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/* @(#)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. * ==================================================== */ #include <sys/cdefs.h> __FBSDID("$FreeBSD: release/9.1.0/lib/msun/src/s_tan.c 218509 2011-02-10 07:37:50Z das $"); /* 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 <float.h> #include "math.h" #define INLINE_REM_PIO2 #include "math_private.h" #include "e_rem_pio2.c" 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 */ if((int)x==0) return x; /* generate inexact */ 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 */ } } #if (LDBL_MANT_DIG == 53) __weak_reference(tan, tanl); #endif