newlib/libm/ld/s_tanl.c

   1 /*-
   2  * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
   3  *
   4  * Copyright (c) 2007 Steven G. Kargl
   5  * All rights reserved.
   6  *
   7  * Redistribution and use in source and binary forms, with or without
   8  * modification, are permitted provided that the following conditions
   9  * are met:
  10  * 1. Redistributions of source code must retain the above copyright
  11  *    notice unmodified, this list of conditions, and the following
  12  *    disclaimer.
  13  * 2. Redistributions in binary form must reproduce the above copyright
  14  *    notice, this list of conditions and the following disclaimer in the
  15  *    documentation and/or other materials provided with the distribution.
  16  *
  17  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  18  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  19  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  20  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  21  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  22  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  23  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  24  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  25  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  26  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  27  */
  28
  29 #include <sys/cdefs.h>
  30 __FBSDID("$FreeBSD$");
  31
  32 /*
  33  * Limited testing on pseudorandom numbers drawn within [0:4e8] shows
  34  * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million
  35  * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%).
  36  */
  37
  38 #include <float.h>
  39 #ifdef __i386__
  40 #include <ieeefp.h>
  41 #endif
  42
  43 #include "math.h"
  44 #include "math_private.h"
  45 #if LDBL_MANT_DIG == 64
  46 #include "../ld80/e_rem_pio2l.h"
  47 #elif LDBL_MANT_DIG == 113
  48 #include "../ld128/e_rem_pio2l.h"
  49 #else
  50 #error "Unsupported long double format"
  51 #endif
  52
  53 long double
  54 tanl(long double x)
  55 {
  56         union IEEEl2bits z;
  57         int e0, s;
  58         long double y[2];
  59         long double hi, lo;
  60
  61         z.e = x;
  62         s = z.bits.sign;
  63         z.bits.sign = 0;
  64
  65         /* If x = +-0 or x is subnormal, then tan(x) = x. */
  66         if (z.bits.exp == 0)
  67                 return (x);
  68
  69         /* If x = NaN or Inf, then tan(x) = NaN. */
  70         if (z.bits.exp == 32767)
  71                 return ((x - x) / (x - x));
  72
  73         ENTERI();
  74
  75         /* Optimize the case where x is already within range. */
  76         if (z.e < M_PI_4) {
  77                 hi = __kernel_tanl(z.e, 0, 0);
  78                 RETURNI(s ? -hi : hi);
  79         }
  80
  81         e0 = __ieee754_rem_pio2l(x, y);
  82         hi = y[0];
  83         lo = y[1];
  84
  85         switch (e0 & 3) {
  86         case 0:
  87         case 2:
  88             hi = __kernel_tanl(hi, lo, 0);
  89             break;
  90         case 1:
  91         case 3:
  92             hi = __kernel_tanl(hi, lo, 1);
  93             break;
  94         }
  95
  96         RETURNI(hi);
  97 }