Correctly rounded functions for better arithmetic

The IEEE 754 standard for floating-point arithmetic requires that the four arithmetic operations and the square root should be correctly rounded. This has improved the accuracy, reliability and portability of numerical software. Unfortunately, such a requirement does not exist for the elementary functions. As a consequence, some libraries that are used everyday are rather poor. The problem of correctly rounding these functions is called the "Table Maker\´s Dilemma". After a survey on this problem, we give some new results. They show that correctly rounded functions could be provided at a reasonable cost.