### Bug Summary

File: | real/remp2.c
Location: | line 202, column 19
Description: | The left operand of '==' is a garbage value

### Annotated Source Code

1 | /* @(#)e_rem_pio2.c 1.4 95/01/18 */
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_rem_pio2.c
29 | *
30 | */
31 |
32 | /*
33 | * ====================================================
34 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
35 | *
36 | * Developed at SunSoft, a Sun Microsystems, Inc. business.
37 | * Permission to use, copy, modify, and distribute this
38 | * software is freely granted, provided that this notice
39 | * is preserved.
40 | * ====================================================
41 | *
42 | */
43 |
44 | #include "prim.h"
45 | #include "math.h"
46 |
47 | /* rem_pio2(x,y)
48 | *
49 | * return the remainder of x rem pi/2 in y[0]+y[1]
50 | * use __kernel_rem_pio2()
51 | */
52 |
53 |
54 | /*
55 | * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
56 | */
57 |
58 | static const int two_over_pi[] = {
59 | 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
60 | 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
61 | 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
62 | 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
63 | 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
64 | 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
65 | 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
66 | 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
67 | 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
68 | 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
69 | 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
70 | };
71 |
72 | static const int npio2_hw[] = {
73 | 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
74 | 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
75 | 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
76 | 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
77 | 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
78 | 0x404858EB, 0x404921FB,
79 | };
80 |
81 | /*
82 | * invpio2: 53 bits of 2/pi
83 | * pio2_1: first 33 bit of pi/2
84 | * pio2_1t: pi/2 - pio2_1
85 | * pio2_2: second 33 bit of pi/2
86 | * pio2_2t: pi/2 - (pio2_1+pio2_2)
87 | * pio2_3: third 33 bit of pi/2
88 | * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
89 | */
90 |
91 | static const double
92 | zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
93 | half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
94 | two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
95 | invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
96 | pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
97 | pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
98 | pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
99 | pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
100 | pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
101 | pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
102 |
103 | int rempio2(double x, double *y)
104 | {
105 | double z = 0.,w,t,r,fn;
106 | double tx[3];
107 | sword i,j,n,ix,hx;
108 | int e0,nx;
109 | uword low;
110 |
111 | GET_HIGH_WORD(hx,x)do { ieee_double_shape_type gh_u; gh_u.value = (x); (hx) = gh_u .parts.msw; } while (0); /* high word of x */
112 | ix = hx&0x7fffffff;
113 | if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */

1 | Assuming 'ix' is > 1072243195 |

2 |

Taking false branch

114 {
115 y[0] = x;
116 y[1] = 0;
117 return 0;
118 }
119 if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */

3 |

Assuming 'ix' is >= 1073928572

4 |

Taking false branch
120 if(hx>0) {
121 z = x - pio2_1;
122 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
123 y[0] = z - pio2_1t;
124 y[1] = (z-y[0])-pio2_1t;
125 } else { /* near pi/2, use 33+33+53 bit pi */
126 z -= pio2_2;
127 y[0] = z - pio2_2t;
128 y[1] = (z-y[0])-pio2_2t;
129 }
130 return 1;
131 } else { /* negative x */
132 z = x + pio2_1;
133 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
134 y[0] = z + pio2_1t;
135 y[1] = (z-y[0])+pio2_1t;
136 } else { /* near pi/2, use 33+33+53 bit pi */
137 z += pio2_2;
138 y[0] = z + pio2_2t;
139 y[1] = (z-y[0])+pio2_2t;
140 }
141 return -1;
142 }
143 }
144 if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */

5 |

Assuming 'ix' is > 1094263291

6 |

Taking false branch
145 t = fabs(x);
146 n = (sword) (t*invpio2+half);
147 fn = (double)n;
148 r = t-fn*pio2_1;
149 w = fn*pio2_1t; /* 1st round good to 85 bit */
150 if(n<32&&ix!=npio2_hw[n-1]) {
151 y[0] = r-w; /* quick check no cancellation */
152 } else {
153 uword high;
154
155 j = ix>>20;
156 y[0] = r-w;
157 GET_HIGH_WORD(high, y[0])do { ieee_double_shape_type gh_u; gh_u.value = (y[0]); (high)
= gh_u.parts.msw; } while (0);
158 i = j-((high>>20)&0x7ff);
159 if(i>16) { /* 2nd iteration needed, good to 118 */
160 t = r;
161 w = fn*pio2_2;
162 r = t-w;
163 w = fn*pio2_2t-((t-r)-w);
164 y[0] = r-w;
165 GET_HIGH_WORD(high,y[0])do { ieee_double_shape_type gh_u; gh_u.value = (y[0]); (high)
= gh_u.parts.msw; } while (0);
166 i = j-((high>>20)&0x7ff);
167 if(i>49) { /* 3rd iteration need, 151 bits acc */
168 t = r; /* will cover all possible cases */
169 w = fn*pio2_3;
170 r = t-w;
171 w = fn*pio2_3t-((t-r)-w);
172 y[0] = r-w;
173 }
174 }
175 }
176 y[1] = (r-y[0])-w;
177 if(hx<0) {
178 y[0] = -y[0];
179 y[1] = -y[1];
180 return -n;
181 }
182 else return n;
183 }
184 /*
185 * all other (large) arguments
186 */
187 if(ix>=0x7ff00000) { /* x is inf or NaN */

7 |

Assuming 'ix' is < 2146435072

8 |

Taking false branch
188 y[0]=y[1]=x-x;
189 return 0;
190 }
191 /* set z = scalbn(|x|,ilogb(x)-23) */
192 GET_LOW_WORD(low,x)do { ieee_double_shape_type gl_u; gl_u.value = (x); (low) = gl_u
.parts.lsw; } while (0);
193 SET_LOW_WORD(z,low)do { ieee_double_shape_type sl_u; sl_u.value = (z); sl_u.parts
.lsw = (low); (z) = sl_u.value; } while (0);
194 e0 = (sword)(ix>>20)-1046; /* e0 = ilogb(z)-23; */
195 SET_HIGH_WORD(z,ix - (e0<<20))do { ieee_double_shape_type sh_u; sh_u.value = (z); sh_u.parts
.msw = (ix - (e0<<20)); (z) = sh_u.value; } while (0);
196 for(i=0; i<2; i++) {

9 |

Loop condition is true. Entering loop body

10 |

Loop condition is true. Entering loop body

11 |

Loop condition is false. Execution continues on line 200
197 tx[i] = (double)((sword)(z));
198 z = (z-tx[i])*two24;
199 }
200 tx[2] = z;
201 nx = 3;
202 while(tx[nx-1]==zero) nx--; /* skip zero term */

12 |

Loop condition is true. Entering loop body

13 |

Loop condition is true. Entering loop body

14 |

Loop condition is true. Entering loop body

15 |

The left operand of '==' is a garbage value
203 n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
204 if(hx<0) {
205 y[0] = -y[0];
206 y[1] = -y[1];
207 return -n;
208 }
209 return n;
210}