Bug Summary

File:src/lib/libm/src/e_j0f.c
Warning:line 239, column 6
Array access (from variable 'p') results in an undefined pointer dereference

Annotated Source Code

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clang -cc1 -cc1 -triple amd64-unknown-openbsd7.0 -analyze -disable-free -disable-llvm-verifier -discard-value-names -main-file-name e_j0f.c -analyzer-store=region -analyzer-opt-analyze-nested-blocks -analyzer-checker=core -analyzer-checker=apiModeling -analyzer-checker=unix -analyzer-checker=deadcode -analyzer-checker=security.insecureAPI.UncheckedReturn -analyzer-checker=security.insecureAPI.getpw -analyzer-checker=security.insecureAPI.gets -analyzer-checker=security.insecureAPI.mktemp -analyzer-checker=security.insecureAPI.mkstemp -analyzer-checker=security.insecureAPI.vfork -analyzer-checker=nullability.NullPassedToNonnull -analyzer-checker=nullability.NullReturnedFromNonnull -analyzer-output plist -w -setup-static-analyzer -mrelocation-model pic -pic-level 1 -fhalf-no-semantic-interposition -mframe-pointer=all -relaxed-aliasing -fno-rounding-math -mconstructor-aliases -munwind-tables -target-cpu x86-64 -target-feature +retpoline-indirect-calls -target-feature +retpoline-indirect-branches -tune-cpu generic -debugger-tuning=gdb -fcoverage-compilation-dir=/usr/src/lib/libm/obj -resource-dir /usr/local/lib/clang/13.0.0 -include namespace.h -I /usr/src/lib/libm/arch/amd64 -I /usr/src/lib/libm/src -I /usr/src/lib/libm/src/ld80 -I /usr/src/lib/libm/hidden -D PIC -internal-isystem /usr/local/lib/clang/13.0.0/include -internal-externc-isystem /usr/include -O2 -fdebug-compilation-dir=/usr/src/lib/libm/obj -ferror-limit 19 -fwrapv -D_RET_PROTECTOR -ret-protector -fgnuc-version=4.2.1 -vectorize-loops -vectorize-slp -fno-builtin-malloc -fno-builtin-calloc -fno-builtin-realloc -fno-builtin-valloc -fno-builtin-free -fno-builtin-strdup -fno-builtin-strndup -analyzer-output=html -faddrsig -D__GCC_HAVE_DWARF2_CFI_ASM=1 -o /home/ben/Projects/vmm/scan-build/2022-01-12-194120-40624-1 -x c /usr/src/lib/libm/src/e_j0f.c
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
19static float pzerof(float), qzerof(float);
20
21static const float
22huge = 1e30,
23one = 1.0,
24invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
25tpi = 6.3661974669e-01, /* 0x3f22f983 */
26 /* R0/S0 on [0, 2.00] */
27R02 = 1.5625000000e-02, /* 0x3c800000 */
28R03 = -1.8997929874e-04, /* 0xb947352e */
29R04 = 1.8295404516e-06, /* 0x35f58e88 */
30R05 = -4.6183270541e-09, /* 0xb19eaf3c */
31S01 = 1.5619102865e-02, /* 0x3c7fe744 */
32S02 = 1.1692678527e-04, /* 0x38f53697 */
33S03 = 5.1354652442e-07, /* 0x3509daa6 */
34S04 = 1.1661400734e-09; /* 0x30a045e8 */
35
36static const float zero = 0.0;
37
38float
39j0f(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}
85DEF_NONSTD(j0f)__asm__(".global " "j0f" " ; " "j0f" " = " "_libm_j0f");
86
87static const float
88u00 = -7.3804296553e-02, /* 0xbd9726b5 */
89u01 = 1.7666645348e-01, /* 0x3e34e80d */
90u02 = -1.3818567619e-02, /* 0xbc626746 */
91u03 = 3.4745343146e-04, /* 0x39b62a69 */
92u04 = -3.8140706238e-06, /* 0xb67ff53c */
93u05 = 1.9559013964e-08, /* 0x32a802ba */
94u06 = -3.9820518410e-11, /* 0xae2f21eb */
95v01 = 1.2730483897e-02, /* 0x3c509385 */
96v02 = 7.6006865129e-05, /* 0x389f65e0 */
97v03 = 2.5915085189e-07, /* 0x348b216c */
98v04 = 4.4111031494e-10; /* 0x2ff280c2 */
99
100float
101y0f(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);
1
Loop condition is false. Exiting loop
→
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);
2
←
Assuming 'ix' is < 2139095040
→
3
←
Taking false branch
→
110 if(ix==0) return -one/zero;
4
←
Assuming 'ix' is not equal to 0
→
5
←
Taking false branch
→
111 if(hx<0) return zero/zero;
6
←
Assuming 'hx' is >= 0
→
7
←
Taking false branch
→
112 if(ix >= 0x40000000) { /* |x| >= 2.0 */
8
←
Assuming 'ix' is >= 1073741824
→
9
←
Taking true branch
→
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 */
10
←
Assuming 'ix' is >= 2130706432
→
11
←
Taking false branch
→
133 z = -cosf(x+x);
134 if ((s*c)<zero) cc = z/ss;
135 else ss = z/cc;
136 }
137 if(ix
11.1
'ix' is <= -2147483648
>0x80000000U) z = (invsqrtpi*ss)/sqrtf(x);
12
←
Taking false branch
→
138 else {
139 u = pzerof(x); v = qzerof(x);
13
←
Calling 'pzerof'
→
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}
152DEF_NONSTD(y0f)__asm__(".global " "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 */
163static 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};
171static 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};
178static 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};
186static 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
194static 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};
202static 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
210static 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};
218static 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
226static float
227pzerof(float x)
228{
229 const float *p,*q;
14
←
'p' declared without an initial value
→
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);
15
←
Loop condition is false. Exiting loop
→
233 ix &= 0x7fffffff;
234 if(ix>=0x41000000) {p = pR8; q= pS8;}
16
←
Assuming 'ix' is < 1090519040
→
17
←
Taking false branch
→
235 else if(ix>=0x40f71c58){p = pR5; q= pS5;}
18
←
Assuming 'ix' is < 1089936472
→
19
←
Taking false branch
→
236 else if(ix>=0x4036db68){p = pR3; q= pS3;}
20
←
Assuming 'ix' is < 1077336936
→
21
←
Taking false branch
→
237 else if(ix>=0x40000000){p = pR2; q= pS2;}
22
←
Assuming 'ix' is < 1073741824
→
23
←
Taking false branch
→
238 z = one/(x*x);
239 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
24
←
Array access (from variable 'p') results in an undefined pointer dereference
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 */
254static 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};
262static 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
271static 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};
279static 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
288static 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};
296static 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
305static 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};
313static 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
322static float
323qzerof(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}