1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_j1.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 | /* j1(x), y1(x) |
13 | * Bessel function of the first and second kinds of order zero. |
14 | * Method -- j1(x): |
15 | * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... |
16 | * 2. Reduce x to |x| since j1(x)=-j1(-x), and |
17 | * for x in (0,2) |
18 | * j1(x) = x/2 + x*z*R0/S0, where z = x*x; |
19 | * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) |
20 | * for x in (2,inf) |
21 | * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) |
22 | * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) |
23 | * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) |
24 | * as follow: |
25 | * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) |
26 | * = 1/sqrt(2) * (sin(x) - cos(x)) |
27 | * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) |
28 | * = -1/sqrt(2) * (sin(x) + cos(x)) |
29 | * (To avoid cancellation, use |
30 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
31 | * to compute the worse one.) |
32 | * |
33 | * 3 Special cases |
34 | * j1(nan)= nan |
35 | * j1(0) = 0 |
36 | * j1(inf) = 0 |
37 | * |
38 | * Method -- y1(x): |
39 | * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN |
40 | * 2. For x<2. |
41 | * Since |
42 | * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) |
43 | * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. |
44 | * We use the following function to approximate y1, |
45 | * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 |
46 | * where for x in [0,2] (abs err less than 2**-65.89) |
47 | * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 |
48 | * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 |
49 | * Note: For tiny x, 1/x dominate y1 and hence |
50 | * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) |
51 | * 3. For x>=2. |
52 | * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) |
53 | * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) |
54 | * by method mentioned above. |
55 | */ |
56 | |
57 | use super::{cos, fabs, get_high_word, get_low_word, log, sin, sqrt}; |
58 | |
59 | const INVSQRTPI: f64 = 5.64189583547756279280e-01; /* 0x3FE20DD7, 0x50429B6D */ |
60 | const TPI: f64 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */ |
61 | |
62 | fn common(ix: u32, x: f64, y1: bool, sign: bool) -> f64 { |
63 | let z: f64; |
64 | let mut s: f64; |
65 | let c: f64; |
66 | let mut ss: f64; |
67 | let mut cc: f64; |
68 | |
69 | /* |
70 | * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x-3pi/4)-q1(x)*sin(x-3pi/4)) |
71 | * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x-3pi/4)+q1(x)*cos(x-3pi/4)) |
72 | * |
73 | * sin(x-3pi/4) = -(sin(x) + cos(x))/sqrt(2) |
74 | * cos(x-3pi/4) = (sin(x) - cos(x))/sqrt(2) |
75 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
76 | */ |
77 | s = sin(x); |
78 | if y1 { |
79 | s = -s; |
80 | } |
81 | c = cos(x); |
82 | cc = s - c; |
83 | if ix < 0x7fe00000 { |
84 | /* avoid overflow in 2*x */ |
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 y1 { |
94 | ss = -ss; |
95 | } |
96 | cc = pone(x) * cc - qone(x) * ss; |
97 | } |
98 | } |
99 | if sign { |
100 | cc = -cc; |
101 | } |
102 | return INVSQRTPI * cc / sqrt(x); |
103 | } |
104 | |
105 | /* R0/S0 on [0,2] */ |
106 | const R00: f64 = -6.25000000000000000000e-02; /* 0xBFB00000, 0x00000000 */ |
107 | const R01: f64 = 1.40705666955189706048e-03; /* 0x3F570D9F, 0x98472C61 */ |
108 | const R02: f64 = -1.59955631084035597520e-05; /* 0xBEF0C5C6, 0xBA169668 */ |
109 | const R03: f64 = 4.96727999609584448412e-08; /* 0x3E6AAAFA, 0x46CA0BD9 */ |
110 | const S01: f64 = 1.91537599538363460805e-02; /* 0x3F939D0B, 0x12637E53 */ |
111 | const S02: f64 = 1.85946785588630915560e-04; /* 0x3F285F56, 0xB9CDF664 */ |
112 | const S03: f64 = 1.17718464042623683263e-06; /* 0x3EB3BFF8, 0x333F8498 */ |
113 | const S04: f64 = 5.04636257076217042715e-09; /* 0x3E35AC88, 0xC97DFF2C */ |
114 | const S05: f64 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ |
115 | |
116 | pub fn j1(x: f64) -> f64 { |
117 | let mut z: f64; |
118 | let r: f64; |
119 | let s: f64; |
120 | let mut ix: u32; |
121 | let sign: bool; |
122 | |
123 | ix = get_high_word(x); |
124 | sign = (ix >> 31) != 0; |
125 | ix &= 0x7fffffff; |
126 | if ix >= 0x7ff00000 { |
127 | return 1.0 / (x * x); |
128 | } |
129 | if ix >= 0x40000000 { |
130 | /* |x| >= 2 */ |
131 | return common(ix, fabs(x), false, sign); |
132 | } |
133 | if ix >= 0x38000000 { |
134 | /* |x| >= 2**-127 */ |
135 | z = x * x; |
136 | r = z * (R00 + z * (R01 + z * (R02 + z * R03))); |
137 | s = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * (S04 + z * S05)))); |
138 | z = r / s; |
139 | } else { |
140 | /* avoid underflow, raise inexact if x!=0 */ |
141 | z = x; |
142 | } |
143 | return (0.5 + z) * x; |
144 | } |
145 | |
146 | const U0: [f64; 5] = [ |
147 | -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ |
148 | 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ |
149 | -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ |
150 | 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ |
151 | -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ |
152 | ]; |
153 | const V0: [f64; 5] = [ |
154 | 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ |
155 | 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ |
156 | 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ |
157 | 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ |
158 | 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ |
159 | ]; |
160 | |
161 | pub fn y1(x: f64) -> f64 { |
162 | let z: f64; |
163 | let u: f64; |
164 | let v: f64; |
165 | let ix: u32; |
166 | let lx: u32; |
167 | |
168 | ix = get_high_word(x); |
169 | lx = get_low_word(x); |
170 | |
171 | /* y1(nan)=nan, y1(<0)=nan, y1(0)=-inf, y1(inf)=0 */ |
172 | if (ix << 1 | lx) == 0 { |
173 | return -1.0 / 0.0; |
174 | } |
175 | if (ix >> 31) != 0 { |
176 | return 0.0 / 0.0; |
177 | } |
178 | if ix >= 0x7ff00000 { |
179 | return 1.0 / x; |
180 | } |
181 | |
182 | if ix >= 0x40000000 { |
183 | /* x >= 2 */ |
184 | return common(ix, x, true, false); |
185 | } |
186 | if ix < 0x3c900000 { |
187 | /* x < 2**-54 */ |
188 | return -TPI / x; |
189 | } |
190 | z = x * x; |
191 | u = U0[0] + z * (U0[1] + z * (U0[2] + z * (U0[3] + z * U0[4]))); |
192 | v = 1.0 + z * (V0[0] + z * (V0[1] + z * (V0[2] + z * (V0[3] + z * V0[4])))); |
193 | return x * (u / v) + TPI * (j1(x) * log(x) - 1.0 / x); |
194 | } |
195 | |
196 | /* For x >= 8, the asymptotic expansions of pone is |
197 | * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. |
198 | * We approximate pone by |
199 | * pone(x) = 1 + (R/S) |
200 | * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 |
201 | * S = 1 + ps0*s^2 + ... + ps4*s^10 |
202 | * and |
203 | * | pone(x)-1-R/S | <= 2 ** ( -60.06) |
204 | */ |
205 | |
206 | const PR8: [f64; 6] = [ |
207 | /* for x in [inf, 8]=1/[0,0.125] */ |
208 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
209 | 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ |
210 | 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ |
211 | 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ |
212 | 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ |
213 | 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ |
214 | ]; |
215 | const PS8: [f64; 5] = [ |
216 | 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ |
217 | 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ |
218 | 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ |
219 | 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ |
220 | 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ |
221 | ]; |
222 | |
223 | const PR5: [f64; 6] = [ |
224 | /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
225 | 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ |
226 | 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ |
227 | 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ |
228 | 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ |
229 | 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ |
230 | 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ |
231 | ]; |
232 | const PS5: [f64; 5] = [ |
233 | 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ |
234 | 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ |
235 | 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ |
236 | 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ |
237 | 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ |
238 | ]; |
239 | |
240 | const PR3: [f64; 6] = [ |
241 | 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ |
242 | 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ |
243 | 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ |
244 | 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ |
245 | 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ |
246 | 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ |
247 | ]; |
248 | const PS3: [f64; 5] = [ |
249 | 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ |
250 | 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ |
251 | 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ |
252 | 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ |
253 | 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ |
254 | ]; |
255 | |
256 | const PR2: [f64; 6] = [ |
257 | /* for x in [2.8570,2]=1/[0.3499,0.5] */ |
258 | 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ |
259 | 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ |
260 | 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ |
261 | 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ |
262 | 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ |
263 | 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ |
264 | ]; |
265 | const PS2: [f64; 5] = [ |
266 | 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ |
267 | 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ |
268 | 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ |
269 | 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ |
270 | 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ |
271 | ]; |
272 | |
273 | fn pone(x: f64) -> f64 { |
274 | let p: &[f64; 6]; |
275 | let q: &[f64; 5]; |
276 | let z: f64; |
277 | let r: f64; |
278 | let s: f64; |
279 | let mut ix: u32; |
280 | |
281 | ix = get_high_word(x); |
282 | ix &= 0x7fffffff; |
283 | if ix >= 0x40200000 { |
284 | p = &PR8; |
285 | q = &PS8; |
286 | } else if ix >= 0x40122E8B { |
287 | p = &PR5; |
288 | q = &PS5; |
289 | } else if ix >= 0x4006DB6D { |
290 | p = &PR3; |
291 | q = &PS3; |
292 | } else |
293 | /*ix >= 0x40000000*/ |
294 | { |
295 | p = &PR2; |
296 | q = &PS2; |
297 | } |
298 | z = 1.0 / (x * x); |
299 | r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5])))); |
300 | s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4])))); |
301 | return 1.0 + r / s; |
302 | } |
303 | |
304 | /* For x >= 8, the asymptotic expansions of qone is |
305 | * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. |
306 | * We approximate pone by |
307 | * qone(x) = s*(0.375 + (R/S)) |
308 | * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 |
309 | * S = 1 + qs1*s^2 + ... + qs6*s^12 |
310 | * and |
311 | * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) |
312 | */ |
313 | |
314 | const QR8: [f64; 6] = [ |
315 | /* for x in [inf, 8]=1/[0,0.125] */ |
316 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
317 | -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ |
318 | -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ |
319 | -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ |
320 | -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ |
321 | -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ |
322 | ]; |
323 | const QS8: [f64; 6] = [ |
324 | 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ |
325 | 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ |
326 | 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ |
327 | 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ |
328 | 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ |
329 | -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ |
330 | ]; |
331 | |
332 | const QR5: [f64; 6] = [ |
333 | /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
334 | -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ |
335 | -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ |
336 | -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ |
337 | -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ |
338 | -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ |
339 | -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ |
340 | ]; |
341 | const QS5: [f64; 6] = [ |
342 | 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ |
343 | 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ |
344 | 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ |
345 | 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ |
346 | 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ |
347 | -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ |
348 | ]; |
349 | |
350 | const QR3: [f64; 6] = [ |
351 | -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ |
352 | -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ |
353 | -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ |
354 | -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ |
355 | -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ |
356 | -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ |
357 | ]; |
358 | const QS3: [f64; 6] = [ |
359 | 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ |
360 | 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ |
361 | 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ |
362 | 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ |
363 | 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ |
364 | -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ |
365 | ]; |
366 | |
367 | const QR2: [f64; 6] = [ |
368 | /* for x in [2.8570,2]=1/[0.3499,0.5] */ |
369 | -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ |
370 | -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ |
371 | -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ |
372 | -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ |
373 | -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ |
374 | -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ |
375 | ]; |
376 | const QS2: [f64; 6] = [ |
377 | 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ |
378 | 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ |
379 | 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ |
380 | 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ |
381 | 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ |
382 | -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ |
383 | ]; |
384 | |
385 | fn qone(x: f64) -> f64 { |
386 | let p: &[f64; 6]; |
387 | let q: &[f64; 6]; |
388 | let s: f64; |
389 | let r: f64; |
390 | let z: f64; |
391 | let mut ix: u32; |
392 | |
393 | ix = get_high_word(x); |
394 | ix &= 0x7fffffff; |
395 | if ix >= 0x40200000 { |
396 | p = &QR8; |
397 | q = &QS8; |
398 | } else if ix >= 0x40122E8B { |
399 | p = &QR5; |
400 | q = &QS5; |
401 | } else if ix >= 0x4006DB6D { |
402 | p = &QR3; |
403 | q = &QS3; |
404 | } else |
405 | /*ix >= 0x40000000*/ |
406 | { |
407 | p = &QR2; |
408 | q = &QS2; |
409 | } |
410 | z = 1.0 / (x * x); |
411 | r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5])))); |
412 | s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5]))))); |
413 | return (0.375 + r / s) / x; |
414 | } |
415 | |