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11210 libm should be cstyle(1ONBLD) clean
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--- old/usr/src/lib/libm/common/C/sincos.c
+++ new/usr/src/lib/libm/common/C/sincos.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 __sincos = sincos
30 32
31 -/* INDENT OFF */
32 33 /*
33 34 * sincos(x,s,c)
34 35 * Accurate Table look-up algorithm by K.C. Ng, 2000.
35 36 *
36 37 * 1. Reduce x to x>0 by cos(-x)=cos(x), sin(-x)=-sin(x).
37 38 * 2. For 0<= x < 8, let i = (64*x chopped)-10. Let d = x - a[i], where
38 39 * a[i] is a double that is close to (i+10.5)/64 (and hence |d|< 10.5/64)
39 40 * and such that sin(a[i]) and cos(a[i]) is close to a double (with error
40 41 * less than 2**-8 ulp). Then
41 42 *
42 43 * cos(x) = cos(a[i]+d) = cos(a[i])cos(d) - sin(a[i])*sin(d)
43 44 * = TBL_cos_a[i]*(1+QQ1*d^2+QQ2*d^4) -
44 45 * TBL_sin_a[i]*(d+PP1*d^3+PP2*d^5)
45 46 * = TBL_cos_a[i] + (TBL_cos_a[i]*d^2*(QQ1+QQ2*d^2) -
46 47 * TBL_sin_a[i]*(d+PP1*d^3+PP2*d^5))
47 48 *
48 49 * sin(x) = sin(a[i]+d) = sin(a[i])cos(d) + cos(a[i])*sin(d)
49 50 * = TBL_sin_a[i]*(1+QQ1*d^2+QQ2*d^4) +
50 51 * TBL_cos_a[i]*(d+PP1*d^3+PP2*d^5)
51 52 * = TBL_sin_a[i] + (TBL_sin_a[i]*d^2*(QQ1+QQ2*d^2) +
52 53 * TBL_cos_a[i]*(d+PP1*d^3+PP2*d^5))
53 54 *
54 55 * Note: for x close to n*pi/2, special treatment is need for either
55 56 * sin or cos:
56 57 * i in [81, 100] ( pi/2 +-10.5/64 => tiny cos(x) = sin(pi/2-x)
57 58 * i in [181,200] ( pi +-10.5/64 => tiny sin(x) = sin(pi-x)
58 59 * i in [282,301] ( 3pi/2+-10.5/64 => tiny cos(x) = sin(x-3pi/2)
59 60 * i in [382,401] ( 2pi +-10.5/64 => tiny sin(x) = sin(x-2pi)
60 61 * i in [483,502] ( 5pi/2+-10.5/64 => tiny cos(x) = sin(5pi/2-x)
61 62 *
62 63 * 3. For x >= 8.0, use kernel function __rem_pio2 to perform argument
63 64 * reduction and call __k_sincos_ to compute sin and cos.
64 65 *
65 66 * kernel function:
66 67 * __rem_pio2 ... argument reduction routine
67 68 * __k_sincos_ ... sine and cosine function on [-pi/4,pi/4]
68 69 *
69 70 * Method.
70 71 * Let S and C denote the sin and cos respectively on [-PI/4, +PI/4].
71 72 * 1. Assume the argument x is reduced to y1+y2 = x-k*pi/2 in
72 73 * [-pi/2 , +pi/2], and let n = k mod 4.
73 74 * 2. Let S=S(y1+y2), C=C(y1+y2). Depending on n, we have
74 75 *
75 76 * n sin(x) cos(x) tan(x)
76 77 * ----------------------------------------------------------
77 78 * 0 S C S/C
78 79 * 1 C -S -C/S
79 80 * 2 -S -C S/C
80 81 * 3 -C S -C/S
81 82 * ----------------------------------------------------------
82 83 *
83 84 * Special cases:
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84 85 * Let trig be any of sin, cos, or tan.
85 86 * trig(+-INF) is NaN, with signals;
86 87 * trig(NaN) is that NaN;
87 88 *
88 89 * Accuracy:
89 90 * TRIG(x) returns trig(x) nearly rounded (less than 1 ulp)
90 91 */
91 92
92 93 #include "libm.h"
93 94
95 +/* BEGIN CSTYLED */
94 96 static const double sc[] = {
95 -/* ONE = */ 1.0,
97 +/* ONE = */
98 + 1.0,
96 99 /* NONE = */ -1.0,
100 +
97 101 /*
98 102 * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008
99 103 */
100 -/* PP1 = */ -0.166666666666316558867252052378889521480627858683055567,
101 -/* PP2 = */ .008333315652997472323564894248466758248475374977974017927,
104 +/* PP1 = */-0.166666666666316558867252052378889521480627858683055567,
105 +/* PP2 = */.008333315652997472323564894248466758248475374977974017927,
106 +
102 107 /*
103 108 * |(sin(x) - (x+p1*x^3+...+p4*x^9)|
104 109 * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125
105 110 * | x |
106 111 */
107 -/* P1 = */ -1.666666666666629669805215138920301589656e-0001,
108 -/* P2 = */ 8.333333332390951295683993455280336376663e-0003,
109 -/* P3 = */ -1.984126237997976692791551778230098403960e-0004,
110 -/* P4 = */ 2.753403624854277237649987622848330351110e-0006,
112 +/* P1 = */ -1.666666666666629669805215138920301589656e-0001,
113 +/* P2 = */ 8.333333332390951295683993455280336376663e-0003,
114 +/* P3 = */ -1.984126237997976692791551778230098403960e-0004,
115 +/* P4 = */ 2.753403624854277237649987622848330351110e-0006,
116 +
111 117 /*
112 118 * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d)
113 119 */
114 -/* QQ1 = */ -0.4999999999975492381842911981948418542742729,
115 -/* QQ2 = */ 0.041666542904352059294545209158357640398771740,
116 -/* Q1 = */ -0.5,
117 -/* Q2 = */ 4.166666666500350703680945520860748617445e-0002,
118 -/* Q3 = */ -1.388888596436972210694266290577848696006e-0003,
119 -/* Q4 = */ 2.478563078858589473679519517892953492192e-0005,
120 -/* PIO2_H = */ 1.570796326794896557999,
121 -/* PIO2_L = */ 6.123233995736765886130e-17,
122 -/* PIO2_L0 = */ 6.123233995727922165564e-17,
123 -/* PIO2_L1 = */ 8.843720566135701120255e-29,
124 -/* PI_H = */ 3.1415926535897931159979634685,
125 -/* PI_L = */ 1.22464679914735317722606593227425e-16,
126 -/* PI_L0 = */ 1.22464679914558443311283879205095e-16,
127 -/* PI_L1 = */ 1.768744113227140223300005233735517376e-28,
128 -/* PI3O2_H = */ 4.712388980384689673997,
129 -/* PI3O2_L = */ 1.836970198721029765839e-16,
130 -/* PI3O2_L0 = */ 1.836970198720396133587e-16,
131 -/* PI3O2_L1 = */ 6.336322524749201142226e-29,
132 -/* PI2_H = */ 6.2831853071795862319959269370,
133 -/* PI2_L = */ 2.44929359829470635445213186454850e-16,
134 -/* PI2_L0 = */ 2.44929359829116886622567758410190e-16,
135 -/* PI2_L1 = */ 3.537488226454280446600010467471034752e-28,
136 -/* PI5O2_H = */ 7.853981633974482789995,
137 -/* PI5O2_L = */ 3.061616997868382943065e-16,
138 -/* PI5O2_L0 = */ 3.061616997861941598865e-16,
139 -/* PI5O2_L1 = */ 6.441344200433640781982e-28,
120 +/* QQ1 = */-0.4999999999975492381842911981948418542742729,
121 +/* QQ2 = */0.041666542904352059294545209158357640398771740,
122 +/* Q1 = */ -0.5,
123 +/* Q2 = */ 4.166666666500350703680945520860748617445e-0002,
124 +/* Q3 = */ -1.388888596436972210694266290577848696006e-0003,
125 +/* Q4 = */ 2.478563078858589473679519517892953492192e-0005,
126 +/* PIO2_H = */ 1.570796326794896557999,
127 +/* PIO2_L = */ 6.123233995736765886130e-17,
128 +/* PIO2_L0 = */ 6.123233995727922165564e-17,
129 +/* PIO2_L1 = */ 8.843720566135701120255e-29,
130 +/* PI_H = */ 3.1415926535897931159979634685,
131 +/* PI_L = */ 1.22464679914735317722606593227425e-16,
132 +/* PI_L0 = */ 1.22464679914558443311283879205095e-16,
133 +/* PI_L1 = */ 1.768744113227140223300005233735517376e-28,
134 +/* PI3O2_H = */ 4.712388980384689673997,
135 +/* PI3O2_L = */ 1.836970198721029765839e-16,
136 +/* PI3O2_L0 = */ 1.836970198720396133587e-16,
137 +/* PI3O2_L1 = */ 6.336322524749201142226e-29,
138 +/* PI2_H = */ 6.2831853071795862319959269370,
139 +/* PI2_L = */ 2.44929359829470635445213186454850e-16,
140 +/* PI2_L0 = */ 2.44929359829116886622567758410190e-16,
141 +/* PI2_L1 = */ 3.537488226454280446600010467471034752e-28,
142 +/* PI5O2_H = */ 7.853981633974482789995,
143 +/* PI5O2_L = */ 3.061616997868382943065e-16,
144 +/* PI5O2_L0 = */ 3.061616997861941598865e-16,
145 +/* PI5O2_L1 = */ 6.441344200433640781982e-28,
140 146 };
141 -/* INDENT ON */
147 +/* END CSTYLED */
142 148
143 -#define ONE sc[0]
144 -#define PP1 sc[2]
145 -#define PP2 sc[3]
146 -#define P1 sc[4]
147 -#define P2 sc[5]
148 -#define P3 sc[6]
149 -#define P4 sc[7]
150 -#define QQ1 sc[8]
151 -#define QQ2 sc[9]
152 -#define Q1 sc[10]
153 -#define Q2 sc[11]
154 -#define Q3 sc[12]
155 -#define Q4 sc[13]
156 -#define PIO2_H sc[14]
157 -#define PIO2_L sc[15]
158 -#define PIO2_L0 sc[16]
159 -#define PIO2_L1 sc[17]
160 -#define PI_H sc[18]
161 -#define PI_L sc[19]
162 -#define PI_L0 sc[20]
163 -#define PI_L1 sc[21]
164 -#define PI3O2_H sc[22]
165 -#define PI3O2_L sc[23]
166 -#define PI3O2_L0 sc[24]
167 -#define PI3O2_L1 sc[25]
168 -#define PI2_H sc[26]
169 -#define PI2_L sc[27]
170 -#define PI2_L0 sc[28]
171 -#define PI2_L1 sc[29]
172 -#define PI5O2_H sc[30]
173 -#define PI5O2_L sc[31]
174 -#define PI5O2_L0 sc[32]
175 -#define PI5O2_L1 sc[33]
176 -#define PoS(x, z) ((x * z) * (PP1 + z * PP2))
177 -#define PoL(x, z) ((x * z) * ((P1 + z * P2) + (z * z) * (P3 + z * P4)))
149 +#define ONE sc[0]
150 +#define PP1 sc[2]
151 +#define PP2 sc[3]
152 +#define P1 sc[4]
153 +#define P2 sc[5]
154 +#define P3 sc[6]
155 +#define P4 sc[7]
156 +#define QQ1 sc[8]
157 +#define QQ2 sc[9]
158 +#define Q1 sc[10]
159 +#define Q2 sc[11]
160 +#define Q3 sc[12]
161 +#define Q4 sc[13]
162 +#define PIO2_H sc[14]
163 +#define PIO2_L sc[15]
164 +#define PIO2_L0 sc[16]
165 +#define PIO2_L1 sc[17]
166 +#define PI_H sc[18]
167 +#define PI_L sc[19]
168 +#define PI_L0 sc[20]
169 +#define PI_L1 sc[21]
170 +#define PI3O2_H sc[22]
171 +#define PI3O2_L sc[23]
172 +#define PI3O2_L0 sc[24]
173 +#define PI3O2_L1 sc[25]
174 +#define PI2_H sc[26]
175 +#define PI2_L sc[27]
176 +#define PI2_L0 sc[28]
177 +#define PI2_L1 sc[29]
178 +#define PI5O2_H sc[30]
179 +#define PI5O2_L sc[31]
180 +#define PI5O2_L0 sc[32]
181 +#define PI5O2_L1 sc[33]
182 +#define PoS(x, z) ((x * z) * (PP1 + z * PP2))
183 +#define PoL(x, z) ((x * z) * ((P1 + z * P2) + (z * z) * \
184 + (P3 + z * P4)))
178 185
179 186 extern const double _TBL_sincos[], _TBL_sincosx[];
180 187
181 188 void
182 -sincos(double x, double *s, double *c) {
183 - double z, y[2], w, t, v, p, q;
184 - int i, j, n, hx, ix, lx;
189 +sincos(double x, double *s, double *c)
190 +{
191 + double z, y[2], w, t, v, p, q;
192 + int i, j, n, hx, ix, lx;
185 193
186 194 hx = ((int *)&x)[HIWORD];
187 195 lx = ((int *)&x)[LOWORD];
188 196 ix = hx & ~0x80000000;
189 197
190 - if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */
198 + if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */
191 199 if (ix < 0x3e400000) { /* |x| < 2**-27 */
192 200 if ((int)x == 0)
193 201 *c = ONE;
202 +
194 203 *s = x;
195 204 } else {
196 205 z = x * x;
206 +
197 207 if (ix < 0x3f800000) { /* |x| < 0.008 */
198 208 q = z * (QQ1 + z * QQ2);
199 209 p = PoS(x, z);
200 210 } else {
201 - q = z * ((Q1 + z * Q2) + (z * z) *
202 - (Q3 + z * Q4));
211 + q = z * ((Q1 + z * Q2) + (z * z) * (Q3 + z *
212 + Q4));
203 213 p = PoL(x, z);
204 214 }
215 +
205 216 *c = ONE + q;
206 217 *s = x + p;
207 218 }
219 +
208 220 return;
209 221 }
210 222
211 223 n = ix >> 20;
212 224 i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
213 225 j = i - 10;
214 - if (n < 0x402) { /* |x| < 8 */
226 +
227 + if (n < 0x402) { /* |x| < 8 */
215 228 x = fabs(x);
216 229 v = x - _TBL_sincosx[j];
217 230 t = v * v;
218 - w = _TBL_sincos[(j<<1)];
219 - z = _TBL_sincos[(j<<1)+1];
231 + w = _TBL_sincos[(j << 1)];
232 + z = _TBL_sincos[(j << 1) + 1];
220 233 p = v + PoS(v, t);
221 234 q = t * (QQ1 + t * QQ2);
222 - if ((((j - 81) ^ (j - 101)) |
223 - ((j - 282) ^ (j - 302)) |
224 - ((j - 483) ^ (j - 503)) |
225 - ((j - 181) ^ (j - 201)) |
226 - ((j - 382) ^ (j - 402))) < 0) {
235 +
236 + if ((((j - 81) ^ (j - 101)) | ((j - 282) ^ (j - 302)) | ((j -
237 + 483) ^ (j - 503)) | ((j - 181) ^ (j - 201)) | ((j - 382) ^
238 + (j - 402))) < 0) {
227 239 if (j <= 101) {
228 240 /* near pi/2, cos(x) = sin(pi/2-x) */
229 241 t = w * q + z * p;
230 - *s = (hx >= 0)? w + t : -w - t;
242 + *s = (hx >= 0) ? w + t : -w - t;
231 243 p = PIO2_H - x;
232 244 i = ix - 0x3ff921fb;
233 245 x = p + PIO2_L;
234 - if ((i | ((lx - 0x54442D00) &
235 - 0xffffff00)) == 0) {
246 +
247 + if ((i | ((lx - 0x54442D00) & 0xffffff00)) ==
248 + 0) {
236 249 /* very close to pi/2 */
237 250 x = p + PIO2_L0;
238 251 *c = x + PIO2_L1;
239 252 } else {
240 253 z = x * x;
254 +
241 255 if (((ix - 0x3ff92000) >> 12) == 0) {
242 256 /* |pi/2-x|<2**-8 */
243 257 w = PIO2_L + PoS(x, z);
244 258 } else {
245 259 w = PIO2_L + PoL(x, z);
246 260 }
261 +
247 262 *c = p + w;
248 263 }
249 264 } else if (j <= 201) {
250 265 /* near pi, sin(x) = sin(pi-x) */
251 266 *c = z - (w * p - z * q);
252 267 p = PI_H - x;
253 268 i = ix - 0x400921fb;
254 269 x = p + PI_L;
255 - if ((i | ((lx - 0x54442D00) &
256 - 0xffffff00)) == 0) {
270 +
271 + if ((i | ((lx - 0x54442D00) & 0xffffff00)) ==
272 + 0) {
257 273 /* very close to pi */
258 274 x = p + PI_L0;
259 - *s = (hx >= 0)? x + PI_L1 :
260 - -(x + PI_L1);
275 + *s = (hx >= 0) ? x + PI_L1 : -(x +
276 + PI_L1);
261 277 } else {
262 278 z = x * x;
279 +
263 280 if (((ix - 0x40092000) >> 11) == 0) {
264 281 /* |pi-x|<2**-8 */
265 282 w = PI_L + PoS(x, z);
266 283 } else {
267 284 w = PI_L + PoL(x, z);
268 285 }
269 - *s = (hx >= 0)? p + w : -p - w;
286 +
287 + *s = (hx >= 0) ? p + w : -p - w;
270 288 }
271 289 } else if (j <= 302) {
272 290 /* near 3/2pi, cos(x)=sin(x-3/2pi) */
273 291 t = w * q + z * p;
274 - *s = (hx >= 0)? w + t : -w - t;
292 + *s = (hx >= 0) ? w + t : -w - t;
275 293 p = x - PI3O2_H;
276 294 i = ix - 0x4012D97C;
277 295 x = p - PI3O2_L;
278 - if ((i | ((lx - 0x7f332100) &
279 - 0xffffff00)) == 0) {
296 +
297 + if ((i | ((lx - 0x7f332100) & 0xffffff00)) ==
298 + 0) {
280 299 /* very close to 3/2pi */
281 300 x = p - PI3O2_L0;
282 301 *c = x - PI3O2_L1;
283 302 } else {
284 303 z = x * x;
304 +
285 305 if (((ix - 0x4012D800) >> 9) == 0) {
286 306 /* |3/2pi-x|<2**-8 */
287 307 w = PoS(x, z) - PI3O2_L;
288 308 } else {
289 309 w = PoL(x, z) - PI3O2_L;
290 310 }
311 +
291 312 *c = p + w;
292 313 }
293 314 } else if (j <= 402) {
294 315 /* near 2pi, sin(x)=sin(x-2pi) */
295 316 *c = z - (w * p - z * q);
296 317 p = x - PI2_H;
297 318 i = ix - 0x401921fb;
298 319 x = p - PI2_L;
299 - if ((i | ((lx - 0x54442D00) &
300 - 0xffffff00)) == 0) {
320 +
321 + if ((i | ((lx - 0x54442D00) & 0xffffff00)) ==
322 + 0) {
301 323 /* very close to 2pi */
302 324 x = p - PI2_L0;
303 - *s = (hx >= 0)? x - PI2_L1 :
304 - -(x - PI2_L1);
325 + *s = (hx >= 0) ? x - PI2_L1 : -(x -
326 + PI2_L1);
305 327 } else {
306 328 z = x * x;
329 +
307 330 if (((ix - 0x40192000) >> 10) == 0) {
308 331 /* |x-2pi|<2**-8 */
309 332 w = PoS(x, z) - PI2_L;
310 333 } else {
311 334 w = PoL(x, z) - PI2_L;
312 335 }
313 - *s = (hx >= 0)? p + w : -p - w;
336 +
337 + *s = (hx >= 0) ? p + w : -p - w;
314 338 }
315 339 } else {
316 340 /* near 5pi/2, cos(x) = sin(5pi/2-x) */
317 341 t = w * q + z * p;
318 - *s = (hx >= 0)? w + t : -w - t;
342 + *s = (hx >= 0) ? w + t : -w - t;
319 343 p = PI5O2_H - x;
320 344 i = ix - 0x401F6A7A;
321 345 x = p + PI5O2_L;
322 - if ((i | ((lx - 0x29553800) &
323 - 0xffffff00)) == 0) {
346 +
347 + if ((i | ((lx - 0x29553800) & 0xffffff00)) ==
348 + 0) {
324 349 /* very close to pi/2 */
325 350 x = p + PI5O2_L0;
326 351 *c = x + PI5O2_L1;
327 352 } else {
328 353 z = x * x;
354 +
329 355 if (((ix - 0x401F6A7A) >> 7) == 0) {
330 356 /* |5pi/2-x|<2**-8 */
331 357 w = PI5O2_L + PoS(x, z);
332 358 } else {
333 359 w = PI5O2_L + PoL(x, z);
334 360 }
361 +
335 362 *c = p + w;
336 363 }
337 364 }
338 365 } else {
339 366 *c = z - (w * p - z * q);
340 367 t = w * q + z * p;
341 - *s = (hx >= 0)? w + t : -w - t;
368 + *s = (hx >= 0) ? w + t : -w - t;
342 369 }
370 +
343 371 return;
344 372 }
345 373
346 374 if (ix >= 0x7ff00000) {
347 375 *s = *c = x / x;
348 376 return;
349 377 }
350 378
351 379 /* argument reduction needed */
352 380 n = __rem_pio2(x, y);
381 +
353 382 switch (n & 3) {
354 383 case 0:
355 384 *s = __k_sincos(y[0], y[1], c);
356 385 break;
357 386 case 1:
358 387 *c = -__k_sincos(y[0], y[1], s);
359 388 break;
360 389 case 2:
361 390 *s = -__k_sincos(y[0], y[1], c);
362 391 *c = -*c;
363 392 break;
364 393 default:
365 394 *c = __k_sincos(y[0], y[1], s);
366 395 *s = -*s;
367 396 }
368 397 }
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