-/* origin: FreeBSD /usr/src/lib/msun/src/s_tanl.c */
-/*-
- * Copyright (c) 2007 Steven G. Kargl
- * All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- * 1. Redistributions of source code must retain the above copyright
- * notice unmodified, this list of conditions, and the following
- * disclaimer.
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
- * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
- * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
- * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
- * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
- * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
- * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
- * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
- * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
- * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
- */
-/*
- * Limited testing on pseudorandom numbers drawn within [0:4e8] shows
- * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million
- * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%).
- */
-
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
long double tanl(long double x)
{
- union IEEEl2bits z;
- int e0, s;
+ union ldshape u = {x};
long double y[2];
- long double hi, lo;
-
- z.e = x;
- s = z.bits.sign;
- z.bits.sign = 0;
-
- /* If x = +-0 or x is subnormal, then tan(x) = x. */
- if (z.bits.exp == 0)
- return x;
-
- /* If x = NaN or Inf, then tan(x) = NaN. */
- if (z.bits.exp == 32767)
- return (x - x) / (x - x);
-
- /* Optimize the case where x is already within range. */
- if (z.e < M_PI_4) {
- hi = __tanl(z.e, 0, 0);
- return s ? -hi : hi;
- }
-
- e0 = __rem_pio2l(x, y);
- hi = y[0];
- lo = y[1];
-
- switch (e0 & 3) {
- case 0:
- case 2:
- hi = __tanl(hi, lo, 0);
- break;
- case 1:
- case 3:
- hi = __tanl(hi, lo, 1);
- break;
+ unsigned n;
+
+ u.i.se &= 0x7fff;
+ if (u.i.se == 0x7fff)
+ return x - x;
+ if (u.f < M_PI_4) {
+ if (u.i.se < 0x3fff - LDBL_MANT_DIG/2) {
+ /* raise inexact if x!=0 and underflow if subnormal */
+ FORCE_EVAL(u.i.se == 0 ? x*0x1p-120f : x+0x1p120f);
+ return x;
+ }
+ return __tanl(x, 0, 0);
}
- return hi;
+ n = __rem_pio2l(x, y);
+ return __tanl(y[0], y[1], n&1);
}
#endif