Crate scientific

Expand description

Arbitrary precision scientific number

Constants

Use Scientific! in the crate scientific-macro to create constant numbers.

use scientific_macro::Scientific;
let n1 = Scientific!(1e100);
let n2 = Scientific!(1e80);
assert_eq!(&n1 + &n2, Scientific!(1.00000000000000000001e100));
// An f64 has only a precision of about 15.9 digits, this are already 21.

Invocation

All functions expect a reference to the Scientific number. (See example above.)

Conversion

There are From and TryFrom traits for conversion between Scientific and integers, floats and strings.

Converting a scientific number with decimals to an integer will fail.

There is a FromStr instance (which clones the str and calls Scientific::from_string).

The functions Scientific::to_bytes and Scientific::from_bytes use a compressed representation and not ASCII (this format will also be used when using serde with non human-readable formats).

Precision

Most functions work in truly arbitrary precision, please be aware of this.

For example: adding 1e1000 and 1e-1000, which both have only one byte of mantissa, results in 2001 bytes of mantissa.

Scientific::div, and Scientific::sqrt (which depends on div) as also Scientific::round require a precision to be specified, the result is only calculated to that precision.

It can be specified as Decimals or Digits. When using decimals specify the number of decimal places to calculate (2 for 0.01 as the smallest number, 0 for 1 and -2 for 100). When using digits specify the number of digits in the mantissa (using <= 0 digits will always result in zero).

Shortcuts: Precision::INTEGER for integer calculations (aka Decimals(0)) and Precision::F64 for calculations with a slightly better precision as an f64 (aka Digits(16)).

Shifting

The shifting operators do shift by one digit (and not one bit as you may expected).

Rounding

The function round/round_assign support several rounding options. See Rounding.

The functions above should be only used for the final rounding. If rounding in between is required (e.g. to keep the mantissa manageable) use round_rpsp/round_assign with a higher precision than the final one. It’s ok to be just one digit longer. RPSP stands for Rounding to prepare for shorter precision, see Wikipedia for more information.

Features

serde: Enable De-/Serialization with serde.
std: If activated the library requires std and the Error trait is implemented for all error types. Without it the library is no_std.
arc: Use of Arc instead of Rc, which enables Send and Sync for Scientific. Though Arc is more expensive, but since it’s only used during create/clone/drop of the Scientific number it’s probably not that much.
debug: Enabled tracking of pointer operations and some more checks. Very helpful during development of this lib.

Exponent

The exponent is represented as an isize. It is expected that it will never under-/overflow, even when smaller numbers are added/subtracted, like e.g. the length of the mantissa.

This is not checked!