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[glibc.git] / sysdeps / ieee754 / dbl-64 / e_asin.c
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1 /*
2 * IBM Accurate Mathematical Library
3 * Copyright (c) International Business Machines Corp., 2001
4 *
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU Lesser General Public License as published by
7 * the Free Software Foundation; either version 2 of the License, or
8 * (at your option) any later version.
9 *
10 * This program is distributed in the hope that it will be useful,
11 * but WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 * GNU General Public License for more details.
14 *
15 * You should have received a copy of the GNU Lesser General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
18 */
19 /******************************************************************/
20 /* MODULE_NAME:uasncs.c */
21 /* */
22 /* FUNCTIONS: uasin */
23 /* uacos */
24 /* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */
25 /* doasin.c sincos32.c dosincos.c mpa.c */
26 /* sincos.tbl asincos.tbl powtwo.tbl root.tbl */
27 /* */
28 /* Ultimate asin/acos routines. Given an IEEE double machine */
29 /* number x, compute the correctly rounded value of */
30 /* arcsin(x)or arccos(x) according to the function called. */
31 /* Assumption: Machine arithmetic operations are performed in */
32 /* round to nearest mode of IEEE 754 standard. */
33 /* */
34 /******************************************************************/
35 #include "endian.h"
36 #include "mydefs.h"
37 #include "asincos.tbl"
38 #include "root.tbl"
39 #include "powtwo.tbl"
40 #include "MathLib.h"
41 #include "uasncs.h"
42
43 void __doasin(double x, double dx, double w[]);
44 void __dubsin(double x, double dx, double v[]);
45 void __dubcos(double x, double dx, double v[]);
46 void __docos(double x, double dx, double v[]);
47 double __sin32(double x, double res, double res1);
48 double __cos32(double x, double res, double res1);
49
50 /***************************************************************************/
51 /* An ultimate asin routine. Given an IEEE double machine number x */
52 /* it computes the correctly rounded (to nearest) value of arcsin(x) */
53 /***************************************************************************/
54 double __ieee754_asin(double x){
55 double x1,x2,xx,s1,s2,res1,p,t,res,r,cor,cc,y,c,z,w[2];
56 mynumber u,v;
57 int4 k,m,n;
58 #if 0
59 int4 nn;
60 #endif
61
62 u.x = x;
63 m = u.i[HIGH_HALF];
64 k = 0x7fffffff&m; /* no sign */
65
66 if (k < 0x3e500000) return x; /* for x->0 => sin(x)=x */
67 /*----------------------2^-26 <= |x| < 2^ -3 -----------------*/
68 else
69 if (k < 0x3fc00000) {
70 x2 = x*x;
71 t = (((((f6*x2 + f5)*x2 + f4)*x2 + f3)*x2 + f2)*x2 + f1)*(x2*x);
72 res = x+t; /* res=arcsin(x) according to Taylor series */
73 cor = (x-res)+t;
74 if (res == res+1.025*cor) return res;
75 else {
76 x1 = x+big;
77 xx = x*x;
78 x1 -= big;
79 x2 = x - x1;
80 p = x1*x1*x1;
81 s1 = a1.x*p;
82 s2 = ((((((c7*xx + c6)*xx + c5)*xx + c4)*xx + c3)*xx + c2)*xx*xx*x +
83 ((a1.x+a2.x)*x2*x2+ 0.5*x1*x)*x2) + a2.x*p;
84 res1 = x+s1;
85 s2 = ((x-res1)+s1)+s2;
86 res = res1+s2;
87 cor = (res1-res)+s2;
88 if (res == res+1.00014*cor) return res;
89 else {
90 __doasin(x,0,w);
91 if (w[0]==(w[0]+1.00000001*w[1])) return w[0];
92 else {
93 y=ABS(x);
94 res=ABS(w[0]);
95 res1=ABS(w[0]+1.1*w[1]);
96 return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
97 }
98 }
99 }
100 }
101 /*---------------------0.125 <= |x| < 0.5 -----------------------------*/
102 else if (k < 0x3fe00000) {
103 if (k<0x3fd00000) n = 11*((k&0x000fffff)>>15);
104 else n = 11*((k&0x000fffff)>>14)+352;
105 if (m>0) xx = x - asncs.x[n];
106 else xx = -x - asncs.x[n];
107 t = asncs.x[n+1]*xx;
108 p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+xx*(asncs.x[n+5]
109 +xx*asncs.x[n+6]))))+asncs.x[n+7];
110 t+=p;
111 res =asncs.x[n+8] +t;
112 cor = (asncs.x[n+8]-res)+t;
113 if (res == res+1.05*cor) return (m>0)?res:-res;
114 else {
115 r=asncs.x[n+8]+xx*asncs.x[n+9];
116 t=((asncs.x[n+8]-r)+xx*asncs.x[n+9])+(p+xx*asncs.x[n+10]);
117 res = r+t;
118 cor = (r-res)+t;
119 if (res == res+1.0005*cor) return (m>0)?res:-res;
120 else {
121 res1=res+1.1*cor;
122 z=0.5*(res1-res);
123 __dubsin(res,z,w);
124 z=(w[0]-ABS(x))+w[1];
125 if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
126 else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
127 else {
128 y=ABS(x);
129 return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
130 }
131 }
132 }
133 } /* else if (k < 0x3fe00000) */
134 /*-------------------- 0.5 <= |x| < 0.75 -----------------------------*/
135 else
136 if (k < 0x3fe80000) {
137 n = 1056+((k&0x000fe000)>>11)*3;
138 if (m>0) xx = x - asncs.x[n];
139 else xx = -x - asncs.x[n];
140 t = asncs.x[n+1]*xx;
141 p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+xx*(asncs.x[n+5]
142 +xx*(asncs.x[n+6]+xx*asncs.x[n+7])))))+asncs.x[n+8];
143 t+=p;
144 res =asncs.x[n+9] +t;
145 cor = (asncs.x[n+9]-res)+t;
146 if (res == res+1.01*cor) return (m>0)?res:-res;
147 else {
148 r=asncs.x[n+9]+xx*asncs.x[n+10];
149 t=((asncs.x[n+9]-r)+xx*asncs.x[n+10])+(p+xx*asncs.x[n+11]);
150 res = r+t;
151 cor = (r-res)+t;
152 if (res == res+1.0005*cor) return (m>0)?res:-res;
153 else {
154 res1=res+1.1*cor;
155 z=0.5*(res1-res);
156 __dubsin(res,z,w);
157 z=(w[0]-ABS(x))+w[1];
158 if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
159 else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
160 else {
161 y=ABS(x);
162 return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
163 }
164 }
165 }
166 } /* else if (k < 0x3fe80000) */
167 /*--------------------- 0.75 <= |x|< 0.921875 ----------------------*/
168 else
169 if (k < 0x3fed8000) {
170 n = 992+((k&0x000fe000)>>13)*13;
171 if (m>0) xx = x - asncs.x[n];
172 else xx = -x - asncs.x[n];
173 t = asncs.x[n+1]*xx;
174 p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+xx*(asncs.x[n+5]
175 +xx*(asncs.x[n+6]+xx*(asncs.x[n+7]+xx*asncs.x[n+8]))))))+asncs.x[n+9];
176 t+=p;
177 res =asncs.x[n+10] +t;
178 cor = (asncs.x[n+10]-res)+t;
179 if (res == res+1.01*cor) return (m>0)?res:-res;
180 else {
181 r=asncs.x[n+10]+xx*asncs.x[n+11];
182 t=((asncs.x[n+10]-r)+xx*asncs.x[n+11])+(p+xx*asncs.x[n+12]);
183 res = r+t;
184 cor = (r-res)+t;
185 if (res == res+1.0008*cor) return (m>0)?res:-res;
186 else {
187 res1=res+1.1*cor;
188 z=0.5*(res1-res);
189 y=hp0.x-res;
190 z=((hp0.x-y)-res)+(hp1.x-z);
191 __dubcos(y,z,w);
192 z=(w[0]-ABS(x))+w[1];
193 if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
194 else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
195 else {
196 y=ABS(x);
197 return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
198 }
199 }
200 }
201 } /* else if (k < 0x3fed8000) */
202 /*-------------------0.921875 <= |x| < 0.953125 ------------------------*/
203 else
204 if (k < 0x3fee8000) {
205 n = 884+((k&0x000fe000)>>13)*14;
206 if (m>0) xx = x - asncs.x[n];
207 else xx = -x - asncs.x[n];
208 t = asncs.x[n+1]*xx;
209 p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+
210 xx*(asncs.x[n+5]+xx*(asncs.x[n+6]
211 +xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+
212 xx*asncs.x[n+9])))))))+asncs.x[n+10];
213 t+=p;
214 res =asncs.x[n+11] +t;
215 cor = (asncs.x[n+11]-res)+t;
216 if (res == res+1.01*cor) return (m>0)?res:-res;
217 else {
218 r=asncs.x[n+11]+xx*asncs.x[n+12];
219 t=((asncs.x[n+11]-r)+xx*asncs.x[n+12])+(p+xx*asncs.x[n+13]);
220 res = r+t;
221 cor = (r-res)+t;
222 if (res == res+1.0007*cor) return (m>0)?res:-res;
223 else {
224 res1=res+1.1*cor;
225 z=0.5*(res1-res);
226 y=(hp0.x-res)-z;
227 z=y+hp1.x;
228 y=(y-z)+hp1.x;
229 __dubcos(z,y,w);
230 z=(w[0]-ABS(x))+w[1];
231 if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
232 else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
233 else {
234 y=ABS(x);
235 return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
236 }
237 }
238 }
239 } /* else if (k < 0x3fee8000) */
240
241 /*--------------------0.953125 <= |x| < 0.96875 ------------------------*/
242 else
243 if (k < 0x3fef0000) {
244 n = 768+((k&0x000fe000)>>13)*15;
245 if (m>0) xx = x - asncs.x[n];
246 else xx = -x - asncs.x[n];
247 t = asncs.x[n+1]*xx;
248 p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+
249 xx*(asncs.x[n+5]+xx*(asncs.x[n+6]
250 +xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+
251 xx*(asncs.x[n+9]+xx*asncs.x[n+10]))))))))+asncs.x[n+11];
252 t+=p;
253 res =asncs.x[n+12] +t;
254 cor = (asncs.x[n+12]-res)+t;
255 if (res == res+1.01*cor) return (m>0)?res:-res;
256 else {
257 r=asncs.x[n+12]+xx*asncs.x[n+13];
258 t=((asncs.x[n+12]-r)+xx*asncs.x[n+13])+(p+xx*asncs.x[n+14]);
259 res = r+t;
260 cor = (r-res)+t;
261 if (res == res+1.0007*cor) return (m>0)?res:-res;
262 else {
263 res1=res+1.1*cor;
264 z=0.5*(res1-res);
265 y=(hp0.x-res)-z;
266 z=y+hp1.x;
267 y=(y-z)+hp1.x;
268 __dubcos(z,y,w);
269 z=(w[0]-ABS(x))+w[1];
270 if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
271 else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
272 else {
273 y=ABS(x);
274 return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
275 }
276 }
277 }
278 } /* else if (k < 0x3fef0000) */
279 /*--------------------0.96875 <= |x| < 1 --------------------------------*/
280 else
281 if (k<0x3ff00000) {
282 z = 0.5*((m>0)?(1.0-x):(1.0+x));
283 v.x=z;
284 k=v.i[HIGH_HALF];
285 t=inroot[(k&0x001fffff)>>14]*powtwo[511-(k>>21)];
286 r=1.0-t*t*z;
287 t = t*(rt0+r*(rt1+r*(rt2+r*rt3)));
288 c=t*z;
289 t=c*(1.5-0.5*t*c);
290 y=(c+t24)-t24;
291 cc = (z-y*y)/(t+y);
292 p=(((((f6*z+f5)*z+f4)*z+f3)*z+f2)*z+f1)*z;
293 cor = (hp1.x - 2.0*cc)-2.0*(y+cc)*p;
294 res1 = hp0.x - 2.0*y;
295 res =res1 + cor;
296 if (res == res+1.003*((res1-res)+cor)) return (m>0)?res:-res;
297 else {
298 c=y+cc;
299 cc=(y-c)+cc;
300 __doasin(c,cc,w);
301 res1=hp0.x-2.0*w[0];
302 cor=((hp0.x-res1)-2.0*w[0])+(hp1.x-2.0*w[1]);
303 res = res1+cor;
304 cor = (res1-res)+cor;
305 if (res==(res+1.0000001*cor)) return (m>0)?res:-res;
306 else {
307 y=ABS(x);
308 res1=res+1.1*cor;
309 return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
310 }
311 }
312 } /* else if (k < 0x3ff00000) */
313 /*---------------------------- |x|>=1 -------------------------------*/
314 else if (k==0x3ff00000 && u.i[LOW_HALF]==0) return (m>0)?hp0.x:-hp0.x;
315 else
316 if (k>0x7ff00000 || (k == 0x7ff00000 && u.i[LOW_HALF] != 0)) return x;
317 else {
318 u.i[HIGH_HALF]=0x7ff00000;
319 v.i[HIGH_HALF]=0x7ff00000;
320 u.i[LOW_HALF]=0;
321 v.i[LOW_HALF]=0;
322 return u.x/v.x; /* NaN */
323 }
324 }
325
326 /*******************************************************************/
327 /* */
328 /* End of arcsine, below is arccosine */
329 /* */
330 /*******************************************************************/
331
332 double __ieee754_acos(double x)
333 {
334 double x1,x2,xx,s1,s2,res1,p,t,res,r,cor,cc,y,c,z,w[2],eps;
335 #if 0
336 double fc;
337 #endif
338 mynumber u,v;
339 int4 k,m,n;
340 #if 0
341 int4 nn;
342 #endif
343 u.x = x;
344 m = u.i[HIGH_HALF];
345 k = 0x7fffffff&m;
346 /*------------------- |x|<2.77556*10^-17 ----------------------*/
347 if (k < 0x3c880000) return hp0.x;
348
349 /*----------------- 2.77556*10^-17 <= |x| < 2^-3 --------------*/
350 else
351 if (k < 0x3fc00000) {
352 x2 = x*x;
353 t = (((((f6*x2 + f5)*x2 + f4)*x2 + f3)*x2 + f2)*x2 + f1)*(x2*x);
354 r=hp0.x-x;
355 cor=(((hp0.x-r)-x)+hp1.x)-t;
356 res = r+cor;
357 cor = (r-res)+cor;
358 if (res == res+1.004*cor) return res;
359 else {
360 x1 = x+big;
361 xx = x*x;
362 x1 -= big;
363 x2 = x - x1;
364 p = x1*x1*x1;
365 s1 = a1.x*p;
366 s2 = ((((((c7*xx + c6)*xx + c5)*xx + c4)*xx + c3)*xx + c2)*xx*xx*x +
367 ((a1.x+a2.x)*x2*x2+ 0.5*x1*x)*x2) + a2.x*p;
368 res1 = x+s1;
369 s2 = ((x-res1)+s1)+s2;
370 r=hp0.x-res1;
371 cor=(((hp0.x-r)-res1)+hp1.x)-s2;
372 res = r+cor;
373 cor = (r-res)+cor;
374 if (res == res+1.00004*cor) return res;
375 else {
376 __doasin(x,0,w);
377 r=hp0.x-w[0];
378 cor=((hp0.x-r)-w[0])+(hp1.x-w[1]);
379 res=r+cor;
380 cor=(r-res)+cor;
381 if (res ==(res +1.00000001*cor)) return res;
382 else {
383 res1=res+1.1*cor;
384 return __cos32(x,res,res1);
385 }
386 }
387 }
388 } /* else if (k < 0x3fc00000) */
389 /*---------------------- 0.125 <= |x| < 0.5 --------------------*/
390 else
391 if (k < 0x3fe00000) {
392 if (k<0x3fd00000) n = 11*((k&0x000fffff)>>15);
393 else n = 11*((k&0x000fffff)>>14)+352;
394 if (m>0) xx = x - asncs.x[n];
395 else xx = -x - asncs.x[n];
396 t = asncs.x[n+1]*xx;
397 p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+
398 xx*(asncs.x[n+5]+xx*asncs.x[n+6]))))+asncs.x[n+7];
399 t+=p;
400 y = (m>0)?(hp0.x-asncs.x[n+8]):(hp0.x+asncs.x[n+8]);
401 t = (m>0)?(hp1.x-t):(hp1.x+t);
402 res = y+t;
403 if (res == res+1.02*((y-res)+t)) return res;
404 else {
405 r=asncs.x[n+8]+xx*asncs.x[n+9];
406 t=((asncs.x[n+8]-r)+xx*asncs.x[n+9])+(p+xx*asncs.x[n+10]);
407 if (m>0)
408 {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; }
409 else
410 {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); }
411 res = p+t;
412 cor = (p-res)+t;
413 if (res == (res+1.0002*cor)) return res;
414 else {
415 res1=res+1.1*cor;
416 z=0.5*(res1-res);
417 __docos(res,z,w);
418 z=(w[0]-x)+w[1];
419 if (z>1.0e-27) return max(res,res1);
420 else if (z<-1.0e-27) return min(res,res1);
421 else return __cos32(x,res,res1);
422 }
423 }
424 } /* else if (k < 0x3fe00000) */
425
426 /*--------------------------- 0.5 <= |x| < 0.75 ---------------------*/
427 else
428 if (k < 0x3fe80000) {
429 n = 1056+((k&0x000fe000)>>11)*3;
430 if (m>0) {xx = x - asncs.x[n]; eps=1.04; }
431 else {xx = -x - asncs.x[n]; eps=1.02; }
432 t = asncs.x[n+1]*xx;
433 p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+
434 xx*(asncs.x[n+5]+xx*(asncs.x[n+6]+
435 xx*asncs.x[n+7])))))+asncs.x[n+8];
436 t+=p;
437 y = (m>0)?(hp0.x-asncs.x[n+9]):(hp0.x+asncs.x[n+9]);
438 t = (m>0)?(hp1.x-t):(hp1.x+t);
439 res = y+t;
440 if (res == res+eps*((y-res)+t)) return res;
441 else {
442 r=asncs.x[n+9]+xx*asncs.x[n+10];
443 t=((asncs.x[n+9]-r)+xx*asncs.x[n+10])+(p+xx*asncs.x[n+11]);
444 if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0004; }
445 else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0002; }
446 res = p+t;
447 cor = (p-res)+t;
448 if (res == (res+eps*cor)) return res;
449 else {
450 res1=res+1.1*cor;
451 z=0.5*(res1-res);
452 __docos(res,z,w);
453 z=(w[0]-x)+w[1];
454 if (z>1.0e-27) return max(res,res1);
455 else if (z<-1.0e-27) return min(res,res1);
456 else return __cos32(x,res,res1);
457 }
458 }
459 } /* else if (k < 0x3fe80000) */
460
461 /*------------------------- 0.75 <= |x| < 0.921875 -------------*/
462 else
463 if (k < 0x3fed8000) {
464 n = 992+((k&0x000fe000)>>13)*13;
465 if (m>0) {xx = x - asncs.x[n]; eps = 1.04; }
466 else {xx = -x - asncs.x[n]; eps = 1.01; }
467 t = asncs.x[n+1]*xx;
468 p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+
469 xx*(asncs.x[n+5]+xx*(asncs.x[n+6]+xx*(asncs.x[n+7]+
470 xx*asncs.x[n+8]))))))+asncs.x[n+9];
471 t+=p;
472 y = (m>0)?(hp0.x-asncs.x[n+10]):(hp0.x+asncs.x[n+10]);
473 t = (m>0)?(hp1.x-t):(hp1.x+t);
474 res = y+t;
475 if (res == res+eps*((y-res)+t)) return res;
476 else {
477 r=asncs.x[n+10]+xx*asncs.x[n+11];
478 t=((asncs.x[n+10]-r)+xx*asncs.x[n+11])+(p+xx*asncs.x[n+12]);
479 if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0032; }
480 else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0008; }
481 res = p+t;
482 cor = (p-res)+t;
483 if (res == (res+eps*cor)) return res;
484 else {
485 res1=res+1.1*cor;
486 z=0.5*(res1-res);
487 __docos(res,z,w);
488 z=(w[0]-x)+w[1];
489 if (z>1.0e-27) return max(res,res1);
490 else if (z<-1.0e-27) return min(res,res1);
491 else return __cos32(x,res,res1);
492 }
493 }
494 } /* else if (k < 0x3fed8000) */
495
496 /*-------------------0.921875 <= |x| < 0.953125 ------------------*/
497 else
498 if (k < 0x3fee8000) {
499 n = 884+((k&0x000fe000)>>13)*14;
500 if (m>0) {xx = x - asncs.x[n]; eps=1.04; }
501 else {xx = -x - asncs.x[n]; eps =1.005; }
502 t = asncs.x[n+1]*xx;
503 p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+
504 xx*(asncs.x[n+5]+xx*(asncs.x[n+6]
505 +xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+
506 xx*asncs.x[n+9])))))))+asncs.x[n+10];
507 t+=p;
508 y = (m>0)?(hp0.x-asncs.x[n+11]):(hp0.x+asncs.x[n+11]);
509 t = (m>0)?(hp1.x-t):(hp1.x+t);
510 res = y+t;
511 if (res == res+eps*((y-res)+t)) return res;
512 else {
513 r=asncs.x[n+11]+xx*asncs.x[n+12];
514 t=((asncs.x[n+11]-r)+xx*asncs.x[n+12])+(p+xx*asncs.x[n+13]);
515 if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0030; }
516 else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0005; }
517 res = p+t;
518 cor = (p-res)+t;
519 if (res == (res+eps*cor)) return res;
520 else {
521 res1=res+1.1*cor;
522 z=0.5*(res1-res);
523 __docos(res,z,w);
524 z=(w[0]-x)+w[1];
525 if (z>1.0e-27) return max(res,res1);
526 else if (z<-1.0e-27) return min(res,res1);
527 else return __cos32(x,res,res1);
528 }
529 }
530 } /* else if (k < 0x3fee8000) */
531
532 /*--------------------0.953125 <= |x| < 0.96875 ----------------*/
533 else
534 if (k < 0x3fef0000) {
535 n = 768+((k&0x000fe000)>>13)*15;
536 if (m>0) {xx = x - asncs.x[n]; eps=1.04; }
537 else {xx = -x - asncs.x[n]; eps=1.005;}
538 t = asncs.x[n+1]*xx;
539 p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+
540 xx*(asncs.x[n+5]+xx*(asncs.x[n+6]
541 +xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+xx*(asncs.x[n+9]+
542 xx*asncs.x[n+10]))))))))+asncs.x[n+11];
543 t+=p;
544 y = (m>0)?(hp0.x-asncs.x[n+12]):(hp0.x+asncs.x[n+12]);
545 t = (m>0)?(hp1.x-t):(hp1.x+t);
546 res = y+t;
547 if (res == res+eps*((y-res)+t)) return res;
548 else {
549 r=asncs.x[n+12]+xx*asncs.x[n+13];
550 t=((asncs.x[n+12]-r)+xx*asncs.x[n+13])+(p+xx*asncs.x[n+14]);
551 if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0030; }
552 else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0005; }
553 res = p+t;
554 cor = (p-res)+t;
555 if (res == (res+eps*cor)) return res;
556 else {
557 res1=res+1.1*cor;
558 z=0.5*(res1-res);
559 __docos(res,z,w);
560 z=(w[0]-x)+w[1];
561 if (z>1.0e-27) return max(res,res1);
562 else if (z<-1.0e-27) return min(res,res1);
563 else return __cos32(x,res,res1);
564 }
565 }
566 } /* else if (k < 0x3fef0000) */
567 /*-----------------0.96875 <= |x| < 1 ---------------------------*/
568
569 else
570 if (k<0x3ff00000) {
571 z = 0.5*((m>0)?(1.0-x):(1.0+x));
572 v.x=z;
573 k=v.i[HIGH_HALF];
574 t=inroot[(k&0x001fffff)>>14]*powtwo[511-(k>>21)];
575 r=1.0-t*t*z;
576 t = t*(rt0+r*(rt1+r*(rt2+r*rt3)));
577 c=t*z;
578 t=c*(1.5-0.5*t*c);
579 y = (t27*c+c)-t27*c;
580 cc = (z-y*y)/(t+y);
581 p=(((((f6*z+f5)*z+f4)*z+f3)*z+f2)*z+f1)*z;
582 if (m<0) {
583 cor = (hp1.x - cc)-(y+cc)*p;
584 res1 = hp0.x - y;
585 res =res1 + cor;
586 if (res == res+1.002*((res1-res)+cor)) return (res+res);
587 else {
588 c=y+cc;
589 cc=(y-c)+cc;
590 __doasin(c,cc,w);
591 res1=hp0.x-w[0];
592 cor=((hp0.x-res1)-w[0])+(hp1.x-w[1]);
593 res = res1+cor;
594 cor = (res1-res)+cor;
595 if (res==(res+1.000001*cor)) return (res+res);
596 else {
597 res=res+res;
598 res1=res+1.2*cor;
599 return __cos32(x,res,res1);
600 }
601 }
602 }
603 else {
604 cor = cc+p*(y+cc);
605 res = y + cor;
606 if (res == res+1.03*((y-res)+cor)) return (res+res);
607 else {
608 c=y+cc;
609 cc=(y-c)+cc;
610 __doasin(c,cc,w);
611 res = w[0];
612 cor=w[1];
613 if (res==(res+1.000001*cor)) return (res+res);
614 else {
615 res=res+res;
616 res1=res+1.2*cor;
617 return __cos32(x,res,res1);
618 }
619 }
620 }
621 } /* else if (k < 0x3ff00000) */
622
623 /*---------------------------- |x|>=1 -----------------------*/
624 else
625 if (k==0x3ff00000 && u.i[LOW_HALF]==0) return (m>0)?0:2.0*hp0.x;
626 else
627 if (k>0x7ff00000 || (k == 0x7ff00000 && u.i[LOW_HALF] != 0)) return x;
628 else {
629 u.i[HIGH_HALF]=0x7ff00000;
630 v.i[HIGH_HALF]=0x7ff00000;
631 u.i[LOW_HALF]=0;
632 v.i[LOW_HALF]=0;
633 return u.x/v.x;
634 }
635 }
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