Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Jaume Timoneda Salat[en] Libquadmath is a library from the GNU GCC Project. It implements mathematical functions in C for 128 bits floating point values with a quad precision according to IEEE 754-2008 standard. The computing of these functions is based on functional approximations and numerical methods such as: Taylor series, Newton-Raphson method and, mainly, in Chebyshev polynomials expansion and minimax approximation. This paper analyses the implemented methods used for an efficient and fast computing of quad precision for square root, cube root, trigonometric, exponential and hyperbolic functions.