2026-10-16 · main ad7db3d · arm64, macOS-26.6.2-arm64-arm-64bit-Mach-O
Mojo 1.1.0 (8189361e) · CPython 3.14.6 · libmpdec 4.0.1 and GMP 6.3.0, both linked from C
Each figure is the minimum over several rounds, on an idle machine.
Regenerate with pixi run benchdoc.
Operands of digits decimal digits at working precision, so that
precision grows with the operands. libmpdec is the C library behind
CPython’s decimal, timed without the interpreter. round drops the
low half of the operand; parse builds the value from its string.
Verified this run: decimo and libmpdec produce the same 2000-digit product from the same 1000-digit operands.
| Digits / precision | Operation | decimo | libmpdec | CPython decimal |
||
|---|---|---|---|---|---|---|
| 9 / 28 | add | 11.2 ns | 35.3 ns | 3.16× faster | 47.1 ns | 4.21× faster |
| 9 / 28 | subtract | 12.0 ns | 34.8 ns | 2.91× faster | 46.9 ns | 3.92× faster |
| 9 / 28 | multiply | 13.5 ns | 27.3 ns | 2.03× faster | 44.8 ns | 3.33× faster |
| 9 / 28 | divide | 59.5 ns | 51.2 ns | 1.16× slower | 69.6 ns | 1.17× faster |
| 9 / 28 | round | 7.8 ns | 32.5 ns | 4.19× faster | 71.5 ns | 9.21× faster |
| 9 / 28 | parse | 53.8 ns | 42.2 ns | 1.27× slower | 82.1 ns | 1.53× faster |
| 1,000 / 1,000 | add | 50.1 ns | 116.5 ns | 2.32× faster | 112.5 ns | 2.24× faster |
| 1,000 / 1,000 | subtract | 60.6 ns | 97.5 ns | 1.61× faster | 86.1 ns | 1.42× faster |
| 1,000 / 1,000 | multiply | 1.07 µs | 9.09 µs | 8.51× faster | 9.89 µs | 9.26× faster |
| 1,000 / 1,000 | divide | 5.82 µs | 14.51 µs | 2.50× faster | 15.68 µs | 2.70× faster |
| 1,000 / 1,000 | round | 51.4 ns | 101.5 ns | 1.97× faster | 124.7 ns | 2.43× faster |
| 1,000 / 1,000 | parse | 1.26 µs | 1.65 µs | 1.30× faster | 2.06 µs | 1.63× faster |
| 100,000 / 100,000 | add | 2.50 µs | 6.00 µs | 2.40× faster | 6.77 µs | 2.71× faster |
| 100,000 / 100,000 | subtract | 3.00 µs | 3.70 µs | 1.23× faster | 4.05 µs | 1.35× faster |
| 100,000 / 100,000 | multiply | 1.85 ms | 2.92 ms | 1.58× faster | 3.06 ms | 1.66× faster |
| 100,000 / 100,000 | divide | 4.66 ms | 14.22 ms | 3.05× faster | 14.81 ms | 3.18× faster |
| 100,000 / 100,000 | round | 2.65 µs | 4.25 µs | 1.60× faster | 4.82 µs | 1.82× faster |
| 100,000 / 100,000 | parse | 119.50 µs | 160.40 µs | 1.34× faster | 177.10 µs | 1.48× faster |
| 1,000,000 / 1,000,000 | add | 24.50 µs | 58.50 µs | 2.39× faster | 69.38 µs | 2.83× faster |
| 1,000,000 / 1,000,000 | subtract | 30.00 µs | 35.50 µs | 1.18× faster | 40.88 µs | 1.36× faster |
| 1,000,000 / 1,000,000 | multiply | 25.30 ms | 30.76 ms | 1.22× faster | 32.33 ms | 1.28× faster |
| 1,000,000 / 1,000,000 | divide | 123.80 ms | 161.11 ms | 1.30× faster | 169.77 ms | 1.37× faster |
| 1,000,000 / 1,000,000 | round | 29.50 µs | 45.50 µs | 1.54× faster | 43.81 µs | 1.49× faster |
| 1,000,000 / 1,000,000 | parse | 1.20 ms | 1.58 ms | 1.32× faster | 2.02 ms | 1.68× faster |
A fixed set, chosen before the results were seen. 2.3456789, and
** 1.5 for power. 100 000 digits is left out because mpd_exp
needs 82 seconds there and mpd_ln 239 seconds.
| Precision | Operation | decimo | libmpdec | |
|---|---|---|---|---|
| 28 | sqrt | 374.6 ns | 902.5 ns | 2.41× faster |
| 28 | exp | 5.13 µs | 4.59 µs | 1.12× slower |
| 28 | ln | 3.01 µs | 13.28 µs | 4.42× faster |
| 28 | power | 9.28 µs | 36.61 µs | 3.95× faster |
| 100 | sqrt | 2.13 µs | 4.16 µs | 1.96× faster |
| 100 | exp | 6.61 µs | 15.18 µs | 2.30× faster |
| 100 | ln | 10.03 µs | 40.42 µs | 4.03× faster |
| 100 | power | 19.37 µs | 84.42 µs | 4.36× faster |
| 1,000 | sqrt | 21.82 µs | 232.02 µs | 10.63× faster |
| 1,000 | exp | 237.69 µs | 4.81 ms | 20.25× faster |
| 1,000 | ln | 157.59 µs | 5.56 ms | 35.30× faster |
| 1,000 | power | 313.32 µs | 11.33 ms | 36.16× faster |
| 10,000 | sqrt | 528.50 µs | 22.66 ms | 42.87× faster |
| 10,000 | exp | 15.46 ms | 1.983 s | 128.26× faster |
| 10,000 | ln | 8.43 ms | 3.527 s | 418.58× faster |
| 10,000 | power | 24.43 ms | 5.020 s | 205.46× faster |
GMP is the reference implementation for big integers and the harder opponent, timed in C. CPython’s integers can only be reached through the interpreter, so those include its overhead — read the large sizes as the real ones. Division is 2n-by-n; two operands of the same width would give a one-digit quotient and measure nothing.
An mpz_t always lives on the heap. Adding two 100-digit values
costs GMP 19.3 ns into a fresh result against 5.2 ns
into a reused one, so most of it is malloc and free. decimo
keeps small values inside the struct, which is why it leads at the
small end and trails at the large one, where the algorithm is all
that is left.
| Digits | Operation | decimo | GMP | CPython int |
||
|---|---|---|---|---|---|---|
| 10 | add | 5.9 ns | 17.0 ns | 2.85× faster | 23.4 ns | 3.94× faster |
| 10 | multiply | 7.4 ns | 16.6 ns | 2.25× faster | 29.1 ns | 3.94× faster |
| 10 | floor divide | 11.3 ns | 24.1 ns | 2.14× faster | 52.6 ns | 4.66× faster |
| 10 | sqrt | 2.7 ns | 16.4 ns | 6.16× faster | 30.4 ns | 11.42× faster |
| 100 | add | 7.2 ns | 19.3 ns | 2.70× faster | 29.3 ns | 4.10× faster |
| 100 | multiply | 41.8 ns | 29.9 ns | 1.40× slower | 119.5 ns | 2.86× faster |
| 100 | floor divide | 117.2 ns | 83.1 ns | 1.41× slower | 317.8 ns | 2.71× faster |
| 100 | sqrt | 126.2 ns | 61.0 ns | 2.07× slower | 335.4 ns | 2.66× faster |
| 1,000 | add | 33.4 ns | 29.2 ns | 1.14× slower | 94.5 ns | 2.83× faster |
| 1,000 | multiply | 1.06 µs | 627.8 ns | 1.69× slower | 5.72 µs | 5.38× faster |
| 1,000 | floor divide | 1.96 µs | 1.33 µs | 1.47× slower | 13.73 µs | 6.99× faster |
| 1,000 | sqrt | 1.65 µs | 391.6 ns | 4.22× slower | 4.74 µs | 2.87× faster |
| 10,000 | add | 180.0 ns | 150.0 ns | 1.20× slower | 861.2 ns | 4.78× faster |
| 10,000 | multiply | 45.56 µs | 20.39 µs | 2.23× slower | 280.83 µs | 6.16× faster |
| 10,000 | floor divide | 92.19 µs | 52.16 µs | 1.77× slower | 575.90 µs | 6.25× faster |
| 10,000 | sqrt | 24.32 µs | 8.61 µs | 2.83× slower | 289.32 µs | 11.90× faster |
| 100,000 | add | 1.75 µs | 1.45 µs | 1.21× slower | 8.60 µs | 4.91× faster |
| 100,000 | multiply | 1.23 ms | 446.25 µs | 2.76× slower | 9.17 ms | 7.44× faster |
| 100,000 | floor divide | 3.81 ms | 1.16 ms | 3.27× slower | 18.93 ms | 4.97× faster |
| 100,000 | sqrt | 984.85 µs | 312.05 µs | 3.16× slower | 8.81 ms | 8.95× faster |
| 1,000,000 | add | 19.00 µs | 13.50 µs | 1.41× slower | 86.17 µs | 4.54× faster |
| 1,000,000 | multiply | 24.78 ms | 6.49 ms | 3.82× slower | 387.56 ms | 15.64× faster |
| 1,000,000 | floor divide | 108.03 ms | 17.13 ms | 6.31× slower | 784.35 ms | 7.26× faster |
| 1,000,000 | sqrt | 32.39 ms | 6.05 ms | 5.35× slower | 359.62 ms | 11.10× faster |
Each measurement in a fresh process, since mpmath and MPFR cache the constant. Includes conversion to a decimal string, for every library.
The two decimo columns compute the same series through the same
integer code and differ only in where the digits end up; BigFloat
is asked for the computation its own cache would have missed on, so
that it is measured cold like the rest.
| Digits | decimo (BigDecimal) | decimo (BigFloat) | mpmath + GMP | MPFR | mpmath (pure Python) |
|---|---|---|---|---|---|
| 100 | 2.49 µs | 3.25 µs | 53.79 µs | 50.62 µs | 37.42 µs |
| 1,000 | 22.33 µs | 23.94 µs | 120.75 µs | 72.62 µs | 176.96 µs |
| 10,000 | 722.60 µs | 715.30 µs | 936.12 µs | 748.71 µs | 6.29 ms |
| 100,000 | 27.24 ms | 26.61 ms | 16.12 ms | 24.02 ms | 191.05 ms |
| 1,000,000 | 720.61 ms | 719.20 ms | 275.24 ms | 440.40 ms | 8.869 s |