DeciMojo
An arbitrary-precision decimal and integer mathematics library for Mojo.
Overview
DeciMojo provides an arbitrary-precision decimal and integer mathematics library for Mojo, delivering exact calculations for financial modeling, scientific computing, and applications where floating-point approximation errors are unacceptable. Beyond basic arithmetic, the library includes advanced mathematical functions with guaranteed precision.
The core types are:
- A base-10 arbitrary-precision signed integer type (
BigInt) and a base-10 arbitrary-precision unsigned integer type (BigUInt) supporting unlimited digits. It features comprehensive arithmetic operations, comparison functions, and supports extremely large integer calculations efficiently. - An arbitrary-precision decimal implementation (
BigDecimal) allowing for calculations with unlimited digits and decimal places. It provides a complete set of arithmetic operations, comparisons, and mathematical functions like logarithms, exponentiation, roots, trigonometric functions, etc. It also supports rounding modes and conversions to/from built-in types. - A 128-bit fixed-point decimal implementation (
Decimal128) supporting up to 29 significant digits with a maximum of 28 decimal places. It features a complete set of mathematical functions including logarithms, exponentiation, roots, etc.
This repository includes TOMLMojo, a lightweight TOML parser in pure Mojo. It parses configuration files and test data, supporting basic types, arrays, and nested tables. While created for DeciMojo’s testing framework, it offers general-purpose structured data parsing with a clean, simple API.
| type | alias | information | internal representation |
|---|---|---|---|
BigUInt |
BUInt |
arbitrary-precision unsigned integer | List[UInt32] |
BigInt |
BInt |
arbitrary-precision integer | BigUInt, Bool |
BigDecimal |
BDec, Decimal |
arbitrary-precision decimal | BigUInt, Int, Bool |
Decimal128 |
Dec128 |
128-bit fixed-precision decimal | UInt32,UInt32,UInt32,UInt32 |
Examples
Here are some examples showcasing the arbitrary-precision feature of the BigDecimal type (aliases: BDec and Decimal). For some mathematical operations, the default precision (number of significant digits) is set to 36. You can change the precision by passing the precision argument to the function. This default precision will be configurable globally in future when Mojo supports global variables.
from decimojo.prelude import *
fn main() raises:
var a = BDec("123456789.123456789") # BDec is an alias for BigDecimal
var b = Decimal(
"1234.56789"
) # Decimal is a Python-like alias for BigDecimal
# === Basic Arithmetic === #
print(a + b) # 123458023.691346789
print(a - b) # 123455554.555566789
print(a * b) # 152415787654.32099750190521
print(a.true_divide(b + 1)) # 99919.0656560820700835791386582569736
# === Exponential Functions === #
print(a.sqrt(precision=80))
# 11111.111066111110969430554981749302328338130654689094538188579359566416821203641
print(a.cbrt(precision=80))
# 497.93385938415242742001134219007635925452951248903093962731782327785111102410518
print(a.root(b, precision=80))
# 1.0152058862996527138602610522640944903320735973237537866713119992581006582644107
print(a.power(b, precision=80))
# 3.3463611024190802340238135400789468682196324482030786573104956727660098625641520E+9989
print(a.exp(precision=80))
# 1.8612755889649587035842377856492201091251654136588338983610243887893287518637652E+53616602
print(a.log(b, precision=80))
# 2.6173300266565482999078843564152939771708486260101032293924082259819624360226238
print(a.ln(precision=80))
# 18.631401767168018032693933348296537542797015174553735308351756611901741276655161
# === Trigonometric Functions === #
print(a.sin(precision=200))
# 0.99985093087193092464780008002600992896256609588456
# 91036188395766389946401881352599352354527727927177
# 79589259132243649550891532070326452232864052771477
# 31418817041042336608522984511928095747763538486886
print(b.cos(precision=1000))
# -0.9969577603867772005841841569997528013669868536239849713029893885930748434064450375775817720425329394
# 9756020177557431933434791661179643984869397089102223199519409695771607230176923201147218218258755323
# 7563476302904118661729889931783126826250691820526961290122532541861737355873869924820906724540889765
# 5940445990824482174517106016800118438405307801022739336016834311018727787337447844118359555063575166
# 5092352912854884589824773945355279792977596081915868398143592738704592059567683083454055626123436523
# 6998108941189617922049864138929932713499431655377552668020889456390832876383147018828166124313166286
# 6004871998201597316078894718748251490628361253685772937806895692619597915005978762245497623003811386
# 0913693867838452088431084666963414694032898497700907783878500297536425463212578556546527017688874265
# 0785862902484462361413598747384083001036443681873292719322642381945064144026145428927304407689433744
# 5821277763016669042385158254006302666602333649775547203560187716156055524418512492782302125286330865
# === Internal representation of the number === #
(
Decimal(
"3.141592653589793238462643383279502884197169399375105820974944"
).power(2, precision=60)
).print_internal_representation()
# Internal Representation Details of BigDecimal
# ----------------------------------------------
# number: 9.8696044010893586188344909998
# 761511353136994072407906264133
# 5
# coefficient: 986960440108935861883449099987
# 615113531369940724079062641335
# negative: False
# scale: 59
# word 0: 62641335
# word 1: 940724079
# word 2: 113531369
# word 3: 99987615
# word 4: 861883449
# word 5: 440108935
# word 6: 986960
# ----------------------------------------------
Here is a comprehensive quick-start guide showcasing each major function of the BigInt type (BInt).
from decimojo.prelude import *
fn main() raises:
# === Construction ===
var a = BigInt("12345678901234567890") # From string
var b = BInt(12345) # From integer
# === Basic Arithmetic ===
print(a + b) # Addition: 12345678901234580235
print(a - b) # Subtraction: 12345678901234555545
print(a * b) # Multiplication: 152415787814108380241050
# === Division Operations ===
print(a // b) # Floor division: 999650944609516
print(a.truncate_divide(b)) # Truncate division: 999650944609516
print(a % b) # Modulo: 9615
# === Power Operation ===
print(BInt(2).power(10)) # Power: 1024
print(BInt(2) ** 10) # Power (using ** operator): 1024
# === Comparison ===
print(a > b) # Greater than: True
print(a == BInt("12345678901234567890")) # Equality: True
print(a.is_zero()) # Check for zero: False
# === Type Conversions ===
print(String(a)) # To string: "12345678901234567890"
# === Sign Handling ===
print(-a) # Negation: -12345678901234567890
print(abs(BInt("-12345678901234567890"))) # Absolute value: 12345678901234567890
print(a.is_negative()) # Check if negative: False
# === Extremely large numbers ===
# 3600 digits // 1800 digits
print(BInt("123456789" * 400) // BInt("987654321" * 200))
Nomenclature
DeciMojo combines “Deci” and “Mojo” - reflecting its purpose and implementation language. “Deci” (from Latin “decimus” meaning “tenth”) highlights our focus on the decimal numeral system that humans naturally use for counting and calculations.
Although the name emphasizes decimals with fractional parts, DeciMojo embraces the full spectrum of decimal mathematics. Our BigInt type, while handling only integers, is designed specifically for the decimal numeral system with its base-10 internal representation. This approach offers optimal performance while maintaining human-readable decimal semantics, contrasting with binary-focused libraries. Furthermore, BigInt serves as the foundation for our BigDecimal implementation, enabling arbitrary-precision calculations across both integer and fractional domains.
The name ultimately emphasizes our mission: bringing precise, reliable decimal calculations to the Mojo ecosystem, addressing the fundamental need for exact arithmetic that floating-point representations cannot provide.
Status
Rome wasn’t built in a day. DeciMojo is currently under active development. It has successfully progressed through the “make it work” phase and is now well into the “make it right” phase with many optimizations already in place. Bug reports and feature requests are welcome! If you encounter issues, please file them here.
Would love to get it added to the 