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573b56c2 ZAL |
1 | /* |
2 | * Copyright (c) 1985 Regents of the University of California. | |
3 | * | |
4 | * Use and reproduction of this software are granted in accordance with | |
5 | * the terms and conditions specified in the Berkeley Software License | |
6 | * Agreement (in particular, this entails acknowledgement of the programs' | |
7 | * source, and inclusion of this notice) with the additional understanding | |
8 | * that all recipients should regard themselves as participants in an | |
9 | * ongoing research project and hence should feel obligated to report | |
10 | * their experiences (good or bad) with these elementary function codes, | |
11 | * using "sendbug 4bsd-bugs@BERKELEY", to the authors. | |
12 | */ | |
13 | ||
14 | #ifndef lint | |
27c51c7b | 15 | static char sccsid[] = |
859dc438 ZAL |
16 | "@(#)trig.c 1.2 (Berkeley) 8/22/85; 1.7 (ucb.elefunt) %G%"; |
17 | #endif /* not lint */ | |
573b56c2 ZAL |
18 | |
19 | /* SIN(X), COS(X), TAN(X) | |
20 | * RETURN THE SINE, COSINE, AND TANGENT OF X RESPECTIVELY | |
21 | * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) | |
22 | * CODED IN C BY K.C. NG, 1/8/85; | |
23 | * REVISED BY W. Kahan and K.C. NG, 8/17/85. | |
24 | * | |
25 | * Required system supported functions: | |
26 | * copysign(x,y) | |
27 | * finite(x) | |
28 | * drem(x,p) | |
29 | * | |
30 | * Static kernel functions: | |
31 | * sin__S(z) ....sin__S(x*x) return (sin(x)-x)/x | |
32 | * cos__C(z) ....cos__C(x*x) return cos(x)-1-x*x/2 | |
33 | * | |
34 | * Method. | |
35 | * Let S and C denote the polynomial approximations to sin and cos | |
36 | * respectively on [-PI/4, +PI/4]. | |
37 | * | |
38 | * SIN and COS: | |
39 | * 1. Reduce the argument into [-PI , +PI] by the remainder function. | |
40 | * 2. For x in (-PI,+PI), there are three cases: | |
41 | * case 1: |x| < PI/4 | |
42 | * case 2: PI/4 <= |x| < 3PI/4 | |
43 | * case 3: 3PI/4 <= |x|. | |
44 | * SIN and COS of x are computed by: | |
45 | * | |
46 | * sin(x) cos(x) remark | |
47 | * ---------------------------------------------------------- | |
48 | * case 1 S(x) C(x) | |
49 | * case 2 sign(x)*C(y) S(y) y=PI/2-|x| | |
50 | * case 3 S(y) -C(y) y=sign(x)*(PI-|x|) | |
51 | * ---------------------------------------------------------- | |
52 | * | |
53 | * TAN: | |
54 | * 1. Reduce the argument into [-PI/2 , +PI/2] by the remainder function. | |
55 | * 2. For x in (-PI/2,+PI/2), there are two cases: | |
56 | * case 1: |x| < PI/4 | |
57 | * case 2: PI/4 <= |x| < PI/2 | |
58 | * TAN of x is computed by: | |
59 | * | |
60 | * tan (x) remark | |
61 | * ---------------------------------------------------------- | |
62 | * case 1 S(x)/C(x) | |
63 | * case 2 C(y)/S(y) y=sign(x)*(PI/2-|x|) | |
64 | * ---------------------------------------------------------- | |
65 | * | |
66 | * Notes: | |
67 | * 1. S(y) and C(y) were computed by: | |
68 | * S(y) = y+y*sin__S(y*y) | |
69 | * C(y) = 1-(y*y/2-cos__C(x*x)) ... if y*y/2 < thresh, | |
70 | * = 0.5-((y*y/2-0.5)-cos__C(x*x)) ... if y*y/2 >= thresh. | |
71 | * where | |
72 | * thresh = 0.5*(acos(3/4)**2) | |
73 | * | |
74 | * 2. For better accuracy, we use the following formula for S/C for tan | |
75 | * (k=0): let ss=sin__S(y*y), and cc=cos__C(y*y), then | |
76 | * | |
77 | * y+y*ss (y*y/2-cc)+ss | |
78 | * S(y)/C(y) = -------- = y + y * ---------------. | |
79 | * C C | |
80 | * | |
81 | * | |
82 | * Special cases: | |
83 | * Let trig be any of sin, cos, or tan. | |
84 | * trig(+-INF) is NaN, with signals; | |
85 | * trig(NaN) is that NaN; | |
86 | * trig(n*PI/2) is exact for any integer n, provided n*PI is | |
87 | * representable; otherwise, trig(x) is inexact. | |
88 | * | |
89 | * Accuracy: | |
90 | * trig(x) returns the exact trig(x*pi/PI) nearly rounded, where | |
91 | * | |
92 | * Decimal: | |
93 | * pi = 3.141592653589793 23846264338327 ..... | |
94 | * 53 bits PI = 3.141592653589793 115997963 ..... , | |
95 | * 56 bits PI = 3.141592653589793 227020265 ..... , | |
96 | * | |
97 | * Hexadecimal: | |
98 | * pi = 3.243F6A8885A308D313198A2E.... | |
99 | * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps | |
100 | * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps | |
101 | * | |
102 | * In a test run with 1,024,000 random arguments on a VAX, the maximum | |
103 | * observed errors (compared with the exact trig(x*pi/PI)) were | |
104 | * tan(x) : 2.09 ulps (around 4.716340404662354) | |
105 | * sin(x) : .861 ulps | |
106 | * cos(x) : .857 ulps | |
107 | * | |
108 | * Constants: | |
109 | * The hexadecimal values are the intended ones for the following constants. | |
110 | * The decimal values may be used, provided that the compiler will convert | |
111 | * from decimal to binary accurately enough to produce the hexadecimal values | |
112 | * shown. | |
113 | */ | |
114 | ||
859dc438 ZAL |
115 | #if defined(vax)||defined(tahoe) |
116 | #ifdef vax | |
f77d20bd | 117 | #define _0x(A,B) 0x/**/A/**/B |
859dc438 | 118 | #else /* vax */ |
f77d20bd | 119 | #define _0x(A,B) 0x/**/B/**/A |
859dc438 | 120 | #endif /* vax */ |
573b56c2 ZAL |
121 | /*thresh = 2.6117239648121182150E-1 , Hex 2^ -1 * .85B8636B026EA0 */ |
122 | /*PIo4 = 7.8539816339744830676E-1 , Hex 2^ 0 * .C90FDAA22168C2 */ | |
123 | /*PIo2 = 1.5707963267948966135E0 , Hex 2^ 1 * .C90FDAA22168C2 */ | |
124 | /*PI3o4 = 2.3561944901923449203E0 , Hex 2^ 2 * .96CBE3F9990E92 */ | |
125 | /*PI = 3.1415926535897932270E0 , Hex 2^ 2 * .C90FDAA22168C2 */ | |
126 | /*PI2 = 6.2831853071795864540E0 ; Hex 2^ 3 * .C90FDAA22168C2 */ | |
f77d20bd | 127 | static long threshx[] = { _0x(b863,3f85), _0x(6ea0,6b02)}; |
573b56c2 | 128 | #define thresh (*(double*)threshx) |
f77d20bd | 129 | static long PIo4x[] = { _0x(0fda,4049), _0x(68c2,a221)}; |
573b56c2 | 130 | #define PIo4 (*(double*)PIo4x) |
f77d20bd | 131 | static long PIo2x[] = { _0x(0fda,40c9), _0x(68c2,a221)}; |
573b56c2 | 132 | #define PIo2 (*(double*)PIo2x) |
f77d20bd | 133 | static long PI3o4x[] = { _0x(cbe3,4116), _0x(0e92,f999)}; |
573b56c2 | 134 | #define PI3o4 (*(double*)PI3o4x) |
f77d20bd | 135 | static long PIx[] = { _0x(0fda,4149), _0x(68c2,a221)}; |
573b56c2 | 136 | #define PI (*(double*)PIx) |
f77d20bd | 137 | static long PI2x[] = { _0x(0fda,41c9), _0x(68c2,a221)}; |
573b56c2 | 138 | #define PI2 (*(double*)PI2x) |
859dc438 | 139 | #else /* defined(vax)||defined(tahoe) */ |
573b56c2 ZAL |
140 | static double |
141 | thresh = 2.6117239648121182150E-1 , /*Hex 2^ -2 * 1.0B70C6D604DD4 */ | |
142 | PIo4 = 7.8539816339744827900E-1 , /*Hex 2^ -1 * 1.921FB54442D18 */ | |
143 | PIo2 = 1.5707963267948965580E0 , /*Hex 2^ 0 * 1.921FB54442D18 */ | |
144 | PI3o4 = 2.3561944901923448370E0 , /*Hex 2^ 1 * 1.2D97C7F3321D2 */ | |
145 | PI = 3.1415926535897931160E0 , /*Hex 2^ 1 * 1.921FB54442D18 */ | |
146 | PI2 = 6.2831853071795862320E0 ; /*Hex 2^ 2 * 1.921FB54442D18 */ | |
859dc438 | 147 | #ifdef national |
0e3f0d63 ZAL |
148 | static long fmaxx[] = { 0xffffffff, 0x7fefffff}; |
149 | #define fmax (*(double*)fmaxx) | |
859dc438 ZAL |
150 | #endif /* national */ |
151 | #endif /* defined(vax)||defined(tahoe) */ | |
573b56c2 ZAL |
152 | static double zero=0, one=1, negone= -1, half=1.0/2.0, |
153 | small=1E-10, /* 1+small**2==1; better values for small: | |
154 | small = 1.5E-9 for VAX D | |
155 | = 1.2E-8 for IEEE Double | |
156 | = 2.8E-10 for IEEE Extended */ | |
157 | big=1E20; /* big = 1/(small**2) */ | |
158 | ||
159 | double tan(x) | |
160 | double x; | |
161 | { | |
162 | double copysign(),drem(),cos__C(),sin__S(),a,z,ss,cc,c; | |
859dc438 ZAL |
163 | int finite(),k; |
164 | ||
573b56c2 | 165 | /* tan(NaN) and tan(INF) must be NaN */ |
859dc438 | 166 | if(!finite(x)) return(x-x); |
573b56c2 ZAL |
167 | x=drem(x,PI); /* reduce x into [-PI/2, PI/2] */ |
168 | a=copysign(x,one); /* ... = abs(x) */ | |
169 | if ( a >= PIo4 ) {k=1; x = copysign( PIo2 - a , x ); } | |
170 | else { k=0; if(a < small ) { big + a; return(x); }} | |
171 | ||
172 | z = x*x; | |
173 | cc = cos__C(z); | |
174 | ss = sin__S(z); | |
175 | z = z*half ; /* Next get c = cos(x) accurately */ | |
176 | c = (z >= thresh )? half-((z-half)-cc) : one-(z-cc); | |
177 | if (k==0) return ( x + (x*(z-(cc-ss)))/c ); /* sin/cos */ | |
859dc438 | 178 | #ifdef national |
0e3f0d63 | 179 | else if(x==0.0) return copysign(fmax,x); /* no inf on 32k */ |
859dc438 | 180 | #endif /* national */ |
0e3f0d63 | 181 | else return( c/(x+x*ss) ); /* ... cos/sin */ |
573b56c2 ZAL |
182 | |
183 | ||
184 | } | |
185 | double sin(x) | |
186 | double x; | |
187 | { | |
188 | double copysign(),drem(),sin__S(),cos__C(),a,c,z; | |
859dc438 ZAL |
189 | int finite(); |
190 | ||
573b56c2 | 191 | /* sin(NaN) and sin(INF) must be NaN */ |
859dc438 | 192 | if(!finite(x)) return(x-x); |
573b56c2 ZAL |
193 | x=drem(x,PI2); /* reduce x into [-PI, PI] */ |
194 | a=copysign(x,one); | |
195 | if( a >= PIo4 ) { | |
196 | if( a >= PI3o4 ) /* .. in [3PI/4, PI ] */ | |
197 | x=copysign((a=PI-a),x); | |
198 | ||
199 | else { /* .. in [PI/4, 3PI/4] */ | |
200 | a=PIo2-a; /* return sign(x)*C(PI/2-|x|) */ | |
201 | z=a*a; | |
202 | c=cos__C(z); | |
203 | z=z*half; | |
204 | a=(z>=thresh)?half-((z-half)-c):one-(z-c); | |
205 | return(copysign(a,x)); | |
206 | } | |
207 | } | |
208 | ||
209 | /* return S(x) */ | |
210 | if( a < small) { big + a; return(x);} | |
211 | return(x+x*sin__S(x*x)); | |
212 | } | |
213 | ||
214 | double cos(x) | |
215 | double x; | |
216 | { | |
217 | double copysign(),drem(),sin__S(),cos__C(),a,c,z,s=1.0; | |
859dc438 ZAL |
218 | int finite(); |
219 | ||
573b56c2 | 220 | /* cos(NaN) and cos(INF) must be NaN */ |
859dc438 | 221 | if(!finite(x)) return(x-x); |
573b56c2 ZAL |
222 | x=drem(x,PI2); /* reduce x into [-PI, PI] */ |
223 | a=copysign(x,one); | |
224 | if ( a >= PIo4 ) { | |
225 | if ( a >= PI3o4 ) /* .. in [3PI/4, PI ] */ | |
226 | { a=PI-a; s= negone; } | |
227 | ||
228 | else /* .. in [PI/4, 3PI/4] */ | |
229 | /* return S(PI/2-|x|) */ | |
230 | { a=PIo2-a; return(a+a*sin__S(a*a));} | |
231 | } | |
232 | ||
233 | ||
234 | /* return s*C(a) */ | |
235 | if( a < small) { big + a; return(s);} | |
236 | z=a*a; | |
237 | c=cos__C(z); | |
238 | z=z*half; | |
239 | a=(z>=thresh)?half-((z-half)-c):one-(z-c); | |
240 | return(copysign(a,s)); | |
241 | } | |
242 | ||
243 | ||
244 | /* sin__S(x*x) | |
245 | * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) | |
246 | * STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X) | |
247 | * CODED IN C BY K.C. NG, 1/21/85; | |
248 | * REVISED BY K.C. NG on 8/13/85. | |
249 | * | |
250 | * sin(x*k) - x | |
251 | * RETURN --------------- on [-PI/4,PI/4] , where k=pi/PI, PI is the rounded | |
252 | * x | |
253 | * value of pi in machine precision: | |
254 | * | |
255 | * Decimal: | |
256 | * pi = 3.141592653589793 23846264338327 ..... | |
257 | * 53 bits PI = 3.141592653589793 115997963 ..... , | |
258 | * 56 bits PI = 3.141592653589793 227020265 ..... , | |
259 | * | |
260 | * Hexadecimal: | |
261 | * pi = 3.243F6A8885A308D313198A2E.... | |
262 | * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 | |
263 | * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 | |
264 | * | |
265 | * Method: | |
266 | * 1. Let z=x*x. Create a polynomial approximation to | |
267 | * (sin(k*x)-x)/x = z*(S0 + S1*z^1 + ... + S5*z^5). | |
268 | * Then | |
269 | * sin__S(x*x) = z*(S0 + S1*z^1 + ... + S5*z^5) | |
270 | * | |
271 | * The coefficient S's are obtained by a special Remez algorithm. | |
272 | * | |
273 | * Accuracy: | |
274 | * In the absence of rounding error, the approximation has absolute error | |
275 | * less than 2**(-61.11) for VAX D FORMAT, 2**(-57.45) for IEEE DOUBLE. | |
276 | * | |
277 | * Constants: | |
278 | * The hexadecimal values are the intended ones for the following constants. | |
279 | * The decimal values may be used, provided that the compiler will convert | |
280 | * from decimal to binary accurately enough to produce the hexadecimal values | |
281 | * shown. | |
282 | * | |
283 | */ | |
284 | ||
859dc438 | 285 | #if defined(vax)||defined(tahoe) |
573b56c2 ZAL |
286 | /*S0 = -1.6666666666666646660E-1 , Hex 2^ -2 * -.AAAAAAAAAAAA71 */ |
287 | /*S1 = 8.3333333333297230413E-3 , Hex 2^ -6 * .8888888888477F */ | |
288 | /*S2 = -1.9841269838362403710E-4 , Hex 2^-12 * -.D00D00CF8A1057 */ | |
289 | /*S3 = 2.7557318019967078930E-6 , Hex 2^-18 * .B8EF1CA326BEDC */ | |
290 | /*S4 = -2.5051841873876551398E-8 , Hex 2^-25 * -.D73195374CE1D3 */ | |
291 | /*S5 = 1.6028995389845827653E-10 , Hex 2^-32 * .B03D9C6D26CCCC */ | |
292 | /*S6 = -6.2723499671769283121E-13 ; Hex 2^-40 * -.B08D0B7561EA82 */ | |
f77d20bd | 293 | static long S0x[] = { _0x(aaaa,bf2a), _0x(aa71,aaaa)}; |
573b56c2 | 294 | #define S0 (*(double*)S0x) |
f77d20bd | 295 | static long S1x[] = { _0x(8888,3d08), _0x(477f,8888)}; |
573b56c2 | 296 | #define S1 (*(double*)S1x) |
f77d20bd | 297 | static long S2x[] = { _0x(0d00,ba50), _0x(1057,cf8a)}; |
573b56c2 | 298 | #define S2 (*(double*)S2x) |
f77d20bd | 299 | static long S3x[] = { _0x(ef1c,3738), _0x(bedc,a326)}; |
573b56c2 | 300 | #define S3 (*(double*)S3x) |
f77d20bd | 301 | static long S4x[] = { _0x(3195,b3d7), _0x(e1d3,374c)}; |
573b56c2 | 302 | #define S4 (*(double*)S4x) |
f77d20bd | 303 | static long S5x[] = { _0x(3d9c,3030), _0x(cccc,6d26)}; |
573b56c2 | 304 | #define S5 (*(double*)S5x) |
f77d20bd | 305 | static long S6x[] = { _0x(8d0b,ac30), _0x(ea82,7561)}; |
573b56c2 ZAL |
306 | #define S6 (*(double*)S6x) |
307 | #else /* IEEE double */ | |
308 | static double | |
309 | S0 = -1.6666666666666463126E-1 , /*Hex 2^ -3 * -1.555555555550C */ | |
310 | S1 = 8.3333333332992771264E-3 , /*Hex 2^ -7 * 1.111111110C461 */ | |
311 | S2 = -1.9841269816180999116E-4 , /*Hex 2^-13 * -1.A01A019746345 */ | |
312 | S3 = 2.7557309793219876880E-6 , /*Hex 2^-19 * 1.71DE3209CDCD9 */ | |
313 | S4 = -2.5050225177523807003E-8 , /*Hex 2^-26 * -1.AE5C0E319A4EF */ | |
314 | S5 = 1.5868926979889205164E-10 ; /*Hex 2^-33 * 1.5CF61DF672B13 */ | |
315 | #endif | |
316 | ||
317 | static double sin__S(z) | |
318 | double z; | |
319 | { | |
859dc438 | 320 | #if defined(vax)||defined(tahoe) |
573b56c2 | 321 | return(z*(S0+z*(S1+z*(S2+z*(S3+z*(S4+z*(S5+z*S6))))))); |
859dc438 | 322 | #else /* defined(vax)||defined(tahoe) */ |
573b56c2 | 323 | return(z*(S0+z*(S1+z*(S2+z*(S3+z*(S4+z*S5)))))); |
859dc438 | 324 | #endif /* defined(vax)||defined(tahoe) */ |
573b56c2 ZAL |
325 | } |
326 | ||
327 | ||
328 | /* cos__C(x*x) | |
329 | * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) | |
330 | * STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X) | |
331 | * CODED IN C BY K.C. NG, 1/21/85; | |
332 | * REVISED BY K.C. NG on 8/13/85. | |
333 | * | |
334 | * x*x | |
335 | * RETURN cos(k*x) - 1 + ----- on [-PI/4,PI/4], where k = pi/PI, | |
336 | * 2 | |
337 | * PI is the rounded value of pi in machine precision : | |
338 | * | |
339 | * Decimal: | |
340 | * pi = 3.141592653589793 23846264338327 ..... | |
341 | * 53 bits PI = 3.141592653589793 115997963 ..... , | |
342 | * 56 bits PI = 3.141592653589793 227020265 ..... , | |
343 | * | |
344 | * Hexadecimal: | |
345 | * pi = 3.243F6A8885A308D313198A2E.... | |
346 | * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 | |
347 | * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 | |
348 | * | |
349 | * | |
350 | * Method: | |
351 | * 1. Let z=x*x. Create a polynomial approximation to | |
352 | * cos(k*x)-1+z/2 = z*z*(C0 + C1*z^1 + ... + C5*z^5) | |
353 | * then | |
354 | * cos__C(z) = z*z*(C0 + C1*z^1 + ... + C5*z^5) | |
355 | * | |
356 | * The coefficient C's are obtained by a special Remez algorithm. | |
357 | * | |
358 | * Accuracy: | |
359 | * In the absence of rounding error, the approximation has absolute error | |
360 | * less than 2**(-64) for VAX D FORMAT, 2**(-58.3) for IEEE DOUBLE. | |
361 | * | |
362 | * | |
363 | * Constants: | |
364 | * The hexadecimal values are the intended ones for the following constants. | |
365 | * The decimal values may be used, provided that the compiler will convert | |
366 | * from decimal to binary accurately enough to produce the hexadecimal values | |
367 | * shown. | |
368 | * | |
369 | */ | |
370 | ||
859dc438 | 371 | #if defined(vax)||defined(tahoe) |
573b56c2 ZAL |
372 | /*C0 = 4.1666666666666504759E-2 , Hex 2^ -4 * .AAAAAAAAAAA9F0 */ |
373 | /*C1 = -1.3888888888865302059E-3 , Hex 2^ -9 * -.B60B60B60A0CCA */ | |
374 | /*C2 = 2.4801587285601038265E-5 , Hex 2^-15 * .D00D00CDCD098F */ | |
375 | /*C3 = -2.7557313470902390219E-7 , Hex 2^-21 * -.93F27BB593E805 */ | |
376 | /*C4 = 2.0875623401082232009E-9 , Hex 2^-28 * .8F74C8FA1E3FF0 */ | |
377 | /*C5 = -1.1355178117642986178E-11 ; Hex 2^-36 * -.C7C32D0A5C5A63 */ | |
f77d20bd | 378 | static long C0x[] = { _0x(aaaa,3e2a), _0x(a9f0,aaaa)}; |
573b56c2 | 379 | #define C0 (*(double*)C0x) |
f77d20bd | 380 | static long C1x[] = { _0x(0b60,bbb6), _0x(0cca,b60a)}; |
573b56c2 | 381 | #define C1 (*(double*)C1x) |
f77d20bd | 382 | static long C2x[] = { _0x(0d00,38d0), _0x(098f,cdcd)}; |
573b56c2 | 383 | #define C2 (*(double*)C2x) |
f77d20bd | 384 | static long C3x[] = { _0x(f27b,b593), _0x(e805,b593)}; |
573b56c2 | 385 | #define C3 (*(double*)C3x) |
f77d20bd | 386 | static long C4x[] = { _0x(74c8,320f), _0x(3ff0,fa1e)}; |
573b56c2 | 387 | #define C4 (*(double*)C4x) |
f77d20bd | 388 | static long C5x[] = { _0x(c32d,ae47), _0x(5a63,0a5c)}; |
573b56c2 | 389 | #define C5 (*(double*)C5x) |
859dc438 | 390 | #else /* defined(vax)||defined(tahoe) */ |
573b56c2 ZAL |
391 | static double |
392 | C0 = 4.1666666666666504759E-2 , /*Hex 2^ -5 * 1.555555555553E */ | |
393 | C1 = -1.3888888888865301516E-3 , /*Hex 2^-10 * -1.6C16C16C14199 */ | |
394 | C2 = 2.4801587269650015769E-5 , /*Hex 2^-16 * 1.A01A01971CAEB */ | |
395 | C3 = -2.7557304623183959811E-7 , /*Hex 2^-22 * -1.27E4F1314AD1A */ | |
396 | C4 = 2.0873958177697780076E-9 , /*Hex 2^-29 * 1.1EE3B60DDDC8C */ | |
397 | C5 = -1.1250289076471311557E-11 ; /*Hex 2^-37 * -1.8BD5986B2A52E */ | |
859dc438 | 398 | #endif /* defined(vax)||defined(tahoe) */ |
573b56c2 ZAL |
399 | |
400 | static double cos__C(z) | |
401 | double z; | |
402 | { | |
403 | return(z*z*(C0+z*(C1+z*(C2+z*(C3+z*(C4+z*C5)))))); | |
404 | } |