Bug Summary

File:src/lib/libm/src/ld80/e_lgammal.c
Warning:line 386, column 7
Value stored to 't' is never read

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_lgammal.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 -pic-is-pie -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 -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/ld80/e_lgammal.c
1/*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12/*
13 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
14 *
15 * Permission to use, copy, modify, and distribute this software for any
16 * purpose with or without fee is hereby granted, provided that the above
17 * copyright notice and this permission notice appear in all copies.
18 *
19 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
20 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
21 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
22 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
23 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
24 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
25 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
26 */
27
28/* lgammal(x)
29 * Reentrant version of the logarithm of the Gamma function
30 * with user provide pointer for the sign of Gamma(x).
31 *
32 * Method:
33 * 1. Argument Reduction for 0 < x <= 8
34 * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may
35 * reduce x to a number in [1.5,2.5] by
36 * lgamma(1+s) = log(s) + lgamma(s)
37 * for example,
38 * lgamma(7.3) = log(6.3) + lgamma(6.3)
39 * = log(6.3*5.3) + lgamma(5.3)
40 * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3)
41 * 2. Polynomial approximation of lgamma around its
42 * minimun ymin=1.461632144968362245 to maintain monotonicity.
43 * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use
44 * Let z = x-ymin;
45 * lgamma(x) = -1.214862905358496078218 + z^2*poly(z)
46 * 2. Rational approximation in the primary interval [2,3]
47 * We use the following approximation:
48 * s = x-2.0;
49 * lgamma(x) = 0.5*s + s*P(s)/Q(s)
50 * Our algorithms are based on the following observation
51 *
52 * zeta(2)-1 2 zeta(3)-1 3
53 * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ...
54 * 2 3
55 *
56 * where Euler = 0.5771... is the Euler constant, which is very
57 * close to 0.5.
58 *
59 * 3. For x>=8, we have
60 * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+....
61 * (better formula:
62 * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...)
63 * Let z = 1/x, then we approximation
64 * f(z) = lgamma(x) - (x-0.5)(log(x)-1)
65 * by
66 * 3 5 11
67 * w = w0 + w1*z + w2*z + w3*z + ... + w6*z
68 *
69 * 4. For negative x, since (G is gamma function)
70 * -x*G(-x)*G(x) = pi/sin(pi*x),
71 * we have
72 * G(x) = pi/(sin(pi*x)*(-x)*G(-x))
73 * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0
74 * Hence, for x<0, signgam = sign(sin(pi*x)) and
75 * lgamma(x) = log(|Gamma(x)|)
76 * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x);
77 * Note: one should avoid compute pi*(-x) directly in the
78 * computation of sin(pi*(-x)).
79 *
80 * 5. Special Cases
81 * lgamma(2+s) ~ s*(1-Euler) for tiny s
82 * lgamma(1)=lgamma(2)=0
83 * lgamma(x) ~ -log(x) for tiny x
84 * lgamma(0) = lgamma(inf) = inf
85 * lgamma(-integer) = +-inf
86 *
87 */
88
89#include <math.h>
90
91#include "math_private.h"
92
93static const long double
94 half = 0.5L,
95 one = 1.0L,
96 pi = 3.14159265358979323846264L,
97 two63 = 9.223372036854775808e18L,
98
99 /* lgam(1+x) = 0.5 x + x a(x)/b(x)
100 -0.268402099609375 <= x <= 0
101 peak relative error 6.6e-22 */
102 a0 = -6.343246574721079391729402781192128239938E2L,
103 a1 = 1.856560238672465796768677717168371401378E3L,
104 a2 = 2.404733102163746263689288466865843408429E3L,
105 a3 = 8.804188795790383497379532868917517596322E2L,
106 a4 = 1.135361354097447729740103745999661157426E2L,
107 a5 = 3.766956539107615557608581581190400021285E0L,
108
109 b0 = 8.214973713960928795704317259806842490498E3L,
110 b1 = 1.026343508841367384879065363925870888012E4L,
111 b2 = 4.553337477045763320522762343132210919277E3L,
112 b3 = 8.506975785032585797446253359230031874803E2L,
113 b4 = 6.042447899703295436820744186992189445813E1L,
114 /* b5 = 1.000000000000000000000000000000000000000E0 */
115
116
117 tc = 1.4616321449683623412626595423257213284682E0L,
118 tf = -1.2148629053584961146050602565082954242826E-1,/* double precision */
119/* tt = (tail of tf), i.e. tf + tt has extended precision. */
120 tt = 3.3649914684731379602768989080467587736363E-18L,
121 /* lgam ( 1.4616321449683623412626595423257213284682E0 ) =
122-1.2148629053584960809551455717769158215135617312999903886372437313313530E-1 */
123
124 /* lgam (x + tc) = tf + tt + x g(x)/h(x)
125 - 0.230003726999612341262659542325721328468 <= x
126 <= 0.2699962730003876587373404576742786715318
127 peak relative error 2.1e-21 */
128 g0 = 3.645529916721223331888305293534095553827E-18L,
129 g1 = 5.126654642791082497002594216163574795690E3L,
130 g2 = 8.828603575854624811911631336122070070327E3L,
131 g3 = 5.464186426932117031234820886525701595203E3L,
132 g4 = 1.455427403530884193180776558102868592293E3L,
133 g5 = 1.541735456969245924860307497029155838446E2L,
134 g6 = 4.335498275274822298341872707453445815118E0L,
135
136 h0 = 1.059584930106085509696730443974495979641E4L,
137 h1 = 2.147921653490043010629481226937850618860E4L,
138 h2 = 1.643014770044524804175197151958100656728E4L,
139 h3 = 5.869021995186925517228323497501767586078E3L,
140 h4 = 9.764244777714344488787381271643502742293E2L,
141 h5 = 6.442485441570592541741092969581997002349E1L,
142 /* h6 = 1.000000000000000000000000000000000000000E0 */
143
144
145 /* lgam (x+1) = -0.5 x + x u(x)/v(x)
146 -0.100006103515625 <= x <= 0.231639862060546875
147 peak relative error 1.3e-21 */
148 u0 = -8.886217500092090678492242071879342025627E1L,
149 u1 = 6.840109978129177639438792958320783599310E2L,
150 u2 = 2.042626104514127267855588786511809932433E3L,
151 u3 = 1.911723903442667422201651063009856064275E3L,
152 u4 = 7.447065275665887457628865263491667767695E2L,
153 u5 = 1.132256494121790736268471016493103952637E2L,
154 u6 = 4.484398885516614191003094714505960972894E0L,
155
156 v0 = 1.150830924194461522996462401210374632929E3L,
157 v1 = 3.399692260848747447377972081399737098610E3L,
158 v2 = 3.786631705644460255229513563657226008015E3L,
159 v3 = 1.966450123004478374557778781564114347876E3L,
160 v4 = 4.741359068914069299837355438370682773122E2L,
161 v5 = 4.508989649747184050907206782117647852364E1L,
162 /* v6 = 1.000000000000000000000000000000000000000E0 */
163
164
165 /* lgam (x+2) = .5 x + x s(x)/r(x)
166 0 <= x <= 1
167 peak relative error 7.2e-22 */
168 s0 = 1.454726263410661942989109455292824853344E6L,
169 s1 = -3.901428390086348447890408306153378922752E6L,
170 s2 = -6.573568698209374121847873064292963089438E6L,
171 s3 = -3.319055881485044417245964508099095984643E6L,
172 s4 = -7.094891568758439227560184618114707107977E5L,
173 s5 = -6.263426646464505837422314539808112478303E4L,
174 s6 = -1.684926520999477529949915657519454051529E3L,
175
176 r0 = -1.883978160734303518163008696712983134698E7L,
177 r1 = -2.815206082812062064902202753264922306830E7L,
178 r2 = -1.600245495251915899081846093343626358398E7L,
179 r3 = -4.310526301881305003489257052083370058799E6L,
180 r4 = -5.563807682263923279438235987186184968542E5L,
181 r5 = -3.027734654434169996032905158145259713083E4L,
182 r6 = -4.501995652861105629217250715790764371267E2L,
183 /* r6 = 1.000000000000000000000000000000000000000E0 */
184
185
186/* lgam(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x w(1/x^2)
187 x >= 8
188 Peak relative error 1.51e-21
189 w0 = LS2PI - 0.5 */
190 w0 = 4.189385332046727417803e-1L,
191 w1 = 8.333333333333331447505E-2L,
192 w2 = -2.777777777750349603440E-3L,
193 w3 = 7.936507795855070755671E-4L,
194 w4 = -5.952345851765688514613E-4L,
195 w5 = 8.412723297322498080632E-4L,
196 w6 = -1.880801938119376907179E-3L,
197 w7 = 4.885026142432270781165E-3L;
198
199static const long double zero = 0.0L;
200
201static long double
202sin_pi(long double x)
203{
204 long double y, z;
205 int n, ix;
206 u_int32_t se, i0, i1;
207
208 GET_LDOUBLE_WORDS (se, i0, i1, x)do { ieee_extended_shape_type ew_u; ew_u.value = (x); (se) = ew_u
.parts.exp; (i0) = ew_u.parts.msw; (i1) = ew_u.parts.lsw; } while
(0)
;
209 ix = se & 0x7fff;
210 ix = (ix << 16) | (i0 >> 16);
211 if (ix < 0x3ffd8000) /* 0.25 */
212 return sinl (pi * x);
213 y = -x; /* x is assume negative */
214
215 /*
216 * argument reduction, make sure inexact flag not raised if input
217 * is an integer
218 */
219 z = floorl (y);
220 if (z != y)
221 { /* inexact anyway */
222 y *= 0.5;
223 y = 2.0*(y - floorl(y)); /* y = |x| mod 2.0 */
224 n = (int) (y*4.0);
225 }
226 else
227 {
228 if (ix >= 0x403f8000) /* 2^64 */
229 {
230 y = zero; n = 0; /* y must be even */
231 }
232 else
233 {
234 if (ix < 0x403e8000) /* 2^63 */
235 z = y + two63; /* exact */
236 GET_LDOUBLE_WORDS (se, i0, i1, z)do { ieee_extended_shape_type ew_u; ew_u.value = (z); (se) = ew_u
.parts.exp; (i0) = ew_u.parts.msw; (i1) = ew_u.parts.lsw; } while
(0)
;
237 n = i1 & 1;
238 y = n;
239 n <<= 2;
240 }
241 }
242
243 switch (n)
244 {
245 case 0:
246 y = sinl (pi * y);
247 break;
248 case 1:
249 case 2:
250 y = cosl (pi * (half - y));
251 break;
252 case 3:
253 case 4:
254 y = sinl (pi * (one - y));
255 break;
256 case 5:
257 case 6:
258 y = -cosl (pi * (y - 1.5));
259 break;
260 default:
261 y = sinl (pi * (y - 2.0));
262 break;
263 }
264 return -y;
265}
266
267
268long double
269lgammal(long double x)
270{
271 long double t, y, z, nadj, p, p1, p2, q, r, w;
272 int i, ix;
273 u_int32_t se, i0, i1;
274
275 signgam = 1;
276 GET_LDOUBLE_WORDS (se, i0, i1, x)do { ieee_extended_shape_type ew_u; ew_u.value = (x); (se) = ew_u
.parts.exp; (i0) = ew_u.parts.msw; (i1) = ew_u.parts.lsw; } while
(0)
;
277 ix = se & 0x7fff;
278
279 if ((ix | i0 | i1) == 0)
280 {
281 if (se & 0x8000)
282 signgam = -1;
283 return one / fabsl (x);
284 }
285
286 ix = (ix << 16) | (i0 >> 16);
287
288 /* purge off +-inf, NaN, +-0, and negative arguments */
289 if (ix >= 0x7fff0000)
290 return x * x;
291
292 if (ix < 0x3fc08000) /* 2^-63 */
293 { /* |x|<2**-63, return -log(|x|) */
294 if (se & 0x8000)
295 {
296 signgam = -1;
297 return -logl (-x);
298 }
299 else
300 return -logl (x);
301 }
302 if (se & 0x8000)
303 {
304 t = sin_pi (x);
305 if (t == zero)
306 return one / fabsl (t); /* -integer */
307 nadj = logl (pi / fabsl (t * x));
308 if (t < zero)
309 signgam = -1;
310 x = -x;
311 }
312
313 /* purge off 1 and 2 */
314 if ((((ix - 0x3fff8000) | i0 | i1) == 0)
315 || (((ix - 0x40008000) | i0 | i1) == 0))
316 r = 0;
317 else if (ix < 0x40008000) /* 2.0 */
318 {
319 /* x < 2.0 */
320 if (ix <= 0x3ffee666) /* 8.99993896484375e-1 */
321 {
322 /* lgamma(x) = lgamma(x+1) - log(x) */
323 r = -logl (x);
324 if (ix >= 0x3ffebb4a) /* 7.31597900390625e-1 */
325 {
326 y = x - one;
327 i = 0;
328 }
329 else if (ix >= 0x3ffced33)/* 2.31639862060546875e-1 */
330 {
331 y = x - (tc - one);
332 i = 1;
333 }
334 else
335 {
336 /* x < 0.23 */
337 y = x;
338 i = 2;
339 }
340 }
341 else
342 {
343 r = zero;
344 if (ix >= 0x3fffdda6) /* 1.73162841796875 */
345 {
346 /* [1.7316,2] */
347 y = x - 2.0;
348 i = 0;
349 }
350 else if (ix >= 0x3fff9da6)/* 1.23162841796875 */
351 {
352 /* [1.23,1.73] */
353 y = x - tc;
354 i = 1;
355 }
356 else
357 {
358 /* [0.9, 1.23] */
359 y = x - one;
360 i = 2;
361 }
362 }
363 switch (i)
364 {
365 case 0:
366 p1 = a0 + y * (a1 + y * (a2 + y * (a3 + y * (a4 + y * a5))));
367 p2 = b0 + y * (b1 + y * (b2 + y * (b3 + y * (b4 + y))));
368 r += half * y + y * p1/p2;
369 break;
370 case 1:
371 p1 = g0 + y * (g1 + y * (g2 + y * (g3 + y * (g4 + y * (g5 + y * g6)))));
372 p2 = h0 + y * (h1 + y * (h2 + y * (h3 + y * (h4 + y * (h5 + y)))));
373 p = tt + y * p1/p2;
374 r += (tf + p);
375 break;
376 case 2:
377 p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * (u5 + y * u6))))));
378 p2 = v0 + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * (v5 + y)))));
379 r += (-half * y + p1 / p2);
380 }
381 }
382 else if (ix < 0x40028000) /* 8.0 */
383 {
384 /* x < 8.0 */
385 i = (int) x;
386 t = zero;
Value stored to 't' is never read
387 y = x - (double) i;
388 p = y *
389 (s0 + y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6))))));
390 q = r0 + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * (r6 + y))))));
391 r = half * y + p / q;
392 z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
393 switch (i)
394 {
395 case 7:
396 z *= (y + 6.0); /* FALLTHRU */
397 case 6:
398 z *= (y + 5.0); /* FALLTHRU */
399 case 5:
400 z *= (y + 4.0); /* FALLTHRU */
401 case 4:
402 z *= (y + 3.0); /* FALLTHRU */
403 case 3:
404 z *= (y + 2.0); /* FALLTHRU */
405 r += logl (z);
406 break;
407 }
408 }
409 else if (ix < 0x40418000) /* 2^66 */
410 {
411 /* 8.0 <= x < 2**66 */
412 t = logl (x);
413 z = one / x;
414 y = z * z;
415 w = w0 + z * (w1
416 + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * (w6 + y * w7))))));
417 r = (x - half) * (t - one) + w;
418 }
419 else
420 /* 2**66 <= x <= inf */
421 r = x * (logl (x) - one);
422 if (se & 0x8000)
423 r = nadj - r;
424 return r;
425}
426DEF_STD(lgammal)__asm__(".global " "lgammal" " ; " "lgammal" " = " "_libm_lgammal"
)
;