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Commit | Line | Data |
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1da177e4 LT |
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 | | | |
e00d82d0 MW |
46 | | For details on the license for this file, please see the |
47 | | file, README, in this same directory. | |
1da177e4 LT |
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 |