public function testSemiFactorial()
{
$this->assertEquals(1, Math::SemiFactorial(0));
$this->assertEquals(1, Math::SemiFactorial(1));
$this->assertEquals(2, Math::SemiFactorial(2));
$this->assertEquals(3, Math::SemiFactorial(3));
$this->assertEquals(8, Math::SemiFactorial(4));
$this->assertEquals(15, Math::SemiFactorial(5));
$this->assertEquals(48, Math::SemiFactorial(6));
$this->assertEquals(105, Math::SemiFactorial(7));
}
/**
* Normalize, i.e. make sure the denominator is positive and that
* the numerator and denominator have no common factors
*/
private function normalize()
{
$gcd = Math::gcd($this->p, $this->q);
if ($gcd == 0) {
throw new DivisionByZeroException();
}
$this->p = $this->p / $gcd;
$this->q = $this->q / $gcd;
if ($this->q < 0) {
$this->p = -$this->p;
$this->q = -$this->q;
}
}
/**
* Evaluate a FunctionNode
*
* Computes the value of a FunctionNode `f(x)`, where f is
* an elementary function recognized by StdMathLexer and StdMathParser.
*
* @see \MathParser\Lexer\StdMathLexer StdMathLexer
* @see \MathParser\StdMathParser StdMathParser
* @throws UnknownFunctionException if the function respresented by the
* FunctionNode is *not* recognized.
*
* @param FunctionNode $node AST to be evaluated
* @retval float
*/
public function visitFunctionNode(FunctionNode $node)
{
$inner = $node->getOperand()->accept($this);
switch ($node->getName()) {
// Trigonometric functions
case 'sin':
case 'cos':
case 'tan':
case 'cot':
case 'arcsin':
case 'arccos':
case 'arctan':
case 'arccot':
case 'exp':
case 'log':
case 'lg':
case 'sinh':
case 'cosh':
case 'tanh':
case 'coth':
case 'arsinh':
case 'arcosh':
case 'artanh':
case 'arcoth':
throw new \UnexpectedValueException("Expecting rational expression");
case 'abs':
return new RationalNode(abs($inner->getNumerator()), $inner->getDenominator());
case 'sgn':
if ($inner->getNumerator() >= 0) {
return new RationalNode(1, 0);
} else {
return new RationalNode(-1, 0);
}
// Powers
// Powers
case 'sqrt':
return $this->rpow($inner, new RationalNode(1, 2));
case '!':
if ($inner->getDenominator() == 1 && $inner->getNumerator() >= 0) {
return new RationalNode(Math::Factorial($inner->getNumerator()), 1);
}
throw new \UnexpectedValueException("Expecting positive integer (factorial)");
case '!!':
if ($inner->getDenominator() == 1 && $inner->getNumerator() >= 0) {
return new RationalNode(Math::SemiFactorial($inner->getNumerator()), 1);
}
throw new \UnexpectedValueException("Expecting positive integer (factorial)");
default:
throw new UnknownFunctionException($node->getName());
}
}
/**
* Evaluate a FunctionNode
*
* Computes the value of a FunctionNode `f(x)`, where f is
* an elementary function recognized by StdMathLexer and StdMathParser.
*
* @see \MathParser\Lexer\StdMathLexer StdMathLexer
* @see \MathParser\StdMathParser StdMathParser
* @throws UnknownFunctionException if the function respresented by the
* FunctionNode is *not* recognized.
*
* @param FunctionNode $node AST to be evaluated
* @retval float
*/
public function visitFunctionNode(FunctionNode $node)
{
$inner = $node->getOperand()->accept($this);
switch ($node->getName()) {
// Trigonometric functions
case 'sin':
return sin($inner);
case 'cos':
return cos($inner);
case 'tan':
return tan($inner);
case 'cot':
return 1 / tan($inner);
// Trigonometric functions, argument in degrees
// Trigonometric functions, argument in degrees
case 'sind':
return sin(deg2rad($inner));
case 'cosd':
return cos(deg2rad($inner));
case 'tand':
return tan(deg2rad($inner));
case 'cotd':
return 1 / tan(deg2rad($inner));
// Inverse trigonometric functions
// Inverse trigonometric functions
case 'arcsin':
return asin($inner);
case 'arccos':
return acos($inner);
case 'arctan':
return atan($inner);
case 'arccot':
return pi() / 2 - atan($inner);
// Exponentials and logarithms
// Exponentials and logarithms
case 'exp':
return exp($inner);
case 'log':
return log($inner);
case 'lg':
return log10($inner);
// Powers
// Powers
case 'sqrt':
return sqrt($inner);
// Hyperbolic functions
// Hyperbolic functions
case 'sinh':
return sinh($inner);
case 'cosh':
return cosh($inner);
case 'tanh':
return tanh($inner);
case 'coth':
return 1 / tanh($inner);
// Inverse hyperbolic functions
// Inverse hyperbolic functions
case 'arsinh':
return asinh($inner);
case 'arcosh':
return acosh($inner);
case 'artanh':
return atanh($inner);
case 'arcoth':
return atanh(1 / $inner);
case 'abs':
return abs($inner);
case 'sgn':
return $inner >= 0 ? 1 : 0;
case '!':
$logGamma = Math::logGamma(1 + $inner);
return exp($logGamma);
case '!!':
if (round($inner) != $inner) {
throw new \UnexpectedValueException("Expecting positive integer (semifactorial)");
}
return Math::SemiFactorial($inner);
default:
throw new UnknownFunctionException($node->getName());
}
}
