tinytrig.c

CD_高级PALM编程

	double 	result, prevResult, numerator, denominator, term, sign, factorial, diff;

// Scale input angle to proper value between -2 PI and + 2 PI.\
// The power series is not as  accurate outside that range.

	if (( x > TWO_PI )  || ( x < - TWO_PI ))
		x = ScaleNearZero ( x, TWO_PI );
	
// initialize everything
	
	result 				= x;
	numerator 		= x;
	denominator		= 1.0;
	factorial 			= -1.0;
	sign 				= 1.0;

// Add the next term to the power series until within allowable limits.

	do 
	{
		
// prepare for next term calculation
	
		factorial 		= factorial + 2.0;
		prevResult 	= result;
		sign 			= sign * - 1.0;
		
// calculate the next term
	
		numerator 	= numerator * x * x;
		denominator	= denominator * ( factorial + 1.0 ) * ( factorial + 2.0 );
		term			= numerator / denominator;
		result 			= result + ( sign * term );
		
// Prep for termination check. Stop when the library's accuracy is reached.

		diff 			= _abs ( _abs ( prevResult ) - _abs ( result));
	}
	while ( diff > TT_ACCURACY );
	
	return result;
}


/*****************************************************
 * FUNCTION:    	_cos
 *
 * DESCRIPTION: 	Calculate the cosine of a double radians number
 *					using  the power series cos x = 1 - 
 *					( x**2 / 2! ) + ( x**4 / 4! ) - ( x**6 / 6! ) + .....
 *
 * RETURNED:    	The result.
*****************************************************/
double _cos		// ( out ) the result
(
	double x		// ( in ) The number to get the cosine of
)
{
	double 	result, prevResult, diff, numerator, denominator, term, sign, factorial;
	UInt8		cnt = 0;
	
// Scale input angle to proper value between -2 PI and + 2 PI.\
// The power series is not as  accurate outside that range.

	if (( x > TWO_PI )  || ( x < - TWO_PI ))
		x = ScaleNearZero ( x, TWO_PI );	

// initialize everything
	
	result 				= 1.0;
	prevResult		= 1.0;
	numerator 		= x * x;
	denominator 	= 2.0;
	factorial 			= 0.0;
	sign 				= 1.0;

	do
	{
	
// Prep for the next calculation

		prevResult 	= result;
		sign 			= -sign;
		factorial 		= factorial + 2.0;
		
// Calculate the next term
	
		term			= numerator / denominator;
		result 			= result + ( sign * term );
		
// Prepare for next sequence thru loop

		numerator 	= numerator * x * x;
		denominator	= denominator * ( factorial + 1.0 ) * ( factorial + 2.0 );
		
// Check for loop termination. Stop when the library's accuracy is reached.
	
		diff 			= _abs ( _abs ( prevResult ) - _abs ( result));
	}
	while ( diff > TT_ACCURACY );
	
	return result;	
}


/*****************************************************
 * FUNCTION:    	_tan
 *
 * DESCRIPTION: 	Calculate the tangent of a double radians number.
 *
 * RETURNED:    	The result. If the cosine is zero, the
 *					value returned is either very small or very large.
*****************************************************/
double _tan		// ( out ) the result
(
	double x		// ( in ) the number to get the tangent of
)
{
	double sinx, cosx, result;

// Scale input angle to proper value between -2 PI and + 2 PI.
// The sin and cos power equations are not as  accurate outside that range.
// Do it here once instead of within both sin and cos.

	if (( x > TWO_PI ) || ( x < - TWO_PI ))
		x = ScaleNearZero ( x, TWO_PI );
	
// Get the sine and cosine of the number.

	sinx 	= _sin ( x );
	cosx 	= _cos ( x );
	result = sinx / cosx;
		
// Eliminate divide by zero problems

	if ( cosx == 0.0 )
	{
		if ( sinx >= 0.0 )
			result = POS_INFINITY;
		else
			result = NEG_INFINITY;
	}
	
// Otherwise, calculate the result

	else result = sinx / cosx;
		
	return result;	
}


/*****************************************************
 * FUNCTION:    	_asin
 *
 * DESCRIPTION: 	Calculate the inverse sine of a double value.
 *
 * RETURNED:    	The matching value in radians.
 *					Returns zero if incoming value is not
 *					a valid sine value between -1 and +1.
*****************************************************/
double _asin		// ( out ) the result
(
	double x		// ( in ) the sine to calculate the inverse of
)
{
	double	sinx = 0.0;

// Check for valid incoming sine value

	if (( x >= - 1.0 ) && ( x <= 1.0 ))
	{
	
// Make suitable for table lookup, lookup the radians equivalent,
// and readjust the resulting sign if appropriate.

		sinx = _abs ( x );
		sinx = TTLookup ( sinx, sines, radians );
		if ( x < 0.0 )
			sinx = -1.0 * sinx;
	}	
	return sinx;	
}


/*****************************************************
 * FUNCTION:    	_acos
 *
 * DESCRIPTION: 	Calculate the inverse cosine of a double value.
 *
 * RETURNED:    	The matching value in radians.
 *					Returns zero if the incoming value is not
 *					a valid cosine value between -1 and +1.
*****************************************************/
double _acos		// ( out ) the result
(
	double x		// ( in ) the number to get th inverse cosine of
)
{
	double	cosx = 0.0;

// Check for valid incoming cosine value

	if (( x >=  - 1.0 ) && ( x <= 1.0 ))
	{

// Make suitable for table lookup, lookup the radians equivalent,
// and readjust the resulting sign if appropriate.

		cosx = _abs ( x );
		cosx = TTLookup ( cosx, cosines, radians );
		if ( x < 0.0 ) 
			cosx = PI - cosx;
	}
	return cosx;
}


/*****************************************************
 * FUNCTION:    	_atan
 *
 * DESCRIPTION: 	Calculate the inverse tangent of a double value.
 *
 * RETURNED:    	The matching value in radians.
 *					Returns -PI/2 or + PI/2 if the incoming value is not
 *					a valid tangent value between -552.0 and +552
 *					( -89.9 <-> 89.9 degrees).
*****************************************************/
double _atan		// ( out ) the result
(
	double 	x	// ( in ) the number to get the inverse tangent of
)
{
	double	tanx = 0.0;
	
// Check for valid incoming tangent value.

	if ( x < TAN_MIN_VALUE ) 
		tanx = - HALF_PI;
	else if ( x > TAN_MAX_VALUE )
		tanx = HALF_PI;
	else
	{
	
// Make suitable for table lookup, lookup the radians equivalent,
// and readjust the resulting sign if appropriate.

		tanx = _abs ( x );
		tanx = TTLookup ( tanx, tangents, radians );
		if ( x < 0.0 )
			tanx = - 1.0 * tanx;
	}
	return tanx;
}


/*****************************************************
 * FUNCTION:    	_sin2
 *
 * DESCRIPTION: 	Lookup the sine of a double radians number.
  *
 * RETURNED:    	The result.
*****************************************************/
double _sin2		// ( out ) the result
(
	double x		// ( in ) the number to get the sine of
)
{
	double	result = 0.0, xRange = x, xval;

// Scale input angle to between -2 PI and + 2 PI and
// adjust for negative value.

	if (( x >  TWO_PI ) || ( x < - TWO_PI))
		xRange = ScaleNearZero ( x, TWO_PI );
	xval	= _abs ( xRange );
		
// Convert to proper sign & range for table lookup

	if (( xval > ( HALF_PI )) && ( xval <= PI ))
		xval = PI  - xval;
	else if (( xval > PI ) && ( xval <= ( 3.0 * HALF_PI )))
		xval = xval - PI;
	else if ( xval > ( 3.0 * HALF_PI ))
		xval = ( TWO_PI ) - xval;
		
// Lookup the radians equivalent

	result = TTLookup ( xval, radians, sines );
	
// Adjust the final sign if necessary

	if (( xRange > PI ) || (( xRange < 0.0 ) && ( xRange > - PI )))
		result = - result;
	return result;	
}


/*****************************************************
 * FUNCTION:    	_cos2
 *
 * DESCRIPTION: 	Lookup the cosine of a double radians number.
  *
 * RETURNED:    	The result.
*****************************************************/
double _cos2		// ( out ) the result
(
	double x		// ( in ) the number to get the sine of
)
{
	double	result = 0.0, xRange = x, xval;

// Scale input angle to between - PI and + PI and
// adjust for negative value.

	if (( x > TWO_PI ) || ( x < - TWO_PI ))
		xRange = ScaleNearZero ( x, TWO_PI );
	xval 	= _abs ( xRange );
		
// Convert to proper sign & range for table lookup

	if (( xval > ( HALF_PI )) && ( xval <= PI ))
		xval = PI  - xval;
	else if (( xval > PI ) && ( xval <= ( 3.0 * HALF_PI )))
		xval = xval - PI;
	else if ( xval > ( 3.0 * HALF_PI ))
		xval = TWO_PI - xval;
		
// Lookup the radians equivalent

	result = TTLookup ( xval, radians, cosines );
	
// Adjust the final sign if necessary

	if ((( xRange > ( - 3.0 * HALF_PI )) && ( xRange < - HALF_PI))  || 
		(( xRange > HALF_PI ) && ( xRange < ( 3.0 * HALF_PI ))))
		result = - result;	
	return result;	
}

/*****************************************************
 * FUNCTION:    	_tan2
 *
 * DESCRIPTION: 	Calculate the tangent of a double radians number.
 *
 * RETURNED:    	The result. If the cosine is zero, the
 *					value returned is either "NEG_INFINITY"
 *					or "POS_INFINITY", very small and very large values.
*****************************************************/
double _tan2		// ( out ) the result
(
	double x		// ( in ) the number to get the tangent of
)
{
	double sinx, cosx,  result, xval = x;

// Scale input angle to proper value between -2 PI and + 2 PI.
// The sin and cos power series are not as  accurate outside that range.
// Do it here once instead of within both sin and cos.

	if (( x > TWO_PI ) || ( x < - TWO_PI ))
		x = ScaleNearZero ( x, TWO_PI );
	
// Get the sine and cosine of the number.

	sinx 	= _sin2 ( x );
	cosx 	= _cos2 ( x );

// Eliminate divide by zero problems

	if ( cosx == 0.0 )
	{
		if ( sinx >= 0.0 )
			result = POS_INFINITY;
		else
			result = NEG_INFINITY;
	}
	
// Otherwise, calculate the result

	else result = sinx / cosx;

	return result;	
}