#arbitrary #precision #no-std

no-std scientific

Arbitrary precision scientific number (no_std capable, in pure Rust)

9 releases

0.5.2 Nov 15, 2023
0.5.1 Aug 30, 2023
0.2.2 Jul 15, 2023
0.2.0 Dec 15, 2022
0.1.0 Jun 25, 2021

#116 in Math

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Used in 2 crates (via serde_taml)

MIT license

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crate scientific

Arbitrary precision scientific number


Use Scientific! to create constant numbers.

use scientific::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.


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


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).


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.

Functions for division and square root (which depends on div) as also all rounding functions 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)).


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


The functions 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 at least the same precision than the final one. The rounding will create one more digit than you required, to easily use it. RPSP stands for Rounding to prepare for shorter precision, see Wikipedia for more information.

In any case it's preferred to use the *_assign version since it can save reallocation of the mantissa (though not everytime relocation is required or can be avoided).


let precision = Precision::Digits(30); // precision for intermediate roundings and the final one
// do calculations
value.round_rpsp_assign(precision); // round to 31 digits with 'Rounding to prepare for shorter precision'
// do more calculations
value.round_assign(precision, RoundHalfUp); // round to 30 digits with the method 'RoundHalfUp'


The functions truncate/truncate_assign are identical to rounding with RoundTowardsZero but faster.

Also truncate_assign is faster than truncate because it does not need to clone. Either way it does never require relocation of the mantissa (since it's not changed, just maybe referenced to a prefix of it).


  • serde: Enable De-/Serialization with serde.

  • macro: Re-export the Scientific! macro, enabled by default.

  • 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: Enables several checks. Very helpful during development of this lib.


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!