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 
55 BOUNDS1:	.long 0x3FFB8000,0x4002FFFF
56 
57 ONE:	.long 0x3F800000
58 
59 	.long 0x00000000
60 
61 ATANA3:	.long 0xBFF6687E,0x314987D8
62 ATANA2:	.long 0x4002AC69,0x34A26DB3
63 
64 ATANA1:	.long 0xBFC2476F,0x4E1DA28E
65 ATANB6:	.long 0x3FB34444,0x7F876989
66 
67 ATANB5:	.long 0xBFB744EE,0x7FAF45DB
68 ATANB4:	.long 0x3FBC71C6,0x46940220
69 
70 ATANB3:	.long 0xBFC24924,0x921872F9
71 ATANB2:	.long 0x3FC99999,0x99998FA9
72 
73 ATANB1:	.long 0xBFD55555,0x55555555
74 ATANC5:	.long 0xBFB70BF3,0x98539E6A
75 
76 ATANC4:	.long 0x3FBC7187,0x962D1D7D
77 ATANC3:	.long 0xBFC24924,0x827107B8
78 
79 ATANC2:	.long 0x3FC99999,0x9996263E
80 ATANC1:	.long 0xBFD55555,0x55555536
81 
82 PPIBY2:	.long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
83 NPIBY2:	.long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x00000000
84 PTINY:	.long 0x00010000,0x80000000,0x00000000,0x00000000
85 NTINY:	.long 0x80010000,0x80000000,0x00000000,0x00000000
86 
87 ATANTBL:
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
231 satand:
232 |--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
233 
234 	bra		t_extdnrm
235 
236 	.global	satan
237 satan:
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 
251 ATANOK1:
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 
278 ATANMAIN:
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 
340 ATANBORS:
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 
346 ATANSM:
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 
392 ATANTINY:
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 
401 ATANBIG:
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 
452 neg_big:
453 	faddx		NPIBY2,%fp0
454 	bra		t_frcinx
455 
456 pos_big:
457 	faddx		PPIBY2,%fp0
458 	bra		t_frcinx
459 
460 ATANHUGE:
461 |--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
462 	btstb		#7,(%a0)
463 	beqs		pos_huge
464 
465 neg_huge:
466 	fmovex		NPIBY2,%fp0
467 	fmovel		%d1,%fpcr
468 	fsubx		NTINY,%fp0
469 	bra		t_frcinx
470 
471 pos_huge:
472 	fmovex		PPIBY2,%fp0
473 	fmovel		%d1,%fpcr
474 	fsubx		PTINY,%fp0
475 	bra		t_frcinx
476 
477 	|end
478