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sin.c

by Paul McJones last modified 2007-02-02 09:32

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/*#ident	"@(#)cfront:lib/complex/sin.c	1.3"*/

#include "complex.h"
#include "const.h"

complex
sin(complex z)
/*
	sine of z: -i * sinh(i*z)
*/
{
	complex	y = complex(-z.im, z.re);	/*  i * z */
	y = sinh(y);				/*  csinh(y) */
	return complex(y.im, -y.re);		/*  -i * y */
}

complex
sinh(complex z)
/*
	The hyperbolic sine
*/
{
	double cosh_x, sinh_x, cos_y, sin_y;
	c_exception	ex( "sinh", z );
	int write( int , char *, unsigned int );

#define SINH_GOOD	1e7

	if (ABS(z.im) > SINH_GOOD)
	{ 
		ex.type = OVERFLOW;
		if ( !complex_error( ex ))
			errno = ERANGE;
    		return ex.retval;
    	}

    	cos_y = cos(z.im);
    	sin_y = sin(z.im);

	if (z.re > MAX_EXPONENT)
	{
		ex.type = OVERFLOW;
		ex.retval.re = (cos_y >= 0) ? HUGE : -HUGE;
		ex.retval.im = (sin_y >= 0) ? HUGE : -HUGE;
		if ( !complex_error( ex ))
			errno = ERANGE;
		return ex.retval;
    	}
	else if (z.re < MIN_EXPONENT)
	{
		ex.type = OVERFLOW;
		ex.retval.re = (cos_y >= 0) ? -HUGE : HUGE;
		ex.retval.im = (sin_y >= 0) ? HUGE : -HUGE;
		if ( !complex_error( ex ))
			errno = ERANGE;
		return ex.retval;
    	}
	else
	{
    		double pos_exp = exp(z.re); 
    		double neg_exp = 1/pos_exp;
   		cosh_x = (pos_exp + neg_exp)/2;
   		sinh_x = (pos_exp - neg_exp)/2;
    	}

	return complex(cos_y*sinh_x, sin_y*cosh_x);
}
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