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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 <sys/cdefs.h>
     28 __FBSDID("$FreeBSD$");
     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 #ifdef __i386__
     38 #include <ieeefp.h>
     39 #endif
     40 
     41 #include "math.h"
     42 #include "math_private.h"
     43 #if LDBL_MANT_DIG == 64
     44 #include "../ld80/e_rem_pio2l.h"
     45 #elif LDBL_MANT_DIG == 113
     46 #include "../ld128/e_rem_pio2l.h"
     47 #else
     48 #error "Unsupported long double format"
     49 #endif
     50 
     51 long double
     52 tanl(long double x)
     53 {
     54 	union IEEEl2bits z;
     55 	int e0, s;
     56 	long double y[2];
     57 	long double hi, lo;
     58 
     59 	z.e = x;
     60 	s = z.bits.sign;
     61 	z.bits.sign = 0;
     62 
     63 	/* If x = +-0 or x is subnormal, then tan(x) = x. */
     64 	if (z.bits.exp == 0)
     65 		return (x);
     66 
     67 	/* If x = NaN or Inf, then tan(x) = NaN. */
     68 	if (z.bits.exp == 32767)
     69 		return ((x - x) / (x - x));
     70 
     71 	ENTERI();
     72 
     73 	/* Optimize the case where x is already within range. */
     74 	if (z.e < M_PI_4) {
     75 		hi = __kernel_tanl(z.e, 0, 0);
     76 		RETURNI(s ? -hi : hi);
     77 	}
     78 
     79 	e0 = __ieee754_rem_pio2l(x, y);
     80 	hi = y[0];
     81 	lo = y[1];
     82 
     83 	switch (e0 & 3) {
     84 	case 0:
     85 	case 2:
     86 	    hi = __kernel_tanl(hi, lo, 0);
     87 	    break;
     88 	case 1:
     89 	case 3:
     90 	    hi = __kernel_tanl(hi, lo, 1);
     91 	    break;
     92 	}
     93 
     94 	RETURNI(hi);
     95 }
     96