File: | src/lib/libm/src/e_j1f.c |
Warning: | line 331, column 6 Array access (from variable 'p') results in an undefined pointer dereference |
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1 | /* e_j1f.c -- float version of e_j1.c. | |||
2 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. | |||
3 | */ | |||
4 | ||||
5 | /* | |||
6 | * ==================================================== | |||
7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |||
8 | * | |||
9 | * Developed at SunPro, a Sun Microsystems, Inc. business. | |||
10 | * Permission to use, copy, modify, and distribute this | |||
11 | * software is freely granted, provided that this notice | |||
12 | * is preserved. | |||
13 | * ==================================================== | |||
14 | */ | |||
15 | ||||
16 | #include "math.h" | |||
17 | #include "math_private.h" | |||
18 | ||||
19 | static float ponef(float), qonef(float); | |||
20 | ||||
21 | static const float | |||
22 | huge = 1e30, | |||
23 | one = 1.0, | |||
24 | invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ | |||
25 | tpi = 6.3661974669e-01, /* 0x3f22f983 */ | |||
26 | /* R0/S0 on [0,2] */ | |||
27 | r00 = -6.2500000000e-02, /* 0xbd800000 */ | |||
28 | r01 = 1.4070566976e-03, /* 0x3ab86cfd */ | |||
29 | r02 = -1.5995563444e-05, /* 0xb7862e36 */ | |||
30 | r03 = 4.9672799207e-08, /* 0x335557d2 */ | |||
31 | s01 = 1.9153760746e-02, /* 0x3c9ce859 */ | |||
32 | s02 = 1.8594678841e-04, /* 0x3942fab6 */ | |||
33 | s03 = 1.1771846857e-06, /* 0x359dffc2 */ | |||
34 | s04 = 5.0463624390e-09, /* 0x31ad6446 */ | |||
35 | s05 = 1.2354227016e-11; /* 0x2d59567e */ | |||
36 | ||||
37 | static const float zero = 0.0; | |||
38 | ||||
39 | float | |||
40 | j1f(float x) | |||
41 | { | |||
42 | float z, s,c,ss,cc,r,u,v,y; | |||
43 | int32_t hx,ix; | |||
44 | ||||
45 | GET_FLOAT_WORD(hx,x)do { ieee_float_shape_type gf_u; gf_u.value = (x); (hx) = gf_u .word; } while (0); | |||
46 | ix = hx&0x7fffffff; | |||
47 | if(ix>=0x7f800000) return one/x; | |||
48 | y = fabsf(x); | |||
49 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ | |||
50 | s = sinf(y); | |||
51 | c = cosf(y); | |||
52 | ss = -s-c; | |||
53 | cc = s-c; | |||
54 | if(ix<0x7f000000) { /* make sure y+y not overflow */ | |||
55 | z = cosf(y+y); | |||
56 | if ((s*c)>zero) cc = z/ss; | |||
57 | else ss = z/cc; | |||
58 | } | |||
59 | /* | |||
60 | * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) | |||
61 | * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) | |||
62 | */ | |||
63 | if(ix>0x80000000U) z = (invsqrtpi*cc)/sqrtf(y); | |||
64 | else { | |||
65 | u = ponef(y); v = qonef(y); | |||
66 | z = invsqrtpi*(u*cc-v*ss)/sqrtf(y); | |||
67 | } | |||
68 | if(hx<0) return -z; | |||
69 | else return z; | |||
70 | } | |||
71 | if(ix<0x32000000) { /* |x|<2**-27 */ | |||
72 | if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */ | |||
73 | } | |||
74 | z = x*x; | |||
75 | r = z*(r00+z*(r01+z*(r02+z*r03))); | |||
76 | s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); | |||
77 | r *= x; | |||
78 | return(x*(float)0.5+r/s); | |||
79 | } | |||
80 | DEF_NONSTD(j1f)__asm__(".weak " "j1f" " ; " "j1f" " = " "_libm_j1f"); | |||
81 | ||||
82 | static const float U0[5] = { | |||
83 | -1.9605709612e-01, /* 0xbe48c331 */ | |||
84 | 5.0443872809e-02, /* 0x3d4e9e3c */ | |||
85 | -1.9125689287e-03, /* 0xbafaaf2a */ | |||
86 | 2.3525259166e-05, /* 0x37c5581c */ | |||
87 | -9.1909917899e-08, /* 0xb3c56003 */ | |||
88 | }; | |||
89 | static const float V0[5] = { | |||
90 | 1.9916731864e-02, /* 0x3ca3286a */ | |||
91 | 2.0255257550e-04, /* 0x3954644b */ | |||
92 | 1.3560879779e-06, /* 0x35b602d4 */ | |||
93 | 6.2274145840e-09, /* 0x31d5f8eb */ | |||
94 | 1.6655924903e-11, /* 0x2d9281cf */ | |||
95 | }; | |||
96 | ||||
97 | float | |||
98 | y1f(float x) | |||
99 | { | |||
100 | float z, s,c,ss,cc,u,v; | |||
101 | int32_t hx,ix; | |||
102 | ||||
103 | GET_FLOAT_WORD(hx,x)do { ieee_float_shape_type gf_u; gf_u.value = (x); (hx) = gf_u .word; } while (0); | |||
| ||||
104 | ix = 0x7fffffff&hx; | |||
105 | /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ | |||
106 | if(ix>=0x7f800000) return one/(x+x*x); | |||
107 | if(ix==0) return -one/zero; | |||
108 | if(hx<0) return zero/zero; | |||
109 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ | |||
110 | s = sinf(x); | |||
111 | c = cosf(x); | |||
112 | ss = -s-c; | |||
113 | cc = s-c; | |||
114 | if(ix<0x7f000000) { /* make sure x+x not overflow */ | |||
115 | z = cosf(x+x); | |||
116 | if ((s*c)>zero) cc = z/ss; | |||
117 | else ss = z/cc; | |||
118 | } | |||
119 | /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) | |||
120 | * where x0 = x-3pi/4 | |||
121 | * Better formula: | |||
122 | * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) | |||
123 | * = 1/sqrt(2) * (sin(x) - cos(x)) | |||
124 | * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) | |||
125 | * = -1/sqrt(2) * (cos(x) + sin(x)) | |||
126 | * To avoid cancellation, use | |||
127 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) | |||
128 | * to compute the worse one. | |||
129 | */ | |||
130 | if(ix>0x48000000) z = (invsqrtpi*ss)/sqrtf(x); | |||
131 | else { | |||
132 | u = ponef(x); v = qonef(x); | |||
133 | z = invsqrtpi*(u*ss+v*cc)/sqrtf(x); | |||
134 | } | |||
135 | return z; | |||
136 | } | |||
137 | if(ix<=0x24800000) { /* x < 2**-54 */ | |||
138 | return(-tpi/x); | |||
139 | } | |||
140 | z = x*x; | |||
141 | u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); | |||
142 | v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); | |||
143 | return(x*(u/v) + tpi*(j1f(x)*logf(x)-one/x)); | |||
144 | } | |||
145 | DEF_NONSTD(y1f)__asm__(".weak " "y1f" " ; " "y1f" " = " "_libm_y1f"); | |||
146 | ||||
147 | /* For x >= 8, the asymptotic expansions of pone is | |||
148 | * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. | |||
149 | * We approximate pone by | |||
150 | * pone(x) = 1 + (R/S) | |||
151 | * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 | |||
152 | * S = 1 + ps0*s^2 + ... + ps4*s^10 | |||
153 | * and | |||
154 | * | pone(x)-1-R/S | <= 2 ** ( -60.06) | |||
155 | */ | |||
156 | ||||
157 | static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ | |||
158 | 0.0000000000e+00, /* 0x00000000 */ | |||
159 | 1.1718750000e-01, /* 0x3df00000 */ | |||
160 | 1.3239480972e+01, /* 0x4153d4ea */ | |||
161 | 4.1205184937e+02, /* 0x43ce06a3 */ | |||
162 | 3.8747453613e+03, /* 0x45722bed */ | |||
163 | 7.9144794922e+03, /* 0x45f753d6 */ | |||
164 | }; | |||
165 | static const float ps8[5] = { | |||
166 | 1.1420736694e+02, /* 0x42e46a2c */ | |||
167 | 3.6509309082e+03, /* 0x45642ee5 */ | |||
168 | 3.6956207031e+04, /* 0x47105c35 */ | |||
169 | 9.7602796875e+04, /* 0x47bea166 */ | |||
170 | 3.0804271484e+04, /* 0x46f0a88b */ | |||
171 | }; | |||
172 | ||||
173 | static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ | |||
174 | 1.3199052094e-11, /* 0x2d68333f */ | |||
175 | 1.1718749255e-01, /* 0x3defffff */ | |||
176 | 6.8027510643e+00, /* 0x40d9b023 */ | |||
177 | 1.0830818176e+02, /* 0x42d89dca */ | |||
178 | 5.1763616943e+02, /* 0x440168b7 */ | |||
179 | 5.2871520996e+02, /* 0x44042dc6 */ | |||
180 | }; | |||
181 | static const float ps5[5] = { | |||
182 | 5.9280597687e+01, /* 0x426d1f55 */ | |||
183 | 9.9140142822e+02, /* 0x4477d9b1 */ | |||
184 | 5.3532670898e+03, /* 0x45a74a23 */ | |||
185 | 7.8446904297e+03, /* 0x45f52586 */ | |||
186 | 1.5040468750e+03, /* 0x44bc0180 */ | |||
187 | }; | |||
188 | ||||
189 | static const float pr3[6] = { | |||
190 | 3.0250391081e-09, /* 0x314fe10d */ | |||
191 | 1.1718686670e-01, /* 0x3defffab */ | |||
192 | 3.9329774380e+00, /* 0x407bb5e7 */ | |||
193 | 3.5119403839e+01, /* 0x420c7a45 */ | |||
194 | 9.1055007935e+01, /* 0x42b61c2a */ | |||
195 | 4.8559066772e+01, /* 0x42423c7c */ | |||
196 | }; | |||
197 | static const float ps3[5] = { | |||
198 | 3.4791309357e+01, /* 0x420b2a4d */ | |||
199 | 3.3676245117e+02, /* 0x43a86198 */ | |||
200 | 1.0468714600e+03, /* 0x4482dbe3 */ | |||
201 | 8.9081134033e+02, /* 0x445eb3ed */ | |||
202 | 1.0378793335e+02, /* 0x42cf936c */ | |||
203 | }; | |||
204 | ||||
205 | static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ | |||
206 | 1.0771083225e-07, /* 0x33e74ea8 */ | |||
207 | 1.1717621982e-01, /* 0x3deffa16 */ | |||
208 | 2.3685150146e+00, /* 0x401795c0 */ | |||
209 | 1.2242610931e+01, /* 0x4143e1bc */ | |||
210 | 1.7693971634e+01, /* 0x418d8d41 */ | |||
211 | 5.0735230446e+00, /* 0x40a25a4d */ | |||
212 | }; | |||
213 | static const float ps2[5] = { | |||
214 | 2.1436485291e+01, /* 0x41ab7dec */ | |||
215 | 1.2529022980e+02, /* 0x42fa9499 */ | |||
216 | 2.3227647400e+02, /* 0x436846c7 */ | |||
217 | 1.1767937469e+02, /* 0x42eb5bd7 */ | |||
218 | 8.3646392822e+00, /* 0x4105d590 */ | |||
219 | }; | |||
220 | ||||
221 | static float | |||
222 | ponef(float x) | |||
223 | { | |||
224 | const float *p,*q; | |||
225 | float z,r,s; | |||
226 | int32_t ix; | |||
227 | GET_FLOAT_WORD(ix,x)do { ieee_float_shape_type gf_u; gf_u.value = (x); (ix) = gf_u .word; } while (0); | |||
228 | ix &= 0x7fffffff; | |||
229 | if(ix>=0x41000000) {p = pr8; q= ps8;} | |||
230 | else if(ix>=0x40f71c58){p = pr5; q= ps5;} | |||
231 | else if(ix>=0x4036db68){p = pr3; q= ps3;} | |||
232 | else if(ix>=0x40000000){p = pr2; q= ps2;} | |||
233 | z = one/(x*x); | |||
234 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); | |||
235 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); | |||
236 | return one+ r/s; | |||
237 | } | |||
238 | ||||
239 | ||||
240 | /* For x >= 8, the asymptotic expansions of qone is | |||
241 | * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. | |||
242 | * We approximate pone by | |||
243 | * qone(x) = s*(0.375 + (R/S)) | |||
244 | * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 | |||
245 | * S = 1 + qs1*s^2 + ... + qs6*s^12 | |||
246 | * and | |||
247 | * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) | |||
248 | */ | |||
249 | ||||
250 | static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ | |||
251 | 0.0000000000e+00, /* 0x00000000 */ | |||
252 | -1.0253906250e-01, /* 0xbdd20000 */ | |||
253 | -1.6271753311e+01, /* 0xc1822c8d */ | |||
254 | -7.5960174561e+02, /* 0xc43de683 */ | |||
255 | -1.1849806641e+04, /* 0xc639273a */ | |||
256 | -4.8438511719e+04, /* 0xc73d3683 */ | |||
257 | }; | |||
258 | static const float qs8[6] = { | |||
259 | 1.6139537048e+02, /* 0x43216537 */ | |||
260 | 7.8253862305e+03, /* 0x45f48b17 */ | |||
261 | 1.3387534375e+05, /* 0x4802bcd6 */ | |||
262 | 7.1965775000e+05, /* 0x492fb29c */ | |||
263 | 6.6660125000e+05, /* 0x4922be94 */ | |||
264 | -2.9449025000e+05, /* 0xc88fcb48 */ | |||
265 | }; | |||
266 | ||||
267 | static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ | |||
268 | -2.0897993405e-11, /* 0xadb7d219 */ | |||
269 | -1.0253904760e-01, /* 0xbdd1fffe */ | |||
270 | -8.0564479828e+00, /* 0xc100e736 */ | |||
271 | -1.8366960144e+02, /* 0xc337ab6b */ | |||
272 | -1.3731937256e+03, /* 0xc4aba633 */ | |||
273 | -2.6124443359e+03, /* 0xc523471c */ | |||
274 | }; | |||
275 | static const float qs5[6] = { | |||
276 | 8.1276550293e+01, /* 0x42a28d98 */ | |||
277 | 1.9917987061e+03, /* 0x44f8f98f */ | |||
278 | 1.7468484375e+04, /* 0x468878f8 */ | |||
279 | 4.9851425781e+04, /* 0x4742bb6d */ | |||
280 | 2.7948074219e+04, /* 0x46da5826 */ | |||
281 | -4.7191835938e+03, /* 0xc5937978 */ | |||
282 | }; | |||
283 | ||||
284 | static const float qr3[6] = { | |||
285 | -5.0783124372e-09, /* 0xb1ae7d4f */ | |||
286 | -1.0253783315e-01, /* 0xbdd1ff5b */ | |||
287 | -4.6101160049e+00, /* 0xc0938612 */ | |||
288 | -5.7847221375e+01, /* 0xc267638e */ | |||
289 | -2.2824453735e+02, /* 0xc3643e9a */ | |||
290 | -2.1921012878e+02, /* 0xc35b35cb */ | |||
291 | }; | |||
292 | static const float qs3[6] = { | |||
293 | 4.7665153503e+01, /* 0x423ea91e */ | |||
294 | 6.7386511230e+02, /* 0x4428775e */ | |||
295 | 3.3801528320e+03, /* 0x45534272 */ | |||
296 | 5.5477290039e+03, /* 0x45ad5dd5 */ | |||
297 | 1.9031191406e+03, /* 0x44ede3d0 */ | |||
298 | -1.3520118713e+02, /* 0xc3073381 */ | |||
299 | }; | |||
300 | ||||
301 | static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ | |||
302 | -1.7838172539e-07, /* 0xb43f8932 */ | |||
303 | -1.0251704603e-01, /* 0xbdd1f475 */ | |||
304 | -2.7522056103e+00, /* 0xc0302423 */ | |||
305 | -1.9663616180e+01, /* 0xc19d4f16 */ | |||
306 | -4.2325313568e+01, /* 0xc2294d1f */ | |||
307 | -2.1371921539e+01, /* 0xc1aaf9b2 */ | |||
308 | }; | |||
309 | static const float qs2[6] = { | |||
310 | 2.9533363342e+01, /* 0x41ec4454 */ | |||
311 | 2.5298155212e+02, /* 0x437cfb47 */ | |||
312 | 7.5750280762e+02, /* 0x443d602e */ | |||
313 | 7.3939318848e+02, /* 0x4438d92a */ | |||
314 | 1.5594900513e+02, /* 0x431bf2f2 */ | |||
315 | -4.9594988823e+00, /* 0xc09eb437 */ | |||
316 | }; | |||
317 | ||||
318 | static float | |||
319 | qonef(float x) | |||
320 | { | |||
321 | const float *p,*q; | |||
322 | float s,r,z; | |||
323 | int32_t ix; | |||
324 | GET_FLOAT_WORD(ix,x)do { ieee_float_shape_type gf_u; gf_u.value = (x); (ix) = gf_u .word; } while (0); | |||
325 | ix &= 0x7fffffff; | |||
326 | if(ix>=0x40200000) {p = qr8; q= qs8;} | |||
327 | else if(ix
| |||
328 | else if(ix
| |||
329 | else if(ix>=0x40000000){p = qr2; q= qs2;} | |||
330 | z = one/(x*x); | |||
331 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); | |||
| ||||
332 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); | |||
333 | return ((float).375 + r/s)/x; | |||
334 | } |