mirror of https://gitlab.com/rnger/amath
111 lines
3.4 KiB
C
111 lines
3.4 KiB
C
/*-
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* Copyright (c) 2014-2017 Carsten Sonne Larsen <cs@innolan.net>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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* Project homepage:
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* https://amath.innolan.net
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*
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* The original source code can be obtained from:
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* http://www.netlib.org/fdlibm/s_tan.c
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*
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*
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* =================================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* =================================================================
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*/
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/**
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* @file tan.c
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* @brief Tangent function
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*/
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#include "prim.h"
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/**
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* @brief Tangent function
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* @return Tangent function of x
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* @details
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* <pre>
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* Kernel function:
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*
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* __kernel_sin ... sine function on [-pi/4,pi/4]
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* __kernel_cos ... cose function on [-pi/4,pi/4]
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* __ieee754_rem_pio2 ... argument reduction routine
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*
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* Method:
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*
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* Let S,C and T denote the sin, cos and tan respectively on
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* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
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* in [-pi/4 , +pi/4], and let n = k mod 4.
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*
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* We have
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*
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* n sin(x) cos(x) tan(x)
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* ----------------------------------------------------------
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* 0 S C T
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* 1 C -S -1/T
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* 2 -S -C T
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* 3 -C S -1/T
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* ----------------------------------------------------------
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*
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* Special cases:
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*
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* Let trig be any of sin, cos, or tan.
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* trig(+-INF) is NaN
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* trig(NaN) is that NaN
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*
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* Accuracy:
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*
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* TRIG(x) returns trig(x) nearly rounded
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* </pre>
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*/
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double tan(double x)
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{
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double y[2], z = 0.0;
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int32_t n, ix;
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GET_HIGH_WORD(ix, x);
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ix &= 0x7FFFFFFF;
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// |x| ~< pi/4
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if (ix <= 0x3FE921FB)
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{
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return __kernel_tan(x, z, 1);
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}
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// tan(Inf or NaN) is NaN
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if (ix >= 0x7FF00000)
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{
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return NAN;
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}
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// |x| ~< pi/4
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n = rempio2(x, y);
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return __kernel_tan(y[0], y[1], 1 - ((n & 1) << 1));
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}
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