File: | src/lib/libm/src/e_j1.c |
Warning: | line 373, column 6 Array access (from variable 'p') results in an undefined pointer dereference |
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1 | /* @(#)e_j1.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 | ||||
13 | /* j1(x), y1(x) | |||
14 | * Bessel function of the first and second kinds of order zero. | |||
15 | * Method -- j1(x): | |||
16 | * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... | |||
17 | * 2. Reduce x to |x| since j1(x)=-j1(-x), and | |||
18 | * for x in (0,2) | |||
19 | * j1(x) = x/2 + x*z*R0/S0, where z = x*x; | |||
20 | * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) | |||
21 | * for x in (2,inf) | |||
22 | * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) | |||
23 | * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) | |||
24 | * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) | |||
25 | * as follow: | |||
26 | * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) | |||
27 | * = 1/sqrt(2) * (sin(x) - cos(x)) | |||
28 | * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) | |||
29 | * = -1/sqrt(2) * (sin(x) + cos(x)) | |||
30 | * (To avoid cancellation, use | |||
31 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) | |||
32 | * to compute the worse one.) | |||
33 | * | |||
34 | * 3 Special cases | |||
35 | * j1(nan)= nan | |||
36 | * j1(0) = 0 | |||
37 | * j1(inf) = 0 | |||
38 | * | |||
39 | * Method -- y1(x): | |||
40 | * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN | |||
41 | * 2. For x<2. | |||
42 | * Since | |||
43 | * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) | |||
44 | * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. | |||
45 | * We use the following function to approximate y1, | |||
46 | * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 | |||
47 | * where for x in [0,2] (abs err less than 2**-65.89) | |||
48 | * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 | |||
49 | * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 | |||
50 | * Note: For tiny x, 1/x dominate y1 and hence | |||
51 | * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) | |||
52 | * 3. For x>=2. | |||
53 | * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) | |||
54 | * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) | |||
55 | * by method mentioned above. | |||
56 | */ | |||
57 | ||||
58 | #include "math.h" | |||
59 | #include "math_private.h" | |||
60 | ||||
61 | static double pone(double), qone(double); | |||
62 | ||||
63 | static const double | |||
64 | huge = 1e300, | |||
65 | one = 1.0, | |||
66 | invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ | |||
67 | tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ | |||
68 | /* R0/S0 on [0,2] */ | |||
69 | r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ | |||
70 | r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ | |||
71 | r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ | |||
72 | r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ | |||
73 | s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ | |||
74 | s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ | |||
75 | s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ | |||
76 | s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ | |||
77 | s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ | |||
78 | ||||
79 | static const double zero = 0.0; | |||
80 | ||||
81 | double | |||
82 | j1(double x) | |||
83 | { | |||
84 | double z, s,c,ss,cc,r,u,v,y; | |||
85 | int32_t hx,ix; | |||
86 | ||||
87 | GET_HIGH_WORD(hx,x)do { ieee_double_shape_type gh_u; gh_u.value = (x); (hx) = gh_u .parts.msw; } while (0); | |||
88 | ix = hx&0x7fffffff; | |||
89 | if(ix>=0x7ff00000) return one/x; | |||
90 | y = fabs(x); | |||
91 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ | |||
92 | s = sin(y); | |||
93 | c = cos(y); | |||
94 | ss = -s-c; | |||
95 | cc = s-c; | |||
96 | if(ix<0x7fe00000) { /* make sure y+y not overflow */ | |||
97 | z = cos(y+y); | |||
98 | if ((s*c)>zero) cc = z/ss; | |||
99 | else ss = z/cc; | |||
100 | } | |||
101 | /* | |||
102 | * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) | |||
103 | * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) | |||
104 | */ | |||
105 | if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y); | |||
106 | else { | |||
107 | u = pone(y); v = qone(y); | |||
108 | z = invsqrtpi*(u*cc-v*ss)/sqrt(y); | |||
109 | } | |||
110 | if(hx<0) return -z; | |||
111 | else return z; | |||
112 | } | |||
113 | if(ix<0x3e400000) { /* |x|<2**-27 */ | |||
114 | if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ | |||
115 | } | |||
116 | z = x*x; | |||
117 | r = z*(r00+z*(r01+z*(r02+z*r03))); | |||
118 | s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); | |||
119 | r *= x; | |||
120 | return(x*0.5+r/s); | |||
121 | } | |||
122 | DEF_NONSTD(j1)__asm__(".global " "j1" " ; " "j1" " = " "_libm_j1"); | |||
123 | ||||
124 | static const double U0[5] = { | |||
125 | -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ | |||
126 | 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ | |||
127 | -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ | |||
128 | 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ | |||
129 | -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ | |||
130 | }; | |||
131 | static const double V0[5] = { | |||
132 | 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ | |||
133 | 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ | |||
134 | 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ | |||
135 | 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ | |||
136 | 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ | |||
137 | }; | |||
138 | ||||
139 | double | |||
140 | y1(double x) | |||
141 | { | |||
142 | double z, s,c,ss,cc,u,v; | |||
143 | int32_t hx,ix,lx; | |||
144 | ||||
145 | EXTRACT_WORDS(hx,lx,x)do { ieee_double_shape_type ew_u; ew_u.value = (x); (hx) = ew_u .parts.msw; (lx) = ew_u.parts.lsw; } while (0); | |||
| ||||
146 | ix = 0x7fffffff&hx; | |||
147 | /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ | |||
148 | if(ix>=0x7ff00000) return one/(x+x*x); | |||
149 | if((ix|lx)==0) return -one/zero; | |||
150 | if(hx<0) return zero/zero; | |||
151 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ | |||
152 | s = sin(x); | |||
153 | c = cos(x); | |||
154 | ss = -s-c; | |||
155 | cc = s-c; | |||
156 | if(ix<0x7fe00000) { /* make sure x+x not overflow */ | |||
157 | z = cos(x+x); | |||
158 | if ((s*c)>zero) cc = z/ss; | |||
159 | else ss = z/cc; | |||
160 | } | |||
161 | /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) | |||
162 | * where x0 = x-3pi/4 | |||
163 | * Better formula: | |||
164 | * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) | |||
165 | * = 1/sqrt(2) * (sin(x) - cos(x)) | |||
166 | * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) | |||
167 | * = -1/sqrt(2) * (cos(x) + sin(x)) | |||
168 | * To avoid cancellation, use | |||
169 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) | |||
170 | * to compute the worse one. | |||
171 | */ | |||
172 | if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); | |||
173 | else { | |||
174 | u = pone(x); v = qone(x); | |||
175 | z = invsqrtpi*(u*ss+v*cc)/sqrt(x); | |||
176 | } | |||
177 | return z; | |||
178 | } | |||
179 | if(ix<=0x3c900000) { /* x < 2**-54 */ | |||
180 | return(-tpi/x); | |||
181 | } | |||
182 | z = x*x; | |||
183 | u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); | |||
184 | v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); | |||
185 | return(x*(u/v) + tpi*(j1(x)*log(x)-one/x)); | |||
186 | } | |||
187 | DEF_NONSTD(y1)__asm__(".global " "y1" " ; " "y1" " = " "_libm_y1"); | |||
188 | ||||
189 | /* For x >= 8, the asymptotic expansions of pone is | |||
190 | * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. | |||
191 | * We approximate pone by | |||
192 | * pone(x) = 1 + (R/S) | |||
193 | * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 | |||
194 | * S = 1 + ps0*s^2 + ... + ps4*s^10 | |||
195 | * and | |||
196 | * | pone(x)-1-R/S | <= 2 ** ( -60.06) | |||
197 | */ | |||
198 | ||||
199 | static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ | |||
200 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ | |||
201 | 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ | |||
202 | 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ | |||
203 | 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ | |||
204 | 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ | |||
205 | 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ | |||
206 | }; | |||
207 | static const double ps8[5] = { | |||
208 | 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ | |||
209 | 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ | |||
210 | 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ | |||
211 | 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ | |||
212 | 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ | |||
213 | }; | |||
214 | ||||
215 | static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ | |||
216 | 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ | |||
217 | 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ | |||
218 | 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ | |||
219 | 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ | |||
220 | 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ | |||
221 | 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ | |||
222 | }; | |||
223 | static const double ps5[5] = { | |||
224 | 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ | |||
225 | 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ | |||
226 | 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ | |||
227 | 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ | |||
228 | 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ | |||
229 | }; | |||
230 | ||||
231 | static const double pr3[6] = { | |||
232 | 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ | |||
233 | 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ | |||
234 | 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ | |||
235 | 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ | |||
236 | 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ | |||
237 | 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ | |||
238 | }; | |||
239 | static const double ps3[5] = { | |||
240 | 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ | |||
241 | 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ | |||
242 | 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ | |||
243 | 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ | |||
244 | 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ | |||
245 | }; | |||
246 | ||||
247 | static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ | |||
248 | 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ | |||
249 | 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ | |||
250 | 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ | |||
251 | 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ | |||
252 | 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ | |||
253 | 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ | |||
254 | }; | |||
255 | static const double ps2[5] = { | |||
256 | 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ | |||
257 | 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ | |||
258 | 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ | |||
259 | 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ | |||
260 | 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ | |||
261 | }; | |||
262 | ||||
263 | static double | |||
264 | pone(double x) | |||
265 | { | |||
266 | const double *p,*q; | |||
267 | double z,r,s; | |||
268 | int32_t ix; | |||
269 | GET_HIGH_WORD(ix,x)do { ieee_double_shape_type gh_u; gh_u.value = (x); (ix) = gh_u .parts.msw; } while (0); | |||
270 | ix &= 0x7fffffff; | |||
271 | if(ix>=0x40200000) {p = pr8; q= ps8;} | |||
272 | else if(ix>=0x40122E8B){p = pr5; q= ps5;} | |||
273 | else if(ix>=0x4006DB6D){p = pr3; q= ps3;} | |||
274 | else if(ix>=0x40000000){p = pr2; q= ps2;} | |||
275 | z = one/(x*x); | |||
276 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); | |||
277 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); | |||
278 | return one+ r/s; | |||
279 | } | |||
280 | ||||
281 | ||||
282 | /* For x >= 8, the asymptotic expansions of qone is | |||
283 | * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. | |||
284 | * We approximate pone by | |||
285 | * qone(x) = s*(0.375 + (R/S)) | |||
286 | * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 | |||
287 | * S = 1 + qs1*s^2 + ... + qs6*s^12 | |||
288 | * and | |||
289 | * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) | |||
290 | */ | |||
291 | ||||
292 | static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ | |||
293 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ | |||
294 | -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ | |||
295 | -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ | |||
296 | -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ | |||
297 | -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ | |||
298 | -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ | |||
299 | }; | |||
300 | static const double qs8[6] = { | |||
301 | 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ | |||
302 | 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ | |||
303 | 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ | |||
304 | 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ | |||
305 | 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ | |||
306 | -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ | |||
307 | }; | |||
308 | ||||
309 | static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ | |||
310 | -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ | |||
311 | -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ | |||
312 | -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ | |||
313 | -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ | |||
314 | -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ | |||
315 | -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ | |||
316 | }; | |||
317 | static const double qs5[6] = { | |||
318 | 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ | |||
319 | 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ | |||
320 | 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ | |||
321 | 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ | |||
322 | 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ | |||
323 | -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ | |||
324 | }; | |||
325 | ||||
326 | static const double qr3[6] = { | |||
327 | -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ | |||
328 | -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ | |||
329 | -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ | |||
330 | -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ | |||
331 | -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ | |||
332 | -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ | |||
333 | }; | |||
334 | static const double qs3[6] = { | |||
335 | 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ | |||
336 | 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ | |||
337 | 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ | |||
338 | 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ | |||
339 | 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ | |||
340 | -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ | |||
341 | }; | |||
342 | ||||
343 | static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ | |||
344 | -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ | |||
345 | -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ | |||
346 | -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ | |||
347 | -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ | |||
348 | -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ | |||
349 | -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ | |||
350 | }; | |||
351 | static const double qs2[6] = { | |||
352 | 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ | |||
353 | 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ | |||
354 | 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ | |||
355 | 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ | |||
356 | 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ | |||
357 | -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ | |||
358 | }; | |||
359 | ||||
360 | static double | |||
361 | qone(double x) | |||
362 | { | |||
363 | const double *p,*q; | |||
364 | double s,r,z; | |||
365 | int32_t ix; | |||
366 | GET_HIGH_WORD(ix,x)do { ieee_double_shape_type gh_u; gh_u.value = (x); (ix) = gh_u .parts.msw; } while (0); | |||
367 | ix &= 0x7fffffff; | |||
368 | if(ix>=0x40200000) {p = qr8; q= qs8;} | |||
369 | else if(ix>=0x40122E8B){p = qr5; q= qs5;} | |||
370 | else if(ix>=0x4006DB6D){p = qr3; q= qs3;} | |||
371 | else if(ix>=0x40000000){p = qr2; q= qs2;} | |||
372 | z = one/(x*x); | |||
373 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); | |||
| ||||
374 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); | |||
375 | return (.375 + r/s)/x; | |||
376 | } |