```5261 libm should stop using synonyms.h
5298 fabs is 0-sized, confuses dis(1) and others
Reviewed by: Josef 'Jeff' Sipek <jeffpc@josefsipek.net>
Approved by: Gordon Ross <gwr@nexenta.com>```

```   1 /*
3  *
4  * The contents of this file are subject to the terms of the
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
15  * If applicable, add the following below this CDDL HEADER, with the
16  * fields enclosed by brackets "[]" replaced with your own identifying
18  *
20  */
21
22 /*
24  */
25 /*
27  * Use is subject to license terms.
28  */
29

30 /* long double sinpil(long double x),
31  * return long double precision sinl(pi*x).
32  *
33  * Algorithm, 10/17/2002, K.C. Ng
34  * ------------------------------
35  * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary).
36  *      1. If y == z, then x is a multiple of pi/4. Return the following values:
37  *             ---------------------------------------------------
38  *               n  x mod 2    sin(x*pi)    cos(x*pi)   tan(x*pi)
39  *             ---------------------------------------------------
40  *              000  0.00       +0 ___       +1 ___      +0
41  *              001  0.25       +\/0.5       +\/0.5      +1
42  *              010  0.50       +1 ___       +0 ___      +inf
43  *              011  0.75       +\/0.5       -\/0.5      -1
44  *              100  1.00       -0 ___       -1 ___      +0
45  *              101  1.25       -\/0.5       -\/0.5      +1
46  *              110  1.50       -1 ___       -0 ___      +inf
47  *              111  1.75       -\/0.5       +\/0.5      -1
48  *             ---------------------------------------------------
49  *      2. Otherwise,
50  *             ---------------------------------------------------
51  *               n     t        sin(x*pi)    cos(x*pi)   tan(x*pi)
52  *             ---------------------------------------------------
53  *              000  (y-z)/4     sinpi(t)     cospi(t)    tanpi(t)
54  *              001  (z+1-y)/4   cospi(t)     sinpi(t)    1/tanpi(t)
55  *              010  (y-z)/4     cospi(t)    -sinpi(t)   -1/tanpi(t)
56  *              011  (z+1-y)/4   sinpi(t)    -cospi(t)   -tanpi(t)
57  *              100  (y-z)/4    -sinpi(t)    -cospi(t)    tanpi(t)
58  *              101  (z+1-y)/4  -cospi(t)    -sinpi(t)    1/tanpi(t)
59  *              110  (y-z)/4    -cospi(t)     sinpi(t)   -1/tanpi(t)
60  *              111  (z+1-y)/4  -sinpi(t)     cospi(t)   -tanpi(t)
61  *             ---------------------------------------------------
62  *
63  * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0).
64  * This will return a result with error slightly more than one ulp (but less
65  * than 2 ulp). If one wants accurate result,  one may break up pi*t in
66  * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo)
68  */
69
70 #include "libm.h"

71 #include "longdouble.h"
72
73 #include <sys/isa_defs.h>
74
75 #define I(q, m) ((int *) &(q))[m]
76 #define U(q, m) ((unsigned *) &(q))[m]
77 #if defined(__i386) || defined(__amd64)
78 #define LDBL_MOST_SIGNIF_I(ld)  ((I(ld, 2) << 16) | (0xffff & (I(ld, 1) >> 15)))
79 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0)
80 #define PREC    64
81 #define PRECM1  63
82 #define PRECM2  62
83 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L;
84 #else
85 #define LDBL_MOST_SIGNIF_I(ld)  I(ld, 0)
86 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof(long double) / sizeof(int) - 1)
87 #define PREC    113
88 #define PRECM1  112
89 #define PRECM2  111
90 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L;
91 #endif
92
93 static const long double
94 zero    = 0.0L,
95 quater  = 0.25L,
96 one     = 1.0L,
97 pi      = 3.141592653589793238462643383279502884197e+0000L,
98 sqrth   = 0.707106781186547524400844362104849039284835937688474,
99 tiny    = 1.0e-100;
100
101 long double
102 sinpil(long double x) {
103         long double y, z, t;
104         int hx, n, k;
105         unsigned lx;
106
107         hx = LDBL_MOST_SIGNIF_I(x);
108         lx = LDBL_LEAST_SIGNIF_U(x);
109         k = ((hx & 0x7fff0000) >> 16) - 0x3fff;
110         if (k >= PRECM2) {           /* |x| >= 2**(Prec-2) */
111                 if (k >= 16384)
112                         y = x - x;
113                 else {
114                         if (k >= PREC)
115                                 y = zero;
116                         else if (k == PRECM1)
117                                 y = (lx & 1) == 0 ? zero: -zero;
118                         else {  /* k = Prec - 2 */
119                                 y = (lx & 1) == 0 ? zero : one;
120                                 if ((lx & 2) != 0)
121                                         y = -y;
122                         }
123                 }
124         }
125         else if (k < -2)     /* |x| < 0.25 */
126                 y = __k_sinl(pi * fabsl(x), zero);
127         else {
128                 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
129                 y = 4.0L * fabsl(x);
130                 if (k < PRECM2) {
131                         z = y + twoPRECM2;
132                         n = LDBL_LEAST_SIGNIF_U(z) & 7;     /* 3 LSb of z */
133                         t = z - twoPRECM2;
134                         k = 0;
135                         if (t == y)
136                                 k = 1;
137                         else if (t > y) {
138                                 n -= 1;
139                                 t = quater + (y - t) * quater;
140                         }
141                         else
142                                 t = (y - t) * quater;
143                 }
144                 else {  /* k = Prec-3 */
145                         n = LDBL_LEAST_SIGNIF_U(y) & 7;     /* 3 LSb of z */
146                         k = 1;
147                 }
148                 if (k) {        /* x = N/4 */
149                         if ((n & 1) != 0)
150                                 y = sqrth + tiny;
151                         else
152                                 y = (n & 2) == 0 ? zero : one;
153                         if ((n & 4) != 0)
154                                 y = -y;
155                 }
156                 else {
157                         if ((n & 1) != 0)
158                                 t = quater - t;
159                         if (((n + (n & 1)) & 2) == 0)
160                                 y = __k_sinl(pi * t, zero);
161                         else
162                                 y = __k_cosl(pi * t, zero);
163                         if ((n & 4) != 0)
164                                 y = -y;
165                 }
166         }
167         return hx >= 0 ? y : -y;
168 }
169 #undef U
170 #undef LDBL_LEAST_SIGNIF_U
171 #undef I
172 #undef LDBL_MOST_SIGNIF_I
--- EOF ---

```