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11210 libm should be cstyle(1ONBLD) clean
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--- old/usr/src/lib/libm/common/complex/catanl.c
+++ new/usr/src/lib/libm/common/complex/catanl.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 __catanl = catanl
31 32
32 -/* INDENT OFF */
33 +
33 34 /*
34 35 * ldcomplex catanl(ldcomplex z);
35 36 *
36 37 * Atan(z) return A + Bi where,
37 38 * 1
38 39 * A = --- * atan2(2x, 1-x*x-y*y)
39 40 * 2
40 41 *
41 42 * 1 [ x*x + (y+1)*(y+1) ] 1 4y
42 43 * B = --- log [ ----------------- ] = - log (1+ -----------------)
43 44 * 4 [ x*x + (y-1)*(y-1) ] 4 x*x + (y-1)*(y-1)
44 45 *
45 46 * 2 16 3 y
46 47 * = t - 2t + -- t - ..., where t = -----------------
47 48 * 3 x*x + (y-1)*(y-1)
48 49 * Proof:
49 50 * Let w = atan(z=x+yi) = A + B i. Then tan(w) = z.
50 51 * Since sin(w) = (exp(iw)-exp(-iw))/(2i), cos(w)=(exp(iw)+exp(-iw))/(2),
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51 52 * Let p = exp(iw), then z = tan(w) = ((p-1/p)/(p+1/p))/i, or
52 53 * iz = (p*p-1)/(p*p+1), or, after simplification,
53 54 * p*p = (1+iz)/(1-iz) ... (1)
54 55 * LHS of (1) = exp(2iw) = exp(2i(A+Bi)) = exp(-2B)*exp(2iA)
55 56 * = exp(-2B)*(cos(2A)+i*sin(2A)) ... (2)
56 57 * 1-y+ix (1-y+ix)*(1+y+ix) 1-x*x-y*y + 2xi
57 58 * RHS of (1) = ------ = ----------------- = --------------- ... (3)
58 59 * 1+y-ix (1+y)**2 + x**2 (1+y)**2 + x**2
59 60 *
60 61 * Comparing the real and imaginary parts of (2) and (3), we have:
61 - * cos(2A) : 1-x*x-y*y = sin(2A) : 2x
62 + * cos(2A) : 1-x*x-y*y = sin(2A) : 2x
62 63 * and hence
63 64 * tan(2A) = 2x/(1-x*x-y*y), or
64 65 * A = 0.5 * atan2(2x, 1-x*x-y*y) ... (4)
65 66 *
66 67 * For the imaginary part B, Note that |p*p| = exp(-2B), and
67 68 * |1+iz| |i-z| hypot(x,(y-1))
68 69 * |----| = |---| = --------------
69 70 * |1-iz| |i+z| hypot(x,(y+1))
70 71 * Thus
71 72 * x*x + (y+1)*(y+1)
72 73 * exp(4B) = -----------------, or
73 74 * x*x + (y-1)*(y-1)
74 75 *
75 76 * 1 [x^2+(y+1)^2] 1 4y
76 77 * B = - log [-----------] = - log(1+ -------------) ... (5)
77 78 * 4 [x^2+(y-1)^2] 4 x^2+(y-1)^2
78 79 *
79 80 * QED.
80 81 *
81 82 * Note that: if catan( x, y) = ( u, v), then
82 83 * catan(-x, y) = (-u, v)
83 84 * catan( x,-y) = ( u,-v)
84 85 *
85 86 * Also, catan(x,y) = -i*catanh(-y,x), or
86 87 * catanh(x,y) = i*catan(-y,x)
87 88 * So, if catanh(y,x) = (v,u), then catan(x,y) = -i*(-v,u) = (u,v), i.e.,
88 89 * catan(x,y) = (u,v)
89 90 *
90 91 * EXCEPTION CASES (conform to ISO/IEC 9899:1999(E)):
91 92 * catan( 0 , 0 ) = (0 , 0 )
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92 93 * catan( NaN, 0 ) = (NaN , 0 )
93 94 * catan( 0 , 1 ) = (0 , +inf) with divide-by-zero
94 95 * catan( inf, y ) = (pi/2 , 0 ) for finite +y
95 96 * catan( NaN, y ) = (NaN , NaN ) with invalid for finite y != 0
96 97 * catan( x , inf ) = (pi/2 , 0 ) for finite +x
97 98 * catan( inf, inf ) = (pi/2 , 0 )
98 99 * catan( NaN, inf ) = (NaN , 0 )
99 100 * catan( x , NaN ) = (NaN , NaN ) with invalid for finite x
100 101 * catan( inf, NaN ) = (pi/2 , +-0 )
101 102 */
102 -/* INDENT ON */
103 103
104 104 #include "libm.h" /* atan2l/atanl/fabsl/isinfl/iszerol/log1pl/logl */
105 105 #include "complex_wrapper.h"
106 106 #include "longdouble.h"
107 107
108 -/* INDENT OFF */
109 -static const long double
110 -zero = 0.0L,
111 -one = 1.0L,
112 -two = 2.0L,
113 -half = 0.5L,
114 -ln2 = 6.931471805599453094172321214581765680755e-0001L,
115 -pi_2 = 1.570796326794896619231321691639751442098584699687552910487472L,
108 +/* BEGIN CSTYLED */
109 +static const long double zero = 0.0L,
110 + one = 1.0L,
111 + two = 2.0L,
112 + half = 0.5L,
113 + ln2 = 6.931471805599453094172321214581765680755e-0001L,
114 + pi_2 = 1.570796326794896619231321691639751442098584699687552910487472L,
116 115 #if defined(__x86)
117 -E = 2.910383045673370361328125000000000000000e-11L, /* 2**-35 */
118 -Einv = 3.435973836800000000000000000000000000000e+10L; /* 2**+35 */
116 + E = 2.910383045673370361328125000000000000000e-11L, /* 2**-35 */
117 + Einv = 3.435973836800000000000000000000000000000e+10L; /* 2**+35 */
119 118 #else
120 -E = 8.673617379884035472059622406959533691406e-19L, /* 2**-60 */
121 -Einv = 1.152921504606846976000000000000000000000e18L; /* 2**+60 */
119 + E = 8.673617379884035472059622406959533691406e-19L, /* 2**-60 */
120 + Einv = 1.152921504606846976000000000000000000000e18L; /* 2**+60 */
122 121 #endif
123 -/* INDENT ON */
122 +/* END CSTYLED */
124 123
125 124 ldcomplex
126 -catanl(ldcomplex z) {
125 +catanl(ldcomplex z)
126 +{
127 127 ldcomplex ans;
128 128 long double x, y, t1, ax, ay, t;
129 129 int hx, hy, ix, iy;
130 130
131 131 x = LD_RE(z);
132 132 y = LD_IM(z);
133 133 ax = fabsl(x);
134 134 ay = fabsl(y);
135 135 hx = HI_XWORD(x);
136 136 hy = HI_XWORD(y);
137 137 ix = hx & 0x7fffffff;
138 138 iy = hy & 0x7fffffff;
139 139
140 140 /* x is inf or NaN */
141 141 if (ix >= 0x7fff0000) {
142 142 if (isinfl(x)) {
143 143 LD_RE(ans) = pi_2;
144 144 LD_IM(ans) = zero;
145 145 } else {
146 146 LD_RE(ans) = x + x;
147 +
147 148 if (iszerol(y) || (isinfl(y)))
148 149 LD_IM(ans) = zero;
149 150 else
150 151 LD_IM(ans) = (fabsl(y) - ay) / (fabsl(y) - ay);
151 152 }
152 153 } else if (iy >= 0x7fff0000) {
153 154 /* y is inf or NaN */
154 155 if (isinfl(y)) {
155 156 LD_RE(ans) = pi_2;
156 157 LD_IM(ans) = zero;
157 158 } else {
158 159 LD_RE(ans) = (fabsl(x) - ax) / (fabsl(x) - ax);
159 160 LD_IM(ans) = y;
160 161 }
161 162 } else if (iszerol(x)) {
162 - /* INDENT OFF */
163 + /* BEGIN CSTYLED */
163 164 /*
164 165 * x = 0
165 166 * 1 1
166 167 * A = --- * atan2(2x, 1-x*x-y*y) = --- atan2(0,1-|y|)
167 168 * 2 2
168 169 *
169 170 * 1 [ (y+1)*(y+1) ] 1 2 1 2y
170 171 * B = - log [ ----------- ] = - log (1+ ---) or - log(1+ ----)
171 172 * 4 [ (y-1)*(y-1) ] 2 y-1 2 1-y
172 173 */
173 - /* INDENT ON */
174 + /* END CSTYLED */
174 175 t = one - ay;
176 +
175 177 if (ay == one) {
176 178 /* y=1: catan(0,1)=(0,+inf) with 1/0 signal */
177 179 LD_IM(ans) = ay / ax;
178 180 LD_RE(ans) = zero;
179 181 } else if (ay > one) { /* y>1 */
180 182 LD_IM(ans) = half * log1pl(two / (-t));
181 183 LD_RE(ans) = pi_2;
182 184 } else { /* y<1 */
183 185 LD_IM(ans) = half * log1pl((ay + ay) / t);
184 186 LD_RE(ans) = zero;
185 187 }
186 188 } else if (ay < E * (one + ax)) {
187 - /* INDENT OFF */
189 + /* BEGIN CSTYLED */
188 190 /*
189 191 * Tiny y (relative to 1+|x|)
190 192 * |y| < E*(1+|x|)
191 193 * where E=2**-29, -35, -60 for double, extended, quad precision
192 194 *
193 195 * 1 [x<=1: atan(x)
194 196 * A = - * atan2(2x,1-x*x-y*y) ~ [ 1 1+x
195 197 * 2 [x>=1: - atan2(2,(1-x)*(-----))
196 198 * 2 x
197 199 *
198 200 * y/x
199 201 * B ~ t*(1-2t), where t = ----------------- is tiny
200 202 * x + (y-1)*(y-1)/x
201 203 *
202 204 * y
203 205 * (when x < 2**-60, t = ----------- )
204 206 * (y-1)*(y-1)
205 207 */
206 - /* INDENT ON */
207 - if (ay == zero)
208 + /* END CSTYLED */
209 + if (ay == zero) {
208 210 LD_IM(ans) = ay;
209 - else {
211 + } else {
210 212 t1 = ay - one;
213 +
211 214 if (ix < 0x3fc30000)
212 215 t = ay / (t1 * t1);
213 216 else if (ix > 0x403b0000)
214 217 t = (ay / ax) / ax;
215 218 else
216 219 t = ay / (ax * ax + t1 * t1);
220 +
217 221 LD_IM(ans) = t * (one - two * t);
218 222 }
223 +
219 224 if (ix < 0x3fff0000)
220 225 LD_RE(ans) = atanl(ax);
221 226 else
222 227 LD_RE(ans) = half * atan2l(two, (one - ax) * (one +
223 - one / ax));
224 -
228 + one / ax));
225 229 } else if (ay > Einv * (one + ax)) {
226 - /* INDENT OFF */
230 + /* BEGIN CSTYLED */
227 231 /*
228 232 * Huge y relative to 1+|x|
229 233 * |y| > Einv*(1+|x|), where Einv~2**(prec/2+3),
230 234 * 1
231 235 * A ~ --- * atan2(2x, -y*y) ~ pi/2
232 236 * 2
233 237 * y
234 238 * B ~ t*(1-2t), where t = --------------- is tiny
235 239 * (y-1)*(y-1)
236 240 */
237 - /* INDENT ON */
241 + /* END CSTYLED */
238 242 LD_RE(ans) = pi_2;
239 243 t = (ay / (ay - one)) / (ay - one);
240 244 LD_IM(ans) = t * (one - (t + t));
241 245 } else if (ay == one) {
242 - /* INDENT OFF */
246 + /* BEGIN CSTYLED */
243 247 /*
244 248 * y=1
245 249 * 1 1
246 250 * A = - * atan2(2x, -x*x) = --- atan2(2,-x)
247 251 * 2 2
248 252 *
249 253 * 1 [ x*x+4] 1 4 [ 0.5(log2-logx) if
250 254 * B = - log [ -----] = - log (1+ ---) = [ |x|<E, else 0.25*
251 255 * 4 [ x*x ] 4 x*x [ log1p((2/x)*(2/x))
252 256 */
253 - /* INDENT ON */
257 + /* END CSTYLED */
254 258 LD_RE(ans) = half * atan2l(two, -ax);
255 - if (ax < E)
259 +
260 + if (ax < E) {
256 261 LD_IM(ans) = half * (ln2 - logl(ax));
257 - else {
262 + } else {
258 263 t = two / ax;
259 264 LD_IM(ans) = 0.25L * log1pl(t * t);
260 265 }
261 266 } else if (ax > Einv * Einv) {
262 - /* INDENT OFF */
267 + /* BEGIN CSTYLED */
263 268 /*
264 269 * Huge x:
265 270 * when |x| > 1/E^2,
266 271 * 1 pi
267 272 * A ~ --- * atan2(2x, -x*x-y*y) ~ ---
268 273 * 2 2
269 274 * y y/x
270 275 * B ~ t*(1-2t), where t = --------------- = (-------------- )/x
271 276 * x*x+(y-1)*(y-1) 1+((y-1)/x)^2
272 277 */
273 - /* INDENT ON */
278 + /* END CSTYLED */
274 279 LD_RE(ans) = pi_2;
275 280 t = ((ay / ax) / (one + ((ay - one) / ax) * ((ay - one) /
276 - ax))) / ax;
281 + ax))) / ax;
277 282 LD_IM(ans) = t * (one - (t + t));
278 283 } else if (ax < E * E * E * E) {
279 - /* INDENT OFF */
284 + /* BEGIN CSTYLED */
280 285 /*
281 286 * Tiny x:
282 287 * when |x| < E^4, (note that y != 1)
283 288 * 1 1
284 289 * A = --- * atan2(2x, 1-x*x-y*y) ~ --- * atan2(2x,1-y*y)
285 290 * 2 2
286 291 *
287 292 * 1 [ (y+1)*(y+1) ] 1 2 1 2y
288 293 * B = - log [ ----------- ] = - log (1+ ---) or - log(1+ ----)
289 294 * 4 [ (y-1)*(y-1) ] 2 y-1 2 1-y
290 295 */
291 - /* INDENT ON */
296 + /* END CSTYLED */
292 297 LD_RE(ans) = half * atan2l(ax + ax, (one - ay) * (one + ay));
293 - if (ay > one) /* y>1 */
298 +
299 + if (ay > one) /* y>1 */
294 300 LD_IM(ans) = half * log1pl(two / (ay - one));
295 - else /* y<1 */
301 + else /* y<1 */
296 302 LD_IM(ans) = half * log1pl((ay + ay) / (one - ay));
297 303 } else {
298 - /* INDENT OFF */
304 + /* BEGIN CSTYLED */
299 305 /*
300 306 * normal x,y
301 307 * 1
302 308 * A = --- * atan2(2x, 1-x*x-y*y)
303 309 * 2
304 310 *
305 311 * 1 [ x*x+(y+1)*(y+1) ] 1 4y
306 312 * B = - log [ --------------- ] = - log (1+ -----------------)
307 313 * 4 [ x*x+(y-1)*(y-1) ] 4 x*x + (y-1)*(y-1)
308 314 */
309 - /* INDENT ON */
315 + /* END CSTYLED */
310 316 t = one - ay;
317 +
311 318 if (iy >= 0x3ffe0000 && iy < 0x40000000) {
312 319 /* y close to 1 */
313 - LD_RE(ans) = half * (atan2l((ax + ax), (t * (one +
314 - ay) - ax * ax)));
320 + LD_RE(ans) = half * (atan2l((ax + ax), (t * (one + ay) -
321 + ax * ax)));
315 322 } else if (ix >= 0x3ffe0000 && ix < 0x40000000) {
316 323 /* x close to 1 */
317 324 LD_RE(ans) = half * atan2l((ax + ax), ((one - ax) *
318 - (one + ax) - ay * ay));
319 - } else
320 - LD_RE(ans) = half * atan2l((ax + ax), ((one - ax *
321 - ax) - ay * ay));
325 + (one + ax) - ay * ay));
326 + } else {
327 + LD_RE(ans) = half * atan2l((ax + ax), ((one - ax * ax) -
328 + ay * ay));
329 + }
330 +
322 331 LD_IM(ans) = 0.25L * log1pl((4.0L * ay) / (ax * ax + t * t));
323 332 }
333 +
324 334 if (hx < 0)
325 335 LD_RE(ans) = -LD_RE(ans);
336 +
326 337 if (hy < 0)
327 338 LD_IM(ans) = -LD_IM(ans);
339 +
328 340 return (ans);
329 341 }
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