Commit | Line | Data |
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1da177e4 LT |
1 | | |
2 | | stan.sa 3.3 7/29/91 | |
3 | | | |
4 | | The entry point stan computes the tangent of | |
5 | | an input argument; | |
6 | | stand does the same except for denormalized input. | |
7 | | | |
8 | | Input: Double-extended number X in location pointed to | |
9 | | by address register a0. | |
10 | | | |
11 | | Output: The value tan(X) returned in floating-point register Fp0. | |
12 | | | |
13 | | Accuracy and Monotonicity: The returned result is within 3 ulp 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 sTAN takes approximately 170 cycles for | |
19 | | input argument X such that |X| < 15Pi, which is the usual | |
20 | | situation. | |
21 | | | |
22 | | Algorithm: | |
23 | | | |
24 | | 1. If |X| >= 15Pi or |X| < 2**(-40), go to 6. | |
25 | | | |
26 | | 2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let | |
27 | | k = N mod 2, so in particular, k = 0 or 1. | |
28 | | | |
29 | | 3. If k is odd, go to 5. | |
30 | | | |
31 | | 4. (k is even) Tan(X) = tan(r) and tan(r) is approximated by a | |
32 | | rational function U/V where | |
33 | | U = r + r*s*(P1 + s*(P2 + s*P3)), and | |
34 | | V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r. | |
35 | | Exit. | |
36 | | | |
37 | | 4. (k is odd) Tan(X) = -cot(r). Since tan(r) is approximated by a | |
38 | | rational function U/V where | |
39 | | U = r + r*s*(P1 + s*(P2 + s*P3)), and | |
40 | | V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r, | |
41 | | -Cot(r) = -V/U. Exit. | |
42 | | | |
43 | | 6. If |X| > 1, go to 8. | |
44 | | | |
45 | | 7. (|X|<2**(-40)) Tan(X) = X. Exit. | |
46 | | | |
47 | | 8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 2. | |
48 | | | |
49 | ||
50 | | Copyright (C) Motorola, Inc. 1990 | |
51 | | All Rights Reserved | |
52 | | | |
e00d82d0 MW |
53 | | For details on the license for this file, please see the |
54 | | file, README, in this same directory. | |
1da177e4 LT |
55 | |
56 | |STAN idnt 2,1 | Motorola 040 Floating Point Software Package | |
57 | ||
58 | |section 8 | |
59 | ||
60 | #include "fpsp.h" | |
61 | ||
62 | BOUNDS1: .long 0x3FD78000,0x4004BC7E | |
63 | TWOBYPI: .long 0x3FE45F30,0x6DC9C883 | |
64 | ||
65 | TANQ4: .long 0x3EA0B759,0xF50F8688 | |
66 | TANP3: .long 0xBEF2BAA5,0xA8924F04 | |
67 | ||
68 | TANQ3: .long 0xBF346F59,0xB39BA65F,0x00000000,0x00000000 | |
69 | ||
70 | TANP2: .long 0x3FF60000,0xE073D3FC,0x199C4A00,0x00000000 | |
71 | ||
72 | TANQ2: .long 0x3FF90000,0xD23CD684,0x15D95FA1,0x00000000 | |
73 | ||
74 | TANP1: .long 0xBFFC0000,0x8895A6C5,0xFB423BCA,0x00000000 | |
75 | ||
76 | TANQ1: .long 0xBFFD0000,0xEEF57E0D,0xA84BC8CE,0x00000000 | |
77 | ||
78 | INVTWOPI: .long 0x3FFC0000,0xA2F9836E,0x4E44152A,0x00000000 | |
79 | ||
80 | TWOPI1: .long 0x40010000,0xC90FDAA2,0x00000000,0x00000000 | |
81 | TWOPI2: .long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000 | |
82 | ||
83 | |--N*PI/2, -32 <= N <= 32, IN A LEADING TERM IN EXT. AND TRAILING | |
84 | |--TERM IN SGL. NOTE THAT PI IS 64-BIT LONG, THUS N*PI/2 IS AT | |
85 | |--MOST 69 BITS LONG. | |
86 | .global PITBL | |
87 | PITBL: | |
88 | .long 0xC0040000,0xC90FDAA2,0x2168C235,0x21800000 | |
89 | .long 0xC0040000,0xC2C75BCD,0x105D7C23,0xA0D00000 | |
90 | .long 0xC0040000,0xBC7EDCF7,0xFF523611,0xA1E80000 | |
91 | .long 0xC0040000,0xB6365E22,0xEE46F000,0x21480000 | |
92 | .long 0xC0040000,0xAFEDDF4D,0xDD3BA9EE,0xA1200000 | |
93 | .long 0xC0040000,0xA9A56078,0xCC3063DD,0x21FC0000 | |
94 | .long 0xC0040000,0xA35CE1A3,0xBB251DCB,0x21100000 | |
95 | .long 0xC0040000,0x9D1462CE,0xAA19D7B9,0xA1580000 | |
96 | .long 0xC0040000,0x96CBE3F9,0x990E91A8,0x21E00000 | |
97 | .long 0xC0040000,0x90836524,0x88034B96,0x20B00000 | |
98 | .long 0xC0040000,0x8A3AE64F,0x76F80584,0xA1880000 | |
99 | .long 0xC0040000,0x83F2677A,0x65ECBF73,0x21C40000 | |
100 | .long 0xC0030000,0xFB53D14A,0xA9C2F2C2,0x20000000 | |
101 | .long 0xC0030000,0xEEC2D3A0,0x87AC669F,0x21380000 | |
102 | .long 0xC0030000,0xE231D5F6,0x6595DA7B,0xA1300000 | |
103 | .long 0xC0030000,0xD5A0D84C,0x437F4E58,0x9FC00000 | |
104 | .long 0xC0030000,0xC90FDAA2,0x2168C235,0x21000000 | |
105 | .long 0xC0030000,0xBC7EDCF7,0xFF523611,0xA1680000 | |
106 | .long 0xC0030000,0xAFEDDF4D,0xDD3BA9EE,0xA0A00000 | |
107 | .long 0xC0030000,0xA35CE1A3,0xBB251DCB,0x20900000 | |
108 | .long 0xC0030000,0x96CBE3F9,0x990E91A8,0x21600000 | |
109 | .long 0xC0030000,0x8A3AE64F,0x76F80584,0xA1080000 | |
110 | .long 0xC0020000,0xFB53D14A,0xA9C2F2C2,0x1F800000 | |
111 | .long 0xC0020000,0xE231D5F6,0x6595DA7B,0xA0B00000 | |
112 | .long 0xC0020000,0xC90FDAA2,0x2168C235,0x20800000 | |
113 | .long 0xC0020000,0xAFEDDF4D,0xDD3BA9EE,0xA0200000 | |
114 | .long 0xC0020000,0x96CBE3F9,0x990E91A8,0x20E00000 | |
115 | .long 0xC0010000,0xFB53D14A,0xA9C2F2C2,0x1F000000 | |
116 | .long 0xC0010000,0xC90FDAA2,0x2168C235,0x20000000 | |
117 | .long 0xC0010000,0x96CBE3F9,0x990E91A8,0x20600000 | |
118 | .long 0xC0000000,0xC90FDAA2,0x2168C235,0x1F800000 | |
119 | .long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x1F000000 | |
120 | .long 0x00000000,0x00000000,0x00000000,0x00000000 | |
121 | .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x9F000000 | |
122 | .long 0x40000000,0xC90FDAA2,0x2168C235,0x9F800000 | |
123 | .long 0x40010000,0x96CBE3F9,0x990E91A8,0xA0600000 | |
124 | .long 0x40010000,0xC90FDAA2,0x2168C235,0xA0000000 | |
125 | .long 0x40010000,0xFB53D14A,0xA9C2F2C2,0x9F000000 | |
126 | .long 0x40020000,0x96CBE3F9,0x990E91A8,0xA0E00000 | |
127 | .long 0x40020000,0xAFEDDF4D,0xDD3BA9EE,0x20200000 | |
128 | .long 0x40020000,0xC90FDAA2,0x2168C235,0xA0800000 | |
129 | .long 0x40020000,0xE231D5F6,0x6595DA7B,0x20B00000 | |
130 | .long 0x40020000,0xFB53D14A,0xA9C2F2C2,0x9F800000 | |
131 | .long 0x40030000,0x8A3AE64F,0x76F80584,0x21080000 | |
132 | .long 0x40030000,0x96CBE3F9,0x990E91A8,0xA1600000 | |
133 | .long 0x40030000,0xA35CE1A3,0xBB251DCB,0xA0900000 | |
134 | .long 0x40030000,0xAFEDDF4D,0xDD3BA9EE,0x20A00000 | |
135 | .long 0x40030000,0xBC7EDCF7,0xFF523611,0x21680000 | |
136 | .long 0x40030000,0xC90FDAA2,0x2168C235,0xA1000000 | |
137 | .long 0x40030000,0xD5A0D84C,0x437F4E58,0x1FC00000 | |
138 | .long 0x40030000,0xE231D5F6,0x6595DA7B,0x21300000 | |
139 | .long 0x40030000,0xEEC2D3A0,0x87AC669F,0xA1380000 | |
140 | .long 0x40030000,0xFB53D14A,0xA9C2F2C2,0xA0000000 | |
141 | .long 0x40040000,0x83F2677A,0x65ECBF73,0xA1C40000 | |
142 | .long 0x40040000,0x8A3AE64F,0x76F80584,0x21880000 | |
143 | .long 0x40040000,0x90836524,0x88034B96,0xA0B00000 | |
144 | .long 0x40040000,0x96CBE3F9,0x990E91A8,0xA1E00000 | |
145 | .long 0x40040000,0x9D1462CE,0xAA19D7B9,0x21580000 | |
146 | .long 0x40040000,0xA35CE1A3,0xBB251DCB,0xA1100000 | |
147 | .long 0x40040000,0xA9A56078,0xCC3063DD,0xA1FC0000 | |
148 | .long 0x40040000,0xAFEDDF4D,0xDD3BA9EE,0x21200000 | |
149 | .long 0x40040000,0xB6365E22,0xEE46F000,0xA1480000 | |
150 | .long 0x40040000,0xBC7EDCF7,0xFF523611,0x21E80000 | |
151 | .long 0x40040000,0xC2C75BCD,0x105D7C23,0x20D00000 | |
152 | .long 0x40040000,0xC90FDAA2,0x2168C235,0xA1800000 | |
153 | ||
154 | .set INARG,FP_SCR4 | |
155 | ||
156 | .set TWOTO63,L_SCR1 | |
157 | .set ENDFLAG,L_SCR2 | |
158 | .set N,L_SCR3 | |
159 | ||
160 | | xref t_frcinx | |
161 | |xref t_extdnrm | |
162 | ||
163 | .global stand | |
164 | stand: | |
165 | |--TAN(X) = X FOR DENORMALIZED X | |
166 | ||
167 | bra t_extdnrm | |
168 | ||
169 | .global stan | |
170 | stan: | |
171 | fmovex (%a0),%fp0 | ...LOAD INPUT | |
172 | ||
173 | movel (%a0),%d0 | |
174 | movew 4(%a0),%d0 | |
175 | andil #0x7FFFFFFF,%d0 | |
176 | ||
177 | cmpil #0x3FD78000,%d0 | ...|X| >= 2**(-40)? | |
178 | bges TANOK1 | |
179 | bra TANSM | |
180 | TANOK1: | |
181 | cmpil #0x4004BC7E,%d0 | ...|X| < 15 PI? | |
182 | blts TANMAIN | |
183 | bra REDUCEX | |
184 | ||
185 | ||
186 | TANMAIN: | |
187 | |--THIS IS THE USUAL CASE, |X| <= 15 PI. | |
188 | |--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP. | |
189 | fmovex %fp0,%fp1 | |
190 | fmuld TWOBYPI,%fp1 | ...X*2/PI | |
191 | ||
192 | |--HIDE THE NEXT TWO INSTRUCTIONS | |
193 | leal PITBL+0x200,%a1 | ...TABLE OF N*PI/2, N = -32,...,32 | |
194 | ||
195 | |--FP1 IS NOW READY | |
196 | fmovel %fp1,%d0 | ...CONVERT TO INTEGER | |
197 | ||
198 | asll #4,%d0 | |
199 | addal %d0,%a1 | ...ADDRESS N*PIBY2 IN Y1, Y2 | |
200 | ||
201 | fsubx (%a1)+,%fp0 | ...X-Y1 | |
202 | |--HIDE THE NEXT ONE | |
203 | ||
204 | fsubs (%a1),%fp0 | ...FP0 IS R = (X-Y1)-Y2 | |
205 | ||
206 | rorl #5,%d0 | |
207 | andil #0x80000000,%d0 | ...D0 WAS ODD IFF D0 < 0 | |
208 | ||
209 | TANCONT: | |
210 | ||
211 | cmpil #0,%d0 | |
212 | blt NODD | |
213 | ||
214 | fmovex %fp0,%fp1 | |
215 | fmulx %fp1,%fp1 | ...S = R*R | |
216 | ||
217 | fmoved TANQ4,%fp3 | |
218 | fmoved TANP3,%fp2 | |
219 | ||
220 | fmulx %fp1,%fp3 | ...SQ4 | |
221 | fmulx %fp1,%fp2 | ...SP3 | |
222 | ||
223 | faddd TANQ3,%fp3 | ...Q3+SQ4 | |
224 | faddx TANP2,%fp2 | ...P2+SP3 | |
225 | ||
226 | fmulx %fp1,%fp3 | ...S(Q3+SQ4) | |
227 | fmulx %fp1,%fp2 | ...S(P2+SP3) | |
228 | ||
229 | faddx TANQ2,%fp3 | ...Q2+S(Q3+SQ4) | |
230 | faddx TANP1,%fp2 | ...P1+S(P2+SP3) | |
231 | ||
232 | fmulx %fp1,%fp3 | ...S(Q2+S(Q3+SQ4)) | |
233 | fmulx %fp1,%fp2 | ...S(P1+S(P2+SP3)) | |
234 | ||
235 | faddx TANQ1,%fp3 | ...Q1+S(Q2+S(Q3+SQ4)) | |
236 | fmulx %fp0,%fp2 | ...RS(P1+S(P2+SP3)) | |
237 | ||
238 | fmulx %fp3,%fp1 | ...S(Q1+S(Q2+S(Q3+SQ4))) | |
239 | ||
240 | ||
241 | faddx %fp2,%fp0 | ...R+RS(P1+S(P2+SP3)) | |
242 | ||
243 | ||
244 | fadds #0x3F800000,%fp1 | ...1+S(Q1+...) | |
245 | ||
246 | fmovel %d1,%fpcr |restore users exceptions | |
247 | fdivx %fp1,%fp0 |last inst - possible exception set | |
248 | ||
249 | bra t_frcinx | |
250 | ||
251 | NODD: | |
252 | fmovex %fp0,%fp1 | |
253 | fmulx %fp0,%fp0 | ...S = R*R | |
254 | ||
255 | fmoved TANQ4,%fp3 | |
256 | fmoved TANP3,%fp2 | |
257 | ||
258 | fmulx %fp0,%fp3 | ...SQ4 | |
259 | fmulx %fp0,%fp2 | ...SP3 | |
260 | ||
261 | faddd TANQ3,%fp3 | ...Q3+SQ4 | |
262 | faddx TANP2,%fp2 | ...P2+SP3 | |
263 | ||
264 | fmulx %fp0,%fp3 | ...S(Q3+SQ4) | |
265 | fmulx %fp0,%fp2 | ...S(P2+SP3) | |
266 | ||
267 | faddx TANQ2,%fp3 | ...Q2+S(Q3+SQ4) | |
268 | faddx TANP1,%fp2 | ...P1+S(P2+SP3) | |
269 | ||
270 | fmulx %fp0,%fp3 | ...S(Q2+S(Q3+SQ4)) | |
271 | fmulx %fp0,%fp2 | ...S(P1+S(P2+SP3)) | |
272 | ||
273 | faddx TANQ1,%fp3 | ...Q1+S(Q2+S(Q3+SQ4)) | |
274 | fmulx %fp1,%fp2 | ...RS(P1+S(P2+SP3)) | |
275 | ||
276 | fmulx %fp3,%fp0 | ...S(Q1+S(Q2+S(Q3+SQ4))) | |
277 | ||
278 | ||
279 | faddx %fp2,%fp1 | ...R+RS(P1+S(P2+SP3)) | |
280 | fadds #0x3F800000,%fp0 | ...1+S(Q1+...) | |
281 | ||
282 | ||
283 | fmovex %fp1,-(%sp) | |
284 | eoril #0x80000000,(%sp) | |
285 | ||
286 | fmovel %d1,%fpcr |restore users exceptions | |
287 | fdivx (%sp)+,%fp0 |last inst - possible exception set | |
288 | ||
289 | bra t_frcinx | |
290 | ||
291 | TANBORS: | |
292 | |--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION. | |
293 | |--IF |X| < 2**(-40), RETURN X OR 1. | |
294 | cmpil #0x3FFF8000,%d0 | |
295 | bgts REDUCEX | |
296 | ||
297 | TANSM: | |
298 | ||
299 | fmovex %fp0,-(%sp) | |
300 | fmovel %d1,%fpcr |restore users exceptions | |
301 | fmovex (%sp)+,%fp0 |last inst - possible exception set | |
302 | ||
303 | bra t_frcinx | |
304 | ||
305 | ||
306 | REDUCEX: | |
307 | |--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW. | |
308 | |--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING | |
309 | |--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE. | |
310 | ||
311 | fmovemx %fp2-%fp5,-(%a7) | ...save FP2 through FP5 | |
312 | movel %d2,-(%a7) | |
313 | fmoves #0x00000000,%fp1 | |
314 | ||
315 | |--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that | |
316 | |--there is a danger of unwanted overflow in first LOOP iteration. In this | |
317 | |--case, reduce argument by one remainder step to make subsequent reduction | |
318 | |--safe. | |
319 | cmpil #0x7ffeffff,%d0 |is argument dangerously large? | |
320 | bnes LOOP | |
321 | movel #0x7ffe0000,FP_SCR2(%a6) |yes | |
322 | | ;create 2**16383*PI/2 | |
323 | movel #0xc90fdaa2,FP_SCR2+4(%a6) | |
324 | clrl FP_SCR2+8(%a6) | |
325 | ftstx %fp0 |test sign of argument | |
326 | movel #0x7fdc0000,FP_SCR3(%a6) |create low half of 2**16383* | |
327 | | ;PI/2 at FP_SCR3 | |
328 | movel #0x85a308d3,FP_SCR3+4(%a6) | |
329 | clrl FP_SCR3+8(%a6) | |
330 | fblt red_neg | |
331 | orw #0x8000,FP_SCR2(%a6) |positive arg | |
332 | orw #0x8000,FP_SCR3(%a6) | |
333 | red_neg: | |
334 | faddx FP_SCR2(%a6),%fp0 |high part of reduction is exact | |
335 | fmovex %fp0,%fp1 |save high result in fp1 | |
336 | faddx FP_SCR3(%a6),%fp0 |low part of reduction | |
337 | fsubx %fp0,%fp1 |determine low component of result | |
338 | faddx FP_SCR3(%a6),%fp1 |fp0/fp1 are reduced argument. | |
339 | ||
340 | |--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4. | |
341 | |--integer quotient will be stored in N | |
342 | |--Intermediate remainder is 66-bit long; (R,r) in (FP0,FP1) | |
343 | ||
344 | LOOP: | |
345 | fmovex %fp0,INARG(%a6) | ...+-2**K * F, 1 <= F < 2 | |
346 | movew INARG(%a6),%d0 | |
347 | movel %d0,%a1 | ...save a copy of D0 | |
348 | andil #0x00007FFF,%d0 | |
349 | subil #0x00003FFF,%d0 | ...D0 IS K | |
350 | cmpil #28,%d0 | |
351 | bles LASTLOOP | |
352 | CONTLOOP: | |
353 | subil #27,%d0 | ...D0 IS L := K-27 | |
354 | movel #0,ENDFLAG(%a6) | |
355 | bras WORK | |
356 | LASTLOOP: | |
357 | clrl %d0 | ...D0 IS L := 0 | |
358 | movel #1,ENDFLAG(%a6) | |
359 | ||
360 | WORK: | |
361 | |--FIND THE REMAINDER OF (R,r) W.R.T. 2**L * (PI/2). L IS SO CHOSEN | |
362 | |--THAT INT( X * (2/PI) / 2**(L) ) < 2**29. | |
363 | ||
364 | |--CREATE 2**(-L) * (2/PI), SIGN(INARG)*2**(63), | |
365 | |--2**L * (PIby2_1), 2**L * (PIby2_2) | |
366 | ||
367 | movel #0x00003FFE,%d2 | ...BIASED EXPO OF 2/PI | |
368 | subl %d0,%d2 | ...BIASED EXPO OF 2**(-L)*(2/PI) | |
369 | ||
370 | movel #0xA2F9836E,FP_SCR1+4(%a6) | |
371 | movel #0x4E44152A,FP_SCR1+8(%a6) | |
372 | movew %d2,FP_SCR1(%a6) | ...FP_SCR1 is 2**(-L)*(2/PI) | |
373 | ||
374 | fmovex %fp0,%fp2 | |
375 | fmulx FP_SCR1(%a6),%fp2 | |
376 | |--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN | |
377 | |--FLOATING POINT FORMAT, THE TWO FMOVE'S FMOVE.L FP <--> N | |
378 | |--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT | |
379 | |--(SIGN(INARG)*2**63 + FP2) - SIGN(INARG)*2**63 WILL GIVE | |
380 | |--US THE DESIRED VALUE IN FLOATING POINT. | |
381 | ||
382 | |--HIDE SIX CYCLES OF INSTRUCTION | |
383 | movel %a1,%d2 | |
384 | swap %d2 | |
385 | andil #0x80000000,%d2 | |
386 | oril #0x5F000000,%d2 | ...D2 IS SIGN(INARG)*2**63 IN SGL | |
387 | movel %d2,TWOTO63(%a6) | |
388 | ||
389 | movel %d0,%d2 | |
390 | addil #0x00003FFF,%d2 | ...BIASED EXPO OF 2**L * (PI/2) | |
391 | ||
392 | |--FP2 IS READY | |
393 | fadds TWOTO63(%a6),%fp2 | ...THE FRACTIONAL PART OF FP1 IS ROUNDED | |
394 | ||
395 | |--HIDE 4 CYCLES OF INSTRUCTION; creating 2**(L)*Piby2_1 and 2**(L)*Piby2_2 | |
396 | movew %d2,FP_SCR2(%a6) | |
397 | clrw FP_SCR2+2(%a6) | |
398 | movel #0xC90FDAA2,FP_SCR2+4(%a6) | |
399 | clrl FP_SCR2+8(%a6) | ...FP_SCR2 is 2**(L) * Piby2_1 | |
400 | ||
401 | |--FP2 IS READY | |
402 | fsubs TWOTO63(%a6),%fp2 | ...FP2 is N | |
403 | ||
404 | addil #0x00003FDD,%d0 | |
405 | movew %d0,FP_SCR3(%a6) | |
406 | clrw FP_SCR3+2(%a6) | |
407 | movel #0x85A308D3,FP_SCR3+4(%a6) | |
408 | clrl FP_SCR3+8(%a6) | ...FP_SCR3 is 2**(L) * Piby2_2 | |
409 | ||
410 | movel ENDFLAG(%a6),%d0 | |
411 | ||
412 | |--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and | |
413 | |--P2 = 2**(L) * Piby2_2 | |
414 | fmovex %fp2,%fp4 | |
415 | fmulx FP_SCR2(%a6),%fp4 | ...W = N*P1 | |
416 | fmovex %fp2,%fp5 | |
417 | fmulx FP_SCR3(%a6),%fp5 | ...w = N*P2 | |
418 | fmovex %fp4,%fp3 | |
419 | |--we want P+p = W+w but |p| <= half ulp of P | |
420 | |--Then, we need to compute A := R-P and a := r-p | |
421 | faddx %fp5,%fp3 | ...FP3 is P | |
422 | fsubx %fp3,%fp4 | ...W-P | |
423 | ||
424 | fsubx %fp3,%fp0 | ...FP0 is A := R - P | |
425 | faddx %fp5,%fp4 | ...FP4 is p = (W-P)+w | |
426 | ||
427 | fmovex %fp0,%fp3 | ...FP3 A | |
428 | fsubx %fp4,%fp1 | ...FP1 is a := r - p | |
429 | ||
430 | |--Now we need to normalize (A,a) to "new (R,r)" where R+r = A+a but | |
431 | |--|r| <= half ulp of R. | |
432 | faddx %fp1,%fp0 | ...FP0 is R := A+a | |
433 | |--No need to calculate r if this is the last loop | |
434 | cmpil #0,%d0 | |
435 | bgt RESTORE | |
436 | ||
437 | |--Need to calculate r | |
438 | fsubx %fp0,%fp3 | ...A-R | |
439 | faddx %fp3,%fp1 | ...FP1 is r := (A-R)+a | |
440 | bra LOOP | |
441 | ||
442 | RESTORE: | |
443 | fmovel %fp2,N(%a6) | |
444 | movel (%a7)+,%d2 | |
445 | fmovemx (%a7)+,%fp2-%fp5 | |
446 | ||
447 | ||
448 | movel N(%a6),%d0 | |
449 | rorl #1,%d0 | |
450 | ||
451 | ||
452 | bra TANCONT | |
453 | ||
454 | |end |