/* tanf.c * * Circular tangent * * * * SYNOPSIS: * * float x, y, tanf(); * * y = tanf( x ); * * * * DESCRIPTION: * * Returns the circular tangent of the radian argument x. * * Range reduction is modulo pi/4. A polynomial approximation * is employed in the basic interval [0, pi/4]. * * * * ACCURACY: * * Relative error: * arithmetic domain # trials peak rms * IEEE +-4096 100000 3.3e-7 4.5e-8 * * ERROR MESSAGES: * * message condition value returned * tanf total loss x > 2^24 0.0 * */ /* cotf.c * * Circular cotangent * * * * SYNOPSIS: * * float x, y, cotf(); * * y = cotf( x ); * * * * DESCRIPTION: * * Returns the circular cotangent of the radian argument x. * A common routine computes either the tangent or cotangent. * * * * ACCURACY: * * Relative error: * arithmetic domain # trials peak rms * IEEE +-4096 100000 3.0e-7 4.5e-8 * * * ERROR MESSAGES: * * message condition value returned * cot total loss x > 2^24 0.0 * cot singularity x = 0 MAXNUMF * */ /* Cephes Math Library Release 2.2: June, 1992 Copyright 1984, 1987, 1989 by Stephen L. Moshier Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */ /* Single precision circular tangent * test interval: [-pi/4, +pi/4] * trials: 10000 * peak relative error: 8.7e-8 * rms relative error: 2.8e-8 */ #include extern float MAXNUMF; static float DP1 = 0.78515625; static float DP2 = 2.4187564849853515625e-4; static float DP3 = 3.77489497744594108e-8; float FOPI = 1.27323954473516; /* 4/pi */ static float lossth = 8192.; /*static float T24M1 = 16777215.;*/ static float tancotf( float xx, int cotflg ) { float x, y, z, zz; long j; int sign; /* make argument positive but save the sign */ if( xx < 0.0 ) { x = -xx; sign = -1; } else { x = xx; sign = 1; } if( x > lossth ) { if( cotflg ) mtherr( "cotf", TLOSS ); else mtherr( "tanf", TLOSS ); return(0.0); } /* compute x mod PIO4 */ j = FOPI * x; /* integer part of x/(PI/4) */ y = j; /* map zeros and singularities to origin */ if( j & 1 ) { j += 1; y += 1.0; } z = ((x - y * DP1) - y * DP2) - y * DP3; zz = z * z; if( x > 1.0e-4 ) { /* 1.7e-8 relative error in [-pi/4, +pi/4] */ y = ((((( 9.38540185543E-3 * zz + 3.11992232697E-3) * zz + 2.44301354525E-2) * zz + 5.34112807005E-2) * zz + 1.33387994085E-1) * zz + 3.33331568548E-1) * zz * z + z; } else { y = z; } if( j & 2 ) { if( cotflg ) y = -y; else y = -1.0/y; } else { if( cotflg ) y = 1.0/y; } if( sign < 0 ) y = -y; return( y ); } float tanf( float x ) { return( tancotf(x,0) ); } float cotf( float x ) { if( x == 0.0 ) { mtherr( "cotf", SING ); return( MAXNUMF ); } return( tancotf(x,1) ); }