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11175 libm should use signbit() correctly
11188 c99 math macros should return strictly backward compatible values
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--- old/usr/src/lib/libm/common/LD/jnl.c
+++ new/usr/src/lib/libm/common/LD/jnl.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.
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 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 27 * Use is subject to license terms.
28 28 */
29 29
30 30 #pragma weak __jnl = jnl
31 31 #pragma weak __ynl = ynl
32 32
33 33 /*
34 34 * floating point Bessel's function of the 1st and 2nd kind
35 35 * of order n: jn(n,x),yn(n,x);
36 36 *
37 37 * Special cases:
38 38 * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
39 39 * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
40 40 * Note 2. About jn(n,x), yn(n,x)
41 41 * For n=0, j0(x) is called,
42 42 * for n=1, j1(x) is called,
43 43 * for n<x, forward recursion us used starting
44 44 * from values of j0(x) and j1(x).
45 45 * for n>x, a continued fraction approximation to
46 46 * j(n,x)/j(n-1,x) is evaluated and then backward
47 47 * recursion is used starting from a supposed value
48 48 * for j(n,x). The resulting value of j(0,x) is
49 49 * compared with the actual value to correct the
50 50 * supposed value of j(n,x).
51 51 *
52 52 * yn(n,x) is similar in all respects, except
53 53 * that forward recursion is used for all
54 54 * values of n>1.
55 55 *
56 56 */
57 57
58 58 #include "libm.h"
59 59 #include "longdouble.h"
60 60 #include <float.h> /* LDBL_MAX */
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61 61
62 62 #define GENERIC long double
63 63
64 64 static const GENERIC
65 65 invsqrtpi = 5.641895835477562869480794515607725858441e-0001L,
66 66 two = 2.0L,
67 67 zero = 0.0L,
68 68 one = 1.0L;
69 69
70 70 GENERIC
71 -jnl(n, x) int n; GENERIC x; {
71 +jnl(int n, GENERIC x)
72 +{
72 73 int i, sgn;
73 74 GENERIC a, b, temp = 0, z, w;
74 75
75 76 /*
76 77 * J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
77 78 * Thus, J(-n,x) = J(n,-x)
78 79 */
79 80 if (n < 0) {
80 81 n = -n;
81 82 x = -x;
82 83 }
83 - if (n == 0) return (j0l(x));
84 - if (n == 1) return (j1l(x));
85 - if (x != x) return x+x;
84 + if (n == 0)
85 + return (j0l(x));
86 + if (n == 1)
87 + return (j1l(x));
88 + if (x != x)
89 + return (x+x);
86 90 if ((n&1) == 0)
87 - sgn = 0; /* even n */
91 + sgn = 0; /* even n */
88 92 else
89 93 sgn = signbitl(x); /* old n */
90 94 x = fabsl(x);
91 95 if (x == zero || !finitel(x)) b = zero;
92 96 else if ((GENERIC)n <= x) {
93 97 /*
94 98 * Safe to use
95 99 * J(n+1,x)=2n/x *J(n,x)-J(n-1,x)
96 100 */
97 - if (x > 1.0e91L) {
101 + if (x > 1.0e91L) {
98 102 /*
99 103 * x >> n**2
100 104 * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
101 105 * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
102 106 * Let s=sin(x), c=cos(x),
103 107 * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
104 108 *
105 109 * n sin(xn)*sqt2 cos(xn)*sqt2
106 110 * ----------------------------------
107 111 * 0 s-c c+s
108 - * 1 -s-c -c+s
112 + * 1 -s-c -c+s
109 113 * 2 -s+c -c-s
110 114 * 3 s+c c-s
111 115 */
112 - switch (n&3) {
113 - case 0: temp = cosl(x)+sinl(x); break;
114 - case 1: temp = -cosl(x)+sinl(x); break;
115 - case 2: temp = -cosl(x)-sinl(x); break;
116 - case 3: temp = cosl(x)-sinl(x); break;
117 - }
118 - b = invsqrtpi*temp/sqrtl(x);
119 - } else {
116 + switch (n&3) {
117 + case 0:
118 + temp = cosl(x)+sinl(x);
119 + break;
120 + case 1:
121 + temp = -cosl(x)+sinl(x);
122 + break;
123 + case 2:
124 + temp = -cosl(x)-sinl(x);
125 + break;
126 + case 3:
127 + temp = cosl(x)-sinl(x);
128 + break;
129 + }
130 + b = invsqrtpi*temp/sqrtl(x);
131 + } else {
120 132 a = j0l(x);
121 133 b = j1l(x);
122 134 for (i = 1; i < n; i++) {
123 - temp = b;
124 - b = b*((GENERIC)(i+i)/x) - a; /* avoid underflow */
125 - a = temp;
135 + temp = b;
136 + /* avoid underflow */
137 + b = b*((GENERIC)(i+i)/x) - a;
138 + a = temp;
126 139 }
127 - }
128 - } else {
129 - if (x < 1e-17L) { /* use J(n,x) = 1/n!*(x/2)^n */
130 - b = powl(0.5L*x, (GENERIC) n);
131 - if (b != zero) {
132 - for (a = one, i = 1; i <= n; i++) a *= (GENERIC)i;
133 - b = b/a;
134 - }
135 - } else {
136 - /*
137 - * use backward recurrence
138 - * x x^2 x^2
139 - * J(n,x)/J(n-1,x) = ---- ------ ------ .....
140 - * 2n - 2(n+1) - 2(n+2)
141 - *
142 - * 1 1 1
143 - * (for large x) = ---- ------ ------ .....
144 - * 2n 2(n+1) 2(n+2)
145 - * -- - ------ - ------ -
146 - * x x x
147 - *
148 - * Let w = 2n/x and h=2/x, then the above quotient
149 - * is equal to the continued fraction:
150 - * 1
151 - * = -----------------------
152 - * 1
153 - * w - -----------------
154 - * 1
155 - * w+h - ---------
156 - * w+2h - ...
157 - *
158 - * To determine how many terms needed, let
159 - * Q(0) = w, Q(1) = w(w+h) - 1,
160 - * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
161 - * When Q(k) > 1e4 good for single
162 - * When Q(k) > 1e9 good for double
163 - * When Q(k) > 1e17 good for quaduple
164 - */
165 - /* determin k */
166 - GENERIC t, v;
167 - double q0, q1, h, tmp; int k, m;
168 - w = (n+n)/(double)x; h = 2.0/(double)x;
169 - q0 = w; z = w+h; q1 = w*z - 1.0; k = 1;
170 - while (q1 < 1.0e17) {
171 - k += 1; z += h;
172 - tmp = z*q1 - q0;
173 - q0 = q1;
174 - q1 = tmp;
175 140 }
176 - m = n+n;
177 - for (t = zero, i = 2*(n+k); i >= m; i -= 2) t = one/(i/x-t);
178 - a = t;
179 - b = one;
141 + } else {
142 + if (x < 1e-17L) { /* use J(n,x) = 1/n!*(x/2)^n */
143 + b = powl(0.5L*x, (GENERIC)n);
144 + if (b != zero) {
145 + for (a = one, i = 1; i <= n; i++)
146 + a *= (GENERIC)i;
147 + b = b/a;
148 + }
149 + } else {
150 + /*
151 + * use backward recurrence
152 + * x x^2 x^2
153 + * J(n,x)/J(n-1,x) = ---- ------ ------ .....
154 + * 2n - 2(n+1) - 2(n+2)
155 + *
156 + * 1 1 1
157 + * (for large x) = ---- ------ ------ .....
158 + * 2n 2(n+1) 2(n+2)
159 + * -- - ------ - ------ -
160 + * x x x
161 + *
162 + * Let w = 2n/x and h=2/x, then the above quotient
163 + * is equal to the continued fraction:
164 + * 1
165 + * = -----------------------
166 + * 1
167 + * w - -----------------
168 + * 1
169 + * w+h - ---------
170 + * w+2h - ...
171 + *
172 + * To determine how many terms needed, let
173 + * Q(0) = w, Q(1) = w(w+h) - 1,
174 + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
175 + * When Q(k) > 1e4 good for single
176 + * When Q(k) > 1e9 good for double
177 + * When Q(k) > 1e17 good for quaduple
178 + */
179 + /* determine k */
180 + GENERIC t, v;
181 + double q0, q1, h, tmp;
182 + int k, m;
183 + w = (n+n)/(double)x;
184 + h = 2.0/(double)x;
185 + q0 = w;
186 + z = w+h;
187 + q1 = w*z - 1.0;
188 + k = 1;
189 + while (q1 < 1.0e17) {
190 + k += 1;
191 + z += h;
192 + tmp = z*q1 - q0;
193 + q0 = q1;
194 + q1 = tmp;
195 + }
196 + m = n+n;
197 + for (t = zero, i = 2*(n+k); i >= m; i -= 2)
198 + t = one/(i/x-t);
199 + a = t;
200 + b = one;
180 201 /*
181 202 * Estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
182 203 * hence, if n*(log(2n/x)) > ...
183 204 * single 8.8722839355e+01
184 205 * double 7.09782712893383973096e+02
185 206 * long double 1.1356523406294143949491931077970765006170e+04
186 207 * then recurrent value may overflow and the result is
187 208 * likely underflow to zero.
188 209 */
189 - tmp = n;
190 - v = two/x;
191 - tmp = tmp*logl(fabsl(v*tmp));
192 - if (tmp < 1.1356523406294143949491931077970765e+04L) {
210 + tmp = n;
211 + v = two/x;
212 + tmp = tmp*logl(fabsl(v*tmp));
213 + if (tmp < 1.1356523406294143949491931077970765e+04L) {
193 214 for (i = n-1; i > 0; i--) {
194 - temp = b;
195 - b = ((i+i)/x)*b - a;
196 - a = temp;
215 + temp = b;
216 + b = ((i+i)/x)*b - a;
217 + a = temp;
197 218 }
198 - } else {
219 + } else {
199 220 for (i = n-1; i > 0; i--) {
200 - temp = b;
201 - b = ((i+i)/x)*b - a;
202 - a = temp;
203 - if (b > 1e1000L) {
221 + temp = b;
222 + b = ((i+i)/x)*b - a;
223 + a = temp;
224 + if (b > 1e1000L) {
204 225 a /= b;
205 226 t /= b;
206 227 b = 1.0;
207 228 }
208 229 }
209 - }
230 + }
210 231 b = (t*j0l(x)/b);
211 - }
232 + }
212 233 }
213 - if (sgn == 1)
214 - return -b;
234 + if (sgn != 0)
235 + return (-b);
215 236 else
216 - return b;
237 + return (b);
217 238 }
218 239
219 240 GENERIC
220 -ynl(n, x) int n; GENERIC x; {
241 +ynl(int n, GENERIC x)
242 +{
221 243 int i;
222 244 int sign;
223 245 GENERIC a, b, temp = 0;
224 246
225 247 if (x != x)
226 - return x+x;
248 + return (x+x);
227 249 if (x <= zero) {
228 250 if (x == zero)
229 - return -one/zero;
251 + return (-one/zero);
230 252 else
231 - return zero/zero;
253 + return (zero/zero);
232 254 }
233 255 sign = 1;
234 256 if (n < 0) {
235 257 n = -n;
236 - if ((n&1) == 1) sign = -1;
258 + if ((n&1) == 1)
259 + sign = -1;
237 260 }
238 - if (n == 0) return (y0l(x));
239 - if (n == 1) return (sign*y1l(x));
240 - if (!finitel(x)) return zero;
261 + if (n == 0)
262 + return (y0l(x));
263 + if (n == 1)
264 + return (sign*y1l(x));
265 + if (!finitel(x))
266 + return (zero);
241 267
242 268 if (x > 1.0e91L) {
243 269 /*
244 270 * x >> n**2
245 271 * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
246 272 * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
247 273 * Let s=sin(x), c=cos(x),
248 274 * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
249 275 *
250 276 * n sin(xn)*sqt2 cos(xn)*sqt2
251 277 * ----------------------------------
252 - * 0 s-c c+s
253 - * 1 -s-c -c+s
254 - * 2 -s+c -c-s
278 + * 0 s-c c+s
279 + * 1 -s-c -c+s
280 + * 2 -s+c -c-s
255 281 * 3 s+c c-s
256 282 */
257 283 switch (n&3) {
258 - case 0: temp = sinl(x)-cosl(x); break;
259 - case 1: temp = -sinl(x)-cosl(x); break;
260 - case 2: temp = -sinl(x)+cosl(x); break;
261 - case 3: temp = sinl(x)+cosl(x); break;
284 + case 0:
285 + temp = sinl(x)-cosl(x);
286 + break;
287 + case 1:
288 + temp = -sinl(x)-cosl(x);
289 + break;
290 + case 2:
291 + temp = -sinl(x)+cosl(x);
292 + break;
293 + case 3:
294 + temp = sinl(x)+cosl(x);
295 + break;
262 296 }
263 297 b = invsqrtpi*temp/sqrtl(x);
264 298 } else {
265 299 a = y0l(x);
266 300 b = y1l(x);
267 301 /*
268 302 * fix 1262058 and take care of non-default rounding
269 303 */
270 304 for (i = 1; i < n; i++) {
271 305 temp = b;
272 306 b *= (GENERIC) (i + i) / x;
273 307 if (b <= -LDBL_MAX)
274 308 break;
275 309 b -= a;
276 310 a = temp;
277 311 }
278 312 }
279 313 if (sign > 0)
280 - return b;
314 + return (b);
281 315 else
282 - return -b;
316 + return (-b);
283 317 }
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