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11210 libm should be cstyle(1ONBLD) clean
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--- old/usr/src/lib/libm/common/C/expm1.c
+++ new/usr/src/lib/libm/common/C/expm1.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
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.
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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 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 24 */
25 +
25 26 /*
26 27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 28 * Use is subject to license terms.
28 29 */
29 30
30 31 #pragma weak __expm1 = expm1
31 32
32 -/* INDENT OFF */
33 +
33 34 /*
34 35 * expm1(x)
35 36 * Returns exp(x)-1, the exponential of x minus 1.
36 37 *
37 38 * Method
38 39 * 1. Arugment reduction:
39 40 * Given x, find r and integer k such that
40 41 *
41 42 * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658
42 43 *
43 44 * Here a correction term c will be computed to compensate
44 45 * the error in r when rounded to a floating-point number.
45 46 *
46 47 * 2. Approximating expm1(r) by a special rational function on
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47 48 * the interval [0,0.34658]:
48 49 * Since
49 50 * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
50 51 * we define R1(r*r) by
51 52 * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
52 53 * That is,
53 54 * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
54 55 * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
55 56 * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
56 57 * We use a special Reme algorithm on [0,0.347] to generate
57 - * a polynomial of degree 5 in r*r to approximate R1. The
58 + * a polynomial of degree 5 in r*r to approximate R1. The
58 59 * maximum error of this polynomial approximation is bounded
59 60 * by 2**-61. In other words,
60 61 * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
61 - * where Q1 = -1.6666666666666567384E-2,
62 - * Q2 = 3.9682539681370365873E-4,
63 - * Q3 = -9.9206344733435987357E-6,
64 - * Q4 = 2.5051361420808517002E-7,
65 - * Q5 = -6.2843505682382617102E-9;
66 - * (where z=r*r, and the values of Q1 to Q5 are listed below)
62 + * where Q1 = -1.6666666666666567384E-2,
63 + * Q2 = 3.9682539681370365873E-4,
64 + * Q3 = -9.9206344733435987357E-6,
65 + * Q4 = 2.5051361420808517002E-7,
66 + * Q5 = -6.2843505682382617102E-9;
67 + * (where z=r*r, and the values of Q1 to Q5 are listed below)
67 68 * with error bounded by
68 69 * | 5 | -61
69 70 * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
70 71 * | |
71 72 *
72 73 * expm1(r) = exp(r)-1 is then computed by the following
73 - * specific way which minimize the accumulation rounding error:
74 + * specific way which minimize the accumulation rounding error:
74 75 * 2 3
75 76 * r r [ 3 - (R1 + R1*r/2) ]
76 77 * expm1(r) = r + --- + --- * [--------------------]
77 78 * 2 2 [ 6 - r*(3 - R1*r/2) ]
78 79 *
79 80 * To compensate the error in the argument reduction, we use
80 81 * expm1(r+c) = expm1(r) + c + expm1(r)*c
81 82 * ~ expm1(r) + c + r*c
82 83 * Thus c+r*c will be added in as the correction terms for
83 84 * expm1(r+c). Now rearrange the term to avoid optimization
84 - * screw up:
85 + * screw up:
85 86 * ( 2 2 )
86 87 * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
87 88 * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
88 89 * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
89 90 * ( )
90 91 *
91 92 * = r - E
92 93 * 3. Scale back to obtain expm1(x):
93 94 * From step 1, we have
94 95 * expm1(x) = either 2^k*[expm1(r)+1] - 1
95 96 * = or 2^k*[expm1(r) + (1-2^-k)]
96 97 * 4. Implementation notes:
97 98 * (A). To save one multiplication, we scale the coefficient Qi
98 99 * to Qi*2^i, and replace z by (x^2)/2.
99 100 * (B). To achieve maximum accuracy, we compute expm1(x) by
100 101 * (i) if x < -56*ln2, return -1.0, (raise inexact if x != inf)
101 102 * (ii) if k=0, return r-E
102 103 * (iii) if k=-1, return 0.5*(r-E)-0.5
103 104 * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
104 105 * else return 1.0+2.0*(r-E);
105 106 * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
106 107 * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
107 108 * (vii) return 2^k(1-((E+2^-k)-r))
108 109 *
109 110 * Special cases:
110 111 * expm1(INF) is INF, expm1(NaN) is NaN;
111 112 * expm1(-INF) is -1, and
112 113 * for finite argument, only expm1(0)=0 is exact.
113 114 *
114 115 * Accuracy:
115 116 * according to an error analysis, the error is always less than
116 117 * 1 ulp (unit in the last place).
117 118 *
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118 119 * Misc. info.
119 120 * For IEEE double
120 121 * if x > 7.09782712893383973096e+02 then expm1(x) overflow
121 122 *
122 123 * Constants:
123 124 * The hexadecimal values are the intended ones for the following
124 125 * constants. The decimal values may be used, provided that the
125 126 * compiler will convert from decimal to binary accurately enough
126 127 * to produce the hexadecimal values shown.
127 128 */
128 -/* INDENT ON */
129 129
130 130 #include "libm_macros.h"
131 131 #include <math.h>
132 132
133 133 static const double xxx[] = {
134 -/* one */ 1.0,
135 -/* huge */ 1.0e+300,
136 -/* tiny */ 1.0e-300,
137 -/* o_threshold */ 7.09782712893383973096e+02, /* 40862E42 FEFA39EF */
138 -/* ln2_hi */ 6.93147180369123816490e-01, /* 3FE62E42 FEE00000 */
139 -/* ln2_lo */ 1.90821492927058770002e-10, /* 3DEA39EF 35793C76 */
140 -/* invln2 */ 1.44269504088896338700e+00, /* 3FF71547 652B82FE */
141 -/* scaled coefficients related to expm1 */
142 -/* Q1 */ -3.33333333333331316428e-02, /* BFA11111 111110F4 */
143 -/* Q2 */ 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
144 -/* Q3 */ -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
145 -/* Q4 */ 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
146 -/* Q5 */ -2.01099218183624371326e-07 /* BE8AFDB7 6E09C32D */
134 +/* one */
135 + 1.0,
136 +/* huge */ 1.0e+300,
137 +/* tiny */ 1.0e-300,
138 +/* o_threshold */ 7.09782712893383973096e+02, /* 40862E42 FEFA39EF */
139 +/* ln2_hi */ 6.93147180369123816490e-01, /* 3FE62E42 FEE00000 */
140 +/* ln2_lo */ 1.90821492927058770002e-10, /* 3DEA39EF 35793C76 */
141 +/* invln2 */ 1.44269504088896338700e+00, /* 3FF71547 652B82FE */
142 +
143 +/*
144 + * scaled coefficients related to expm1
145 + * Q1
146 + */
147 + -3.33333333333331316428e-02, /* BFA11111 111110F4 */
148 +/* Q2 */ 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
149 +/* Q3 */ -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
150 +/* Q4 */ 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
151 +/* Q5 */ -2.01099218183624371326e-07 /* BE8AFDB7 6E09C32D */
147 152 };
148 -#define one xxx[0]
149 -#define huge xxx[1]
150 -#define tiny xxx[2]
151 -#define o_threshold xxx[3]
152 -#define ln2_hi xxx[4]
153 -#define ln2_lo xxx[5]
154 -#define invln2 xxx[6]
155 -#define Q1 xxx[7]
156 -#define Q2 xxx[8]
157 -#define Q3 xxx[9]
158 -#define Q4 xxx[10]
159 -#define Q5 xxx[11]
153 +
154 +#define one xxx[0]
155 +#define huge xxx[1]
156 +#define tiny xxx[2]
157 +#define o_threshold xxx[3]
158 +#define ln2_hi xxx[4]
159 +#define ln2_lo xxx[5]
160 +#define invln2 xxx[6]
161 +#define Q1 xxx[7]
162 +#define Q2 xxx[8]
163 +#define Q3 xxx[9]
164 +#define Q4 xxx[10]
165 +#define Q5 xxx[11]
160 166
161 167 double
162 -expm1(double x) {
168 +expm1(double x)
169 +{
163 170 double y, hi, lo, c = 0.0L, t, e, hxs, hfx, r1;
164 171 int k, xsb;
165 172 unsigned hx;
166 173
167 - hx = ((unsigned *) &x)[HIWORD]; /* high word of x */
168 - xsb = hx & 0x80000000; /* sign bit of x */
174 + hx = ((unsigned *)&x)[HIWORD]; /* high word of x */
175 + xsb = hx & 0x80000000; /* sign bit of x */
176 +
169 177 if (xsb == 0)
170 178 y = x;
171 179 else
172 - y = -x; /* y = |x| */
173 - hx &= 0x7fffffff; /* high word of |x| */
180 + y = -x; /* y = |x| */
181 +
182 + hx &= 0x7fffffff; /* high word of |x| */
174 183
175 - /* filter out huge and non-finite argument */
176 - /* for example exp(38)-1 is approximately 3.1855932e+16 */
184 + /*
185 + * filter out huge and non-finite argument
186 + * for example exp(38)-1 is approximately 3.1855932e+16
187 + */
177 188 if (hx >= 0x4043687A) {
178 189 /* if |x|>=56*ln2 (~38.8162...) */
179 - if (hx >= 0x40862E42) { /* if |x|>=709.78... -> inf */
190 + if (hx >= 0x40862E42) { /* if |x|>=709.78... -> inf */
180 191 if (hx >= 0x7ff00000) {
181 - if (((hx & 0xfffff) | ((int *) &x)[LOWORD])
182 - != 0)
192 + if (((hx & 0xfffff) | ((int *)&x)[LOWORD]) != 0)
183 193 return (x * x); /* + -> * for Cheetah */
184 194 else
185 195 /* exp(+-inf)={inf,-1} */
186 196 return (xsb == 0 ? x : -1.0);
187 197 }
198 +
188 199 if (x > o_threshold)
189 200 return (huge * huge); /* overflow */
190 201 }
191 - if (xsb != 0) { /* x < -56*ln2, return -1.0 w/inexact */
202 +
203 + if (xsb != 0) { /* x < -56*ln2, return -1.0 w/inexact */
192 204 if (x + tiny < 0.0) /* raise inexact */
193 205 return (tiny - one); /* return -1 */
194 206 }
195 207 }
196 208
197 209 /* argument reduction */
198 - if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
199 - if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
200 - if (xsb == 0) { /* positive number */
210 + if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
211 + if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
212 + if (xsb == 0) { /* positive number */
201 213 hi = x - ln2_hi;
202 214 lo = ln2_lo;
203 215 k = 1;
204 216 } else {
205 217 /* negative number */
206 218 hi = x + ln2_hi;
207 219 lo = -ln2_lo;
208 220 k = -1;
209 221 }
210 222 } else {
211 223 /* |x| > 1.5 ln2 */
212 - k = (int) (invln2 * x + (xsb == 0 ? 0.5 : -0.5));
224 + k = (int)(invln2 * x + (xsb == 0 ? 0.5 : -0.5));
213 225 t = k;
214 226 hi = x - t * ln2_hi; /* t*ln2_hi is exact here */
215 227 lo = t * ln2_lo;
216 228 }
229 +
217 230 x = hi - lo;
218 - c = (hi - x) - lo; /* still at |x| > 0.5 ln2 */
231 + c = (hi - x) - lo; /* still at |x| > 0.5 ln2 */
219 232 } else if (hx < 0x3c900000) {
220 233 /* when |x|<2**-54, return x */
221 234 t = huge + x; /* return x w/inexact when x != 0 */
222 235 return (x - (t - (huge + x)));
223 - } else
236 + } else {
224 237 /* |x| <= 0.5 ln2 */
225 238 k = 0;
239 + }
226 240
227 241 /* x is now in primary range */
228 242 hfx = 0.5 * x;
229 243 hxs = x * hfx;
230 244 r1 = one + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
231 245 t = 3.0 - r1 * hfx;
232 246 e = hxs * ((r1 - t) / (6.0 - x * t));
233 - if (k == 0) /* |x| <= 0.5 ln2 */
247 +
248 + if (k == 0) { /* |x| <= 0.5 ln2 */
234 249 return (x - (x * e - hxs));
235 - else { /* |x| > 0.5 ln2 */
250 + } else { /* |x| > 0.5 ln2 */
236 251 e = (x * (e - c) - c);
237 252 e -= hxs;
253 +
238 254 if (k == -1)
239 255 return (0.5 * (x - e) - 0.5);
256 +
240 257 if (k == 1) {
241 258 if (x < -0.25)
242 259 return (-2.0 * (e - (x + 0.5)));
243 260 else
244 261 return (one + 2.0 * (x - e));
245 262 }
263 +
246 264 if (k <= -2 || k > 56) { /* suffice to return exp(x)-1 */
247 265 y = one - (e - x);
248 - ((int *) &y)[HIWORD] += k << 20;
266 + ((int *)&y)[HIWORD] += k << 20;
249 267 return (y - one);
250 268 }
269 +
251 270 t = one;
271 +
252 272 if (k < 20) {
253 - ((int *) &t)[HIWORD] = 0x3ff00000 - (0x200000 >> k);
254 - /* t = 1 - 2^-k */
273 + ((int *)&t)[HIWORD] = 0x3ff00000 - (0x200000 >> k);
274 + /* t = 1 - 2^-k */
255 275 y = t - (e - x);
256 - ((int *) &y)[HIWORD] += k << 20;
276 + ((int *)&y)[HIWORD] += k << 20;
257 277 } else {
258 - ((int *) &t)[HIWORD] = (0x3ff - k) << 20; /* 2^-k */
278 + ((int *)&t)[HIWORD] = (0x3ff - k) << 20; /* 2^-k */
259 279 y = x - (e + t);
260 280 y += one;
261 - ((int *) &y)[HIWORD] += k << 20;
281 + ((int *)&y)[HIWORD] += k << 20;
262 282 }
263 283 }
284 +
264 285 return (y);
265 286 }
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