Comparisons¶

How decimal-scaled compares on speed against other fixed-precision Rust decimal crates, timed on the same golden set. Each peer works at a fixed precision, so decimal-scaled is timed at four matching precisions — 17, 28, 37 and 152 fractional digits (see Effective precision per library below) — and each peer is read against the decimal-scaled line doing a similar amount of work. Each function has a chart: decimal-scaled as one line per comparison precision across its width tiers (with a shaded min–max band), and each peer as a single marker at its significant-digit capacity (with a min–max whisker). Generated from CI (lib-perf); refreshed on each release PR. The per-function tables and graphs are split across Arithmetic, Roots and Exponents, and Trigonometry.

Unit	In nanoseconds
ns	10⁰ ns
µs	10³ ns
ms	10⁶ ns

Effective precision per library¶

decimal-scaled supports any scale up to each tier's maximum; this comparison times it at four fixed precisions, one per peer-precision level, so each peer is matched against decimal-scaled doing a comparable amount of work. Each line is drawn across every width that can hold that scale.

Comparison scale	Matches
`@17`	the narrow D18 ceiling — 18 significant digits
`@28`	`rust_decimal` — 28 significant digits
`@37`	the D38 ceiling = `decimal-rs` / `g_math` — 38 significant digits
`@152`	the D153 ceiling ≈ `fastnum` — ~154 significant digits

The libraries don't all measure precision the same way. decimal-scaled and g_math are fixed-point — precision is a fixed number of fractional digits. The others cap total significant figures, so their fractional-digit count depends on the size of the integer part.

Library	Precision model	Working precision
`decimal-scaled`	Fixed-point — fixed fractional digits (the scale)	the four comparison scales: 17 / 28 / 37 / 152
`g_math`	Fixed-point — Q128.128	~38 fractional digits
`rust_decimal`	Significant-figure, input-driven scale	up to 28 significant digits
`decimal-rs`	Significant-figure, input-driven scale	up to 38 significant digits
`fastnum` (D512)	Significant-figure, fixed coefficient	up to ~154 significant digits

bigdecimal and dashu-float are not timed here: their working width is driven by the input values rather than a fixed capacity, so they have no single marker position on a width axis. Recovering their per-call operating width is deferred to a later release.

Integer in, fractional out. How much work a call does is set by how many output digits the library produces, which depends on the operation:

Arithmetic (add, sub, mul, rem) terminates — an integer in gives an integer out and no library adds fractional digits, so the work is set by the size of the operands. For decimal-scaled that work is set by the tier width, not the scale, so its four scale-lines nearly overlap on the arithmetic pages.
Transcendentals and division don't terminate — even an integer input gives an irrational or repeating result, so each library produces fractional digits up to its own working precision (the table above), and decimal-scaled's cost rises with the comparison scale. That is why the scale-lines fan apart on those pages, and why each peer is read against the decimal-scaled line nearest its precision.

So how to read the timings. At a matching precision decimal-scaled does like-for-like work against each peer. What it does not equalise is storage: a decimal-scaled value keeps its full tier width — D1232 is a 1232-digit fixed type — even when only a few fractional digits are in play, so the wide tiers cost more per call than a small-coefficient library doing the same maths. A peer producing fewer digits than the matching line is doing less work, not the same work faster.

Input distribution¶

The table below characterises the golden inputs each comparison runs over — per function, how many input values it exercises and how their fractional- and significant-digit counts are spread, plus the share that are exact integers (scale 0).

Function	Inputs	Fractional digits (min/mean/max)	Significant digits (min/mean/max)	% integer
`add`	160	0 / 6.8 / 28	0 / 22.8 / 28	61%
`div`	132	0 / 2.8 / 26	1 / 12.9 / 28	86%
`mul`	272	0 / 31.1 / 642	1 / 12.9 / 28	64%
`rem`	130	0 / 2.9 / 26	1 / 13.4 / 28	85%
`sub`	160	0 / 6.8 / 28	0 / 22.8 / 28	61%
`cbrt`	5,680	0 / 14.1 / 1231	0 / 22.5 / 28	42%
`exp`	4,636	0 / 23.2 / 1231	0 / 21.3 / 28	9%
`exp2`	4,725	0 / 22.5 / 1231	0 / 20.7 / 28	12%
`hypot`	260	0 / 3.9 / 27	0 / 16.4 / 28	79%
`ln`	5,051	0 / 17.7 / 924	1 / 21.6 / 119	17%
`log`	3,292	0 / 15.6 / 31	1 / 18.1 / 28	20%
`log10`	5,264	0 / 17.7 / 924	1 / 22.2 / 1232	17%
`log2`	5,034	0 / 17.2 / 924	1 / 21.2 / 28	19%
`powf`	8,046	0 / 19.1 / 31	0 / 20.3 / 28	14%
`sqrt`	5,599	0 / 12.4 / 1231	0 / 22.7 / 28	44%
`acos`	4,015	0 / 23.3 / 118	0 / 23.0 / 28	0%
`acosh`	4,302	0 / 15.7 / 118	1 / 20.5 / 119	20%
`asin`	4,356	0 / 23.6 / 118	0 / 23.2 / 28	0%
`asinh`	5,152	0 / 17.7 / 1231	0 / 24.1 / 28	33%
`atan`	5,026	0 / 14.4 / 118	0 / 24.3 / 28	33%
`atan2`	9,874	0 / 18.5 / 924	0 / 19.0 / 28	24%
`atanh`	4,149	0 / 23.6 / 168	0 / 23.1 / 28	0%
`cos`	4,377	0 / 22.3 / 118	0 / 23.1 / 28	2%
`cosh`	5,123	0 / 24.1 / 1231	0 / 21.8 / 28	8%
`sin`	4,381	0 / 22.3 / 118	0 / 23.1 / 28	2%
`sinh`	4,841	0 / 24.3 / 1231	0 / 21.5 / 28	9%
`tan`	4,418	0 / 22.6 / 118	0 / 23.0 / 28	2%
`tanh`	4,517	0 / 26.2 / 1231	0 / 22.8 / 28	1%