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
53static const double
54bp[] = {1.0, 1.5,},
55dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
56dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
57zero = 0.0,
58one = 1.0,
59two = 2.0,
60two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
61huge = 1.0e300,
62tiny = 1.0e-300,
63 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
64L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
65L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
66L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
67L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
68L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
69L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
70P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
71P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
72P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
73P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
74P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
75lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
76lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
77lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
78ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
79cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
80cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
81cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
82ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
83ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
84ivln2_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
139double 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}