/* origin: FreeBSD /usr/src/lib/msun/src/s_tan.c */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* tan(x) * Return tangent function of x. * * kernel function: * __tan ... tangent function on [-pi/4,pi/4] * __rem_pio2 ... argument reduction routine * * Method. * Let S,C and T denote the sin, cos and tan respectively on * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 * in [-pi/4 , +pi/4], and let n = k mod 4. * We have * * n sin(x) cos(x) tan(x) * ---------------------------------------------------------- * 0 S C T * 1 C -S -1/T * 2 -S -C T * 3 -C S -1/T * ---------------------------------------------------------- * * Special cases: * Let trig be any of sin, cos, or tan. * trig(+-INF) is NaN, with signals; * trig(NaN) is that NaN; * * Accuracy: * TRIG(x) returns trig(x) nearly rounded */ #include "libm.h" double tan(double x) { double y[2], z = 0.0; int32_t n, ix; /* High word of x. */ GET_HIGH_WORD(ix, x); /* |x| ~< pi/4 */ ix &= 0x7fffffff; if (ix <= 0x3fe921fb) { if (ix < 0x3e400000) /* x < 2**-27 */ /* raise inexact if x != 0 */ if ((int)x == 0) return x; return __tan(x, z, 1); } /* tan(Inf or NaN) is NaN */ if (ix >= 0x7ff00000) return x - x; /* argument reduction needed */ n = __rem_pio2(x, y); return __tan(y[0], y[1], 1 - ((n&1)<<1)); /* n even: 1, n odd: -1 */ }