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