/* @(#)s_tan.c 5.1 93/09/24 */ /* * ==================================================== * 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. * ==================================================== */ /* FUNCTION <<tan>>, <<tanf>>---tangent INDEX tan INDEX tanf ANSI_SYNOPSIS #include <math.h> double tan(double <[x]>); float tanf(float <[x]>); TRAD_SYNOPSIS #include <math.h> double tan(<[x]>) double <[x]>; float tanf(<[x]>) float <[x]>; DESCRIPTION <<tan>> computes the tangent of the argument <[x]>. Angles are specified in radians. <<tanf>> is identical, save that it takes and returns <<float>> values. RETURNS The tangent of <[x]> is returned. PORTABILITY <<tan>> is ANSI. <<tanf>> is an extension. */ /* tan(x) * Return tangent function of x. * * kernel function: * __kernel_tan ... tangent function on [-pi/4,pi/4] * __ieee754_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 "fdlibm.h" #ifndef _DOUBLE_IS_32BITS #ifdef __STDC__ double tan(double x) #else double tan(x) double x; #endif { 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) return __kernel_tan(x,z,1); /* tan(Inf or NaN) is NaN */ else if (ix>=0x7ff00000) return x-x; /* NaN */ /* argument reduction needed */ else { n = __ieee754_rem_pio2(x,y); return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even -1 -- n odd */ } } #endif /* _DOUBLE_IS_32BITS */