Companion programs to the article "Integer points close to a transcendental curve and correctly-rounded evaluation of a function" by N. Brisebarre and G. Hanrot

These programs are SageMath ones. Please use a version 9.* of SageMath. You will get faster and more reliable performances if you install fplll and use it instead of using the fplll internal to SageMath.

• Algorithms 1 and 2, the one variable case. You will find some comments, examples and explanations in the file univ.sage. As an example, let's consider the last row of Table 3 in the article.
  • If we want to deal with a single instance, enter "runfile univ.sage" and enter "univ(gamma, 113, 12, 3/2, 3/2+15/2^21, 'dr', 'newton', 2^18, 0, 'extlll')": it tackles Problem 2.6 for gamma and directed roundings over the interval [3/2,3/2+15/2^21] with p = 113 and d = 12.
  • An example of intensive computations. To tackle Problem 2.6 for gamma over the interval [1+1/2^112,1+15/2^8] with p = 113 and d = 12, download test113_univ_gamma_12 and enter "sage < test113_univ_gamma_12".
• Algorithms 3 and 4, the two variable case. You will find some comments, examples and explanations in the file biv.sage. As an example, let's consider the last row of Table 4 in the article.
  • If we want to deal with a single instance, enter "runfile biv.sage" and enter "biv(exp, 113, 12, 1/4, 1/4+5/2^19, 12, 'dr', 'newton', 2^21, 78, 2, 'extlll')": it tackles Problem 2.6 for exp and directed roundings over the interval [1/4,1/4+5/2^19] with p = 113, d = 12 and w = 12p.
  • An example of intensive computations. To tackle Problem 2.6 for exp over the interval [1/4,1/4+5/2^6] with p = 113 and d = 12, download test113_biv_exp_12 and enter "sage < test113_biv_exp_12".