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lib/glm/gtx/fast_exponential.inl

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+/// @ref gtx_fast_exponential
+/// @file glm/gtx/fast_exponential.inl
+
+namespace glm
+{
+	// fastPow:
+	template <typename genType>
+	GLM_FUNC_QUALIFIER genType fastPow(genType x, genType y)
+	{
+		return exp(y * log(x));
+	}
+
+	template <typename T, precision P, template <typename, precision> class vecType>
+	GLM_FUNC_QUALIFIER vecType<T, P> fastPow(vecType<T, P> const & x, vecType<T, P> const & y)
+	{
+		return exp(y * log(x));
+	}
+
+	template <typename T>
+	GLM_FUNC_QUALIFIER T fastPow(T x, int y)
+	{
+		T f = static_cast<T>(1);
+		for(int i = 0; i < y; ++i)
+			f *= x;
+		return f;
+	}
+
+	template <typename T, precision P, template <typename, precision> class vecType>
+	GLM_FUNC_QUALIFIER vecType<T, P> fastPow(vecType<T, P> const & x, vecType<int, P> const & y)
+	{
+		vecType<T, P> Result(uninitialize);
+		for(length_t i = 0, n = x.length(); i < n; ++i)
+			Result[i] = fastPow(x[i], y[i]);
+		return Result;
+	}
+
+	// fastExp
+	// Note: This function provides accurate results only for value between -1 and 1, else avoid it.
+	template <typename T>
+	GLM_FUNC_QUALIFIER T fastExp(T x)
+	{
+		// This has a better looking and same performance in release mode than the following code. However, in debug mode it's slower.
+		// return 1.0f + x * (1.0f + x * 0.5f * (1.0f + x * 0.3333333333f * (1.0f + x * 0.25 * (1.0f + x * 0.2f))));
+		T x2 = x * x;
+		T x3 = x2 * x;
+		T x4 = x3 * x;
+		T x5 = x4 * x;
+		return T(1) + x + (x2 * T(0.5)) + (x3 * T(0.1666666667)) + (x4 * T(0.041666667)) + (x5 * T(0.008333333333));
+	}
+	/*  // Try to handle all values of float... but often shower than std::exp, glm::floor and the loop kill the performance
+	GLM_FUNC_QUALIFIER float fastExp(float x)
+	{
+		const float e = 2.718281828f;
+		const float IntegerPart = floor(x);
+		const float FloatPart = x - IntegerPart;
+		float z = 1.f;
+
+		for(int i = 0; i < int(IntegerPart); ++i)
+			z *= e;
+
+		const float x2 = FloatPart * FloatPart;
+		const float x3 = x2 * FloatPart;
+		const float x4 = x3 * FloatPart;
+		const float x5 = x4 * FloatPart;
+		return z * (1.0f + FloatPart + (x2 * 0.5f) + (x3 * 0.1666666667f) + (x4 * 0.041666667f) + (x5 * 0.008333333333f));
+	}
+
+	// Increase accuracy on number bigger that 1 and smaller than -1 but it's not enough for high and negative numbers
+	GLM_FUNC_QUALIFIER float fastExp(float x)
+	{
+		// This has a better looking and same performance in release mode than the following code. However, in debug mode it's slower.
+		// return 1.0f + x * (1.0f + x * 0.5f * (1.0f + x * 0.3333333333f * (1.0f + x * 0.25 * (1.0f + x * 0.2f))));
+		float x2 = x * x;
+		float x3 = x2 * x;
+		float x4 = x3 * x;
+		float x5 = x4 * x;
+		float x6 = x5 * x;
+		float x7 = x6 * x;
+		float x8 = x7 * x;
+		return 1.0f + x + (x2 * 0.5f) + (x3 * 0.1666666667f) + (x4 * 0.041666667f) + (x5 * 0.008333333333f)+ (x6 * 0.00138888888888f) + (x7 * 0.000198412698f) + (x8 * 0.0000248015873f);;
+	}
+	*/
+
+	template <typename T, precision P, template <typename, precision> class vecType>
+	GLM_FUNC_QUALIFIER vecType<T, P> fastExp(vecType<T, P> const & x)
+	{
+		return detail::functor1<T, T, P, vecType>::call(fastExp, x);
+	}
+
+	// fastLog
+	template <typename genType>
+	GLM_FUNC_QUALIFIER genType fastLog(genType x)
+	{
+		return std::log(x);
+	}
+
+	/* Slower than the VC7.1 function...
+	GLM_FUNC_QUALIFIER float fastLog(float x)
+	{
+		float y1 = (x - 1.0f) / (x + 1.0f);
+		float y2 = y1 * y1;
+		return 2.0f * y1 * (1.0f + y2 * (0.3333333333f + y2 * (0.2f + y2 * 0.1428571429f)));
+	}
+	*/
+
+	template <typename T, precision P, template <typename, precision> class vecType>
+	GLM_FUNC_QUALIFIER vecType<T, P> fastLog(vecType<T, P> const & x)
+	{
+		return detail::functor1<T, T, P, vecType>::call(fastLog, x);
+	}
+
+	//fastExp2, ln2 = 0.69314718055994530941723212145818f
+	template <typename genType>
+	GLM_FUNC_QUALIFIER genType fastExp2(genType x)
+	{
+		return fastExp(0.69314718055994530941723212145818f * x);
+	}
+
+	template <typename T, precision P, template <typename, precision> class vecType>
+	GLM_FUNC_QUALIFIER vecType<T, P> fastExp2(vecType<T, P> const & x)
+	{
+		return detail::functor1<T, T, P, vecType>::call(fastExp2, x);
+	}
+
+	// fastLog2, ln2 = 0.69314718055994530941723212145818f
+	template <typename genType>
+	GLM_FUNC_QUALIFIER genType fastLog2(genType x)
+	{
+		return fastLog(x) / 0.69314718055994530941723212145818f;
+	}
+
+	template <typename T, precision P, template <typename, precision> class vecType>
+	GLM_FUNC_QUALIFIER vecType<T, P> fastLog2(vecType<T, P> const & x)
+	{
+		return detail::functor1<T, T, P, vecType>::call(fastLog2, x);
+	}
+}//namespace glm