| blob | c8a664998f92d659c2a44937657a1b461fa02600 |
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 |
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.
49 |satan idnt 2,1 | Motorola 040 Floating Point Software Package
51 |section 8
53 #include "fpsp.h"
55 BOUNDS1: .long 0x3FFB8000,0x4002FFFF
57 ONE: .long 0x3F800000
59 .long 0x00000000
61 ATANA3: .long 0xBFF6687E,0x314987D8
62 ATANA2: .long 0x4002AC69,0x34A26DB3
64 ATANA1: .long 0xBFC2476F,0x4E1DA28E
65 ATANB6: .long 0x3FB34444,0x7F876989
67 ATANB5: .long 0xBFB744EE,0x7FAF45DB
68 ATANB4: .long 0x3FBC71C6,0x46940220
70 ATANB3: .long 0xBFC24924,0x921872F9
71 ATANB2: .long 0x3FC99999,0x99998FA9
73 ATANB1: .long 0xBFD55555,0x55555555
74 ATANC5: .long 0xBFB70BF3,0x98539E6A
76 ATANC4: .long 0x3FBC7187,0x962D1D7D
77 ATANC3: .long 0xBFC24924,0x827107B8
79 ATANC2: .long 0x3FC99999,0x9996263E
80 ATANC1: .long 0xBFD55555,0x55555536
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
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
217 .set X,FP_SCR1
218 .set XDCARE,X+2
219 .set XFRAC,X+4
220 .set XFRACLO,X+8
222 .set ATANF,FP_SCR2
223 .set ATANFHI,ATANF+4
224 .set ATANFLO,ATANF+8
227 | xref t_frcinx
228 |xref t_extdnrm
230 .global satand
231 satand:
232 |--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
234 bra t_extdnrm
236 .global satan
237 satan:
238 |--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
240 fmovex (%a0),%fp0 | ...LOAD INPUT
242 movel (%a0),%d0
243 movew 4(%a0),%d0
244 fmovex %fp0,X(%a6)
245 andil #0x7FFFFFFF,%d0
247 cmpil #0x3FFB8000,%d0 | ...|X| >= 1/16?
248 bges ATANOK1
249 bra ATANSM
251 ATANOK1:
252 cmpil #0x4002FFFF,%d0 | ...|X| < 16 ?
253 bles ATANMAIN
254 bra ATANBIG
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.
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|).
278 ATANMAIN:
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
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)
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.
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
313 |--THAT'S ALL I HAVE TO DO FOR NOW,
314 |--BUT ALAS, THE DIVIDE IS STILL CRANKING!
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
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))
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
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
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.
353 cmpil #0x3FD78000,%d0
354 blt ATANTINY
355 |--COMPUTE POLYNOMIAL
356 fmulx %fp0,%fp0 | ...FP0 IS Y = X*X
359 movew #0x0000,XDCARE(%a6)
361 fmovex %fp0,%fp1
362 fmulx %fp1,%fp1 | ...FP1 IS Z = Y*Y
364 fmoved ATANB6,%fp2
365 fmoved ATANB5,%fp3
367 fmulx %fp1,%fp2 | ...Z*B6
368 fmulx %fp1,%fp3 | ...Z*B5
370 faddd ATANB4,%fp2 | ...B4+Z*B6
371 faddd ATANB3,%fp3 | ...B3+Z*B5
373 fmulx %fp1,%fp2 | ...Z*(B4+Z*B6)
374 fmulx %fp3,%fp1 | ...Z*(B3+Z*B5)
376 faddd ATANB2,%fp2 | ...B2+Z*(B4+Z*B6)
377 faddd ATANB1,%fp1 | ...B1+Z*(B3+Z*B5)
379 fmulx %fp0,%fp2 | ...Y*(B2+Z*(B4+Z*B6))
380 fmulx X(%a6),%fp0 | ...X*Y
382 faddx %fp2,%fp1 | ...[B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
385 fmulx %fp1,%fp0 | ...X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
387 fmovel %d1,%FPCR |restore users exceptions
388 faddx X(%a6),%fp0
390 bra t_frcinx
392 ATANTINY:
393 |--|X| < 2^(-40), ATAN(X) = X
394 movew #0x0000,XDCARE(%a6)
396 fmovel %d1,%FPCR |restore users exceptions
397 fmovex X(%a6),%fp0 |last inst - possible exception set
399 bra t_frcinx
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
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.
412 fmoves #0xBF800000,%fp1 | ...LOAD -1
413 fdivx %fp0,%fp1 | ...FP1 IS -1/X
416 |--DIVIDE IS STILL CRANKING
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'
422 fmovex %fp0,%fp1
423 fmulx %fp1,%fp1 | ...FP1 IS Z = Y*Y
425 fmoved ATANC5,%fp3
426 fmoved ATANC4,%fp2
428 fmulx %fp1,%fp3 | ...Z*C5
429 fmulx %fp1,%fp2 | ...Z*B4
431 faddd ATANC3,%fp3 | ...C3+Z*C5
432 faddd ATANC2,%fp2 | ...C2+Z*C4
434 fmulx %fp3,%fp1 | ...Z*(C3+Z*C5), FP3 RELEASED
435 fmulx %fp0,%fp2 | ...Y*(C2+Z*C4)
437 faddd ATANC1,%fp1 | ...C1+Z*(C3+Z*C5)
438 fmulx X(%a6),%fp0 | ...X'*Y
440 faddx %fp2,%fp1 | ...[Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
443 fmulx %fp1,%fp0 | ...X'*Y*([B1+Z*(B3+Z*B5)]
444 | ... +[Y*(B2+Z*(B4+Z*B6))])
445 faddx X(%a6),%fp0
447 fmovel %d1,%FPCR |restore users exceptions
449 btstb #7,(%a0)
450 beqs pos_big
452 neg_big:
453 faddx NPIBY2,%fp0
454 bra t_frcinx
456 pos_big:
457 faddx PPIBY2,%fp0
458 bra t_frcinx
460 ATANHUGE:
461 |--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
462 btstb #7,(%a0)
463 beqs pos_huge
465 neg_huge:
466 fmovex NPIBY2,%fp0
467 fmovel %d1,%fpcr
468 fsubx NTINY,%fp0
469 bra t_frcinx
471 pos_huge:
472 fmovex PPIBY2,%fp0
473 fmovel %d1,%fpcr
474 fsubx PTINY,%fp0
475 bra t_frcinx
477 |end