xref: /netbsd/sys/arch/m68k/fpsp/satan.sa (revision 6550d01e) 
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
75satan	IDNT	2,1 Motorola 040 Floating Point Software Package
76
77	section	8
78
79	include fpsp.h
80
81BOUNDS1	DC.L $3FFB8000,$4002FFFF
82
83ONE	DC.L $3F800000
84
85	DC.L $00000000
86
87ATANA3	DC.L $BFF6687E,$314987D8
88ATANA2	DC.L $4002AC69,$34A26DB3
89
90ATANA1	DC.L $BFC2476F,$4E1DA28E
91ATANB6	DC.L $3FB34444,$7F876989
92
93ATANB5	DC.L $BFB744EE,$7FAF45DB
94ATANB4	DC.L $3FBC71C6,$46940220
95
96ATANB3	DC.L $BFC24924,$921872F9
97ATANB2	DC.L $3FC99999,$99998FA9
98
99ATANB1	DC.L $BFD55555,$55555555
100ATANC5	DC.L $BFB70BF3,$98539E6A
101
102ATANC4	DC.L $3FBC7187,$962D1D7D
103ATANC3	DC.L $BFC24924,$827107B8
104
105ATANC2	DC.L $3FC99999,$9996263E
106ATANC1	DC.L $BFD55555,$55555536
107
108PPIBY2	DC.L $3FFF0000,$C90FDAA2,$2168C235,$00000000
109NPIBY2	DC.L $BFFF0000,$C90FDAA2,$2168C235,$00000000
110PTINY	DC.L $00010000,$80000000,$00000000,$00000000
111NTINY	DC.L $80010000,$80000000,$00000000,$00000000
112
113ATANTBL:
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
243X	equ	FP_SCR1
244XDCARE	equ	X+2
245XFRAC	equ	X+4
246XFRACLO	equ	X+8
247
248ATANF	equ	FP_SCR2
249ATANFHI	equ	ATANF+4
250ATANFLO	equ	ATANF+8
251
252
253	xref	t_frcinx
254	xref	t_extdnrm
255
256	xdef	satand
257satand:
258*--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
259
260	bra		t_extdnrm
261
262	xdef	satan
263satan:
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
277ATANOK1:
278	CMPI.L		#$4002FFFF,D0		...|X| < 16 ?
279	BLE.B		ATANMAIN
280	BRA.W		ATANBIG
281
282
283*--THE MOST LIKELY CASE, |X| IN [1/16, 16). WE USE TABLE TECHNIQUE
284*--THE IDEA IS ATAN(X) = ATAN(F) + ATAN( [X-F] / [1+XF] ).
285*--SO IF F IS CHOSEN TO BE CLOSE TO X AND ATAN(F) IS STORED IN
286*--A TABLE, ALL WE NEED IS TO APPROXIMATE ATAN(U) WHERE
287*--U = (X-F)/(1+XF) IS SMALL (REMEMBER F IS CLOSE TO X). IT IS
288*--TRUE THAT A DIVIDE IS NOW NEEDED, BUT THE APPROXIMATION FOR
289*--ATAN(U) IS A VERY SHORT POLYNOMIAL AND THE INDEXING TO
290*--FETCH F AND SAVING OF REGISTERS CAN BE ALL HIDED UNDER THE
291*--DIVIDE. IN THE END THIS METHOD IS MUCH FASTER THAN A TRADITIONAL
292*--ONE. NOTE ALSO THAT THE TRADITIONAL SCHEME THAT APPROXIMATE
293*--ATAN(X) DIRECTLY WILL NEED TO USE A RATIONAL APPROXIMATION
294*--(DIVISION NEEDED) ANYWAY BECAUSE A POLYNOMIAL APPROXIMATION
295*--WILL INVOLVE A VERY LONG POLYNOMIAL.
296
297*--NOW WE SEE X AS +-2^K * 1.BBBBBBB....B <- 1. + 63 BITS
298*--WE CHOSE F TO BE +-2^K * 1.BBBB1
299*--THAT IS IT MATCHES THE EXPONENT AND FIRST 5 BITS OF X, THE
300*--SIXTH BITS IS SET TO BE 1. SINCE K = -4, -3, ..., 3, THERE
301*--ARE ONLY 8 TIMES 16 = 2^7 = 128 |F|'S. SINCE ATAN(-|F|) IS
302*-- -ATAN(|F|), WE NEED TO STORE ONLY ATAN(|F|).
303
304ATANMAIN:
305
306	CLR.W		XDCARE(a6)		...CLEAN UP X JUST IN CASE
307	ANDI.L		#$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
366ATANBORS:
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
372ATANSM:
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
418ATANTINY:
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
427ATANBIG:
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
478neg_big:
479	FADD.X		NPIBY2,FP0
480	bra		t_frcinx
481
482pos_big:
483	FADD.X		PPIBY2,FP0
484	bra		t_frcinx
485
486ATANHUGE:
487*--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
488	btst.b		#7,(a0)
489	beq.b		pos_huge
490
491neg_huge:
492	FMOVE.X		NPIBY2,fp0
493	fmove.l		d1,fpcr
494	fsub.x		NTINY,fp0
495	bra		t_frcinx
496
497pos_huge:
498	FMOVE.X		PPIBY2,fp0
499	fmove.l		d1,fpcr
500	fsub.x		PTINY,fp0
501	bra		t_frcinx
502
503	end
504