1 | /* @(#)e_j0.c 5.1 93/09/24 */ |
2 | /* |
3 | * ==================================================== |
4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
5 | * |
6 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
7 | * Permission to use, copy, modify, and distribute this |
8 | * software is freely granted, provided that this notice |
9 | * is preserved. |
10 | * ==================================================== |
11 | */ |
12 | /* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/26, |
13 | for performance improvement on pipelined processors. |
14 | */ |
15 | |
16 | /* __ieee754_j0(x), __ieee754_y0(x) |
17 | * Bessel function of the first and second kinds of order zero. |
18 | * Method -- j0(x): |
19 | * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... |
20 | * 2. Reduce x to |x| since j0(x)=j0(-x), and |
21 | * for x in (0,2) |
22 | * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; |
23 | * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) |
24 | * for x in (2,inf) |
25 | * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) |
26 | * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) |
27 | * as follow: |
28 | * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) |
29 | * = 1/sqrt(2) * (cos(x) + sin(x)) |
30 | * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) |
31 | * = 1/sqrt(2) * (sin(x) - cos(x)) |
32 | * (To avoid cancellation, use |
33 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
34 | * to compute the worse one.) |
35 | * |
36 | * 3 Special cases |
37 | * j0(nan)= nan |
38 | * j0(0) = 1 |
39 | * j0(inf) = 0 |
40 | * |
41 | * Method -- y0(x): |
42 | * 1. For x<2. |
43 | * Since |
44 | * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) |
45 | * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. |
46 | * We use the following function to approximate y0, |
47 | * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 |
48 | * where |
49 | * U(z) = u00 + u01*z + ... + u06*z^6 |
50 | * V(z) = 1 + v01*z + ... + v04*z^4 |
51 | * with absolute approximation error bounded by 2**-72. |
52 | * Note: For tiny x, U/V = u0 and j0(x)~1, hence |
53 | * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) |
54 | * 2. For x>=2. |
55 | * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) |
56 | * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) |
57 | * by the method mentioned above. |
58 | * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. |
59 | */ |
60 | |
61 | #include <math.h> |
62 | #include <math_private.h> |
63 | |
64 | static double pzero (double), qzero (double); |
65 | |
66 | static const double |
67 | huge = 1e300, |
68 | one = 1.0, |
69 | invsqrtpi = 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ |
70 | tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
71 | /* R0/S0 on [0, 2.00] */ |
72 | R[] = { 0.0, 0.0, 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ |
73 | -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ |
74 | 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ |
75 | -4.61832688532103189199e-09 }, /* 0xBE33D5E7, 0x73D63FCE */ |
76 | S[] = { 0.0, 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ |
77 | 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ |
78 | 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ |
79 | 1.16614003333790000205e-09 }; /* 0x3E1408BC, 0xF4745D8F */ |
80 | |
81 | static const double zero = 0.0; |
82 | |
83 | double |
84 | __ieee754_j0 (double x) |
85 | { |
86 | double z, s, c, ss, cc, r, u, v, r1, r2, s1, s2, z2, z4; |
87 | int32_t hx, ix; |
88 | |
89 | GET_HIGH_WORD (hx, x); |
90 | ix = hx & 0x7fffffff; |
91 | if (ix >= 0x7ff00000) |
92 | return one / (x * x); |
93 | x = fabs (x); |
94 | if (ix >= 0x40000000) /* |x| >= 2.0 */ |
95 | { |
96 | __sincos (x, &s, &c); |
97 | ss = s - c; |
98 | cc = s + c; |
99 | if (ix < 0x7fe00000) /* make sure x+x not overflow */ |
100 | { |
101 | z = -__cos (x + x); |
102 | if ((s * c) < zero) |
103 | cc = z / ss; |
104 | else |
105 | ss = z / cc; |
106 | } |
107 | /* |
108 | * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) |
109 | * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) |
110 | */ |
111 | if (ix > 0x48000000) |
112 | z = (invsqrtpi * cc) / __ieee754_sqrt (x); |
113 | else |
114 | { |
115 | u = pzero (x); v = qzero (x); |
116 | z = invsqrtpi * (u * cc - v * ss) / __ieee754_sqrt (x); |
117 | } |
118 | return z; |
119 | } |
120 | if (ix < 0x3f200000) /* |x| < 2**-13 */ |
121 | { |
122 | math_force_eval (huge + x); /* raise inexact if x != 0 */ |
123 | if (ix < 0x3e400000) |
124 | return one; /* |x|<2**-27 */ |
125 | else |
126 | return one - 0.25 * x * x; |
127 | } |
128 | z = x * x; |
129 | r1 = z * R[2]; z2 = z * z; |
130 | r2 = R[3] + z * R[4]; z4 = z2 * z2; |
131 | r = r1 + z2 * r2 + z4 * R[5]; |
132 | s1 = one + z * S[1]; |
133 | s2 = S[2] + z * S[3]; |
134 | s = s1 + z2 * s2 + z4 * S[4]; |
135 | if (ix < 0x3FF00000) /* |x| < 1.00 */ |
136 | { |
137 | return one + z * (-0.25 + (r / s)); |
138 | } |
139 | else |
140 | { |
141 | u = 0.5 * x; |
142 | return ((one + u) * (one - u) + z * (r / s)); |
143 | } |
144 | } |
145 | strong_alias (__ieee754_j0, __j0_finite) |
146 | |
147 | static const double |
148 | U[] = { -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ |
149 | 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ |
150 | -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ |
151 | 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ |
152 | -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ |
153 | 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ |
154 | -3.98205194132103398453e-11 }, /* 0xBDC5E43D, 0x693FB3C8 */ |
155 | V[] = { 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ |
156 | 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ |
157 | 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ |
158 | 4.41110311332675467403e-10 }; /* 0x3DFE5018, 0x3BD6D9EF */ |
159 | |
160 | double |
161 | __ieee754_y0 (double x) |
162 | { |
163 | double z, s, c, ss, cc, u, v, z2, z4, z6, u1, u2, u3, v1, v2; |
164 | int32_t hx, ix, lx; |
165 | |
166 | EXTRACT_WORDS (hx, lx, x); |
167 | ix = 0x7fffffff & hx; |
168 | /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0, y0(0) is -inf. */ |
169 | if (ix >= 0x7ff00000) |
170 | return one / (x + x * x); |
171 | if ((ix | lx) == 0) |
172 | return -1 / zero; /* -inf and divide by zero exception. */ |
173 | if (hx < 0) |
174 | return zero / (zero * x); |
175 | if (ix >= 0x40000000) /* |x| >= 2.0 */ |
176 | { /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) |
177 | * where x0 = x-pi/4 |
178 | * Better formula: |
179 | * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) |
180 | * = 1/sqrt(2) * (sin(x) + cos(x)) |
181 | * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) |
182 | * = 1/sqrt(2) * (sin(x) - cos(x)) |
183 | * To avoid cancellation, use |
184 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
185 | * to compute the worse one. |
186 | */ |
187 | __sincos (x, &s, &c); |
188 | ss = s - c; |
189 | cc = s + c; |
190 | /* |
191 | * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) |
192 | * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) |
193 | */ |
194 | if (ix < 0x7fe00000) /* make sure x+x not overflow */ |
195 | { |
196 | z = -__cos (x + x); |
197 | if ((s * c) < zero) |
198 | cc = z / ss; |
199 | else |
200 | ss = z / cc; |
201 | } |
202 | if (ix > 0x48000000) |
203 | z = (invsqrtpi * ss) / __ieee754_sqrt (x); |
204 | else |
205 | { |
206 | u = pzero (x); v = qzero (x); |
207 | z = invsqrtpi * (u * ss + v * cc) / __ieee754_sqrt (x); |
208 | } |
209 | return z; |
210 | } |
211 | if (ix <= 0x3e400000) /* x < 2**-27 */ |
212 | { |
213 | return (U[0] + tpi * __ieee754_log (x)); |
214 | } |
215 | z = x * x; |
216 | u1 = U[0] + z * U[1]; z2 = z * z; |
217 | u2 = U[2] + z * U[3]; z4 = z2 * z2; |
218 | u3 = U[4] + z * U[5]; z6 = z4 * z2; |
219 | u = u1 + z2 * u2 + z4 * u3 + z6 * U[6]; |
220 | v1 = one + z * V[0]; |
221 | v2 = V[1] + z * V[2]; |
222 | v = v1 + z2 * v2 + z4 * V[3]; |
223 | return (u / v + tpi * (__ieee754_j0 (x) * __ieee754_log (x))); |
224 | } |
225 | strong_alias (__ieee754_y0, __y0_finite) |
226 | |
227 | /* The asymptotic expansions of pzero is |
228 | * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. |
229 | * For x >= 2, We approximate pzero by |
230 | * pzero(x) = 1 + (R/S) |
231 | * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 |
232 | * S = 1 + pS0*s^2 + ... + pS4*s^10 |
233 | * and |
234 | * | pzero(x)-1-R/S | <= 2 ** ( -60.26) |
235 | */ |
236 | static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
237 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
238 | -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ |
239 | -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ |
240 | -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ |
241 | -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ |
242 | -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ |
243 | }; |
244 | static const double pS8[5] = { |
245 | 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ |
246 | 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ |
247 | 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ |
248 | 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ |
249 | 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ |
250 | }; |
251 | |
252 | static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
253 | -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ |
254 | -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ |
255 | -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ |
256 | -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ |
257 | -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ |
258 | -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ |
259 | }; |
260 | static const double pS5[5] = { |
261 | 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ |
262 | 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ |
263 | 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ |
264 | 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ |
265 | 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ |
266 | }; |
267 | |
268 | static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
269 | -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ |
270 | -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ |
271 | -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ |
272 | -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ |
273 | -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ |
274 | -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ |
275 | }; |
276 | static const double pS3[5] = { |
277 | 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ |
278 | 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ |
279 | 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ |
280 | 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ |
281 | 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ |
282 | }; |
283 | |
284 | static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
285 | -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ |
286 | -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ |
287 | -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ |
288 | -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ |
289 | -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ |
290 | -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ |
291 | }; |
292 | static const double pS2[5] = { |
293 | 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ |
294 | 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ |
295 | 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ |
296 | 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ |
297 | 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ |
298 | }; |
299 | |
300 | static double |
301 | pzero (double x) |
302 | { |
303 | const double *p, *q; |
304 | double z, r, s, z2, z4, r1, r2, r3, s1, s2, s3; |
305 | int32_t ix; |
306 | GET_HIGH_WORD (ix, x); |
307 | ix &= 0x7fffffff; |
308 | /* ix >= 0x40000000 for all calls to this function. */ |
309 | if (ix >= 0x41b00000) |
310 | { |
311 | return one; |
312 | } |
313 | else if (ix >= 0x40200000) |
314 | { |
315 | p = pR8; q = pS8; |
316 | } |
317 | else if (ix >= 0x40122E8B) |
318 | { |
319 | p = pR5; q = pS5; |
320 | } |
321 | else if (ix >= 0x4006DB6D) |
322 | { |
323 | p = pR3; q = pS3; |
324 | } |
325 | else |
326 | { |
327 | p = pR2; q = pS2; |
328 | } |
329 | z = one / (x * x); |
330 | r1 = p[0] + z * p[1]; z2 = z * z; |
331 | r2 = p[2] + z * p[3]; z4 = z2 * z2; |
332 | r3 = p[4] + z * p[5]; |
333 | r = r1 + z2 * r2 + z4 * r3; |
334 | s1 = one + z * q[0]; |
335 | s2 = q[1] + z * q[2]; |
336 | s3 = q[3] + z * q[4]; |
337 | s = s1 + z2 * s2 + z4 * s3; |
338 | return one + r / s; |
339 | } |
340 | |
341 | |
342 | /* For x >= 8, the asymptotic expansions of qzero is |
343 | * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. |
344 | * We approximate pzero by |
345 | * qzero(x) = s*(-1.25 + (R/S)) |
346 | * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 |
347 | * S = 1 + qS0*s^2 + ... + qS5*s^12 |
348 | * and |
349 | * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) |
350 | */ |
351 | static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
352 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
353 | 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ |
354 | 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ |
355 | 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ |
356 | 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ |
357 | 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ |
358 | }; |
359 | static const double qS8[6] = { |
360 | 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ |
361 | 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ |
362 | 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ |
363 | 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ |
364 | 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ |
365 | -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ |
366 | }; |
367 | |
368 | static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
369 | 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ |
370 | 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ |
371 | 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ |
372 | 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ |
373 | 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ |
374 | 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ |
375 | }; |
376 | static const double qS5[6] = { |
377 | 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ |
378 | 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ |
379 | 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ |
380 | 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ |
381 | 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ |
382 | -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ |
383 | }; |
384 | |
385 | static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
386 | 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ |
387 | 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ |
388 | 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ |
389 | 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ |
390 | 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ |
391 | 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ |
392 | }; |
393 | static const double qS3[6] = { |
394 | 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ |
395 | 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ |
396 | 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ |
397 | 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ |
398 | 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ |
399 | -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ |
400 | }; |
401 | |
402 | static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
403 | 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ |
404 | 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ |
405 | 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ |
406 | 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ |
407 | 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ |
408 | 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ |
409 | }; |
410 | static const double qS2[6] = { |
411 | 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ |
412 | 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ |
413 | 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ |
414 | 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ |
415 | 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ |
416 | -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ |
417 | }; |
418 | |
419 | static double |
420 | qzero (double x) |
421 | { |
422 | const double *p, *q; |
423 | double s, r, z, z2, z4, z6, r1, r2, r3, s1, s2, s3; |
424 | int32_t ix; |
425 | GET_HIGH_WORD (ix, x); |
426 | ix &= 0x7fffffff; |
427 | /* ix >= 0x40000000 for all calls to this function. */ |
428 | if (ix >= 0x41b00000) |
429 | { |
430 | return -.125 / x; |
431 | } |
432 | else if (ix >= 0x40200000) |
433 | { |
434 | p = qR8; q = qS8; |
435 | } |
436 | else if (ix >= 0x40122E8B) |
437 | { |
438 | p = qR5; q = qS5; |
439 | } |
440 | else if (ix >= 0x4006DB6D) |
441 | { |
442 | p = qR3; q = qS3; |
443 | } |
444 | else |
445 | { |
446 | p = qR2; q = qS2; |
447 | } |
448 | z = one / (x * x); |
449 | r1 = p[0] + z * p[1]; z2 = z * z; |
450 | r2 = p[2] + z * p[3]; z4 = z2 * z2; |
451 | r3 = p[4] + z * p[5]; z6 = z4 * z2; |
452 | r = r1 + z2 * r2 + z4 * r3; |
453 | s1 = one + z * q[0]; |
454 | s2 = q[1] + z * q[2]; |
455 | s3 = q[3] + z * q[4]; |
456 | s = s1 + z2 * s2 + z4 * s3 + z6 * q[5]; |
457 | return (-.125 + r / s) / x; |
458 | } |
459 | |