File: | src/lib/libm/src/e_j0.c |
Warning: | line 282, column 6 Array access (from variable 'p') results in an undefined pointer dereference |
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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 | ||||
13 | /* j0(x), y0(x) | |||
14 | * Bessel function of the first and second kinds of order zero. | |||
15 | * Method -- j0(x): | |||
16 | * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... | |||
17 | * 2. Reduce x to |x| since j0(x)=j0(-x), and | |||
18 | * for x in (0,2) | |||
19 | * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; | |||
20 | * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) | |||
21 | * for x in (2,inf) | |||
22 | * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) | |||
23 | * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) | |||
24 | * as follow: | |||
25 | * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) | |||
26 | * = 1/sqrt(2) * (cos(x) + sin(x)) | |||
27 | * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/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 | * j0(nan)= nan | |||
35 | * j0(0) = 1 | |||
36 | * j0(inf) = 0 | |||
37 | * | |||
38 | * Method -- y0(x): | |||
39 | * 1. For x<2. | |||
40 | * Since | |||
41 | * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) | |||
42 | * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. | |||
43 | * We use the following function to approximate y0, | |||
44 | * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 | |||
45 | * where | |||
46 | * U(z) = u00 + u01*z + ... + u06*z^6 | |||
47 | * V(z) = 1 + v01*z + ... + v04*z^4 | |||
48 | * with absolute approximation error bounded by 2**-72. | |||
49 | * Note: For tiny x, U/V = u0 and j0(x)~1, hence | |||
50 | * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) | |||
51 | * 2. For x>=2. | |||
52 | * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) | |||
53 | * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) | |||
54 | * by the method mentioned above. | |||
55 | * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. | |||
56 | */ | |||
57 | ||||
58 | #include "math.h" | |||
59 | #include "math_private.h" | |||
60 | ||||
61 | static double pzero(double), qzero(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, 2.00] */ | |||
69 | R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ | |||
70 | R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ | |||
71 | R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ | |||
72 | R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ | |||
73 | S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ | |||
74 | S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ | |||
75 | S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ | |||
76 | S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ | |||
77 | ||||
78 | static const double zero = 0.0; | |||
79 | ||||
80 | double | |||
81 | j0(double x) | |||
82 | { | |||
83 | double z, s,c,ss,cc,r,u,v; | |||
84 | int32_t hx,ix; | |||
85 | ||||
86 | GET_HIGH_WORD(hx,x)do { ieee_double_shape_type gh_u; gh_u.value = (x); (hx) = gh_u .parts.msw; } while (0); | |||
87 | ix = hx&0x7fffffff; | |||
88 | if(ix>=0x7ff00000) return one/(x*x); | |||
89 | x = fabs(x); | |||
90 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ | |||
91 | s = sin(x); | |||
92 | c = cos(x); | |||
93 | ss = s-c; | |||
94 | cc = s+c; | |||
95 | if(ix<0x7fe00000) { /* make sure x+x not overflow */ | |||
96 | z = -cos(x+x); | |||
97 | if ((s*c)<zero) cc = z/ss; | |||
98 | else ss = z/cc; | |||
99 | } | |||
100 | /* | |||
101 | * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) | |||
102 | * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) | |||
103 | */ | |||
104 | if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(x); | |||
105 | else { | |||
106 | u = pzero(x); v = qzero(x); | |||
107 | z = invsqrtpi*(u*cc-v*ss)/sqrt(x); | |||
108 | } | |||
109 | return z; | |||
110 | } | |||
111 | if(ix<0x3f200000) { /* |x| < 2**-13 */ | |||
112 | if(huge+x>one) { /* raise inexact if x != 0 */ | |||
113 | if(ix<0x3e400000) return one; /* |x|<2**-27 */ | |||
114 | else return one - 0.25*x*x; | |||
115 | } | |||
116 | } | |||
117 | z = x*x; | |||
118 | r = z*(R02+z*(R03+z*(R04+z*R05))); | |||
119 | s = one+z*(S01+z*(S02+z*(S03+z*S04))); | |||
120 | if(ix < 0x3FF00000) { /* |x| < 1.00 */ | |||
121 | return one + z*(-0.25+(r/s)); | |||
122 | } else { | |||
123 | u = 0.5*x; | |||
124 | return((one+u)*(one-u)+z*(r/s)); | |||
125 | } | |||
126 | } | |||
127 | DEF_NONSTD(j0)__asm__(".weak " "j0" " ; " "j0" " = " "_libm_j0"); | |||
128 | ||||
129 | static const double | |||
130 | u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ | |||
131 | u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ | |||
132 | u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ | |||
133 | u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ | |||
134 | u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ | |||
135 | u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ | |||
136 | u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ | |||
137 | v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ | |||
138 | v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ | |||
139 | v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ | |||
140 | v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ | |||
141 | ||||
142 | double | |||
143 | y0(double x) | |||
144 | { | |||
145 | double z, s,c,ss,cc,u,v; | |||
146 | int32_t hx,ix,lx; | |||
147 | ||||
148 | 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); | |||
| ||||
149 | ix = 0x7fffffff&hx; | |||
150 | /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ | |||
151 | if(ix>=0x7ff00000) return one/(x+x*x); | |||
152 | if((ix|lx)==0) return -one/zero; | |||
153 | if(hx<0) return zero/zero; | |||
154 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ | |||
155 | /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) | |||
156 | * where x0 = x-pi/4 | |||
157 | * Better formula: | |||
158 | * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) | |||
159 | * = 1/sqrt(2) * (sin(x) + cos(x)) | |||
160 | * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) | |||
161 | * = 1/sqrt(2) * (sin(x) - cos(x)) | |||
162 | * To avoid cancellation, use | |||
163 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) | |||
164 | * to compute the worse one. | |||
165 | */ | |||
166 | s = sin(x); | |||
167 | c = cos(x); | |||
168 | ss = s-c; | |||
169 | cc = s+c; | |||
170 | /* | |||
171 | * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) | |||
172 | * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) | |||
173 | */ | |||
174 | if(ix<0x7fe00000) { /* make sure x+x not overflow */ | |||
175 | z = -cos(x+x); | |||
176 | if ((s*c)<zero) cc = z/ss; | |||
177 | else ss = z/cc; | |||
178 | } | |||
179 | if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); | |||
180 | else { | |||
181 | u = pzero(x); v = qzero(x); | |||
182 | z = invsqrtpi*(u*ss+v*cc)/sqrt(x); | |||
183 | } | |||
184 | return z; | |||
185 | } | |||
186 | if(ix<=0x3e400000) { /* x < 2**-27 */ | |||
187 | return(u00 + tpi*log(x)); | |||
188 | } | |||
189 | z = x*x; | |||
190 | u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); | |||
191 | v = one+z*(v01+z*(v02+z*(v03+z*v04))); | |||
192 | return(u/v + tpi*(j0(x)*log(x))); | |||
193 | } | |||
194 | DEF_NONSTD(y0)__asm__(".weak " "y0" " ; " "y0" " = " "_libm_y0"); | |||
195 | ||||
196 | /* The asymptotic expansions of pzero is | |||
197 | * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. | |||
198 | * For x >= 2, We approximate pzero by | |||
199 | * pzero(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 | * | pzero(x)-1-R/S | <= 2 ** ( -60.26) | |||
204 | */ | |||
205 | static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ | |||
206 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ | |||
207 | -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ | |||
208 | -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ | |||
209 | -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ | |||
210 | -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ | |||
211 | -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ | |||
212 | }; | |||
213 | static const double pS8[5] = { | |||
214 | 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ | |||
215 | 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ | |||
216 | 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ | |||
217 | 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ | |||
218 | 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ | |||
219 | }; | |||
220 | ||||
221 | static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ | |||
222 | -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ | |||
223 | -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ | |||
224 | -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ | |||
225 | -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ | |||
226 | -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ | |||
227 | -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ | |||
228 | }; | |||
229 | static const double pS5[5] = { | |||
230 | 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ | |||
231 | 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ | |||
232 | 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ | |||
233 | 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ | |||
234 | 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ | |||
235 | }; | |||
236 | ||||
237 | static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ | |||
238 | -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ | |||
239 | -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ | |||
240 | -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ | |||
241 | -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ | |||
242 | -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ | |||
243 | -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ | |||
244 | }; | |||
245 | static const double pS3[5] = { | |||
246 | 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ | |||
247 | 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ | |||
248 | 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ | |||
249 | 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ | |||
250 | 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ | |||
251 | }; | |||
252 | ||||
253 | static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ | |||
254 | -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ | |||
255 | -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ | |||
256 | -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ | |||
257 | -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ | |||
258 | -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ | |||
259 | -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ | |||
260 | }; | |||
261 | static const double pS2[5] = { | |||
262 | 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ | |||
263 | 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ | |||
264 | 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ | |||
265 | 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ | |||
266 | 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ | |||
267 | }; | |||
268 | ||||
269 | static double | |||
270 | pzero(double x) | |||
271 | { | |||
272 | const double *p,*q; | |||
273 | double z,r,s; | |||
274 | int32_t ix; | |||
275 | GET_HIGH_WORD(ix,x)do { ieee_double_shape_type gh_u; gh_u.value = (x); (ix) = gh_u .parts.msw; } while (0); | |||
276 | ix &= 0x7fffffff; | |||
277 | if(ix>=0x40200000) {p = pR8; q= pS8;} | |||
278 | else if(ix>=0x40122E8B){p = pR5; q= pS5;} | |||
279 | else if(ix>=0x4006DB6D){p = pR3; q= pS3;} | |||
280 | else if(ix>=0x40000000){p = pR2; q= pS2;} | |||
281 | z = one/(x*x); | |||
282 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); | |||
| ||||
283 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); | |||
284 | return one+ r/s; | |||
285 | } | |||
286 | ||||
287 | ||||
288 | /* For x >= 8, the asymptotic expansions of qzero is | |||
289 | * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. | |||
290 | * We approximate pzero by | |||
291 | * qzero(x) = s*(-1.25 + (R/S)) | |||
292 | * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 | |||
293 | * S = 1 + qS0*s^2 + ... + qS5*s^12 | |||
294 | * and | |||
295 | * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) | |||
296 | */ | |||
297 | static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ | |||
298 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ | |||
299 | 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ | |||
300 | 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ | |||
301 | 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ | |||
302 | 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ | |||
303 | 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ | |||
304 | }; | |||
305 | static const double qS8[6] = { | |||
306 | 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ | |||
307 | 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ | |||
308 | 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ | |||
309 | 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ | |||
310 | 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ | |||
311 | -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ | |||
312 | }; | |||
313 | ||||
314 | static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ | |||
315 | 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ | |||
316 | 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ | |||
317 | 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ | |||
318 | 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ | |||
319 | 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ | |||
320 | 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ | |||
321 | }; | |||
322 | static const double qS5[6] = { | |||
323 | 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ | |||
324 | 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ | |||
325 | 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ | |||
326 | 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ | |||
327 | 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ | |||
328 | -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ | |||
329 | }; | |||
330 | ||||
331 | static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ | |||
332 | 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ | |||
333 | 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ | |||
334 | 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ | |||
335 | 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ | |||
336 | 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ | |||
337 | 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ | |||
338 | }; | |||
339 | static const double qS3[6] = { | |||
340 | 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ | |||
341 | 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ | |||
342 | 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ | |||
343 | 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ | |||
344 | 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ | |||
345 | -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ | |||
346 | }; | |||
347 | ||||
348 | static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ | |||
349 | 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ | |||
350 | 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ | |||
351 | 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ | |||
352 | 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ | |||
353 | 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ | |||
354 | 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ | |||
355 | }; | |||
356 | static const double qS2[6] = { | |||
357 | 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ | |||
358 | 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ | |||
359 | 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ | |||
360 | 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ | |||
361 | 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ | |||
362 | -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ | |||
363 | }; | |||
364 | ||||
365 | static double | |||
366 | qzero(double x) | |||
367 | { | |||
368 | const double *p,*q; | |||
369 | double s,r,z; | |||
370 | int32_t ix; | |||
371 | GET_HIGH_WORD(ix,x)do { ieee_double_shape_type gh_u; gh_u.value = (x); (ix) = gh_u .parts.msw; } while (0); | |||
372 | ix &= 0x7fffffff; | |||
373 | if(ix>=0x40200000) {p = qR8; q= qS8;} | |||
374 | else if(ix>=0x40122E8B){p = qR5; q= qS5;} | |||
375 | else if(ix>=0x4006DB6D){p = qR3; q= qS3;} | |||
376 | else if(ix>=0x40000000){p = qR2; q= qS2;} | |||
377 | z = one/(x*x); | |||
378 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); | |||
379 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); | |||
380 | return (-.125 + r/s)/x; | |||
381 | } |