### Bug Summary

File: | real/pow.c
Location: | line 148, column 5
Description: | Value stored to 'i1' is never read

### Annotated Source Code

1 | /* @(#)e_pow.c 1.5 04/04/22 SMI */
2 |
3 | /*
4 | * Copyright (c) 2015-2017 Carsten Sonne Larsen <cs@innolan.dk>
5 | * All rights reserved.
6 | *
7 | * Redistribution and use in source and binary forms, with or without
8 | * modification, are permitted provided that the following conditions
9 | * are met:
10 | * 1. Redistributions of source code must retain the above copyright
11 | * notice, this list of conditions and the following disclaimer.
12 | * 2. Redistributions in binary form must reproduce the above copyright
13 | * notice, this list of conditions and the following disclaimer in the
14 | * documentation and/or other materials provided with the distribution.
15 | *
16 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
17 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
18 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
19 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
20 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
21 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
22 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
23 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
24 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
25 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
26 | *
27 | * The origin source code can be obtained from:
28 | * http://www.netlib.org/fdlibm/e_pow.c
29 | *
30 | */
31 |
32 | /*
33 | * ====================================================
34 | * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
35 | *
36 | * Permission to use, copy, modify, and distribute this
37 | * software is freely granted, provided that this notice
38 | * is preserved.
39 | * ====================================================
40 | */
41 |
42 | #include "prim.h"
43 | #include "math.h"
44 |
45 | #ifdef __clang__1
46 | # pragma clang diagnostic ignored "-Wunused-variable"
47 | # pragma clang diagnostic ignored "-Wstrict-aliasing"
48 | #elif defined(__GNUC__4) && __GNUC__4 > 2
49 | # pragma GCC diagnostic ignored "-Wunused-but-set-variable"
50 | # pragma GCC diagnostic ignored "-Wstrict-aliasing"
51 | #endif
52 |
53 | static const double
54 | bp[] = {1.0, 1.5,},
55 | dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
56 | dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
57 | zero = 0.0,
58 | one = 1.0,
59 | two = 2.0,
60 | two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
61 | huge = 1.0e300,
62 | tiny = 1.0e-300,
63 | /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
64 | L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
65 | L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
66 | L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
67 | L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
68 | L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
69 | L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
70 | P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
71 | P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
72 | P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
73 | P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
74 | P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
75 | lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
76 | lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
77 | lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
78 | ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
79 | cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
80 | cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
81 | cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
82 | ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
83 | ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
84 | ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
85 |
86 | /**
87 | * @brief Expontation function.
88 | * @version 1.3
89 | * @date 95/01/18
90 | * @details
91 | * <pre>
92 | * Method: Let x = 2 * (1+f)
93 | * 1. Compute and return log2(x) in two pieces:
94 | * log2(x) = w1 + w2,
95 | * where w1 has 53-24 = 29 bit trailing zeros.
96 | * 2. Perform y*log2(x) = n+y' by simulating muti-precision
97 | * arithmetic, where |y'|<=0.5.
98 | * 3. Return x**y = 2**n*exp(y'*log2)
99 | *
100 | * Special cases:
101 | * 1. (anything) ** 0 is 1
102 | * 2. (anything) ** 1 is itself
103 | * 3. (anything) ** NAN is NAN
104 | * 4. NAN ** (anything except 0) is NAN
105 | * 5. +-(|x| > 1) ** +INF is +INF
106 | * 6. +-(|x| > 1) ** -INF is +0
107 | * 7. +-(|x| < 1) ** +INF is +0
108 | * 8. +-(|x| < 1) ** -INF is +INF
109 | * 9. +-1 ** +-INF is NAN
110 | * 10. +0 ** (+anything except 0, NAN) is +0
111 | * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
112 | * 12. +0 ** (-anything except 0, NAN) is +INF
113 | * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
114 | * 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
115 | * 15. +INF ** (+anything except 0,NAN) is +INF
116 | * 16. +INF ** (-anything except 0,NAN) is +0
117 | * 17. -INF ** (anything) = -0 ** (-anything)
118 | * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
119 | * 19. (-anything except 0 and inf) ** (non-integer) is NAN
120 | *
121 | * Accuracy:
122 | * pow(x,y) returns x**y nearly rounded. In particular
123 | * pow(integer,integer)
124 | * always returns the correct integer provided it is
125 | * representable.
126 | *
127 | * Constants :
128 | * The hexadecimal values are the intended ones for the following
129 | * constants. The decimal values may be used, provided that the
130 | * compiler will convert from decimal to binary accurately enough
131 | * to produce the hexadecimal values shown.
132 | * </pre>
133 | * @copyright Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
134 | * @license Developed at SunSoft, a Sun Microsystems, Inc. business. Permission
135 | * to use, copy, modify, and distribute this software is freely granted,
136 | * provided that this notice is preserved.
137 | */
138 |
139 | double pow(double x, double y)
140 | {
141 | double z,ax,z_h,z_l,p_h,p_l;
142 | double y1,t1,t2,r,s,t,u,v,w;
143 | sword i0,i1,i,j,k,yisint,n;
144 | sword hx,hy,ix,iy;
145 | uword lx,ly;
146 |
147 | i0 = ((*(int*)&one)>>29)^1;
148 | i1=1-i0;
| Value stored to 'i1' is never read
149 | 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);
150 | EXTRACT_WORDS(hy,ly,y)do { ieee_double_shape_type ew_u; ew_u.value = (y); (hy) = ew_u .parts.msw; (ly) = ew_u.parts.lsw; } while (0);
151 | ix = hx&0x7fffffff;
152 | iy = hy&0x7fffffff;
153 |
154 | /* y==zero: x**0 = 1 */
155 | if((iy|ly)==0) return one;
156 |
157 | /* +-NaN return x+y */
158 | if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
159 | iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
160 | return x+y;
161 |
162 | /* determine if y is an odd int when x < 0
163 | * yisint = 0 ... y is not an integer
164 | * yisint = 1 ... y is an odd int
165 | * yisint = 2 ... y is an even int
166 | */
167 | yisint = 0;
168 | if(hx<0) {
169 | if(iy>=0x43400000) yisint = 2; /* even integer y */
170 | else if(iy>=0x3ff00000) {
171 | k = (iy>>20)-0x3ff; /* exponent */
172 | if(k>20) {
173 | j = ly>>(52-k);
174 | if((uword)(j<<(52-k))==ly) yisint = 2-(j&1);
175 | } else if(ly==0) {
176 | j = iy>>(20-k);
177 | if((j<<(20-k))==iy) yisint = 2-(j&1);
178 | }
179 | }
180 | }
181 |
182 | /* special value of y */
183 | if(ly==0) {
184 | if (iy==0x7ff00000) { /* y is +-inf */
185 | if(((ix-0x3ff00000)|lx)==0)
186 | return y - y; /* inf**+-1 is NaN */
187 | else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
188 | return (hy>=0)? y: zero;
189 | else /* (|x|<1)**-,+inf = inf,0 */
190 | return (hy<0)?-y: zero;
191 | }
192 | if(iy==0x3ff00000) { /* y is +-1 */
193 | if(hy<0) return one/x;
194 | else return x;
195 | }
196 | if(hy==0x40000000) return x*x; /* y is 2 */
197 | if(hy==0x3fe00000) { /* y is 0.5 */
198 | if(hx>=0) /* x >= +0 */
199 | return sqrt(x);
200 | }
201 | }
202 |
203 | ax = fabs(x);
204 | /* special value of x */
205 | if(lx==0) {
206 | if(ix==0x7ff00000||ix==0||ix==0x3ff00000) {
207 | z = ax; /*x is +-0,+-inf,+-1*/
208 | if(hy<0) z = one/z; /* z = (1/|x|) */
209 | if(hx<0) {
210 | if(((ix-0x3ff00000)|yisint)==0) {
211 | z = (z-z)/(z-z); /* (-1)**non-int is NaN */
212 | } else if(yisint==1)
213 | z = -z; /* (x<0)**odd = -(|x|**odd) */
214 | }
215 | return z;
216 | }
217 | }
218 |
219 | n = (hx>>31)+1;
220 |
221 | /* (x<0)**(non-int) is NaN */
222 | if((n|yisint)==0) return (x-x)/(x-x);
223 |
224 | s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
225 | if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
226 |
227 | /* |y| is huge */
228 | if(iy>0x41e00000) { /* if |y| > 2**31 */
229 | if(iy>0x43f00000) { /* if |y| > 2**64, must o/uflow */
230 | if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
231 | if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
232 | }
233 | /* over/underflow if x is not close to one */
234 | if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
235 | if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
236 | /* now |1-x| is tiny <= 2**-20, suffice to compute
237 | log(x) by x-x^2/2+x^3/3-x^4/4 */
238 | t = ax-one; /* t has 20 trailing zeros */
239 | w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
240 | u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
241 | v = t*ivln2_l-w*ivln2;
242 | t1 = u+v;
243 | SET_LOW_WORD(t1,0)do { ieee_double_shape_type sl_u; sl_u.value = (t1); sl_u.parts .lsw = (0); (t1) = sl_u.value; } while (0);
244 | t2 = v-(t1-u);
245 | } else {
246 | double ss,s2,s_h,s_l,t_h,t_l;
247 | n = 0;
248 | /* take care subnormal number */
249 | if(ix<0x00100000)
250 | {
251 | ax *= two53;
252 | n -= 53;
253 | GET_HIGH_WORD(ix,ax)do { ieee_double_shape_type gh_u; gh_u.value = (ax); (ix) = gh_u .parts.msw; } while (0);
254 | }
255 | n += ((ix)>>20)-0x3ff;
256 | j = ix&0x000fffff;
257 | /* determine interval */
258 | ix = j|0x3ff00000; /* normalize ix */
259 | if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
260 | else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
261 | else {
262 | k=0;
263 | n+=1;
264 | ix -= 0x00100000;
265 | }
266 | SET_HIGH_WORD(ax,ix)do { ieee_double_shape_type sh_u; sh_u.value = (ax); sh_u.parts .msw = (ix); (ax) = sh_u.value; } while (0);
267 |
268 | /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
269 | u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
270 | v = one/(ax+bp[k]);
271 | ss = u*v;
272 | s_h = ss;
273 | SET_LOW_WORD(s_h,0)do { ieee_double_shape_type sl_u; sl_u.value = (s_h); sl_u.parts .lsw = (0); (s_h) = sl_u.value; } while (0);
274 | /* t_h=ax+bp[k] High */
275 | t_h = zero;
276 | SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18))do { ieee_double_shape_type sh_u; sh_u.value = (t_h); sh_u.parts .msw = (((ix>>1)|0x20000000)+0x00080000+(k<<18)); (t_h) = sh_u.value; } while (0);
277 | t_l = ax - (t_h-bp[k]);
278 | s_l = v*((u-s_h*t_h)-s_h*t_l);
279 | /* compute log(ax) */
280 | s2 = ss*ss;
281 | r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
282 | r += s_l*(s_h+ss);
283 | s2 = s_h*s_h;
284 | t_h = 3.0+s2+r;
285 | SET_LOW_WORD(t_h,0)do { ieee_double_shape_type sl_u; sl_u.value = (t_h); sl_u.parts .lsw = (0); (t_h) = sl_u.value; } while (0);
286 | t_l = r-((t_h-3.0)-s2);
287 | /* u+v = ss*(1+...) */
288 | u = s_h*t_h;
289 | v = s_l*t_h+t_l*ss;
290 | /* 2/(3log2)*(ss+...) */
291 | p_h = u+v;
292 | SET_LOW_WORD(p_h,0)do { ieee_double_shape_type sl_u; sl_u.value = (p_h); sl_u.parts .lsw = (0); (p_h) = sl_u.value; } while (0);
293 | p_l = v-(p_h-u);
294 | z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
295 | z_l = cp_l*p_h+p_l*cp+dp_l[k];
296 | /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
297 | t = (double)n;
298 | t1 = (((z_h+z_l)+dp_h[k])+t);
299 | SET_LOW_WORD(t1,0)do { ieee_double_shape_type sl_u; sl_u.value = (t1); sl_u.parts .lsw = (0); (t1) = sl_u.value; } while (0);
300 | t2 = z_l-(((t1-t)-dp_h[k])-z_h);
301 | }
302 |
303 | /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
304 | y1 = y;
305 | SET_LOW_WORD(y1,0)do { ieee_double_shape_type sl_u; sl_u.value = (y1); sl_u.parts .lsw = (0); (y1) = sl_u.value; } while (0);
306 | p_l = (y-y1)*t1+y*t2;
307 | p_h = y1*t1;
308 | z = p_l+p_h;
309 | EXTRACT_WORDS(j,i,z)do { ieee_double_shape_type ew_u; ew_u.value = (z); (j) = ew_u .parts.msw; (i) = ew_u.parts.lsw; } while (0);
310 | if (j>=0x40900000) { /* z >= 1024 */
311 | if(((j-0x40900000)|i)!=0) /* if z > 1024 */
312 | return s*huge*huge; /* overflow */
313 | else {
314 | if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
315 | }
316 | } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
317 | if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
318 | return s*tiny*tiny; /* underflow */
319 | else {
320 | if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
321 | }
322 | }
323 | /*
324 | * compute 2**(p_h+p_l)
325 | */
326 | i = j&0x7fffffff;
327 | k = (i>>20)-0x3ff;
328 | n = 0;
329 | if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
330 | n = j+(0x00100000>>(k+1));
331 | k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
332 | t = zero;
333 | SET_HIGH_WORD(t,(n&~(0x000fffff>>k)))do { ieee_double_shape_type sh_u; sh_u.value = (t); sh_u.parts .msw = ((n&~(0x000fffff>>k))); (t) = sh_u.value; } while (0);
334 | n = ((n&0x000fffff)|0x00100000)>>(20-k);
335 | if(j<0) n = -n;
336 | p_h -= t;
337 | }
338 | t = p_l+p_h;
339 | SET_LOW_WORD(t,0)do { ieee_double_shape_type sl_u; sl_u.value = (t); sl_u.parts .lsw = (0); (t) = sl_u.value; } while (0);
340 | u = t*lg2_h;
341 | v = (p_l-(t-p_h))*lg2+t*lg2_l;
342 | z = u+v;
343 | w = v-(z-u);
344 | t = z*z;
345 | t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
346 | r = (z*t1)/(t1-two)-(w+z*w);
347 | z = one-(r-z);
348 | GET_HIGH_WORD(j,z)do { ieee_double_shape_type gh_u; gh_u.value = (z); (j) = gh_u .parts.msw; } while (0);
349 | j += (n<<20);
350 | if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */
351 | else
352 | {
353 | uword hz;
354 | GET_HIGH_WORD(hz,z)do { ieee_double_shape_type gh_u; gh_u.value = (z); (hz) = gh_u .parts.msw; } while (0);
355 | SET_HIGH_WORD(z,hz + (n<<20))do { ieee_double_shape_type sh_u; sh_u.value = (z); sh_u.parts .msw = (hz + (n<<20)); (z) = sh_u.value; } while (0);
356 | }
357 | return s*z;
358 | }