The document proposes efficient methods for evaluating elementary functions like sin, cos, tan, log, and exp using SIMD instructions. The methods are twice as fast as floating point unit evaluation and have a maximum error of 6 ulps. They avoid conditional branches, gathering/scattering operations, and table lookups. Trigonometric functions are evaluated in two steps - argument reduction followed by a series evaluation. Inverse trigonometric, exponential and logarithmic functions are also efficiently evaluated in a similar manner suitable for SIMD computation. Evaluation accuracy and speed are evaluated against existing methods and the code size is kept small.