1 /* origin: FreeBSD /usr/src/lib/msun/src/s_tanl.c */
3 * Copyright (c) 2007 Steven G. Kargl
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
9 * 1. Redistributions of source code must retain the above copyright
10 * notice unmodified, this list of conditions, and the following
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
17 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
18 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
19 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
20 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
21 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
22 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
23 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
24 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
25 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
28 * Limited testing on pseudorandom numbers drawn within [0:4e8] shows
29 * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million
30 * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%).
35 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
36 long double tanl(long double x)
40 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
41 #include "__rem_pio2l.h"
43 long double tanl(long double x)
54 /* If x = +-0 or x is subnormal, then tan(x) = x. */
58 /* If x = NaN or Inf, then tan(x) = NaN. */
59 if (z.bits.exp == 32767)
60 return (x - x) / (x - x);
62 /* Optimize the case where x is already within range. */
64 hi = __tanl(z.e, 0, 0);
68 e0 = __rem_pio2l(x, y);
75 hi = __tanl(hi, lo, 0);
79 hi = __tanl(hi, lo, 1);