/usr/src/lib/libm/src/e_powf.c

Bug Summary

File:	src/lib/libm/src/e_powf.c
Warning:	line 240, column 9 The result of the left shift is undefined because the left operand is negative

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_powf.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/e_powf.c

1/* e_powf.c -- float version of e_pow.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 const volatile float huge = 1.0e+30, tiny = 1.0e-30;
20 
21static const float
22bp[] = {1.0, 1.5,},
23dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
24dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
25zero    =  0.0,
26one	=  1.0,
27two	=  2.0,
28two24	=  16777216.0,	/* 0x4b800000 */
29	/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
30L1  =  6.0000002384e-01, /* 0x3f19999a */
31L2  =  4.2857143283e-01, /* 0x3edb6db7 */
32L3  =  3.3333334327e-01, /* 0x3eaaaaab */
33L4  =  2.7272811532e-01, /* 0x3e8ba305 */
34L5  =  2.3066075146e-01, /* 0x3e6c3255 */
35L6  =  2.0697501302e-01, /* 0x3e53f142 */
36P1   =  1.6666667163e-01, /* 0x3e2aaaab */
37P2   = -2.7777778450e-03, /* 0xbb360b61 */
38P3   =  6.6137559770e-05, /* 0x388ab355 */
39P4   = -1.6533901999e-06, /* 0xb5ddea0e */
40P5   =  4.1381369442e-08, /* 0x3331bb4c */
41lg2  =  6.9314718246e-01, /* 0x3f317218 */
42lg2_h  =  6.93145752e-01, /* 0x3f317200 */
43lg2_l  =  1.42860654e-06, /* 0x35bfbe8c */
44ovt =  4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
45cp    =  9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
46cp_h  =  9.6179199219e-01, /* 0x3f763800 =head of cp */
47cp_l  =  4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
48ivln2    =  1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
49ivln2_h  =  1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
50ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
51 
52float
53powf(float x, float y)
54{
55	float z,ax,z_h,z_l,p_h,p_l;
56	float yy1,t1,t2,r,s,t,u,v,w;
57	int32_t i,j,k,yisint,n;
58	int32_t hx,hy,ix,iy,is;
59 
60	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→
61	GET_FLOAT_WORD(hy,y)do { ieee_float_shape_type gf_u; gf_u.value = (y); (hy) = gf_u
.word; } while (0);
2
←
Loop condition is false.  Exiting loop→
62	ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
63 
64    /* y==zero: x**0 = 1 */
65	if(iy==0) return one; 	
3
←
Assuming 'iy' is not equal to 0→
4
←
Taking false branch→
66 
67    /* x==1: 1**y = 1, even if y is NaN */
68	if (hx==0x3f800000) return one;
5
←
Assuming 'hx' is not equal to 1065353216→
6
←
Taking false branch→
69 
70    /* +-NaN return x+y */
71	if(ix > 0x7f800000 ||
7
←
Assuming 'ix' is <= 2139095040→
9
←
Taking false branch→
72	   iy > 0x7f800000)
8
←
Assuming 'iy' is <= 2139095040→
73		return x+y;	
74 
75    /* determine if y is an odd int when x < 0
76     * yisint = 0	... y is not an integer
77     * yisint = 1	... y is an odd int
78     * yisint = 2	... y is an even int
79     */
80	yisint  = 0;
81	if(hx<0) {	
10
←
Assuming 'hx' is >= 0→
11
←
Taking false branch→
82	    if(iy>=0x4b800000) yisint = 2; /* even integer y */
83	    else if(iy>=0x3f800000) {
84		k = (iy>>23)-0x7f;	   /* exponent */
85		j = iy>>(23-k);
86		if((j<<(23-k))==iy) yisint = 2-(j&1);
87	    }		
88	} 
89 
90    /* special value of y */
91	if (iy==0x7f800000) {	/* y is +-inf */
12
←
Assuming 'iy' is not equal to 2139095040→
13
←
Taking false branch→
92	    if (ix==0x3f800000)
93	        return  one;	/* (-1)**+-inf is NaN */
94	    else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
95	        return (hy>=0)? y: zero;
96	    else			/* (|x|<1)**-,+inf = inf,0 */
97	        return (hy<0)?-y: zero;
98	} 
99	if(iy==0x3f800000) {	/* y is  +-1 */
14
←
Assuming 'iy' is not equal to 1065353216→
15
←
Taking false branch→
100	    if(hy<0) return one/x; else return x;
101	}
102	if(hy==0x40000000) return x*x; /* y is  2 */
16
←
Assuming 'hy' is not equal to 1073741824→
17
←
Taking false branch→
103	if(hy==0x3f000000) {	/* y is  0.5 */
18
←
Assuming 'hy' is not equal to 1056964608→
19
←
Taking false branch→
104	    if(hx>=0)	/* x >= +0 */
105	    return sqrtf(x);	
106	}
107 
108	ax   = fabsf(x);
109    /* special value of x */
110	if(ix==0x7f800000||ix==0||ix==0x3f800000){
20
←
Assuming 'ix' is not equal to 2139095040→
21
←
Assuming 'ix' is not equal to 0→
22
←
Assuming 'ix' is not equal to 1065353216→
23
←
Taking false branch→
111	    z = ax;			/*x is +-0,+-inf,+-1*/
112	    if(hy<0) z = one/z;	/* z = (1/|x|) */
113	    if(hx<0) {
114		if(((ix-0x3f800000)|yisint)==0) {
115		    z = (z-z)/(z-z); /* (-1)**non-int is NaN */
116		} else if(yisint==1) 
117		    z = -z;		/* (x<0)**odd = -(|x|**odd) */
118	    }
119	    return z;
120	}
121    
122    /* (x<0)**(non-int) is NaN */
123	if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
24
←
Assuming the condition is false→
25
←
Taking false branch→
124 
125    /* |y| is huge */
126	if(iy>0x4d000000) { /* if |y| > 2**27 */
26
←
Assuming 'iy' is > 1291845632→
27
←
Taking true branch→
127	/* over/underflow if x is not close to one */
128	    if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
28
←
Assuming 'ix' is >= 1065353208→
29
←
Taking false branch→
129	    if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
30
←
Assuming 'ix' is <= 1065353223→
31
←
Taking false branch→
130	/* now |1-x| is tiny <= 2**-20, suffice to compute 
131	   log(x) by x-x^2/2+x^3/3-x^4/4 */
132	    t = ax-one;		/* t has 20 trailing zeros */
133	    w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
134	    u = ivln2_h*t;	/* ivln2_h has 16 sig. bits */
135	    v = t*ivln2_l-w*ivln2;
136	    t1 = u+v;
137	    GET_FLOAT_WORD(is,t1)do { ieee_float_shape_type gf_u; gf_u.value = (t1); (is) = gf_u
.word; } while (0);
32
←
Loop condition is false.  Exiting loop→
138	    SET_FLOAT_WORD(t1,is&0xfffff000)do { ieee_float_shape_type sf_u; sf_u.word = (is&0xfffff000
); (t1) = sf_u.value; } while (0);
33
←
Loop condition is false.  Exiting loop→
139	    t2 = v-(t1-u);
140	} else {
141	    float s2,s_h,s_l,t_h,t_l;
142	    n = 0;
143	/* take care subnormal number */
144	    if(ix<0x00800000)
145		{ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax)do { ieee_float_shape_type gf_u; gf_u.value = (ax); (ix) = gf_u
.word; } while (0); }
146	    n  += ((ix)>>23)-0x7f;
147	    j  = ix&0x007fffff;
148	/* determine interval */
149	    ix = j|0x3f800000;		/* normalize ix */
150	    if(j<=0x1cc471) k=0;	/* |x|<sqrt(3/2) */
151	    else if(j<0x5db3d7) k=1;	/* |x|<sqrt(3)   */
152	    else {k=0;n+=1;ix -= 0x00800000;}
153	    SET_FLOAT_WORD(ax,ix)do { ieee_float_shape_type sf_u; sf_u.word = (ix); (ax) = sf_u
.value; } while (0);
154 
155	/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
156	    u = ax-bp[k];		/* bp[0]=1.0, bp[1]=1.5 */
157	    v = one/(ax+bp[k]);
158	    s = u*v;
159	    s_h = s;
160	    GET_FLOAT_WORD(is,s_h)do { ieee_float_shape_type gf_u; gf_u.value = (s_h); (is) = gf_u
.word; } while (0);
161	    SET_FLOAT_WORD(s_h,is&0xfffff000)do { ieee_float_shape_type sf_u; sf_u.word = (is&0xfffff000
); (s_h) = sf_u.value; } while (0);
162	/* t_h=ax+bp[k] High */
163	    SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21))do { ieee_float_shape_type sf_u; sf_u.word = (((ix>>1)|
0x20000000)+0x0040000+(k<<21)); (t_h) = sf_u.value; } while
 (0);
164	    t_l = ax - (t_h-bp[k]);
165	    s_l = v*((u-s_h*t_h)-s_h*t_l);
166	/* compute log(ax) */
167	    s2 = s*s;
168	    r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
169	    r += s_l*(s_h+s);
170	    s2  = s_h*s_h;
171	    t_h = (float)3.0+s2+r;
172	    GET_FLOAT_WORD(is,t_h)do { ieee_float_shape_type gf_u; gf_u.value = (t_h); (is) = gf_u
.word; } while (0);
173	    SET_FLOAT_WORD(t_h,is&0xfffff000)do { ieee_float_shape_type sf_u; sf_u.word = (is&0xfffff000
); (t_h) = sf_u.value; } while (0);
174	    t_l = r-((t_h-(float)3.0)-s2);
175	/* u+v = s*(1+...) */
176	    u = s_h*t_h;
177	    v = s_l*t_h+t_l*s;
178	/* 2/(3log2)*(s+...) */
179	    p_h = u+v;
180	    GET_FLOAT_WORD(is,p_h)do { ieee_float_shape_type gf_u; gf_u.value = (p_h); (is) = gf_u
.word; } while (0);
181	    SET_FLOAT_WORD(p_h,is&0xfffff000)do { ieee_float_shape_type sf_u; sf_u.word = (is&0xfffff000
); (p_h) = sf_u.value; } while (0);
182	    p_l = v-(p_h-u);
183	    z_h = cp_h*p_h;		/* cp_h+cp_l = 2/(3*log2) */
184	    z_l = cp_l*p_h+p_l*cp+dp_l[k];
185	/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
186	    t = (float)n;
187	    t1 = (((z_h+z_l)+dp_h[k])+t);
188	    GET_FLOAT_WORD(is,t1)do { ieee_float_shape_type gf_u; gf_u.value = (t1); (is) = gf_u
.word; } while (0);
189	    SET_FLOAT_WORD(t1,is&0xfffff000)do { ieee_float_shape_type sf_u; sf_u.word = (is&0xfffff000
); (t1) = sf_u.value; } while (0);
190	    t2 = z_l-(((t1-t)-dp_h[k])-z_h);
191	}
192 
193	s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
194	if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
34
←
Taking false branch→
195	    s = -one;	/* (-ve)**(odd int) */
196 
197    /* split up y into yy1+y2 and compute (yy1+y2)*(t1+t2) */
198	GET_FLOAT_WORD(is,y)do { ieee_float_shape_type gf_u; gf_u.value = (y); (is) = gf_u
.word; } while (0);
35
←
Loop condition is false.  Exiting loop→
199	SET_FLOAT_WORD(yy1,is&0xfffff000)do { ieee_float_shape_type sf_u; sf_u.word = (is&0xfffff000
); (yy1) = sf_u.value; } while (0);
36
←
Loop condition is false.  Exiting loop→
200	p_l = (y-yy1)*t1+y*t2;
201	p_h = yy1*t1;
202	z = p_l+p_h;
203	GET_FLOAT_WORD(j,z)do { ieee_float_shape_type gf_u; gf_u.value = (z); (j) = gf_u
.word; } while (0);
37
←
Loop condition is false.  Exiting loop→
204	if (j>0x43000000)				/* if z > 128 */
38
←
Assuming 'j' is <= 1124073472→
39
←
Taking false branch→
205	    return s*huge*huge;				/* overflow */
206	else if (j==0x43000000) {			/* if z == 128 */
40
←
Assuming 'j' is not equal to 1124073472→
41
←
Taking false branch→
207	    if(p_l+ovt>z-p_h) return s*huge*huge;	/* overflow */
208	}
209	else if ((j&0x7fffffff)>0x43160000)		/* z <= -150 */
42
←
Assuming the condition is false→
43
←
Taking false branch→
210	    return s*tiny*tiny;				/* underflow */
211	else if (j==0xc3160000){			/* z == -150 */
44
←
Assuming 'j' is equal to -1021968384→
45
←
Taking true branch→
212	    if(p_l<=z-p_h) return s*tiny*tiny;		/* underflow */
46
←
Assuming the condition is false→
47
←
Taking false branch→
213	}
214    /*
215     * compute 2**(p_h+p_l)
216     */
217	i = j&0x7fffffff;
218	k = (i>>23)-0x7f;
219	n = 0;
220	if(i47.1
'i' is > 1056964608
>0x3f000000) {		/* if |z| > 0.5, set n = [z+0.5] */
48
←
Taking true branch→
221	    n = j+(0x00800000>>(k+1));
222	    k = ((n&0x7fffffff)>>23)-0x7f;	/* new k for n */
223	    SET_FLOAT_WORD(t,n&~(0x007fffff>>k))do { ieee_float_shape_type sf_u; sf_u.word = (n&~(0x007fffff
>>k)); (t) = sf_u.value; } while (0);
49
←
Loop condition is false.  Exiting loop→
224	    n = ((n&0x007fffff)|0x00800000)>>(23-k);
225	    if(j49.1
'j' is < 0
<0) n = -n;
50
←
Taking true branch→
51
←
The value -150 is assigned to 'n'→
226	    p_h -= t;
227	} 
228	t = p_l+p_h;
229	GET_FLOAT_WORD(is,t)do { ieee_float_shape_type gf_u; gf_u.value = (t); (is) = gf_u
.word; } while (0);
52
←
Loop condition is false.  Exiting loop→
230	SET_FLOAT_WORD(t,is&0xfffff000)do { ieee_float_shape_type sf_u; sf_u.word = (is&0xfffff000
); (t) = sf_u.value; } while (0);
53
←
Loop condition is false.  Exiting loop→
231	u = t*lg2_h;
232	v = (p_l-(t-p_h))*lg2+t*lg2_l;
233	z = u+v;
234	w = v-(z-u);
235	t  = z*z;
236	t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
237	r  = (z*t1)/(t1-two)-(w+z*w);
238	z  = one-(r-z);
239	GET_FLOAT_WORD(j,z)do { ieee_float_shape_type gf_u; gf_u.value = (z); (j) = gf_u
.word; } while (0);
54
←
Loop condition is false.  Exiting loop→
240	j += (n<<23);
55
←
The result of the left shift is undefined because the left operand is negative
241	if((j>>23)<=0) z = scalbnf(z,n);	/* subnormal output */
242	else SET_FLOAT_WORD(z,j)do { ieee_float_shape_type sf_u; sf_u.word = (j); (z) = sf_u.
value; } while (0);
243	return s*z;
244}
245DEF_STD(powf)__asm__(".global " "powf" " ; " "powf" " = " "_libm_powf");