The Mpfr Library: Algorithms and Proofs

1. Notations and Assumptions 2 2. Error calculus 2 2.1. Ulp calculus 2 2.2. Relative error analysis 4 2.3. Generic error of addition/subtraction 4 2.4. Generic error of multiplication 5 2.5. Generic error of inverse 5 2.6. Generic error of division 6 2.7. Generic error of square root 7 2.8. Generic error of the exponential 7 2.9. Generic error of the logarithm 8 2.10. Ulp calculus vs relative error 8 3. Low level functions 9 3.1. The mpfr add function 9 3.2. The mpfr cmp2 function 9 3.3. The mpfr sub function 10 3.4. The mpfr mul function 11 3.5. The mpfr div function 11 3.6. The mpfr sqrt function 13 3.7. The inverse square root 13 3.8. The mpfr remainder and mpfr remquo functions 15 4. High level functions 15 4.1. The cosine function 15 4.2. The sine function 16 4.3. The tangent function 17 4.4. The exponential function 17 4.5. The error function 18 4.6. The hyperbolic cosine function 19 4.7. The inverse hyperbolic cosine function 20 4.8. The hyperbolic sine function 21 4.9. The inverse hyperbolic sine function 22 4.10. The hyperbolic tangent function 23 4.11. The inverse hyperbolic tangent function 24 4.12. The arc-sine function 25