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11210 libm should be cstyle(1ONBLD) clean
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--- old/usr/src/lib/libm/common/C/log1p.c
+++ new/usr/src/lib/libm/common/C/log1p.c
1 1 /*
2 2 * CDDL HEADER START
3 3 *
4 4 * The contents of this file are subject to the terms of the
5 5 * Common Development and Distribution License (the "License").
6 6 * You may not use this file except in compliance with the License.
7 7 *
8 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 9 * or http://www.opensolaris.org/os/licensing.
10 10 * See the License for the specific language governing permissions
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11 11 * and limitations under the License.
12 12 *
13 13 * When distributing Covered Code, include this CDDL HEADER in each
14 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 15 * If applicable, add the following below this CDDL HEADER, with the
16 16 * fields enclosed by brackets "[]" replaced with your own identifying
17 17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 18 *
19 19 * CDDL HEADER END
20 20 */
21 +
21 22 /*
22 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 24 */
25 +
24 26 /*
25 27 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 28 * Use is subject to license terms.
27 29 */
28 30
29 31 #pragma weak __log1p = log1p
30 32
31 -/* INDENT OFF */
33 +
32 34 /*
33 35 * Method :
34 36 * 1. Argument Reduction: find k and f such that
35 37 * 1+x = 2^k * (1+f),
36 38 * where sqrt(2)/2 < 1+f < sqrt(2) .
37 39 *
38 40 * Note. If k=0, then f=x is exact. However, if k != 0, then f
39 41 * may not be representable exactly. In that case, a correction
40 42 * term is need. Let u=1+x rounded. Let c = (1+x)-u, then
41 43 * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
42 44 * and add back the correction term c/u.
43 45 * (Note: when x > 2**53, one can simply return log(x))
44 46 *
45 47 * 2. Approximation of log1p(f).
46 48 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
47 49 * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
48 50 * = 2s + s*R
49 51 * We use a special Reme algorithm on [0,0.1716] to generate
50 - * a polynomial of degree 14 to approximate R The maximum error
52 + * a polynomial of degree 14 to approximate R The maximum error
51 53 * of this polynomial approximation is bounded by 2**-58.45. In
52 54 * other words,
53 55 * 2 4 6 8 10 12 14
54 56 * R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s
55 - * (the values of Lp1 to Lp7 are listed in the program)
57 + * (the values of Lp1 to Lp7 are listed in the program)
56 58 * and
57 59 * | 2 14 | -58.45
58 60 * | Lp1*s +...+Lp7*s - R(z) | <= 2
59 61 * | |
60 62 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
61 63 * In order to guarantee error in log below 1ulp, we compute log
62 64 * by
63 65 * log1p(f) = f - (hfsq - s*(hfsq+R)).
64 66 *
65 67 * 3. Finally, log1p(x) = k*ln2 + log1p(f).
66 68 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
67 69 * Here ln2 is splitted into two floating point number:
68 70 * ln2_hi + ln2_lo,
69 71 * where n*ln2_hi is always exact for |n| < 2000.
70 72 *
71 73 * Special cases:
72 74 * log1p(x) is NaN with signal if x < -1 (including -INF) ;
73 75 * log1p(+INF) is +INF; log1p(-1) is -INF with signal;
74 76 * log1p(NaN) is that NaN with no signal.
75 77 *
76 78 * Accuracy:
77 79 * according to an error analysis, the error is always less than
78 80 * 1 ulp (unit in the last place).
79 81 *
80 82 * Constants:
81 83 * The hexadecimal values are the intended ones for the following
82 84 * constants. The decimal values may be used, provided that the
83 85 * compiler will convert from decimal to binary accurately enough
84 86 * to produce the hexadecimal values shown.
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85 87 *
86 88 * Note: Assuming log() return accurate answer, the following
87 89 * algorithm can be used to compute log1p(x) to within a few ULP:
88 90 *
89 91 * u = 1+x;
90 92 * if (u == 1.0) return x ; else
91 93 * return log(u)*(x/(u-1.0));
92 94 *
93 95 * See HP-15C Advanced Functions Handbook, p.193.
94 96 */
95 -/* INDENT ON */
96 97
97 98 #include "libm.h"
98 99
99 100 static const double xxx[] = {
100 -/* ln2_hi */ 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
101 -/* ln2_lo */ 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
102 -/* two54 */ 1.80143985094819840000e+16, /* 43500000 00000000 */
103 -/* Lp1 */ 6.666666666666735130e-01, /* 3FE55555 55555593 */
104 -/* Lp2 */ 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
105 -/* Lp3 */ 2.857142874366239149e-01, /* 3FD24924 94229359 */
106 -/* Lp4 */ 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
107 -/* Lp5 */ 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
108 -/* Lp6 */ 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
109 -/* Lp7 */ 1.479819860511658591e-01, /* 3FC2F112 DF3E5244 */
110 -/* zero */ 0.0
101 +/* ln2_hi */
102 + 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
103 +/* ln2_lo */ 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
104 +/* two54 */ 1.80143985094819840000e+16, /* 43500000 00000000 */
105 +/* Lp1 */ 6.666666666666735130e-01, /* 3FE55555 55555593 */
106 +/* Lp2 */ 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
107 +/* Lp3 */ 2.857142874366239149e-01, /* 3FD24924 94229359 */
108 +/* Lp4 */ 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
109 +/* Lp5 */ 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
110 +/* Lp6 */ 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
111 +/* Lp7 */ 1.479819860511658591e-01, /* 3FC2F112 DF3E5244 */
112 +/* zero */ 0.0
111 113 };
112 -#define ln2_hi xxx[0]
113 -#define ln2_lo xxx[1]
114 -#define two54 xxx[2]
115 -#define Lp1 xxx[3]
116 -#define Lp2 xxx[4]
117 -#define Lp3 xxx[5]
118 -#define Lp4 xxx[6]
119 -#define Lp5 xxx[7]
120 -#define Lp6 xxx[8]
121 -#define Lp7 xxx[9]
122 -#define zero xxx[10]
114 +
115 +#define ln2_hi xxx[0]
116 +#define ln2_lo xxx[1]
117 +#define two54 xxx[2]
118 +#define Lp1 xxx[3]
119 +#define Lp2 xxx[4]
120 +#define Lp3 xxx[5]
121 +#define Lp4 xxx[6]
122 +#define Lp5 xxx[7]
123 +#define Lp6 xxx[8]
124 +#define Lp7 xxx[9]
125 +#define zero xxx[10]
123 126
124 127 double
125 -log1p(double x) {
126 - double hfsq, f, c = 0.0, s, z, R, u;
127 - int k, hx, hu, ax;
128 +log1p(double x)
129 +{
130 + double hfsq, f, c = 0.0, s, z, R, u;
131 + int k, hx, hu, ax;
128 132
129 - hx = ((int *)&x)[HIWORD]; /* high word of x */
133 + hx = ((int *)&x)[HIWORD]; /* high word of x */
130 134 ax = hx & 0x7fffffff;
131 135
132 - if (ax >= 0x7ff00000) { /* x is inf or nan */
136 + if (ax >= 0x7ff00000) { /* x is inf or nan */
133 137 if (((hx - 0xfff00000) | ((int *)&x)[LOWORD]) == 0) /* -inf */
134 138 return (_SVID_libm_err(x, x, 44));
139 +
135 140 return (x * x);
136 141 }
137 142
138 143 k = 1;
139 - if (hx < 0x3FDA827A) { /* x < 0.41422 */
140 - if (ax >= 0x3ff00000) /* x <= -1.0 */
144 +
145 + if (hx < 0x3FDA827A) { /* x < 0.41422 */
146 + if (ax >= 0x3ff00000) /* x <= -1.0 */
141 147 return (_SVID_libm_err(x, x, x == -1.0 ? 43 : 44));
142 - if (ax < 0x3e200000) { /* |x| < 2**-29 */
148 +
149 + if (ax < 0x3e200000) { /* |x| < 2**-29 */
143 150 if (two54 + x > zero && /* raise inexact */
144 151 ax < 0x3c900000) /* |x| < 2**-54 */
145 152 return (x);
146 153 else
147 154 return (x - x * x * 0.5);
148 155 }
156 +
149 157 if (hx > 0 || hx <= (int)0xbfd2bec3) { /* -0.2929<x<0.41422 */
150 158 k = 0;
151 159 f = x;
152 160 hu = 1;
153 161 }
154 162 }
163 +
155 164 /* We will initialize 'c' here. */
156 165 if (k != 0) {
157 166 if (hx < 0x43400000) {
158 167 u = 1.0 + x;
159 168 hu = ((int *)&u)[HIWORD]; /* high word of u */
160 169 k = (hu >> 20) - 1023;
170 +
161 171 /*
162 172 * correction term
163 173 */
164 174 c = k > 0 ? 1.0 - (u - x) : x - (u - 1.0);
165 175 c /= u;
166 176 } else {
167 177 u = x;
168 178 hu = ((int *)&u)[HIWORD]; /* high word of u */
169 179 k = (hu >> 20) - 1023;
170 180 c = 0;
171 181 }
182 +
172 183 hu &= 0x000fffff;
184 +
173 185 if (hu < 0x6a09e) { /* normalize u */
174 186 ((int *)&u)[HIWORD] = hu | 0x3ff00000;
175 - } else { /* normalize u/2 */
187 + } else { /* normalize u/2 */
176 188 k += 1;
177 189 ((int *)&u)[HIWORD] = hu | 0x3fe00000;
178 190 hu = (0x00100000 - hu) >> 2;
179 191 }
192 +
180 193 f = u - 1.0;
181 194 }
195 +
182 196 hfsq = 0.5 * f * f;
183 - if (hu == 0) { /* |f| < 2**-20 */
197 +
198 + if (hu == 0) { /* |f| < 2**-20 */
184 199 if (f == zero) {
185 200 if (k == 0)
186 201 return (zero);
202 +
187 203 /* We already initialized 'c' before, when (k != 0) */
188 204 c += k * ln2_lo;
189 205 return (k * ln2_hi + c);
190 206 }
207 +
191 208 R = hfsq * (1.0 - 0.66666666666666666 * f);
209 +
192 210 if (k == 0)
193 211 return (f - R);
212 +
194 213 return (k * ln2_hi - ((R - (k * ln2_lo + c)) - f));
195 214 }
215 +
196 216 s = f / (2.0 + f);
197 217 z = s * s;
198 - R = z * (Lp1 + z * (Lp2 + z * (Lp3 + z * (Lp4 + z * (Lp5 +
199 - z * (Lp6 + z * Lp7))))));
218 + R = z * (Lp1 + z * (Lp2 + z * (Lp3 + z * (Lp4 + z * (Lp5 + z * (Lp6 +
219 + z * Lp7))))));
220 +
200 221 if (k == 0)
201 222 return (f - (hfsq - s * (hfsq + R)));
202 - return (k * ln2_hi - ((hfsq - (s * (hfsq + R) +
203 - (k * ln2_lo + c))) - f));
223 +
224 + return (k * ln2_hi -
225 + ((hfsq - (s * (hfsq + R) + (k * ln2_lo + c))) - f));
204 226 }
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