contrib/openbsd_libm/src/s_tanl.c

   1 /*      $OpenBSD: s_tanl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $     */
   2 /*-
   3  * Copyright (c) 2007 Steven G. Kargl
   4  * All rights reserved.
   5  *
   6  * Redistribution and use in source and binary forms, with or without
   7  * modification, are permitted provided that the following conditions
   8  * are met:
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice unmodified, this list of conditions, and the following
  11  *    disclaimer.
  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.
  15  *
  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.
  26  */
  27
  28 /*
  29  * Compute tan(x) for x where x is reduced to y = x - k * pi / 2.
  30  * Limited testing on pseudorandom numbers drawn within [0:4e8] shows
  31  * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million
  32  * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%).
  33  */
  34
  35 #include <sys/types.h>
  36 #include <machine/ieee.h>
  37 #include <float.h>
  38 #include <math.h>
  39
  40 #include "math_private.h"
  41
  42 #if LDBL_MANT_DIG == 64
  43 #define NX      3
  44 #define PREC    2
  45 #elif LDBL_MANT_DIG == 113
  46 #define NX      5
  47 #define PREC    3
  48 #else
  49 #error "Unsupported long double format"
  50 #endif
  51
  52 static const long double two24 = 1.67772160000000000000e+07L;
  53
  54 long double
  55 tanl(long double x)
  56 {
  57         union {
  58                 long double e;
  59                 struct ieee_ext bits;
  60         } z;
  61         int i, e0, s;
  62         double xd[NX], yd[PREC];
  63         long double hi, lo;
  64
  65         z.e = x;
  66         s = z.bits.ext_sign;
  67         z.bits.ext_sign = 0;
  68
  69         /* If x = +-0 or x is subnormal, then tan(x) = x. */
  70         if (z.bits.ext_exp == 0)
  71                 return (x);
  72
  73         /* If x = NaN or Inf, then tan(x) = NaN. */
  74         if (z.bits.ext_exp == 32767)
  75                 return ((x - x) / (x - x));
  76
  77         /* Optimize the case where x is already within range. */
  78         if (z.e < M_PI_4) {
  79                 hi = __kernel_tanl(z.e, 0, 0);
  80                 return (s ? -hi : hi);
  81         }
  82
  83         /* Split z.e into a 24-bit representation. */
  84         e0 = ilogbl(z.e) - 23;
  85         z.e = scalbnl(z.e, -e0);
  86         for (i = 0; i < NX; i++) {
  87                 xd[i] = (double)((int32_t)z.e);
  88                 z.e = (z.e - xd[i]) * two24;
  89         }
  90
  91         /* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */
  92         e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC);
  93
  94 #if PREC == 2
  95         hi = (long double)yd[0] + yd[1];
  96         lo = yd[1] - (hi - yd[0]);
  97 #else /* PREC == 3 */
  98         long double t;
  99         t = (long double)yd[2] + yd[1];
 100         hi = t + yd[0];
 101         lo = yd[0] - (hi - t);
 102 #endif
 103
 104         switch (e0 & 3) {
 105         case 0:
 106         case 2:
 107             hi = __kernel_tanl(hi, lo, 0);
 108             break;
 109         case 1:
 110         case 3:
 111             hi = __kernel_tanl(hi, lo, 1);
 112             break;
 113         }
 114
 115         return (s ? -hi : hi);
 116 }