File: | src/lib/libm/src/e_j0f.c |
Warning: | line 335, column 6 Array access (from variable 'p') results in an undefined pointer dereference |
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1 | /* e_j0f.c -- float version of e_j0.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 pzerof(float), qzerof(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, 2.00] */ | |||
27 | R02 = 1.5625000000e-02, /* 0x3c800000 */ | |||
28 | R03 = -1.8997929874e-04, /* 0xb947352e */ | |||
29 | R04 = 1.8295404516e-06, /* 0x35f58e88 */ | |||
30 | R05 = -4.6183270541e-09, /* 0xb19eaf3c */ | |||
31 | S01 = 1.5619102865e-02, /* 0x3c7fe744 */ | |||
32 | S02 = 1.1692678527e-04, /* 0x38f53697 */ | |||
33 | S03 = 5.1354652442e-07, /* 0x3509daa6 */ | |||
34 | S04 = 1.1661400734e-09; /* 0x30a045e8 */ | |||
35 | ||||
36 | static const float zero = 0.0; | |||
37 | ||||
38 | float | |||
39 | j0f(float x) | |||
40 | { | |||
41 | float z, s,c,ss,cc,r,u,v; | |||
42 | int32_t hx,ix; | |||
43 | ||||
44 | GET_FLOAT_WORD(hx,x)do { ieee_float_shape_type gf_u; gf_u.value = (x); (hx) = gf_u .word; } while (0); | |||
45 | ix = hx&0x7fffffff; | |||
46 | if(ix>=0x7f800000) return one/(x*x); | |||
47 | x = fabsf(x); | |||
48 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ | |||
49 | s = sinf(x); | |||
50 | c = cosf(x); | |||
51 | ss = s-c; | |||
52 | cc = s+c; | |||
53 | if(ix<0x7f000000) { /* make sure x+x not overflow */ | |||
54 | z = -cosf(x+x); | |||
55 | if ((s*c)<zero) cc = z/ss; | |||
56 | else ss = z/cc; | |||
57 | } | |||
58 | /* | |||
59 | * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) | |||
60 | * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) | |||
61 | */ | |||
62 | if(ix>0x80000000U) z = (invsqrtpi*cc)/sqrtf(x); | |||
63 | else { | |||
64 | u = pzerof(x); v = qzerof(x); | |||
65 | z = invsqrtpi*(u*cc-v*ss)/sqrtf(x); | |||
66 | } | |||
67 | return z; | |||
68 | } | |||
69 | if(ix<0x39000000) { /* |x| < 2**-13 */ | |||
70 | if(huge+x>one) { /* raise inexact if x != 0 */ | |||
71 | if(ix<0x32000000) return one; /* |x|<2**-27 */ | |||
72 | else return one - (float)0.25*x*x; | |||
73 | } | |||
74 | } | |||
75 | z = x*x; | |||
76 | r = z*(R02+z*(R03+z*(R04+z*R05))); | |||
77 | s = one+z*(S01+z*(S02+z*(S03+z*S04))); | |||
78 | if(ix < 0x3F800000) { /* |x| < 1.00 */ | |||
79 | return one + z*((float)-0.25+(r/s)); | |||
80 | } else { | |||
81 | u = (float)0.5*x; | |||
82 | return((one+u)*(one-u)+z*(r/s)); | |||
83 | } | |||
84 | } | |||
85 | DEF_NONSTD(j0f)__asm__(".weak " "j0f" " ; " "j0f" " = " "_libm_j0f"); | |||
86 | ||||
87 | static const float | |||
88 | u00 = -7.3804296553e-02, /* 0xbd9726b5 */ | |||
89 | u01 = 1.7666645348e-01, /* 0x3e34e80d */ | |||
90 | u02 = -1.3818567619e-02, /* 0xbc626746 */ | |||
91 | u03 = 3.4745343146e-04, /* 0x39b62a69 */ | |||
92 | u04 = -3.8140706238e-06, /* 0xb67ff53c */ | |||
93 | u05 = 1.9559013964e-08, /* 0x32a802ba */ | |||
94 | u06 = -3.9820518410e-11, /* 0xae2f21eb */ | |||
95 | v01 = 1.2730483897e-02, /* 0x3c509385 */ | |||
96 | v02 = 7.6006865129e-05, /* 0x389f65e0 */ | |||
97 | v03 = 2.5915085189e-07, /* 0x348b216c */ | |||
98 | v04 = 4.4111031494e-10; /* 0x2ff280c2 */ | |||
99 | ||||
100 | float | |||
101 | y0f(float x) | |||
102 | { | |||
103 | float z, s,c,ss,cc,u,v; | |||
104 | int32_t hx,ix; | |||
105 | ||||
106 | GET_FLOAT_WORD(hx,x)do { ieee_float_shape_type gf_u; gf_u.value = (x); (hx) = gf_u .word; } while (0); | |||
| ||||
107 | ix = 0x7fffffff&hx; | |||
108 | /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ | |||
109 | if(ix>=0x7f800000) return one/(x+x*x); | |||
110 | if(ix==0) return -one/zero; | |||
111 | if(hx<0) return zero/zero; | |||
112 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ | |||
113 | /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) | |||
114 | * where x0 = x-pi/4 | |||
115 | * Better formula: | |||
116 | * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) | |||
117 | * = 1/sqrt(2) * (sin(x) + cos(x)) | |||
118 | * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) | |||
119 | * = 1/sqrt(2) * (sin(x) - cos(x)) | |||
120 | * To avoid cancellation, use | |||
121 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) | |||
122 | * to compute the worse one. | |||
123 | */ | |||
124 | s = sinf(x); | |||
125 | c = cosf(x); | |||
126 | ss = s-c; | |||
127 | cc = s+c; | |||
128 | /* | |||
129 | * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) | |||
130 | * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) | |||
131 | */ | |||
132 | if(ix<0x7f000000) { /* make sure x+x not overflow */ | |||
133 | z = -cosf(x+x); | |||
134 | if ((s*c)<zero) cc = z/ss; | |||
135 | else ss = z/cc; | |||
136 | } | |||
137 | if(ix
| |||
138 | else { | |||
139 | u = pzerof(x); v = qzerof(x); | |||
140 | z = invsqrtpi*(u*ss+v*cc)/sqrtf(x); | |||
141 | } | |||
142 | return z; | |||
143 | } | |||
144 | if(ix<=0x32000000) { /* x < 2**-27 */ | |||
145 | return(u00 + tpi*logf(x)); | |||
146 | } | |||
147 | z = x*x; | |||
148 | u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); | |||
149 | v = one+z*(v01+z*(v02+z*(v03+z*v04))); | |||
150 | return(u/v + tpi*(j0f(x)*logf(x))); | |||
151 | } | |||
152 | DEF_NONSTD(y0f)__asm__(".weak " "y0f" " ; " "y0f" " = " "_libm_y0f"); | |||
153 | ||||
154 | /* The asymptotic expansions of pzero is | |||
155 | * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. | |||
156 | * For x >= 2, We approximate pzero by | |||
157 | * pzero(x) = 1 + (R/S) | |||
158 | * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 | |||
159 | * S = 1 + pS0*s^2 + ... + pS4*s^10 | |||
160 | * and | |||
161 | * | pzero(x)-1-R/S | <= 2 ** ( -60.26) | |||
162 | */ | |||
163 | static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ | |||
164 | 0.0000000000e+00, /* 0x00000000 */ | |||
165 | -7.0312500000e-02, /* 0xbd900000 */ | |||
166 | -8.0816707611e+00, /* 0xc1014e86 */ | |||
167 | -2.5706311035e+02, /* 0xc3808814 */ | |||
168 | -2.4852163086e+03, /* 0xc51b5376 */ | |||
169 | -5.2530439453e+03, /* 0xc5a4285a */ | |||
170 | }; | |||
171 | static const float pS8[5] = { | |||
172 | 1.1653436279e+02, /* 0x42e91198 */ | |||
173 | 3.8337448730e+03, /* 0x456f9beb */ | |||
174 | 4.0597855469e+04, /* 0x471e95db */ | |||
175 | 1.1675296875e+05, /* 0x47e4087c */ | |||
176 | 4.7627726562e+04, /* 0x473a0bba */ | |||
177 | }; | |||
178 | static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ | |||
179 | -1.1412546255e-11, /* 0xad48c58a */ | |||
180 | -7.0312492549e-02, /* 0xbd8fffff */ | |||
181 | -4.1596107483e+00, /* 0xc0851b88 */ | |||
182 | -6.7674766541e+01, /* 0xc287597b */ | |||
183 | -3.3123129272e+02, /* 0xc3a59d9b */ | |||
184 | -3.4643338013e+02, /* 0xc3ad3779 */ | |||
185 | }; | |||
186 | static const float pS5[5] = { | |||
187 | 6.0753936768e+01, /* 0x42730408 */ | |||
188 | 1.0512523193e+03, /* 0x44836813 */ | |||
189 | 5.9789707031e+03, /* 0x45bad7c4 */ | |||
190 | 9.6254453125e+03, /* 0x461665c8 */ | |||
191 | 2.4060581055e+03, /* 0x451660ee */ | |||
192 | }; | |||
193 | ||||
194 | static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ | |||
195 | -2.5470459075e-09, /* 0xb12f081b */ | |||
196 | -7.0311963558e-02, /* 0xbd8fffb8 */ | |||
197 | -2.4090321064e+00, /* 0xc01a2d95 */ | |||
198 | -2.1965976715e+01, /* 0xc1afba52 */ | |||
199 | -5.8079170227e+01, /* 0xc2685112 */ | |||
200 | -3.1447946548e+01, /* 0xc1fb9565 */ | |||
201 | }; | |||
202 | static const float pS3[5] = { | |||
203 | 3.5856033325e+01, /* 0x420f6c94 */ | |||
204 | 3.6151397705e+02, /* 0x43b4c1ca */ | |||
205 | 1.1936077881e+03, /* 0x44953373 */ | |||
206 | 1.1279968262e+03, /* 0x448cffe6 */ | |||
207 | 1.7358093262e+02, /* 0x432d94b8 */ | |||
208 | }; | |||
209 | ||||
210 | static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ | |||
211 | -8.8753431271e-08, /* 0xb3be98b7 */ | |||
212 | -7.0303097367e-02, /* 0xbd8ffb12 */ | |||
213 | -1.4507384300e+00, /* 0xbfb9b1cc */ | |||
214 | -7.6356959343e+00, /* 0xc0f4579f */ | |||
215 | -1.1193166733e+01, /* 0xc1331736 */ | |||
216 | -3.2336456776e+00, /* 0xc04ef40d */ | |||
217 | }; | |||
218 | static const float pS2[5] = { | |||
219 | 2.2220300674e+01, /* 0x41b1c32d */ | |||
220 | 1.3620678711e+02, /* 0x430834f0 */ | |||
221 | 2.7047027588e+02, /* 0x43873c32 */ | |||
222 | 1.5387539673e+02, /* 0x4319e01a */ | |||
223 | 1.4657617569e+01, /* 0x416a859a */ | |||
224 | }; | |||
225 | ||||
226 | static float | |||
227 | pzerof(float x) | |||
228 | { | |||
229 | const float *p,*q; | |||
230 | float z,r,s; | |||
231 | int32_t ix; | |||
232 | GET_FLOAT_WORD(ix,x)do { ieee_float_shape_type gf_u; gf_u.value = (x); (ix) = gf_u .word; } while (0); | |||
233 | ix &= 0x7fffffff; | |||
234 | if(ix>=0x41000000) {p = pR8; q= pS8;} | |||
235 | else if(ix>=0x40f71c58){p = pR5; q= pS5;} | |||
236 | else if(ix>=0x4036db68){p = pR3; q= pS3;} | |||
237 | else if(ix>=0x40000000){p = pR2; q= pS2;} | |||
238 | z = one/(x*x); | |||
239 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); | |||
240 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); | |||
241 | return one+ r/s; | |||
242 | } | |||
243 | ||||
244 | ||||
245 | /* For x >= 8, the asymptotic expansions of qzero is | |||
246 | * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. | |||
247 | * We approximate pzero by | |||
248 | * qzero(x) = s*(-1.25 + (R/S)) | |||
249 | * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 | |||
250 | * S = 1 + qS0*s^2 + ... + qS5*s^12 | |||
251 | * and | |||
252 | * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) | |||
253 | */ | |||
254 | static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ | |||
255 | 0.0000000000e+00, /* 0x00000000 */ | |||
256 | 7.3242187500e-02, /* 0x3d960000 */ | |||
257 | 1.1768206596e+01, /* 0x413c4a93 */ | |||
258 | 5.5767340088e+02, /* 0x440b6b19 */ | |||
259 | 8.8591972656e+03, /* 0x460a6cca */ | |||
260 | 3.7014625000e+04, /* 0x471096a0 */ | |||
261 | }; | |||
262 | static const float qS8[6] = { | |||
263 | 1.6377603149e+02, /* 0x4323c6aa */ | |||
264 | 8.0983447266e+03, /* 0x45fd12c2 */ | |||
265 | 1.4253829688e+05, /* 0x480b3293 */ | |||
266 | 8.0330925000e+05, /* 0x49441ed4 */ | |||
267 | 8.4050156250e+05, /* 0x494d3359 */ | |||
268 | -3.4389928125e+05, /* 0xc8a7eb69 */ | |||
269 | }; | |||
270 | ||||
271 | static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ | |||
272 | 1.8408595828e-11, /* 0x2da1ec79 */ | |||
273 | 7.3242180049e-02, /* 0x3d95ffff */ | |||
274 | 5.8356351852e+00, /* 0x40babd86 */ | |||
275 | 1.3511157227e+02, /* 0x43071c90 */ | |||
276 | 1.0272437744e+03, /* 0x448067cd */ | |||
277 | 1.9899779053e+03, /* 0x44f8bf4b */ | |||
278 | }; | |||
279 | static const float qS5[6] = { | |||
280 | 8.2776611328e+01, /* 0x42a58da0 */ | |||
281 | 2.0778142090e+03, /* 0x4501dd07 */ | |||
282 | 1.8847289062e+04, /* 0x46933e94 */ | |||
283 | 5.6751113281e+04, /* 0x475daf1d */ | |||
284 | 3.5976753906e+04, /* 0x470c88c1 */ | |||
285 | -5.3543427734e+03, /* 0xc5a752be */ | |||
286 | }; | |||
287 | ||||
288 | static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ | |||
289 | 4.3774099900e-09, /* 0x3196681b */ | |||
290 | 7.3241114616e-02, /* 0x3d95ff70 */ | |||
291 | 3.3442313671e+00, /* 0x405607e3 */ | |||
292 | 4.2621845245e+01, /* 0x422a7cc5 */ | |||
293 | 1.7080809021e+02, /* 0x432acedf */ | |||
294 | 1.6673394775e+02, /* 0x4326bbe4 */ | |||
295 | }; | |||
296 | static const float qS3[6] = { | |||
297 | 4.8758872986e+01, /* 0x42430916 */ | |||
298 | 7.0968920898e+02, /* 0x44316c1c */ | |||
299 | 3.7041481934e+03, /* 0x4567825f */ | |||
300 | 6.4604252930e+03, /* 0x45c9e367 */ | |||
301 | 2.5163337402e+03, /* 0x451d4557 */ | |||
302 | -1.4924745178e+02, /* 0xc3153f59 */ | |||
303 | }; | |||
304 | ||||
305 | static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ | |||
306 | 1.5044444979e-07, /* 0x342189db */ | |||
307 | 7.3223426938e-02, /* 0x3d95f62a */ | |||
308 | 1.9981917143e+00, /* 0x3fffc4bf */ | |||
309 | 1.4495602608e+01, /* 0x4167edfd */ | |||
310 | 3.1666231155e+01, /* 0x41fd5471 */ | |||
311 | 1.6252708435e+01, /* 0x4182058c */ | |||
312 | }; | |||
313 | static const float qS2[6] = { | |||
314 | 3.0365585327e+01, /* 0x41f2ecb8 */ | |||
315 | 2.6934811401e+02, /* 0x4386ac8f */ | |||
316 | 8.4478375244e+02, /* 0x44533229 */ | |||
317 | 8.8293585205e+02, /* 0x445cbbe5 */ | |||
318 | 2.1266638184e+02, /* 0x4354aa98 */ | |||
319 | -5.3109550476e+00, /* 0xc0a9f358 */ | |||
320 | }; | |||
321 | ||||
322 | static float | |||
323 | qzerof(float x) | |||
324 | { | |||
325 | const float *p,*q; | |||
326 | float s,r,z; | |||
327 | int32_t ix; | |||
328 | GET_FLOAT_WORD(ix,x)do { ieee_float_shape_type gf_u; gf_u.value = (x); (ix) = gf_u .word; } while (0); | |||
329 | ix &= 0x7fffffff; | |||
330 | if(ix>=0x41000000) {p = qR8; q= qS8;} | |||
331 | else if(ix>=0x40f71c58){p = qR5; q= qS5;} | |||
332 | else if(ix>=0x4036db68){p = qR3; q= qS3;} | |||
333 | else if(ix>=0x40000000){p = qR2; q= qS2;} | |||
334 | z = one/(x*x); | |||
335 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); | |||
| ||||
336 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); | |||
337 | return (-(float).125 + r/s)/x; | |||
338 | } |