1 /*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
6 * You may not use this file except in compliance with the License.
7 *
8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 * or http://www.opensolaris.org/os/licensing.
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21
22 /*
23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 */
25 /*
26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 * Use is subject to license terms.
28 */
29
30 #include <sys/isa_defs.h>
31 #include "libm_inlines.h"
32
33 #ifdef _LITTLE_ENDIAN
34 #define HI(x) *(1+(int*)x)
35 #define LO(x) *(unsigned*)x
36 #else
37 #define HI(x) *(int*)x
38 #define LO(x) *(1+(unsigned*)x)
39 #endif
40
41 #ifdef __RESTRICT
42 #define restrict _Restrict
43 #else
44 #define restrict
45 #endif
46
47 void
48 __vatan( int n, double * restrict x, int stridex, double * restrict y, int stridey )
49 {
50 double f , z, ans = 0.0L, ansu , ansl , tmp , poly , conup , conlo , dummy;
51 double f1, ans1, ansu1, ansl1, tmp1, poly1, conup1, conlo1;
52 double f2, ans2, ansu2, ansl2, tmp2, poly2, conup2, conlo2;
53 int index, sign, intf, intflo, intz, argcount;
54 int index1, sign1 = 0;
55 int index2, sign2 = 0;
56 double *yaddr,*yaddr1 = 0,*yaddr2 = 0;
57 extern const double __vlibm_TBL_atan1[];
58 extern double fabs( double );
59
60 /* Power series atan(x) = x + p1*x**3 + p2*x**5 + p3*x**7
61 * Error = -3.08254E-18 On the interval |x| < 1/64 */
62
63 /* define dummy names for readability. Use parray to help compiler optimize loads */
64 #define p3 parray[0]
65 #define p2 parray[1]
66 #define p1 parray[2]
67
68 static const double parray[] = {
69 -1.428029046844299722E-01, /* p[3] */
70 1.999999917247000615E-01, /* p[2] */
71 -3.333333333329292858E-01, /* p[1] */
72 1.0, /* not used for p[0], though */
73 -1.0, /* used to flip sign of answer */
74 };
75
76 if( n <= 0 ) return; /* if no. of elements is 0 or neg, do nothing */
77 do
78 {
79 LOOP0:
80
81 f = fabs(*x); /* fetch argument */
82 intf = HI(x); /* upper half of x, as integer */
83 intflo = LO(x); /* lower half of x, as integer */
84 sign = intf & 0x80000000; /* sign of argument */
85 intf = intf & ~0x80000000; /* abs(upper argument) */
86
87 if( (intf > 0x43600000) || (intf < 0x3e300000) ) /* filter out special cases */
88 {
89 if( (intf > 0x7ff00000) || ((intf == 0x7ff00000) && (intflo !=0) ) )
90 {
91 ans = f - f; /* return NaN if x=NaN*/
92 }
93 else if( intf < 0x3e300000 ) /* avoid underflow for small arg */
94 {
95 dummy = 1.0e37 + f;
96 dummy = dummy;
97 ans = f;
98 }
99 else if( intf > 0x43600000 ) /* avoid underflow for big arg */
100 {
101 index = 2;
102 ans = __vlibm_TBL_atan1[index] + __vlibm_TBL_atan1[index+1];/* pi/2 up + pi/2 low */
103 }
104 *y = (sign) ? -ans: ans; /* store answer, with sign bit */
105 x += stridex;
106 y += stridey;
107 argcount = 0; /* initialize argcount */
108 if ( --n <=0 ) break; /* we are done */
109 goto LOOP0; /* otherwise, examine next arg */
110 }
111
112 index = 0; /* points to 0,0 in table */
113 if (intf > 0x40500000) /* if(|x| > 64 */
114 { f = -1.0/f;
115 index = 2; /* point to pi/2 upper, lower */
116 }
117 else if( intf >= 0x3f900000 ) /* if |x| >= (1/64)... */
118 {
119 intz = (intf + 0x00008000) & 0x7fff0000;/* round arg, keep upper */
120 HI(&z) = intz; /* store as a double (z) */
121 LO(&z) = 0; /* ...lower */
122 f = (f - z)/(1.0 + f*z); /* get reduced argument */
123 index = (intz - 0x3f900000) >> 15; /* (index >> 16) << 1) */
124 index = index + 4; /* skip over 0,0,pi/2,pi/2 */
125 }
126 yaddr = y; /* address to store this answer */
127 x += stridex; /* point to next arg */
128 y += stridey; /* point to next result */
129 argcount = 1; /* we now have 1 good argument */
130 if ( --n <=0 )
131 {
132 f1 = 0.0; /* put dummy values in args 1,2 */
133 f2 = 0.0;
134 index1 = 0;
135 index2 = 0;
136 goto UNROLL3; /* finish up with 1 good arg */
137 }
138
139 /*--------------------------------------------------------------------------*/
140 /*--------------------------------------------------------------------------*/
141 /*--------------------------------------------------------------------------*/
142
143 LOOP1:
144
145 f1 = fabs(*x); /* fetch argument */
146 intf = HI(x); /* upper half of x, as integer */
147 intflo = LO(x); /* lower half of x, as integer */
148 sign1 = intf & 0x80000000; /* sign of argument */
149 intf = intf & ~0x80000000; /* abs(upper argument) */
150
151 if( (intf > 0x43600000) || (intf < 0x3e300000) ) /* filter out special cases */
152 {
153 if( (intf > 0x7ff00000) || ((intf == 0x7ff00000) && (intflo !=0) ) )
154 {
155 ans = f1 - f1; /* return NaN if x=NaN*/
156 }
157 else if( intf < 0x3e300000 ) /* avoid underflow for small arg */
158 {
159 dummy = 1.0e37 + f1;
160 dummy = dummy;
161 ans = f1;
162 }
163 else if( intf > 0x43600000 ) /* avoid underflow for big arg */
164 {
165 index1 = 2;
166 ans = __vlibm_TBL_atan1[index1] + __vlibm_TBL_atan1[index1+1];/* pi/2 up + pi/2 low */
167 }
168 *y = (sign1) ? -ans: ans; /* store answer, with sign bit */
169 x += stridex;
170 y += stridey;
171 argcount = 1; /* we still have 1 good arg */
172 if ( --n <=0 )
173 {
174 f1 = 0.0; /* put dummy values in args 1,2 */
175 f2 = 0.0;
176 index1 = 0;
177 index2 = 0;
178 goto UNROLL3; /* finish up with 1 good arg */
179 }
180 goto LOOP1; /* otherwise, examine next arg */
181 }
182
183 index1 = 0; /* points to 0,0 in table */
184 if (intf > 0x40500000) /* if(|x| > 64 */
185 { f1 = -1.0/f1;
186 index1 = 2; /* point to pi/2 upper, lower */
187 }
188 else if( intf >= 0x3f900000 ) /* if |x| >= (1/64)... */
189 {
190 intz = (intf + 0x00008000) & 0x7fff0000;/* round arg, keep upper */
191 HI(&z) = intz; /* store as a double (z) */
192 LO(&z) = 0; /* ...lower */
193 f1 = (f1 - z)/(1.0 + f1*z); /* get reduced argument */
194 index1 = (intz - 0x3f900000) >> 15; /* (index >> 16) << 1) */
195 index1 = index1 + 4; /* skip over 0,0,pi/2,pi/2 */
196 }
197 yaddr1 = y; /* address to store this answer */
198 x += stridex; /* point to next arg */
199 y += stridey; /* point to next result */
200 argcount = 2; /* we now have 2 good arguments */
201 if ( --n <=0 )
202 {
203 f2 = 0.0; /* put dummy value in arg 2 */
204 index2 = 0;
205 goto UNROLL3; /* finish up with 2 good args */
206 }
207
208 /*--------------------------------------------------------------------------*/
209 /*--------------------------------------------------------------------------*/
210 /*--------------------------------------------------------------------------*/
211
212 LOOP2:
213
214 f2 = fabs(*x); /* fetch argument */
215 intf = HI(x); /* upper half of x, as integer */
216 intflo = LO(x); /* lower half of x, as integer */
217 sign2 = intf & 0x80000000; /* sign of argument */
218 intf = intf & ~0x80000000; /* abs(upper argument) */
219
220 if( (intf > 0x43600000) || (intf < 0x3e300000) ) /* filter out special cases */
221 {
222 if( (intf > 0x7ff00000) || ((intf == 0x7ff00000) && (intflo !=0) ) )
223 {
224 ans = f2 - f2; /* return NaN if x=NaN*/
225 }
226 else if( intf < 0x3e300000 ) /* avoid underflow for small arg */
227 {
228 dummy = 1.0e37 + f2;
229 dummy = dummy;
230 ans = f2;
231 }
232 else if( intf > 0x43600000 ) /* avoid underflow for big arg */
233 {
234 index2 = 2;
235 ans = __vlibm_TBL_atan1[index2] + __vlibm_TBL_atan1[index2+1];/* pi/2 up + pi/2 low */
236 }
237 *y = (sign2) ? -ans: ans; /* store answer, with sign bit */
238 x += stridex;
239 y += stridey;
240 argcount = 2; /* we still have 2 good args */
241 if ( --n <=0 )
242 {
243 f2 = 0.0; /* put dummy value in arg 2 */
244 index2 = 0;
245 goto UNROLL3; /* finish up with 2 good args */
246 }
247 goto LOOP2; /* otherwise, examine next arg */
248 }
249
250 index2 = 0; /* points to 0,0 in table */
251 if (intf > 0x40500000) /* if(|x| > 64 */
252 { f2 = -1.0/f2;
253 index2 = 2; /* point to pi/2 upper, lower */
254 }
255 else if( intf >= 0x3f900000 ) /* if |x| >= (1/64)... */
256 {
257 intz = (intf + 0x00008000) & 0x7fff0000;/* round arg, keep upper */
258 HI(&z) = intz; /* store as a double (z) */
259 LO(&z) = 0; /* ...lower */
260 f2 = (f2 - z)/(1.0 + f2*z); /* get reduced argument */
261 index2 = (intz - 0x3f900000) >> 15; /* (index >> 16) << 1) */
262 index2 = index2 + 4; /* skip over 0,0,pi/2,pi/2 */
263 }
264 yaddr2 = y; /* address to store this answer */
265 x += stridex; /* point to next arg */
266 y += stridey; /* point to next result */
267 argcount = 3; /* we now have 3 good arguments */
268
269
270 /* here is the 3 way unrolled section,
271 note, we may actually only have
272 1,2, or 3 'real' arguments at this point
273 */
274
275 UNROLL3:
276
277 conup = __vlibm_TBL_atan1[index ]; /* upper table */
278 conup1 = __vlibm_TBL_atan1[index1]; /* upper table */
279 conup2 = __vlibm_TBL_atan1[index2]; /* upper table */
280
281 conlo = __vlibm_TBL_atan1[index +1]; /* lower table */
282 conlo1 = __vlibm_TBL_atan1[index1+1]; /* lower table */
283 conlo2 = __vlibm_TBL_atan1[index2+1]; /* lower table */
284
285 tmp = f *f ;
286 tmp1 = f1*f1;
287 tmp2 = f2*f2;
288
289 poly = f *((p3*tmp + p2)*tmp + p1)*tmp ;
290 poly1 = f1*((p3*tmp1 + p2)*tmp1 + p1)*tmp1;
291 poly2 = f2*((p3*tmp2 + p2)*tmp2 + p1)*tmp2;
292
293 ansu = conup + f ; /* compute atan(f) upper */
294 ansu1 = conup1 + f1; /* compute atan(f) upper */
295 ansu2 = conup2 + f2; /* compute atan(f) upper */
296
297 ansl = (((conup - ansu ) + f ) + poly ) + conlo ;
298 ansl1 = (((conup1 - ansu1) + f1) + poly1) + conlo1;
299 ansl2 = (((conup2 - ansu2) + f2) + poly2) + conlo2;
300
301 ans = ansu + ansl ;
302 ans1 = ansu1 + ansl1;
303 ans2 = ansu2 + ansl2;
304
305 /* now check to see if these are 'real' or 'dummy' arguments BEFORE storing */
306
307 *yaddr = sign ? -ans: ans; /* this one is always good */
308 if(argcount < 3) break; /* end loop and finish up */
309 *yaddr1 = sign1 ? -ans1: ans1;
310 *yaddr2 = sign2 ? -ans2: ans2;
311
312 } while (--n > 0);
313
314 if(argcount == 2)
315 { *yaddr1 = sign1 ? -ans1: ans1;
316 }
317 }