 	FMOVE.X		NPIBY2,fp0
    493 	fmove.l		d1,fpcr
    494 	fsub.x		NTINY,fp0
    495 	bra		t_frcinx
    496 
    497 pos_huge:
    498 	FMOVE.X		PPIBY2,fp0
    499 	fmove.l		d1,fpcr
    500 	fsub.x		PTINY,fp0
    501 	bra		t_frcinx
    502 	
    503 	end
    504