Numeric Limits
Integer Arithmetic[Bearbeiten]
Expecco supports arbitrary precision integer arithmetic, arbitrary precision fractions and limited precision floating point numbers.
For integer operations, there is no overflow or error in the result for any legal operation. I.e. operations on two big numbers deliver a correct result:
4294967295 (0xFFFFFFFF) + 1 -> 4294967296 (0x100000000)
18446744073709551615 (0xFFFFFFFFFFFFFFFF) + 1 -> 18446744073709551616 (0x10000000000000000)
when dividing integers, the "/" operator will deliver an exact result, possibly as a fraction:
5 / 3 -> 5/3
and the truncating division "//" will deliver an integer, truncated towards negative infinity (i.e. the next smaller integer):
5 // 3 -> 2 -5 // 3 -> -3
Trigonmetric and other Math Functions[Bearbeiten]
Trigonometric and other math functions (sqrt, log, exp) will first convert the number to a limited precision real number (a C-double), and therefore may have a limited input value range and also generate inexact results.
For example, you will not get a valid result for:
10000 factorial sin
because it is not possible to represent that large number as real number. (expecco will signal a domain error, as the input to sin will be +INF)
Also, the result from:
(9 / 64) sqrt
will be the (inexact) 0.75 (a double), instead of the exact 3/4 (a fraction).
