xref: /linux/arch/m68k/fpsp040/satan.S (revision cc04a46f11ea046ed53e2c832ae29e4790f7e35f) 
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|       For details on the license for this file, please see the
47|       file, README, in this same directory.
48
49|satan	idnt	2,1 | Motorola 040 Floating Point Software Package
50
51	|section	8
52
53#include "fpsp.h"
54
55BOUNDS1:	.long 0x3FFB8000,0x4002FFFF
56
57ONE:	.long 0x3F800000
58
59	.long 0x00000000
60
61ATANA3:	.long 0xBFF6687E,0x314987D8
62ATANA2:	.long 0x4002AC69,0x34A26DB3
63
64ATANA1:	.long 0xBFC2476F,0x4E1DA28E
65ATANB6:	.long 0x3FB34444,0x7F876989
66
67ATANB5:	.long 0xBFB744EE,0x7FAF45DB
68ATANB4:	.long 0x3FBC71C6,0x46940220
69
70ATANB3:	.long 0xBFC24924,0x921872F9
71ATANB2:	.long 0x3FC99999,0x99998FA9
72
73ATANB1:	.long 0xBFD55555,0x55555555
74ATANC5:	.long 0xBFB70BF3,0x98539E6A
75
76ATANC4:	.long 0x3FBC7187,0x962D1D7D
77ATANC3:	.long 0xBFC24924,0x827107B8
78
79ATANC2:	.long 0x3FC99999,0x9996263E
80ATANC1:	.long 0xBFD55555,0x55555536
81
82PPIBY2:	.long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
83NPIBY2:	.long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x00000000
84PTINY:	.long 0x00010000,0x80000000,0x00000000,0x00000000
85NTINY:	.long 0x80010000,0x80000000,0x00000000,0x00000000
86
87ATANTBL:
88	.long	0x3FFB0000,0x83D152C5,0x060B7A51,0x00000000
89	.long	0x3FFB0000,0x8BC85445,0x65498B8B,0x00000000
90	.long	0x3FFB0000,0x93BE4060,0x17626B0D,0x00000000
91	.long	0x3FFB0000,0x9BB3078D,0x35AEC202,0x00000000
92	.long	0x3FFB0000,0xA3A69A52,0x5DDCE7DE,0x00000000
93	.long	0x3FFB0000,0xAB98E943,0x62765619,0x00000000
94	.long	0x3FFB0000,0xB389E502,0xF9C59862,0x00000000
95	.long	0x3FFB0000,0xBB797E43,0x6B09E6FB,0x00000000
96	.long	0x3FFB0000,0xC367A5C7,0x39E5F446,0x00000000
97	.long	0x3FFB0000,0xCB544C61,0xCFF7D5C6,0x00000000
98	.long	0x3FFB0000,0xD33F62F8,0x2488533E,0x00000000
99	.long	0x3FFB0000,0xDB28DA81,0x62404C77,0x00000000
100	.long	0x3FFB0000,0xE310A407,0x8AD34F18,0x00000000
101	.long	0x3FFB0000,0xEAF6B0A8,0x188EE1EB,0x00000000
102	.long	0x3FFB0000,0xF2DAF194,0x9DBE79D5,0x00000000
103	.long	0x3FFB0000,0xFABD5813,0x61D47E3E,0x00000000
104	.long	0x3FFC0000,0x8346AC21,0x0959ECC4,0x00000000
105	.long	0x3FFC0000,0x8B232A08,0x304282D8,0x00000000
106	.long	0x3FFC0000,0x92FB70B8,0xD29AE2F9,0x00000000
107	.long	0x3FFC0000,0x9ACF476F,0x5CCD1CB4,0x00000000
108	.long	0x3FFC0000,0xA29E7630,0x4954F23F,0x00000000
109	.long	0x3FFC0000,0xAA68C5D0,0x8AB85230,0x00000000
110	.long	0x3FFC0000,0xB22DFFFD,0x9D539F83,0x00000000
111	.long	0x3FFC0000,0xB9EDEF45,0x3E900EA5,0x00000000
112	.long	0x3FFC0000,0xC1A85F1C,0xC75E3EA5,0x00000000
113	.long	0x3FFC0000,0xC95D1BE8,0x28138DE6,0x00000000
114	.long	0x3FFC0000,0xD10BF300,0x840D2DE4,0x00000000
115	.long	0x3FFC0000,0xD8B4B2BA,0x6BC05E7A,0x00000000
116	.long	0x3FFC0000,0xE0572A6B,0xB42335F6,0x00000000
117	.long	0x3FFC0000,0xE7F32A70,0xEA9CAA8F,0x00000000
118	.long	0x3FFC0000,0xEF888432,0x64ECEFAA,0x00000000
119	.long	0x3FFC0000,0xF7170A28,0xECC06666,0x00000000
120	.long	0x3FFD0000,0x812FD288,0x332DAD32,0x00000000
121	.long	0x3FFD0000,0x88A8D1B1,0x218E4D64,0x00000000
122	.long	0x3FFD0000,0x9012AB3F,0x23E4AEE8,0x00000000
123	.long	0x3FFD0000,0x976CC3D4,0x11E7F1B9,0x00000000
124	.long	0x3FFD0000,0x9EB68949,0x3889A227,0x00000000
125	.long	0x3FFD0000,0xA5EF72C3,0x4487361B,0x00000000
126	.long	0x3FFD0000,0xAD1700BA,0xF07A7227,0x00000000
127	.long	0x3FFD0000,0xB42CBCFA,0xFD37EFB7,0x00000000
128	.long	0x3FFD0000,0xBB303A94,0x0BA80F89,0x00000000
129	.long	0x3FFD0000,0xC22115C6,0xFCAEBBAF,0x00000000
130	.long	0x3FFD0000,0xC8FEF3E6,0x86331221,0x00000000
131	.long	0x3FFD0000,0xCFC98330,0xB4000C70,0x00000000
132	.long	0x3FFD0000,0xD6807AA1,0x102C5BF9,0x00000000
133	.long	0x3FFD0000,0xDD2399BC,0x31252AA3,0x00000000
134	.long	0x3FFD0000,0xE3B2A855,0x6B8FC517,0x00000000
135	.long	0x3FFD0000,0xEA2D764F,0x64315989,0x00000000
136	.long	0x3FFD0000,0xF3BF5BF8,0xBAD1A21D,0x00000000
137	.long	0x3FFE0000,0x801CE39E,0x0D205C9A,0x00000000
138	.long	0x3FFE0000,0x8630A2DA,0xDA1ED066,0x00000000
139	.long	0x3FFE0000,0x8C1AD445,0xF3E09B8C,0x00000000
140	.long	0x3FFE0000,0x91DB8F16,0x64F350E2,0x00000000
141	.long	0x3FFE0000,0x97731420,0x365E538C,0x00000000
142	.long	0x3FFE0000,0x9CE1C8E6,0xA0B8CDBA,0x00000000
143	.long	0x3FFE0000,0xA22832DB,0xCADAAE09,0x00000000
144	.long	0x3FFE0000,0xA746F2DD,0xB7602294,0x00000000
145	.long	0x3FFE0000,0xAC3EC0FB,0x997DD6A2,0x00000000
146	.long	0x3FFE0000,0xB110688A,0xEBDC6F6A,0x00000000
147	.long	0x3FFE0000,0xB5BCC490,0x59ECC4B0,0x00000000
148	.long	0x3FFE0000,0xBA44BC7D,0xD470782F,0x00000000
149	.long	0x3FFE0000,0xBEA94144,0xFD049AAC,0x00000000
150	.long	0x3FFE0000,0xC2EB4ABB,0x661628B6,0x00000000
151	.long	0x3FFE0000,0xC70BD54C,0xE602EE14,0x00000000
152	.long	0x3FFE0000,0xCD000549,0xADEC7159,0x00000000
153	.long	0x3FFE0000,0xD48457D2,0xD8EA4EA3,0x00000000
154	.long	0x3FFE0000,0xDB948DA7,0x12DECE3B,0x00000000
155	.long	0x3FFE0000,0xE23855F9,0x69E8096A,0x00000000
156	.long	0x3FFE0000,0xE8771129,0xC4353259,0x00000000
157	.long	0x3FFE0000,0xEE57C16E,0x0D379C0D,0x00000000
158	.long	0x3FFE0000,0xF3E10211,0xA87C3779,0x00000000
159	.long	0x3FFE0000,0xF919039D,0x758B8D41,0x00000000
160	.long	0x3FFE0000,0xFE058B8F,0x64935FB3,0x00000000
161	.long	0x3FFF0000,0x8155FB49,0x7B685D04,0x00000000
162	.long	0x3FFF0000,0x83889E35,0x49D108E1,0x00000000
163	.long	0x3FFF0000,0x859CFA76,0x511D724B,0x00000000
164	.long	0x3FFF0000,0x87952ECF,0xFF8131E7,0x00000000
165	.long	0x3FFF0000,0x89732FD1,0x9557641B,0x00000000
166	.long	0x3FFF0000,0x8B38CAD1,0x01932A35,0x00000000
167	.long	0x3FFF0000,0x8CE7A8D8,0x301EE6B5,0x00000000
168	.long	0x3FFF0000,0x8F46A39E,0x2EAE5281,0x00000000
169	.long	0x3FFF0000,0x922DA7D7,0x91888487,0x00000000
170	.long	0x3FFF0000,0x94D19FCB,0xDEDF5241,0x00000000
171	.long	0x3FFF0000,0x973AB944,0x19D2A08B,0x00000000
172	.long	0x3FFF0000,0x996FF00E,0x08E10B96,0x00000000
173	.long	0x3FFF0000,0x9B773F95,0x12321DA7,0x00000000
174	.long	0x3FFF0000,0x9D55CC32,0x0F935624,0x00000000
175	.long	0x3FFF0000,0x9F100575,0x006CC571,0x00000000
176	.long	0x3FFF0000,0xA0A9C290,0xD97CC06C,0x00000000
177	.long	0x3FFF0000,0xA22659EB,0xEBC0630A,0x00000000
178	.long	0x3FFF0000,0xA388B4AF,0xF6EF0EC9,0x00000000
179	.long	0x3FFF0000,0xA4D35F10,0x61D292C4,0x00000000
180	.long	0x3FFF0000,0xA60895DC,0xFBE3187E,0x00000000
181	.long	0x3FFF0000,0xA72A51DC,0x7367BEAC,0x00000000
182	.long	0x3FFF0000,0xA83A5153,0x0956168F,0x00000000
183	.long	0x3FFF0000,0xA93A2007,0x7539546E,0x00000000
184	.long	0x3FFF0000,0xAA9E7245,0x023B2605,0x00000000
185	.long	0x3FFF0000,0xAC4C84BA,0x6FE4D58F,0x00000000
186	.long	0x3FFF0000,0xADCE4A4A,0x606B9712,0x00000000
187	.long	0x3FFF0000,0xAF2A2DCD,0x8D263C9C,0x00000000
188	.long	0x3FFF0000,0xB0656F81,0xF22265C7,0x00000000
189	.long	0x3FFF0000,0xB1846515,0x0F71496A,0x00000000
190	.long	0x3FFF0000,0xB28AAA15,0x6F9ADA35,0x00000000
191	.long	0x3FFF0000,0xB37B44FF,0x3766B895,0x00000000
192	.long	0x3FFF0000,0xB458C3DC,0xE9630433,0x00000000
193	.long	0x3FFF0000,0xB525529D,0x562246BD,0x00000000
194	.long	0x3FFF0000,0xB5E2CCA9,0x5F9D88CC,0x00000000
195	.long	0x3FFF0000,0xB692CADA,0x7ACA1ADA,0x00000000
196	.long	0x3FFF0000,0xB736AEA7,0xA6925838,0x00000000
197	.long	0x3FFF0000,0xB7CFAB28,0x7E9F7B36,0x00000000
198	.long	0x3FFF0000,0xB85ECC66,0xCB219835,0x00000000
199	.long	0x3FFF0000,0xB8E4FD5A,0x20A593DA,0x00000000
200	.long	0x3FFF0000,0xB99F41F6,0x4AFF9BB5,0x00000000
201	.long	0x3FFF0000,0xBA7F1E17,0x842BBE7B,0x00000000
202	.long	0x3FFF0000,0xBB471285,0x7637E17D,0x00000000
203	.long	0x3FFF0000,0xBBFABE8A,0x4788DF6F,0x00000000
204	.long	0x3FFF0000,0xBC9D0FAD,0x2B689D79,0x00000000
205	.long	0x3FFF0000,0xBD306A39,0x471ECD86,0x00000000
206	.long	0x3FFF0000,0xBDB6C731,0x856AF18A,0x00000000
207	.long	0x3FFF0000,0xBE31CAC5,0x02E80D70,0x00000000
208	.long	0x3FFF0000,0xBEA2D55C,0xE33194E2,0x00000000
209	.long	0x3FFF0000,0xBF0B10B7,0xC03128F0,0x00000000
210	.long	0x3FFF0000,0xBF6B7A18,0xDACB778D,0x00000000
211	.long	0x3FFF0000,0xBFC4EA46,0x63FA18F6,0x00000000
212	.long	0x3FFF0000,0xC0181BDE,0x8B89A454,0x00000000
213	.long	0x3FFF0000,0xC065B066,0xCFBF6439,0x00000000
214	.long	0x3FFF0000,0xC0AE345F,0x56340AE6,0x00000000
215	.long	0x3FFF0000,0xC0F22291,0x9CB9E6A7,0x00000000
216
217	.set	X,FP_SCR1
218	.set	XDCARE,X+2
219	.set	XFRAC,X+4
220	.set	XFRACLO,X+8
221
222	.set	ATANF,FP_SCR2
223	.set	ATANFHI,ATANF+4
224	.set	ATANFLO,ATANF+8
225
226
227	| xref	t_frcinx
228	|xref	t_extdnrm
229
230	.global	satand
231satand:
232|--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
233
234	bra		t_extdnrm
235
236	.global	satan
237satan:
238|--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
239
240	fmovex		(%a0),%fp0	| ...LOAD INPUT
241
242	movel		(%a0),%d0
243	movew		4(%a0),%d0
244	fmovex		%fp0,X(%a6)
245	andil		#0x7FFFFFFF,%d0
246
247	cmpil		#0x3FFB8000,%d0		| ...|X| >= 1/16?
248	bges		ATANOK1
249	bra		ATANSM
250
251ATANOK1:
252	cmpil		#0x4002FFFF,%d0		| ...|X| < 16 ?
253	bles		ATANMAIN
254	bra		ATANBIG
255
256
257|--THE MOST LIKELY CASE, |X| IN [1/16, 16). WE USE TABLE TECHNIQUE
258|--THE IDEA IS ATAN(X) = ATAN(F) + ATAN( [X-F] / [1+XF] ).
259|--SO IF F IS CHOSEN TO BE CLOSE TO X AND ATAN(F) IS STORED IN
260|--A TABLE, ALL WE NEED IS TO APPROXIMATE ATAN(U) WHERE
261|--U = (X-F)/(1+XF) IS SMALL (REMEMBER F IS CLOSE TO X). IT IS
262|--TRUE THAT A DIVIDE IS NOW NEEDED, BUT THE APPROXIMATION FOR
263|--ATAN(U) IS A VERY SHORT POLYNOMIAL AND THE INDEXING TO
264|--FETCH F AND SAVING OF REGISTERS CAN BE ALL HIDED UNDER THE
265|--DIVIDE. IN THE END THIS METHOD IS MUCH FASTER THAN A TRADITIONAL
266|--ONE. NOTE ALSO THAT THE TRADITIONAL SCHEME THAT APPROXIMATE
267|--ATAN(X) DIRECTLY WILL NEED TO USE A RATIONAL APPROXIMATION
268|--(DIVISION NEEDED) ANYWAY BECAUSE A POLYNOMIAL APPROXIMATION
269|--WILL INVOLVE A VERY LONG POLYNOMIAL.
270
271|--NOW WE SEE X AS +-2^K * 1.BBBBBBB....B <- 1. + 63 BITS
272|--WE CHOSE F TO BE +-2^K * 1.BBBB1
273|--THAT IS IT MATCHES THE EXPONENT AND FIRST 5 BITS OF X, THE
274|--SIXTH BITS IS SET TO BE 1. SINCE K = -4, -3, ..., 3, THERE
275|--ARE ONLY 8 TIMES 16 = 2^7 = 128 |F|'S. SINCE ATAN(-|F|) IS
276|-- -ATAN(|F|), WE NEED TO STORE ONLY ATAN(|F|).
277
278ATANMAIN:
279
280	movew		#0x0000,XDCARE(%a6)	| ...CLEAN UP X JUST IN CASE
281	andil		#0xF8000000,XFRAC(%a6)	| ...FIRST 5 BITS
282	oril		#0x04000000,XFRAC(%a6)	| ...SET 6-TH BIT TO 1
283	movel		#0x00000000,XFRACLO(%a6)	| ...LOCATION OF X IS NOW F
284
285	fmovex		%fp0,%fp1			| ...FP1 IS X
286	fmulx		X(%a6),%fp1		| ...FP1 IS X*F, NOTE THAT X*F > 0
287	fsubx		X(%a6),%fp0		| ...FP0 IS X-F
288	fadds		#0x3F800000,%fp1		| ...FP1 IS 1 + X*F
289	fdivx		%fp1,%fp0			| ...FP0 IS U = (X-F)/(1+X*F)
290
291|--WHILE THE DIVISION IS TAKING ITS TIME, WE FETCH ATAN(|F|)
292|--CREATE ATAN(F) AND STORE IT IN ATANF, AND
293|--SAVE REGISTERS FP2.
294
295	movel		%d2,-(%a7)	| ...SAVE d2 TEMPORARILY
296	movel		%d0,%d2		| ...THE EXPO AND 16 BITS OF X
297	andil		#0x00007800,%d0	| ...4 VARYING BITS OF F'S FRACTION
298	andil		#0x7FFF0000,%d2	| ...EXPONENT OF F
299	subil		#0x3FFB0000,%d2	| ...K+4
300	asrl		#1,%d2
301	addl		%d2,%d0		| ...THE 7 BITS IDENTIFYING F
302	asrl		#7,%d0		| ...INDEX INTO TBL OF ATAN(|F|)
303	lea		ATANTBL,%a1
304	addal		%d0,%a1		| ...ADDRESS OF ATAN(|F|)
305	movel		(%a1)+,ATANF(%a6)
306	movel		(%a1)+,ATANFHI(%a6)
307	movel		(%a1)+,ATANFLO(%a6)	| ...ATANF IS NOW ATAN(|F|)
308	movel		X(%a6),%d0		| ...LOAD SIGN AND EXPO. AGAIN
309	andil		#0x80000000,%d0	| ...SIGN(F)
310	orl		%d0,ATANF(%a6)	| ...ATANF IS NOW SIGN(F)*ATAN(|F|)
311	movel		(%a7)+,%d2	| ...RESTORE d2
312
313|--THAT'S ALL I HAVE TO DO FOR NOW,
314|--BUT ALAS, THE DIVIDE IS STILL CRANKING!
315
316|--U IN FP0, WE ARE NOW READY TO COMPUTE ATAN(U) AS
317|--U + A1*U*V*(A2 + V*(A3 + V)), V = U*U
318|--THE POLYNOMIAL MAY LOOK STRANGE, BUT IS NEVERTHELESS CORRECT.
319|--THE NATURAL FORM IS U + U*V*(A1 + V*(A2 + V*A3))
320|--WHAT WE HAVE HERE IS MERELY	A1 = A3, A2 = A1/A3, A3 = A2/A3.
321|--THE REASON FOR THIS REARRANGEMENT IS TO MAKE THE INDEPENDENT
322|--PARTS A1*U*V AND (A2 + ... STUFF) MORE LOAD-BALANCED
323
324
325	fmovex		%fp0,%fp1
326	fmulx		%fp1,%fp1
327	fmoved		ATANA3,%fp2
328	faddx		%fp1,%fp2		| ...A3+V
329	fmulx		%fp1,%fp2		| ...V*(A3+V)
330	fmulx		%fp0,%fp1		| ...U*V
331	faddd		ATANA2,%fp2	| ...A2+V*(A3+V)
332	fmuld		ATANA1,%fp1	| ...A1*U*V
333	fmulx		%fp2,%fp1		| ...A1*U*V*(A2+V*(A3+V))
334
335	faddx		%fp1,%fp0		| ...ATAN(U), FP1 RELEASED
336	fmovel		%d1,%FPCR		|restore users exceptions
337	faddx		ATANF(%a6),%fp0	| ...ATAN(X)
338	bra		t_frcinx
339
340ATANBORS:
341|--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED.
342|--FP0 IS X AND |X| <= 1/16 OR |X| >= 16.
343	cmpil		#0x3FFF8000,%d0
344	bgt		ATANBIG	| ...I.E. |X| >= 16
345
346ATANSM:
347|--|X| <= 1/16
348|--IF |X| < 2^(-40), RETURN X AS ANSWER. OTHERWISE, APPROXIMATE
349|--ATAN(X) BY X + X*Y*(B1+Y*(B2+Y*(B3+Y*(B4+Y*(B5+Y*B6)))))
350|--WHICH IS X + X*Y*( [B1+Z*(B3+Z*B5)] + [Y*(B2+Z*(B4+Z*B6)] )
351|--WHERE Y = X*X, AND Z = Y*Y.
352
353	cmpil		#0x3FD78000,%d0
354	blt		ATANTINY
355|--COMPUTE POLYNOMIAL
356	fmulx		%fp0,%fp0	| ...FP0 IS Y = X*X
357
358
359	movew		#0x0000,XDCARE(%a6)
360
361	fmovex		%fp0,%fp1
362	fmulx		%fp1,%fp1		| ...FP1 IS Z = Y*Y
363
364	fmoved		ATANB6,%fp2
365	fmoved		ATANB5,%fp3
366
367	fmulx		%fp1,%fp2		| ...Z*B6
368	fmulx		%fp1,%fp3		| ...Z*B5
369
370	faddd		ATANB4,%fp2	| ...B4+Z*B6
371	faddd		ATANB3,%fp3	| ...B3+Z*B5
372
373	fmulx		%fp1,%fp2		| ...Z*(B4+Z*B6)
374	fmulx		%fp3,%fp1		| ...Z*(B3+Z*B5)
375
376	faddd		ATANB2,%fp2	| ...B2+Z*(B4+Z*B6)
377	faddd		ATANB1,%fp1	| ...B1+Z*(B3+Z*B5)
378
379	fmulx		%fp0,%fp2		| ...Y*(B2+Z*(B4+Z*B6))
380	fmulx		X(%a6),%fp0		| ...X*Y
381
382	faddx		%fp2,%fp1		| ...[B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
383
384
385	fmulx		%fp1,%fp0	| ...X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
386
387	fmovel		%d1,%FPCR		|restore users exceptions
388	faddx		X(%a6),%fp0
389
390	bra		t_frcinx
391
392ATANTINY:
393|--|X| < 2^(-40), ATAN(X) = X
394	movew		#0x0000,XDCARE(%a6)
395
396	fmovel		%d1,%FPCR		|restore users exceptions
397	fmovex		X(%a6),%fp0	|last inst - possible exception set
398
399	bra		t_frcinx
400
401ATANBIG:
402|--IF |X| > 2^(100), RETURN	SIGN(X)*(PI/2 - TINY). OTHERWISE,
403|--RETURN SIGN(X)*PI/2 + ATAN(-1/X).
404	cmpil		#0x40638000,%d0
405	bgt		ATANHUGE
406
407|--APPROXIMATE ATAN(-1/X) BY
408|--X'+X'*Y*(C1+Y*(C2+Y*(C3+Y*(C4+Y*C5)))), X' = -1/X, Y = X'*X'
409|--THIS CAN BE RE-WRITTEN AS
410|--X'+X'*Y*( [C1+Z*(C3+Z*C5)] + [Y*(C2+Z*C4)] ), Z = Y*Y.
411
412	fmoves		#0xBF800000,%fp1	| ...LOAD -1
413	fdivx		%fp0,%fp1		| ...FP1 IS -1/X
414
415
416|--DIVIDE IS STILL CRANKING
417
418	fmovex		%fp1,%fp0		| ...FP0 IS X'
419	fmulx		%fp0,%fp0		| ...FP0 IS Y = X'*X'
420	fmovex		%fp1,X(%a6)		| ...X IS REALLY X'
421
422	fmovex		%fp0,%fp1
423	fmulx		%fp1,%fp1		| ...FP1 IS Z = Y*Y
424
425	fmoved		ATANC5,%fp3
426	fmoved		ATANC4,%fp2
427
428	fmulx		%fp1,%fp3		| ...Z*C5
429	fmulx		%fp1,%fp2		| ...Z*B4
430
431	faddd		ATANC3,%fp3	| ...C3+Z*C5
432	faddd		ATANC2,%fp2	| ...C2+Z*C4
433
434	fmulx		%fp3,%fp1		| ...Z*(C3+Z*C5), FP3 RELEASED
435	fmulx		%fp0,%fp2		| ...Y*(C2+Z*C4)
436
437	faddd		ATANC1,%fp1	| ...C1+Z*(C3+Z*C5)
438	fmulx		X(%a6),%fp0		| ...X'*Y
439
440	faddx		%fp2,%fp1		| ...[Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
441
442
443	fmulx		%fp1,%fp0		| ...X'*Y*([B1+Z*(B3+Z*B5)]
444|					...	+[Y*(B2+Z*(B4+Z*B6))])
445	faddx		X(%a6),%fp0
446
447	fmovel		%d1,%FPCR		|restore users exceptions
448
449	btstb		#7,(%a0)
450	beqs		pos_big
451
452neg_big:
453	faddx		NPIBY2,%fp0
454	bra		t_frcinx
455
456pos_big:
457	faddx		PPIBY2,%fp0
458	bra		t_frcinx
459
460ATANHUGE:
461|--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
462	btstb		#7,(%a0)
463	beqs		pos_huge
464
465neg_huge:
466	fmovex		NPIBY2,%fp0
467	fmovel		%d1,%fpcr
468	fsubx		NTINY,%fp0
469	bra		t_frcinx
470
471pos_huge:
472	fmovex		PPIBY2,%fp0
473	fmovel		%d1,%fpcr
474	fsubx		PTINY,%fp0
475	bra		t_frcinx
476
477	|end
478