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       1                 :             : /*-
       2                 :             :  * Copyright (c) 2007 Steven G. Kargl
       3                 :             :  * All rights reserved.
       4                 :             :  *
       5                 :             :  * Redistribution and use in source and binary forms, with or without
       6                 :             :  * modification, are permitted provided that the following conditions
       7                 :             :  * are met:
       8                 :             :  * 1. Redistributions of source code must retain the above copyright
       9                 :             :  *    notice unmodified, this list of conditions, and the following
      10                 :             :  *    disclaimer.
      11                 :             :  * 2. Redistributions in binary form must reproduce the above copyright
      12                 :             :  *    notice, this list of conditions and the following disclaimer in the
      13                 :             :  *    documentation and/or other materials provided with the distribution.
      14                 :             :  *
      15                 :             :  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
      16                 :             :  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
      17                 :             :  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
      18                 :             :  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
      19                 :             :  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
      20                 :             :  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
      21                 :             :  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
      22                 :             :  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
      23                 :             :  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
      24                 :             :  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
      25                 :             :  */
      26                 :             : 
      27                 :             : #include "cdefs-compat.h"
      28                 :             : //__FBSDID("$FreeBSD: src/lib/msun/src/s_tanl.c,v 1.3 2011/05/30 19:41:28 kargl Exp $");
      29                 :             : 
      30                 :             : /*
      31                 :             :  * Limited testing on pseudorandom numbers drawn within [0:4e8] shows
      32                 :             :  * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million
      33                 :             :  * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%).
      34                 :             :  */
      35                 :             : 
      36                 :             : #include <float.h>
      37                 :             : #include <openlibm_math.h>
      38                 :             : 
      39                 :             : #include "math_private.h"
      40                 :             : #if LDBL_MANT_DIG == 64
      41                 :             : #include "../ld80/e_rem_pio2l.h"
      42                 :             : #elif LDBL_MANT_DIG == 113
      43                 :             : #include "../ld128/e_rem_pio2l.h"
      44                 :             : #else
      45                 :             : #error "Unsupported long double format"
      46                 :             : #endif
      47                 :             : 
      48                 :             : OLM_DLLEXPORT long double
      49                 :           0 : tanl(long double x)
      50                 :             : {
      51                 :             :         union IEEEl2bits z;
      52                 :             :         int e0, s;
      53                 :             :         long double y[2];
      54                 :             :         long double hi, lo;
      55                 :             : 
      56                 :           0 :         z.e = x;
      57                 :           0 :         s = z.bits.sign;
      58                 :           0 :         z.bits.sign = 0;
      59                 :             : 
      60                 :             :         /* If x = +-0 or x is subnormal, then tan(x) = x. */
      61         [ #  # ]:           0 :         if (z.bits.exp == 0)
      62                 :           0 :                 return (x);
      63                 :             : 
      64                 :             :         /* If x = NaN or Inf, then tan(x) = NaN. */
      65         [ #  # ]:           0 :         if (z.bits.exp == 32767)
      66                 :           0 :                 return ((x - x) / (x - x));
      67                 :             : 
      68                 :             :         /* Optimize the case where x is already within range. */
      69         [ #  # ]:           0 :         if (z.e < M_PI_4) {
      70                 :           0 :                 hi = __kernel_tanl(z.e, 0, 0);
      71         [ #  # ]:           0 :                 return (s ? -hi : hi);
      72                 :             :         }
      73                 :             : 
      74                 :           0 :         e0 = __ieee754_rem_pio2l(x, y);
      75                 :           0 :         hi = y[0];
      76                 :           0 :         lo = y[1];
      77                 :             : 
      78      [ #  #  # ]:           0 :         switch (e0 & 3) {
      79                 :           0 :         case 0:
      80                 :             :         case 2:
      81                 :           0 :             hi = __kernel_tanl(hi, lo, 0);
      82                 :           0 :             break;
      83                 :           0 :         case 1:
      84                 :             :         case 3:
      85                 :           0 :             hi = __kernel_tanl(hi, lo, 1);
      86                 :           0 :             break;
      87                 :             :         }
      88                 :             : 
      89                 :           0 :         return (hi);
      90                 :             : }