1|
2|	satan.sa 3.3 12/19/90
3|
4|	The entry point satan computes the arctangent of an
5|	input value. satand does the same except the input value is a
6|	denormalized number.
7|
8|	Input: Double-extended value in memory location pointed to by address
9|		register a0.
10|
11|	Output:	Arctan(X) returned in floating-point register Fp0.
12|
13|	Accuracy and Monotonicity: The returned result is within 2 ulps in
14|		64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
15|		result is subsequently rounded to double precision. The
16|		result is provably monotonic in double precision.
17|
18|	Speed: The program satan takes approximately 160 cycles for input
19|		argument X such that 1/16 < |X| < 16. For the other arguments,
20|		the program will run no worse than 10% slower.
21|
22|	Algorithm:
23|	Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5.
24|
25|	Step 2. Let X = sgn * 2**k * 1.xxxxxxxx...x. Note that k = -4, -3,..., or 3.
26|		Define F = sgn * 2**k * 1.xxxx1, i.e. the first 5 significant bits
27|		of X with a bit-1 attached at the 6-th bit position. Define u
28|		to be u = (X-F) / (1 + X*F).
29|
30|	Step 3. Approximate arctan(u) by a polynomial poly.
31|
32|	Step 4. Return arctan(F) + poly, arctan(F) is fetched from a table of values
33|		calculated beforehand. Exit.
34|
35|	Step 5. If |X| >= 16, go to Step 7.
36|
37|	Step 6. Approximate arctan(X) by an odd polynomial in X. Exit.
38|
39|	Step 7. Define X' = -1/X. Approximate arctan(X') by an odd polynomial in X'.
40|		Arctan(X) = sign(X)*Pi/2 + arctan(X'). Exit.
41|
42
43|		Copyright (C) Motorola, Inc. 1990
44|			All Rights Reserved
45|
46|	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
47|	The copyright notice above does not evidence any
48|	actual or intended publication of such source code.
49
50|satan	idnt	2,1 | Motorola 040 Floating Point Software Package
51
52	|section	8
53
54	.include "fpsp.h"
55
56BOUNDS1:	.long 0x3FFB8000,0x4002FFFF
57
58ONE:	.long 0x3F800000
59
60	.long 0x00000000
61
62ATANA3:	.long 0xBFF6687E,0x314987D8
63ATANA2:	.long 0x4002AC69,0x34A26DB3
64
65ATANA1:	.long 0xBFC2476F,0x4E1DA28E
66ATANB6:	.long 0x3FB34444,0x7F876989
67
68ATANB5:	.long 0xBFB744EE,0x7FAF45DB
69ATANB4:	.long 0x3FBC71C6,0x46940220
70
71ATANB3:	.long 0xBFC24924,0x921872F9
72ATANB2:	.long 0x3FC99999,0x99998FA9
73
74ATANB1:	.long 0xBFD55555,0x55555555
75ATANC5:	.long 0xBFB70BF3,0x98539E6A
76
77ATANC4:	.long 0x3FBC7187,0x962D1D7D
78ATANC3:	.long 0xBFC24924,0x827107B8
79
80ATANC2:	.long 0x3FC99999,0x9996263E
81ATANC1:	.long 0xBFD55555,0x55555536
82
83PPIBY2:	.long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
84NPIBY2:	.long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x00000000
85PTINY:	.long 0x00010000,0x80000000,0x00000000,0x00000000
86NTINY:	.long 0x80010000,0x80000000,0x00000000,0x00000000
87
88ATANTBL:
89	.long	0x3FFB0000,0x83D152C5,0x060B7A51,0x00000000
90	.long	0x3FFB0000,0x8BC85445,0x65498B8B,0x00000000
91	.long	0x3FFB0000,0x93BE4060,0x17626B0D,0x00000000
92	.long	0x3FFB0000,0x9BB3078D,0x35AEC202,0x00000000
93	.long	0x3FFB0000,0xA3A69A52,0x5DDCE7DE,0x00000000
94	.long	0x3FFB0000,0xAB98E943,0x62765619,0x00000000
95	.long	0x3FFB0000,0xB389E502,0xF9C59862,0x00000000
96	.long	0x3FFB0000,0xBB797E43,0x6B09E6FB,0x00000000
97	.long	0x3FFB0000,0xC367A5C7,0x39E5F446,0x00000000
98	.long	0x3FFB0000,0xCB544C61,0xCFF7D5C6,0x00000000
99	.long	0x3FFB0000,0xD33F62F8,0x2488533E,0x00000000
100	.long	0x3FFB0000,0xDB28DA81,0x62404C77,0x00000000
101	.long	0x3FFB0000,0xE310A407,0x8AD34F18,0x00000000
102	.long	0x3FFB0000,0xEAF6B0A8,0x188EE1EB,0x00000000
103	.long	0x3FFB0000,0xF2DAF194,0x9DBE79D5,0x00000000
104	.long	0x3FFB0000,0xFABD5813,0x61D47E3E,0x00000000
105	.long	0x3FFC0000,0x8346AC21,0x0959ECC4,0x00000000
106	.long	0x3FFC0000,0x8B232A08,0x304282D8,0x00000000
107	.long	0x3FFC0000,0x92FB70B8,0xD29AE2F9,0x00000000
108	.long	0x3FFC0000,0x9ACF476F,0x5CCD1CB4,0x00000000
109	.long	0x3FFC0000,0xA29E7630,0x4954F23F,0x00000000
110	.long	0x3FFC0000,0xAA68C5D0,0x8AB85230,0x00000000
111	.long	0x3FFC0000,0xB22DFFFD,0x9D539F83,0x00000000
112	.long	0x3FFC0000,0xB9EDEF45,0x3E900EA5,0x00000000
113	.long	0x3FFC0000,0xC1A85F1C,0xC75E3EA5,0x00000000
114	.long	0x3FFC0000,0xC95D1BE8,0x28138DE6,0x00000000
115	.long	0x3FFC0000,0xD10BF300,0x840D2DE4,0x00000000
116	.long	0x3FFC0000,0xD8B4B2BA,0x6BC05E7A,0x00000000
117	.long	0x3FFC0000,0xE0572A6B,0xB42335F6,0x00000000
118	.long	0x3FFC0000,0xE7F32A70,0xEA9CAA8F,0x00000000
119	.long	0x3FFC0000,0xEF888432,0x64ECEFAA,0x00000000
120	.long	0x3FFC0000,0xF7170A28,0xECC06666,0x00000000
121	.long	0x3FFD0000,0x812FD288,0x332DAD32,0x00000000
122	.long	0x3FFD0000,0x88A8D1B1,0x218E4D64,0x00000000
123	.long	0x3FFD0000,0x9012AB3F,0x23E4AEE8,0x00000000
124	.long	0x3FFD0000,0x976CC3D4,0x11E7F1B9,0x00000000
125	.long	0x3FFD0000,0x9EB68949,0x3889A227,0x00000000
126	.long	0x3FFD0000,0xA5EF72C3,0x4487361B,0x00000000
127	.long	0x3FFD0000,0xAD1700BA,0xF07A7227,0x00000000
128	.long	0x3FFD0000,0xB42CBCFA,0xFD37EFB7,0x00000000
129	.long	0x3FFD0000,0xBB303A94,0x0BA80F89,0x00000000
130	.long	0x3FFD0000,0xC22115C6,0xFCAEBBAF,0x00000000
131	.long	0x3FFD0000,0xC8FEF3E6,0x86331221,0x00000000
132	.long	0x3FFD0000,0xCFC98330,0xB4000C70,0x00000000
133	.long	0x3FFD0000,0xD6807AA1,0x102C5BF9,0x00000000
134	.long	0x3FFD0000,0xDD2399BC,0x31252AA3,0x00000000
135	.long	0x3FFD0000,0xE3B2A855,0x6B8FC517,0x00000000
136	.long	0x3FFD0000,0xEA2D764F,0x64315989,0x00000000
137	.long	0x3FFD0000,0xF3BF5BF8,0xBAD1A21D,0x00000000
138	.long	0x3FFE0000,0x801CE39E,0x0D205C9A,0x00000000
139	.long	0x3FFE0000,0x8630A2DA,0xDA1ED066,0x00000000
140	.long	0x3FFE0000,0x8C1AD445,0xF3E09B8C,0x00000000
141	.long	0x3FFE0000,0x91DB8F16,0x64F350E2,0x00000000
142	.long	0x3FFE0000,0x97731420,0x365E538C,0x00000000
143	.long	0x3FFE0000,0x9CE1C8E6,0xA0B8CDBA,0x00000000
144	.long	0x3FFE0000,0xA22832DB,0xCADAAE09,0x00000000
145	.long	0x3FFE0000,0xA746F2DD,0xB7602294,0x00000000
146	.long	0x3FFE0000,0xAC3EC0FB,0x997DD6A2,0x00000000
147	.long	0x3FFE0000,0xB110688A,0xEBDC6F6A,0x00000000
148	.long	0x3FFE0000,0xB5BCC490,0x59ECC4B0,0x00000000
149	.long	0x3FFE0000,0xBA44BC7D,0xD470782F,0x00000000
150	.long	0x3FFE0000,0xBEA94144,0xFD049AAC,0x00000000
151	.long	0x3FFE0000,0xC2EB4ABB,0x661628B6,0x00000000
152	.long	0x3FFE0000,0xC70BD54C,0xE602EE14,0x00000000
153	.long	0x3FFE0000,0xCD000549,0xADEC7159,0x00000000
154	.long	0x3FFE0000,0xD48457D2,0xD8EA4EA3,0x00000000
155	.long	0x3FFE0000,0xDB948DA7,0x12DECE3B,0x00000000
156	.long	0x3FFE0000,0xE23855F9,0x69E8096A,0x00000000
157	.long	0x3FFE0000,0xE8771129,0xC4353259,0x00000000
158	.long	0x3FFE0000,0xEE57C16E,0x0D379C0D,0x00000000
159	.long	0x3FFE0000,0xF3E10211,0xA87C3779,0x00000000
160	.long	0x3FFE0000,0xF919039D,0x758B8D41,0x00000000
161	.long	0x3FFE0000,0xFE058B8F,0x64935FB3,0x00000000
162	.long	0x3FFF0000,0x8155FB49,0x7B685D04,0x00000000
163	.long	0x3FFF0000,0x83889E35,0x49D108E1,0x00000000
164	.long	0x3FFF0000,0x859CFA76,0x511D724B,0x00000000
165	.long	0x3FFF0000,0x87952ECF,0xFF8131E7,0x00000000
166	.long	0x3FFF0000,0x89732FD1,0x9557641B,0x00000000
167	.long	0x3FFF0000,0x8B38CAD1,0x01932A35,0x00000000
168	.long	0x3FFF0000,0x8CE7A8D8,0x301EE6B5,0x00000000
169	.long	0x3FFF0000,0x8F46A39E,0x2EAE5281,0x00000000
170	.long	0x3FFF0000,0x922DA7D7,0x91888487,0x00000000
171	.long	0x3FFF0000,0x94D19FCB,0xDEDF5241,0x00000000
172	.long	0x3FFF0000,0x973AB944,0x19D2A08B,0x00000000
173	.long	0x3FFF0000,0x996FF00E,0x08E10B96,0x00000000
174	.long	0x3FFF0000,0x9B773F95,0x12321DA7,0x00000000
175	.long	0x3FFF0000,0x9D55CC32,0x0F935624,0x00000000
176	.long	0x3FFF0000,0x9F100575,0x006CC571,0x00000000
177	.long	0x3FFF0000,0xA0A9C290,0xD97CC06C,0x00000000
178	.long	0x3FFF0000,0xA22659EB,0xEBC0630A,0x00000000
179	.long	0x3FFF0000,0xA388B4AF,0xF6EF0EC9,0x00000000
180	.long	0x3FFF0000,0xA4D35F10,0x61D292C4,0x00000000
181	.long	0x3FFF0000,0xA60895DC,0xFBE3187E,0x00000000
182	.long	0x3FFF0000,0xA72A51DC,0x7367BEAC,0x00000000
183	.long	0x3FFF0000,0xA83A5153,0x0956168F,0x00000000
184	.long	0x3FFF0000,0xA93A2007,0x7539546E,0x00000000
185	.long	0x3FFF0000,0xAA9E7245,0x023B2605,0x00000000
186	.long	0x3FFF0000,0xAC4C84BA,0x6FE4D58F,0x00000000
187	.long	0x3FFF0000,0xADCE4A4A,0x606B9712,0x00000000
188	.long	0x3FFF0000,0xAF2A2DCD,0x8D263C9C,0x00000000
189	.long	0x3FFF0000,0xB0656F81,0xF22265C7,0x00000000
190	.long	0x3FFF0000,0xB1846515,0x0F71496A,0x00000000
191	.long	0x3FFF0000,0xB28AAA15,0x6F9ADA35,0x00000000
192	.long	0x3FFF0000,0xB37B44FF,0x3766B895,0x00000000
193	.long	0x3FFF0000,0xB458C3DC,0xE9630433,0x00000000
194	.long	0x3FFF0000,0xB525529D,0x562246BD,0x00000000
195	.long	0x3FFF0000,0xB5E2CCA9,0x5F9D88CC,0x00000000
196	.long	0x3FFF0000,0xB692CADA,0x7ACA1ADA,0x00000000
197	.long	0x3FFF0000,0xB736AEA7,0xA6925838,0x00000000
198	.long	0x3FFF0000,0xB7CFAB28,0x7E9F7B36,0x00000000
199	.long	0x3FFF0000,0xB85ECC66,0xCB219835,0x00000000
200	.long	0x3FFF0000,0xB8E4FD5A,0x20A593DA,0x00000000
201	.long	0x3FFF0000,0xB99F41F6,0x4AFF9BB5,0x00000000
202	.long	0x3FFF0000,0xBA7F1E17,0x842BBE7B,0x00000000
203	.long	0x3FFF0000,0xBB471285,0x7637E17D,0x00000000
204	.long	0x3FFF0000,0xBBFABE8A,0x4788DF6F,0x00000000
205	.long	0x3FFF0000,0xBC9D0FAD,0x2B689D79,0x00000000
206	.long	0x3FFF0000,0xBD306A39,0x471ECD86,0x00000000
207	.long	0x3FFF0000,0xBDB6C731,0x856AF18A,0x00000000
208	.long	0x3FFF0000,0xBE31CAC5,0x02E80D70,0x00000000
209	.long	0x3FFF0000,0xBEA2D55C,0xE33194E2,0x00000000
210	.long	0x3FFF0000,0xBF0B10B7,0xC03128F0,0x00000000
211	.long	0x3FFF0000,0xBF6B7A18,0xDACB778D,0x00000000
212	.long	0x3FFF0000,0xBFC4EA46,0x63FA18F6,0x00000000
213	.long	0x3FFF0000,0xC0181BDE,0x8B89A454,0x00000000
214	.long	0x3FFF0000,0xC065B066,0xCFBF6439,0x00000000
215	.long	0x3FFF0000,0xC0AE345F,0x56340AE6,0x00000000
216	.long	0x3FFF0000,0xC0F22291,0x9CB9E6A7,0x00000000
217
218	.set	X,FP_SCR1
219	.set	XDCARE,X+2
220	.set	XFRAC,X+4
221	.set	XFRACLO,X+8
222
223	.set	ATANF,FP_SCR2
224	.set	ATANFHI,ATANF+4
225	.set	ATANFLO,ATANF+8
226
227
228	| xref	t_frcinx
229	|xref	t_extdnrm
230
231	.global	satand
232satand:
233|--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
234
235	bra		t_extdnrm
236
237	.global	satan
238satan:
239|--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
240
241	fmovex		(%a0),%fp0	| ...LOAD INPUT
242
243	movel		(%a0),%d0
244	movew		4(%a0),%d0
245	fmovex		%fp0,X(%a6)
246	andil		#0x7FFFFFFF,%d0
247
248	cmpil		#0x3FFB8000,%d0		| ...|X| >= 1/16?
249	bges		ATANOK1
250	bra		ATANSM
251
252ATANOK1:
253	cmpil		#0x4002FFFF,%d0		| ...|X| < 16 ?
254	bles		ATANMAIN
255	bra		ATANBIG
256
257
258|--THE MOST LIKELY CASE, |X| IN [1/16, 16). WE USE TABLE TECHNIQUE
259|--THE IDEA IS ATAN(X) = ATAN(F) + ATAN( [X-F] / [1+XF] ).
260|--SO IF F IS CHOSEN TO BE CLOSE TO X AND ATAN(F) IS STORED IN
261|--A TABLE, ALL WE NEED IS TO APPROXIMATE ATAN(U) WHERE
262|--U = (X-F)/(1+XF) IS SMALL (REMEMBER F IS CLOSE TO X). IT IS
263|--TRUE THAT A DIVIDE IS NOW NEEDED, BUT THE APPROXIMATION FOR
264|--ATAN(U) IS A VERY SHORT POLYNOMIAL AND THE INDEXING TO
265|--FETCH F AND SAVING OF REGISTERS CAN BE ALL HIDED UNDER THE
266|--DIVIDE. IN THE END THIS METHOD IS MUCH FASTER THAN A TRADITIONAL
267|--ONE. NOTE ALSO THAT THE TRADITIONAL SCHEME THAT APPROXIMATE
268|--ATAN(X) DIRECTLY WILL NEED TO USE A RATIONAL APPROXIMATION
269|--(DIVISION NEEDED) ANYWAY BECAUSE A POLYNOMIAL APPROXIMATION
270|--WILL INVOLVE A VERY LONG POLYNOMIAL.
271
272|--NOW WE SEE X AS +-2^K * 1.BBBBBBB....B <- 1. + 63 BITS
273|--WE CHOSE F TO BE +-2^K * 1.BBBB1
274|--THAT IS IT MATCHES THE EXPONENT AND FIRST 5 BITS OF X, THE
275|--SIXTH BITS IS SET TO BE 1. SINCE K = -4, -3, ..., 3, THERE
276|--ARE ONLY 8 TIMES 16 = 2^7 = 128 |F|'S. SINCE ATAN(-|F|) IS
277|-- -ATAN(|F|), WE NEED TO STORE ONLY ATAN(|F|).
278
279ATANMAIN:
280
281	movew		#0x0000,XDCARE(%a6)	| ...CLEAN UP X JUST IN CASE
282	andil		#0xF8000000,XFRAC(%a6)	| ...FIRST 5 BITS
283	oril		#0x04000000,XFRAC(%a6)	| ...SET 6-TH BIT TO 1
284	movel		#0x00000000,XFRACLO(%a6)	| ...LOCATION OF X IS NOW F
285
286	fmovex		%fp0,%fp1			| ...FP1 IS X
287	fmulx		X(%a6),%fp1		| ...FP1 IS X*F, NOTE THAT X*F > 0
288	fsubx		X(%a6),%fp0		| ...FP0 IS X-F
289	fadds		#0x3F800000,%fp1		| ...FP1 IS 1 + X*F
290	fdivx		%fp1,%fp0			| ...FP0 IS U = (X-F)/(1+X*F)
291
292|--WHILE THE DIVISION IS TAKING ITS TIME, WE FETCH ATAN(|F|)
293|--CREATE ATAN(F) AND STORE IT IN ATANF, AND
294|--SAVE REGISTERS FP2.
295
296	movel		%d2,-(%a7)	| ...SAVE d2 TEMPORARILY
297	movel		%d0,%d2		| ...THE EXPO AND 16 BITS OF X
298	andil		#0x00007800,%d0	| ...4 VARYING BITS OF F'S FRACTION
299	andil		#0x7FFF0000,%d2	| ...EXPONENT OF F
300	subil		#0x3FFB0000,%d2	| ...K+4
301	asrl		#1,%d2
302	addl		%d2,%d0		| ...THE 7 BITS IDENTIFYING F
303	asrl		#7,%d0		| ...INDEX INTO TBL OF ATAN(|F|)
304	lea		ATANTBL,%a1
305	addal		%d0,%a1		| ...ADDRESS OF ATAN(|F|)
306	movel		(%a1)+,ATANF(%a6)
307	movel		(%a1)+,ATANFHI(%a6)
308	movel		(%a1)+,ATANFLO(%a6)	| ...ATANF IS NOW ATAN(|F|)
309	movel		X(%a6),%d0		| ...LOAD SIGN AND EXPO. AGAIN
310	andil		#0x80000000,%d0	| ...SIGN(F)
311	orl		%d0,ATANF(%a6)	| ...ATANF IS NOW SIGN(F)*ATAN(|F|)
312	movel		(%a7)+,%d2	| ...RESTORE d2
313
314|--THAT'S ALL I HAVE TO DO FOR NOW,
315|--BUT ALAS, THE DIVIDE IS STILL CRANKING!
316
317|--U IN FP0, WE ARE NOW READY TO COMPUTE ATAN(U) AS
318|--U + A1*U*V*(A2 + V*(A3 + V)), V = U*U
319|--THE POLYNOMIAL MAY LOOK STRANGE, BUT IS NEVERTHELESS CORRECT.
320|--THE NATURAL FORM IS U + U*V*(A1 + V*(A2 + V*A3))
321|--WHAT WE HAVE HERE IS MERELY	A1 = A3, A2 = A1/A3, A3 = A2/A3.
322|--THE REASON FOR THIS REARRANGEMENT IS TO MAKE THE INDEPENDENT
323|--PARTS A1*U*V AND (A2 + ... STUFF) MORE LOAD-BALANCED
324
325
326	fmovex		%fp0,%fp1
327	fmulx		%fp1,%fp1
328	fmoved		ATANA3,%fp2
329	faddx		%fp1,%fp2		| ...A3+V
330	fmulx		%fp1,%fp2		| ...V*(A3+V)
331	fmulx		%fp0,%fp1		| ...U*V
332	faddd		ATANA2,%fp2	| ...A2+V*(A3+V)
333	fmuld		ATANA1,%fp1	| ...A1*U*V
334	fmulx		%fp2,%fp1		| ...A1*U*V*(A2+V*(A3+V))
335
336	faddx		%fp1,%fp0		| ...ATAN(U), FP1 RELEASED
337	fmovel		%d1,%FPCR		|restore users exceptions
338	faddx		ATANF(%a6),%fp0	| ...ATAN(X)
339	bra		t_frcinx
340
341ATANBORS:
342|--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED.
343|--FP0 IS X AND |X| <= 1/16 OR |X| >= 16.
344	cmpil		#0x3FFF8000,%d0
345	bgt		ATANBIG	| ...I.E. |X| >= 16
346
347ATANSM:
348|--|X| <= 1/16
349|--IF |X| < 2^(-40), RETURN X AS ANSWER. OTHERWISE, APPROXIMATE
350|--ATAN(X) BY X + X*Y*(B1+Y*(B2+Y*(B3+Y*(B4+Y*(B5+Y*B6)))))
351|--WHICH IS X + X*Y*( [B1+Z*(B3+Z*B5)] + [Y*(B2+Z*(B4+Z*B6)] )
352|--WHERE Y = X*X, AND Z = Y*Y.
353
354	cmpil		#0x3FD78000,%d0
355	blt		ATANTINY
356|--COMPUTE POLYNOMIAL
357	fmulx		%fp0,%fp0	| ...FP0 IS Y = X*X
358
359
360	movew		#0x0000,XDCARE(%a6)
361
362	fmovex		%fp0,%fp1
363	fmulx		%fp1,%fp1		| ...FP1 IS Z = Y*Y
364
365	fmoved		ATANB6,%fp2
366	fmoved		ATANB5,%fp3
367
368	fmulx		%fp1,%fp2		| ...Z*B6
369	fmulx		%fp1,%fp3		| ...Z*B5
370
371	faddd		ATANB4,%fp2	| ...B4+Z*B6
372	faddd		ATANB3,%fp3	| ...B3+Z*B5
373
374	fmulx		%fp1,%fp2		| ...Z*(B4+Z*B6)
375	fmulx		%fp3,%fp1		| ...Z*(B3+Z*B5)
376
377	faddd		ATANB2,%fp2	| ...B2+Z*(B4+Z*B6)
378	faddd		ATANB1,%fp1	| ...B1+Z*(B3+Z*B5)
379
380	fmulx		%fp0,%fp2		| ...Y*(B2+Z*(B4+Z*B6))
381	fmulx		X(%a6),%fp0		| ...X*Y
382
383	faddx		%fp2,%fp1		| ...[B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
384
385
386	fmulx		%fp1,%fp0	| ...X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
387
388	fmovel		%d1,%FPCR		|restore users exceptions
389	faddx		X(%a6),%fp0
390
391	bra		t_frcinx
392
393ATANTINY:
394|--|X| < 2^(-40), ATAN(X) = X
395	movew		#0x0000,XDCARE(%a6)
396
397	fmovel		%d1,%FPCR		|restore users exceptions
398	fmovex		X(%a6),%fp0	|last inst - possible exception set
399
400	bra		t_frcinx
401
402ATANBIG:
403|--IF |X| > 2^(100), RETURN	SIGN(X)*(PI/2 - TINY). OTHERWISE,
404|--RETURN SIGN(X)*PI/2 + ATAN(-1/X).
405	cmpil		#0x40638000,%d0
406	bgt		ATANHUGE
407
408|--APPROXIMATE ATAN(-1/X) BY
409|--X'+X'*Y*(C1+Y*(C2+Y*(C3+Y*(C4+Y*C5)))), X' = -1/X, Y = X'*X'
410|--THIS CAN BE RE-WRITTEN AS
411|--X'+X'*Y*( [C1+Z*(C3+Z*C5)] + [Y*(C2+Z*C4)] ), Z = Y*Y.
412
413	fmoves		#0xBF800000,%fp1	| ...LOAD -1
414	fdivx		%fp0,%fp1		| ...FP1 IS -1/X
415
416
417|--DIVIDE IS STILL CRANKING
418
419	fmovex		%fp1,%fp0		| ...FP0 IS X'
420	fmulx		%fp0,%fp0		| ...FP0 IS Y = X'*X'
421	fmovex		%fp1,X(%a6)		| ...X IS REALLY X'
422
423	fmovex		%fp0,%fp1
424	fmulx		%fp1,%fp1		| ...FP1 IS Z = Y*Y
425
426	fmoved		ATANC5,%fp3
427	fmoved		ATANC4,%fp2
428
429	fmulx		%fp1,%fp3		| ...Z*C5
430	fmulx		%fp1,%fp2		| ...Z*B4
431
432	faddd		ATANC3,%fp3	| ...C3+Z*C5
433	faddd		ATANC2,%fp2	| ...C2+Z*C4
434
435	fmulx		%fp3,%fp1		| ...Z*(C3+Z*C5), FP3 RELEASED
436	fmulx		%fp0,%fp2		| ...Y*(C2+Z*C4)
437
438	faddd		ATANC1,%fp1	| ...C1+Z*(C3+Z*C5)
439	fmulx		X(%a6),%fp0		| ...X'*Y
440
441	faddx		%fp2,%fp1		| ...[Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
442
443
444	fmulx		%fp1,%fp0		| ...X'*Y*([B1+Z*(B3+Z*B5)]
445|					...	+[Y*(B2+Z*(B4+Z*B6))])
446	faddx		X(%a6),%fp0
447
448	fmovel		%d1,%FPCR		|restore users exceptions
449
450	btstb		#7,(%a0)
451	beqs		pos_big
452
453neg_big:
454	faddx		NPIBY2,%fp0
455	bra		t_frcinx
456
457pos_big:
458	faddx		PPIBY2,%fp0
459	bra		t_frcinx
460
461ATANHUGE:
462|--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
463	btstb		#7,(%a0)
464	beqs		pos_huge
465
466neg_huge:
467	fmovex		NPIBY2,%fp0
468	fmovel		%d1,%fpcr
469	fsubx		NTINY,%fp0
470	bra		t_frcinx
471
472pos_huge:
473	fmovex		PPIBY2,%fp0
474	fmovel		%d1,%fpcr
475	fsubx		PTINY,%fp0
476	bra		t_frcinx
477
478	|end
479