decimo

A drop-in replacement for Python's decimal, written in Mojo.

⚠️ Development release. The API is settled enough to use, but the versions carry a timestamp: 0.14.0.devYYYYMMDDHHMMSS, where 0.14.0 is the version of the Mojo library the wheel packages. Wheels: macOS arm64 (11 and later) and Linux x86_64 and arm64 (glibc 2.35 and later), CPython 3.13 and 3.14. Everywhere else, build from source.

Change one import and your program keeps working:

# from decimal import Decimal, getcontext
from decimo import Decimal, getcontext

getcontext().prec = 50
print(Decimal(1) / Decimal(7))
# 0.14285714285714285714285714285714285714285714285714

The two libraries agree digit for digit. The test suite checks every operation against the standard library rather than against a table of expected strings, so "agrees with decimal" is a property that is measured, not a claim.

How fast is it?

The same benchmark file run against both libraries -- python/benchmarks/compare.py in the repository, which imports one or the other and runs identical code. Best of five, on an Apple M-series laptop:

Program	decimo	decimal
add/sub/mul/div, 28 digits	90.6 ns	73.0 ns	1.24× slower
add/sub/mul/div, 200 digits	331.8 ns	409.0 ns	1.23× faster
add/sub/mul/div, 1000 digits	2.02 µs	5.89 µs	2.91× faster
compound interest, 150 years	12.71 µs	13.08 µs	about the same
e from its series, 500 digits	197.92 µs	162.75 µs	1.22× slower
sqrt by Newton, 1000 digits	143.29 µs	232.29 µs	1.62× faster
pi by Machin, 500 digits	620.12 µs	520.17 µs	1.19× slower
parse and print, 1000 digits	3.28 µs	2.60 µs	1.26× slower

decimo is faster once the numbers are large, and 20-25% behind on small ones. The small-number gap is not the arithmetic: measured against libmpdec directly, without an interpreter in the way, decimo is 2-4× faster at 9 digits on add, subtract, multiply and round, and faster at every operation at 1000 digits. What is left is the cost of the Python call itself -- building the result object and converting the operands -- which CPython's decimal has had thirty years to shave. See the benchmarks.

What works

Everything a decimal program normally touches:

all the operators, including //, %, divmod() and **
getcontext().prec and getcontext().rounding, setcontext(), localcontext() (with keyword overrides), Context objects
all the rounding modes: ROUND_HALF_EVEN, ROUND_HALF_UP, ROUND_HALF_DOWN, ROUND_DOWN, ROUND_UP, ROUND_CEILING, ROUND_FLOOR, exact for arithmetic, quantize, round() and to_integral_value()
int(), float(), round(), math.floor/ceil/trunc, hash(), format()
Context you can compute with: ctx.divide(x, y), ctx.sqrt(x), ctx.quantize(x, y) and the rest, none of them touching the current context
keyword arguments where decimal takes them: quantize(exp, rounding=ROUND_HALF_UP), to_integral_value(rounding=...), sqrt(context=...)
Decimal((sign, digits, exponent)), so as_tuple() round-trips
pow(x, y, modulus), by modular exponentiation
quantize, normalize, as_tuple, as_integer_ratio, compare, fma, sqrt, exp, ln, log10, scaleb, adjusted, copy_abs, copy_negate, copy_sign, same_quantum, to_eng_string, max, min
the rest of the specification's surface: remainder_near, next_plus, next_minus, next_toward, shift, rotate, logical_and, logical_or, logical_xor, logical_invert, logb, compare_total, compare_total_mag, compare_signal, max_mag, min_mag, number_class, to_integral_exact, is_normal, is_subnormal, from_number
the same coercion rules: int converts in arithmetic, float does not, and both convert in a comparison
copy, deepcopy and pickle
ZeroDivisionError where you expect it, and hashes that agree with int, float and decimal.Decimal

Three things `decimal` does not have

decimo.pi(1000)   # 1000 digits of pi, by Chudnovsky with binary splitting
decimo.e(50)      # 50 digits of e
Decimal(2).sqrt(rounding=ROUND_FLOOR)   # and exp, ln, log10 too

pi() and e() use the context precision when given no argument; decimal has neither, and its documentation gives a recipe to write your own.

rounding= on sqrt, exp, ln and log10 is decimo's own: decimal ignores the context mode for these and always rounds half to even. And the answer under any mode is decided rather than approximated. The library computes wider than you asked, takes the interval its own error bound allows, and checks that the whole of it rounds to one answer; if a boundary falls inside, it widens and looks again. The same check now guards the default half to even, where before the last digit was assumed rather than known -- so ROUND_FLOOR really does stay under the true value, and a tie really is a tie.

A second type for money

Decimal is arbitrary precision and is what a program reaching for decimal.Decimal wants. Decimal128 is the other one: 96 bits of coefficient and a scale from 0 to 28, in sixteen bytes that own nothing -- the layout .NET's System.Decimal and Rust's rust_decimal use.

from decimo import Decimal128        # Dec128 is the same type

price = Decimal128("19.99")
line = (price * 3).quantize(Decimal128("0.01"))     # 59.97
Decimal128(2).sqrt()                                # and exp, ln, log10, sin, cos, tan
Decimal128("1").to_ieee754()                        # the IEEE 754 interchange bytes

It does arithmetic, compares, hashes and rounds like Decimal, mixes with int, float and str on either side of an operator, and converts both ways (Decimal128(x).to_decimal(), Decimal(x)). Its results never allocate, so it is quicker than Decimal on every operation where the values are money and the shape of them is known, and quicker than decimal on all of them but str().

A mixed expression settles in the wider type: Decimal128(x) + Decimal(y) is a Decimal, either way round, because widening loses nothing.

What it does not do: it stops at 7.9E+28 and 28 decimal places and raises rather than rounding into a context, it has no Context of its own beyond the rounding mode, and its scale is never negative -- Decimal128("1.23E+5") is 123000, where decimal keeps a coefficient of 123 with an exponent of 3 and can print it as 123E+3. Decimal128(0.1) is 0.1 rather than the whole binary expansion, since 55 digits do not fit 28; what is promised is that float(Decimal128(x)) == x.

What does not

decimo refuses these rather than answering differently:

NaN and infinity. decimo has no non-finite values. is_nan() and is_infinite() are always False.
ROUND_05UP. Nothing implements it; setting it raises NotImplementedError.
sqrt, exp, ln and log10 ignore the context rounding, as they do in decimal, and round half to even unless you pass rounding=. ** follows the context, also as in decimal. All of them are correctly rounded whichever mode applies, as are arithmetic, quantize and round().
//, %, divmod() and remainder_near with a long quotient. decimal raises InvalidOperation when the integer quotient has more digits than the precision; decimo answers. The remainder is rounded to the context, as in decimal.
Emin only reaches four methods. Exponents are unbounded, so Emin changes nothing except what next_plus(0), next_minus(0), is_subnormal() and number_class() say, where decimal's answers need a smallest exponent.
Signals and traps. Context.flags and Context.traps exist and stay empty. Inexact, Rounded and the rest are importable but never raised.
Emin / Emax. Exponents are unbounded, so nothing ever underflows to zero or overflows to infinity. A loop that waits for a term to become exactly zero will not stop; wait for the sum to stop changing instead.
One context per process, not per thread.

DivisionByZero and InvalidOperation are aliases for ZeroDivisionError and ValueError, which is what decimo actually raises, so except clauses written against decimal still catch.

Installing

pip install decimo

Wheels are built for macOS arm64 (macOS 11 and later) and for Linux on x86_64 and arm64 (glibc 2.35 and later), for CPython 3.13 and 3.14. On anything else, build from source with pixi:

git clone https://github.com/forfudan/decimo && cd decimo
pixi run -e py314 release        # or py313; the wheel lands in python/dist/
pip install python/dist/*.whl

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