certums

Crates.io	certums
lib.rs	certums
version	0.2.1
created_at	2025-10-13 23:23:14.94672+00
updated_at	2025-10-23 18:12:15.901063+00
description	(INDEV) Yet another fixed-point number system
homepage
repository	https://github.com/MisterSirCode/certums
max_upload_size
id	1881310
size	72,298

Taylor Schneider (MisterSirCode)

documentation

README

Certums

This is a simple numeric extension in rust that implements low-level fixed-sized fixed-point numbers as well as extensions and utilities for them in many different forms.

Certums and their variants are fixed-point values with whole number and fractional components. Acutes are fractional numbers with no whole number components.

The goal is to have a flexible and high-precision number system for tasks that rely largely on fractional components over supporting whole-number values.

These values are easily (Though lossily) convertable between eachother through simple bit-shifts, making them a convenient and easy-to-use format.

Changelog

V0.2.0 - Fix algebra (again) and add comparison checks, upgrade constants and features

NOTE: Due to the lack of widespread support, conversion of Certums (and variants) to f16s and f128s is not supported

Currently Implemented Types and Operands

8-128 bit Certums, 8-128 bit Unsigned Certums
Casting / Float conversion for all types
Negation for all types
Addition and Subtraction for all types
MIN/MAX/MINF/MAXF constants for all types
PI and E constants for all types (Except u8 for practicality reasons)
==, >, <, >=, <= checks for all types

More information:

Certums (and variants) and Acutes are quite simple and defined by simple structures, n representing bit count:

Unsigned Certum:

log_2(n) - 1 whole bits, n - log_2(n) + 1 fractional bits.

Signed Certums:

1 sign bit, log_2(n) - 2 whole bits, n - log_2(n) + 1 fractional bits.

Unsigned Quarta:

n / 4 whole bits, n - n / 4 fractional bits.

Signed Quarta:

1 sign bit, n / 4 - 1 whole bits, n - n / 4 fractional bits.

Unsigned Dimid:

n / 2 whole bits, n - n / 2 fractional bits.

Signed Dimid:

1 sign bit, n / 2 - 1 whole bits, n - n / 2 fractional bits.

Unsigned Acutes:

n fractional bits.

Signed Acutes:

1 sign bit, n - 1 fractional bits.

For data ranges, type any value into wolframalpha to see its full decimal format.

Certum Data Ranges:

Bit Depth	Min Signed	Max Signed	Max Unsigned	Integer:Fraction Signed	Integer:Fraction Unsigned
8 Bits	-2 + 2^-6	2 - 2^-6	4 - 2^-6	1:6	2:6
16 Bits	-4 + 2^-13	4 - 2^-13	8 - 2^-13	2:13	3:13
32 Bits	-8 + 2^-28	8 - 2^-28	16 - 2^-28	3:28	4:28
64 Bits	-16 + 2^-59	16 - 2^-59	32 - 2^-59	4:59	5:59
128 Bits	-32 + 2^-122	32 - 2^-122	64 - 2^-122	5:122	6:122

Quarta Data Ranges:

Bit Depth	Min Signed	Max Signed	Max Unsigned	Integer:Fraction Signed	Integer:Fraction Unsigned
8 Bits	-2 + 2^-6	2 - 2^-6	4 - 2^-6	1:6	2:6
16 Bits	-8 + 2^-12	8 - 2^-12	16 - 2^-12	3:12	4:12
32 Bits	-128 + 2^-24	128 - 2^-24	256 - 2^-24	7:24	8:24
64 Bits	-2¹⁵ + 2^-48	2¹⁵ - 2^-48	2¹⁶ - 2^-48	15:48	16:48
128 Bits	-2³¹ + 2^-96	2³¹ - 2^-96	2³² - 2^-96	31:96	32:96

Dimid Data Ranges:

Bit Depth	Min Signed	Max Signed	Max Unsigned	Integer:Fraction Signed	Integer:Fraction Unsigned
8 Bits	-8 + 2^-4	8 - 2^-4	16 - 2^-4	3:4	4:4
16 Bits	-128 + 2^-8	128 - 2^-8	256 - 2^-8	7:8	8:8
32 Bits	-2¹⁵ + 2^-16	2¹⁵ - 2^-16	2¹⁶ - 2^-16	15:16	16:16
64 Bits	-2³¹ + 2^-32	2³¹ - 2^-32	2³² - 2^-32	31:32	32:32
128 Bits	-2⁶³ + 2^-64	2⁶³ - 2^-64	2⁶⁴ - 2^-64	63:64	64:64

Acute Data Ranges:

Bit Depth	Min Signed	Max Signed	Max Unsigned
8 Bits	-1 + 2^-7	1 - 2^-7	1 - 2^-8
16 Bits	-1 + 2^-15	1 - 2^-15	1 - 2^-16
32 Bits	-1 + 2^-31	1 - 2^-31	1 - 2^-32
64 Bits	-1 + 2^-63	1 - 2^-63	1 - 2^-64
128 Bits	-1 + 2^-127	1 - 2^-127	1 - 2^-128

Translated:
Certum - Fixed
Quarta - Quarter
Dimidium - Half
Acute - Sharp

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