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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46| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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
generated by cgit v1.2.2 (git 2.25.0) at 2024-11-17 04:56:45 -0500