1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_j0.c */ |
2 | /* |
3 | * ==================================================== |
4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
5 | * |
6 | * Developed at SunSoft, 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 | /* j0(x), y0(x) |
13 | * Bessel function of the first and second kinds of order zero. |
14 | * Method -- j0(x): |
15 | * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... |
16 | * 2. Reduce x to |x| since j0(x)=j0(-x), and |
17 | * for x in (0,2) |
18 | * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; |
19 | * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) |
20 | * for x in (2,inf) |
21 | * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) |
22 | * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) |
23 | * as follow: |
24 | * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) |
25 | * = 1/sqrt(2) * (cos(x) + sin(x)) |
26 | * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) |
27 | * = 1/sqrt(2) * (sin(x) - cos(x)) |
28 | * (To avoid cancellation, use |
29 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
30 | * to compute the worse one.) |
31 | * |
32 | * 3 Special cases |
33 | * j0(nan)= nan |
34 | * j0(0) = 1 |
35 | * j0(inf) = 0 |
36 | * |
37 | * Method -- y0(x): |
38 | * 1. For x<2. |
39 | * Since |
40 | * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) |
41 | * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. |
42 | * We use the following function to approximate y0, |
43 | * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 |
44 | * where |
45 | * U(z) = u00 + u01*z + ... + u06*z^6 |
46 | * V(z) = 1 + v01*z + ... + v04*z^4 |
47 | * with absolute approximation error bounded by 2**-72. |
48 | * Note: For tiny x, U/V = u0 and j0(x)~1, hence |
49 | * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) |
50 | * 2. For x>=2. |
51 | * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) |
52 | * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) |
53 | * by the method mentioned above. |
54 | * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. |
55 | */ |
56 | |
57 | use super::{cos, fabs, get_high_word, get_low_word, log, sin, sqrt}; |
58 | const INVSQRTPI: f64 = 5.64189583547756279280e-01; /* 0x3FE20DD7, 0x50429B6D */ |
59 | const TPI: f64 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */ |
60 | |
61 | /* common method when |x|>=2 */ |
62 | fn common(ix: u32, x: f64, y0: bool) -> f64 { |
63 | let s: f64; |
64 | let mut c: f64; |
65 | let mut ss: f64; |
66 | let mut cc: f64; |
67 | let z: f64; |
68 | |
69 | /* |
70 | * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x-pi/4)-q0(x)*sin(x-pi/4)) |
71 | * y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x-pi/4)+q0(x)*cos(x-pi/4)) |
72 | * |
73 | * sin(x-pi/4) = (sin(x) - cos(x))/sqrt(2) |
74 | * cos(x-pi/4) = (sin(x) + cos(x))/sqrt(2) |
75 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
76 | */ |
77 | s = sin(x); |
78 | c = cos(x); |
79 | if y0 { |
80 | c = -c; |
81 | } |
82 | cc = s + c; |
83 | /* avoid overflow in 2*x, big ulp error when x>=0x1p1023 */ |
84 | if ix < 0x7fe00000 { |
85 | ss = s - c; |
86 | z = -cos(2.0 * x); |
87 | if s * c < 0.0 { |
88 | cc = z / ss; |
89 | } else { |
90 | ss = z / cc; |
91 | } |
92 | if ix < 0x48000000 { |
93 | if y0 { |
94 | ss = -ss; |
95 | } |
96 | cc = pzero(x) * cc - qzero(x) * ss; |
97 | } |
98 | } |
99 | return INVSQRTPI * cc / sqrt(x); |
100 | } |
101 | |
102 | /* R0/S0 on [0, 2.00] */ |
103 | const R02: f64 = 1.56249999999999947958e-02; /* 0x3F8FFFFF, 0xFFFFFFFD */ |
104 | const R03: f64 = -1.89979294238854721751e-04; /* 0xBF28E6A5, 0xB61AC6E9 */ |
105 | const R04: f64 = 1.82954049532700665670e-06; /* 0x3EBEB1D1, 0x0C503919 */ |
106 | const R05: f64 = -4.61832688532103189199e-09; /* 0xBE33D5E7, 0x73D63FCE */ |
107 | const S01: f64 = 1.56191029464890010492e-02; /* 0x3F8FFCE8, 0x82C8C2A4 */ |
108 | const S02: f64 = 1.16926784663337450260e-04; /* 0x3F1EA6D2, 0xDD57DBF4 */ |
109 | const S03: f64 = 5.13546550207318111446e-07; /* 0x3EA13B54, 0xCE84D5A9 */ |
110 | const S04: f64 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ |
111 | |
112 | pub fn j0(mut x: f64) -> f64 { |
113 | let z: f64; |
114 | let r: f64; |
115 | let s: f64; |
116 | let mut ix: u32; |
117 | |
118 | ix = get_high_word(x); |
119 | ix &= 0x7fffffff; |
120 | |
121 | /* j0(+-inf)=0, j0(nan)=nan */ |
122 | if ix >= 0x7ff00000 { |
123 | return 1.0 / (x * x); |
124 | } |
125 | x = fabs(x); |
126 | |
127 | if ix >= 0x40000000 { |
128 | /* |x| >= 2 */ |
129 | /* large ulp error near zeros: 2.4, 5.52, 8.6537,.. */ |
130 | return common(ix, x, false); |
131 | } |
132 | |
133 | /* 1 - x*x/4 + x*x*R(x^2)/S(x^2) */ |
134 | if ix >= 0x3f200000 { |
135 | /* |x| >= 2**-13 */ |
136 | /* up to 4ulp error close to 2 */ |
137 | z = x * x; |
138 | r = z * (R02 + z * (R03 + z * (R04 + z * R05))); |
139 | s = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * S04))); |
140 | return (1.0 + x / 2.0) * (1.0 - x / 2.0) + z * (r / s); |
141 | } |
142 | |
143 | /* 1 - x*x/4 */ |
144 | /* prevent underflow */ |
145 | /* inexact should be raised when x!=0, this is not done correctly */ |
146 | if ix >= 0x38000000 { |
147 | /* |x| >= 2**-127 */ |
148 | x = 0.25 * x * x; |
149 | } |
150 | return 1.0 - x; |
151 | } |
152 | |
153 | const U00: f64 = -7.38042951086872317523e-02; /* 0xBFB2E4D6, 0x99CBD01F */ |
154 | const U01: f64 = 1.76666452509181115538e-01; /* 0x3FC69D01, 0x9DE9E3FC */ |
155 | const U02: f64 = -1.38185671945596898896e-02; /* 0xBF8C4CE8, 0xB16CFA97 */ |
156 | const U03: f64 = 3.47453432093683650238e-04; /* 0x3F36C54D, 0x20B29B6B */ |
157 | const U04: f64 = -3.81407053724364161125e-06; /* 0xBECFFEA7, 0x73D25CAD */ |
158 | const U05: f64 = 1.95590137035022920206e-08; /* 0x3E550057, 0x3B4EABD4 */ |
159 | const U06: f64 = -3.98205194132103398453e-11; /* 0xBDC5E43D, 0x693FB3C8 */ |
160 | const V01: f64 = 1.27304834834123699328e-02; /* 0x3F8A1270, 0x91C9C71A */ |
161 | const V02: f64 = 7.60068627350353253702e-05; /* 0x3F13ECBB, 0xF578C6C1 */ |
162 | const V03: f64 = 2.59150851840457805467e-07; /* 0x3E91642D, 0x7FF202FD */ |
163 | const V04: f64 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ |
164 | |
165 | pub fn y0(x: f64) -> f64 { |
166 | let z: f64; |
167 | let u: f64; |
168 | let v: f64; |
169 | let ix: u32; |
170 | let lx: u32; |
171 | |
172 | ix = get_high_word(x); |
173 | lx = get_low_word(x); |
174 | |
175 | /* y0(nan)=nan, y0(<0)=nan, y0(0)=-inf, y0(inf)=0 */ |
176 | if ((ix << 1) | lx) == 0 { |
177 | return -1.0 / 0.0; |
178 | } |
179 | if (ix >> 31) != 0 { |
180 | return 0.0 / 0.0; |
181 | } |
182 | if ix >= 0x7ff00000 { |
183 | return 1.0 / x; |
184 | } |
185 | |
186 | if ix >= 0x40000000 { |
187 | /* x >= 2 */ |
188 | /* large ulp errors near zeros: 3.958, 7.086,.. */ |
189 | return common(ix, x, true); |
190 | } |
191 | |
192 | /* U(x^2)/V(x^2) + (2/pi)*j0(x)*log(x) */ |
193 | if ix >= 0x3e400000 { |
194 | /* x >= 2**-27 */ |
195 | /* large ulp error near the first zero, x ~= 0.89 */ |
196 | z = x * x; |
197 | u = U00 + z * (U01 + z * (U02 + z * (U03 + z * (U04 + z * (U05 + z * U06))))); |
198 | v = 1.0 + z * (V01 + z * (V02 + z * (V03 + z * V04))); |
199 | return u / v + TPI * (j0(x) * log(x)); |
200 | } |
201 | return U00 + TPI * log(x); |
202 | } |
203 | |
204 | /* The asymptotic expansions of pzero is |
205 | * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. |
206 | * For x >= 2, We approximate pzero by |
207 | * pzero(x) = 1 + (R/S) |
208 | * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 |
209 | * S = 1 + pS0*s^2 + ... + pS4*s^10 |
210 | * and |
211 | * | pzero(x)-1-R/S | <= 2 ** ( -60.26) |
212 | */ |
213 | const PR8: [f64; 6] = [ |
214 | /* for x in [inf, 8]=1/[0,0.125] */ |
215 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
216 | -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ |
217 | -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ |
218 | -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ |
219 | -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ |
220 | -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ |
221 | ]; |
222 | const PS8: [f64; 5] = [ |
223 | 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ |
224 | 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ |
225 | 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ |
226 | 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ |
227 | 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ |
228 | ]; |
229 | |
230 | const PR5: [f64; 6] = [ |
231 | /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
232 | -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ |
233 | -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ |
234 | -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ |
235 | -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ |
236 | -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ |
237 | -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ |
238 | ]; |
239 | const PS5: [f64; 5] = [ |
240 | 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ |
241 | 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ |
242 | 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ |
243 | 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ |
244 | 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ |
245 | ]; |
246 | |
247 | const PR3: [f64; 6] = [ |
248 | /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
249 | -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ |
250 | -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ |
251 | -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ |
252 | -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ |
253 | -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ |
254 | -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ |
255 | ]; |
256 | const PS3: [f64; 5] = [ |
257 | 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ |
258 | 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ |
259 | 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ |
260 | 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ |
261 | 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ |
262 | ]; |
263 | |
264 | const PR2: [f64; 6] = [ |
265 | /* for x in [2.8570,2]=1/[0.3499,0.5] */ |
266 | -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ |
267 | -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ |
268 | -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ |
269 | -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ |
270 | -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ |
271 | -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ |
272 | ]; |
273 | const PS2: [f64; 5] = [ |
274 | 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ |
275 | 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ |
276 | 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ |
277 | 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ |
278 | 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ |
279 | ]; |
280 | |
281 | fn pzero(x: f64) -> f64 { |
282 | let p: &[f64; 6]; |
283 | let q: &[f64; 5]; |
284 | let z: f64; |
285 | let r: f64; |
286 | let s: f64; |
287 | let mut ix: u32; |
288 | |
289 | ix = get_high_word(x); |
290 | ix &= 0x7fffffff; |
291 | if ix >= 0x40200000 { |
292 | p = &PR8; |
293 | q = &PS8; |
294 | } else if ix >= 0x40122E8B { |
295 | p = &PR5; |
296 | q = &PS5; |
297 | } else if ix >= 0x4006DB6D { |
298 | p = &PR3; |
299 | q = &PS3; |
300 | } else |
301 | /*ix >= 0x40000000*/ |
302 | { |
303 | p = &PR2; |
304 | q = &PS2; |
305 | } |
306 | z = 1.0 / (x * x); |
307 | r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5])))); |
308 | s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4])))); |
309 | return 1.0 + r / s; |
310 | } |
311 | |
312 | /* For x >= 8, the asymptotic expansions of qzero is |
313 | * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. |
314 | * We approximate pzero by |
315 | * qzero(x) = s*(-1.25 + (R/S)) |
316 | * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 |
317 | * S = 1 + qS0*s^2 + ... + qS5*s^12 |
318 | * and |
319 | * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) |
320 | */ |
321 | const QR8: [f64; 6] = [ |
322 | /* for x in [inf, 8]=1/[0,0.125] */ |
323 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
324 | 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ |
325 | 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ |
326 | 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ |
327 | 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ |
328 | 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ |
329 | ]; |
330 | const QS8: [f64; 6] = [ |
331 | 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ |
332 | 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ |
333 | 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ |
334 | 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ |
335 | 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ |
336 | -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ |
337 | ]; |
338 | |
339 | const QR5: [f64; 6] = [ |
340 | /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
341 | 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ |
342 | 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ |
343 | 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ |
344 | 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ |
345 | 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ |
346 | 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ |
347 | ]; |
348 | const QS5: [f64; 6] = [ |
349 | 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ |
350 | 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ |
351 | 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ |
352 | 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ |
353 | 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ |
354 | -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ |
355 | ]; |
356 | |
357 | const QR3: [f64; 6] = [ |
358 | /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
359 | 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ |
360 | 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ |
361 | 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ |
362 | 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ |
363 | 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ |
364 | 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ |
365 | ]; |
366 | const QS3: [f64; 6] = [ |
367 | 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ |
368 | 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ |
369 | 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ |
370 | 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ |
371 | 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ |
372 | -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ |
373 | ]; |
374 | |
375 | const QR2: [f64; 6] = [ |
376 | /* for x in [2.8570,2]=1/[0.3499,0.5] */ |
377 | 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ |
378 | 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ |
379 | 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ |
380 | 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ |
381 | 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ |
382 | 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ |
383 | ]; |
384 | const QS2: [f64; 6] = [ |
385 | 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ |
386 | 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ |
387 | 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ |
388 | 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ |
389 | 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ |
390 | -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ |
391 | ]; |
392 | |
393 | fn qzero(x: f64) -> f64 { |
394 | let p: &[f64; 6]; |
395 | let q: &[f64; 6]; |
396 | let s: f64; |
397 | let r: f64; |
398 | let z: f64; |
399 | let mut ix: u32; |
400 | |
401 | ix = get_high_word(x); |
402 | ix &= 0x7fffffff; |
403 | if ix >= 0x40200000 { |
404 | p = &QR8; |
405 | q = &QS8; |
406 | } else if ix >= 0x40122E8B { |
407 | p = &QR5; |
408 | q = &QS5; |
409 | } else if ix >= 0x4006DB6D { |
410 | p = &QR3; |
411 | q = &QS3; |
412 | } else |
413 | /*ix >= 0x40000000*/ |
414 | { |
415 | p = &QR2; |
416 | q = &QS2; |
417 | } |
418 | z = 1.0 / (x * x); |
419 | r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5])))); |
420 | s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5]))))); |
421 | return (-0.125 + r / s) / x; |
422 | } |
423 | |