Blockulator: the definitive source for precision

two formats

38 digits fixed, 71 floating

FP127 is fixed point with 128 bits after the point. FP19 is a 256-bit float that reaches 10^±78,913. WAD gives the fraction 60 bits.

measured

Against 300-digit arithmetic

FP127, FP19 and 15 other libraries, run through 14 scenarios of up to 10,000 steps each.

two forms

Deploy it or inline it

Each format is one Yul source, built into a deployed contract and an inline library that are fuzzed equal on every int256.

trust

No owner, no upgrades

No contract has storage, a proxy or an admin key. A new version gets a new address, and the old ones stay.

Leave a market alone and its interest goes wrong

Put $10,000 in at 5% a year and accrue it in one step after N days. Aave and Morpho approximate e^x with three terms, so the longer a market waits for an update, the fewer digits survive: after 10,000 days, one. FP127 and FP19 lose less than two digits over the whole range.

Correct digits against exact arithmetic, each capped at what the library's format holds. OpenZeppelin, Uniswap and Maker have no exponential, so they are not here. The input is the continuous-accrual scenario's; data: ladder.json.

Every library, every N

library · correct digits after	1 day	10 days	100 days	365 days	1,000 days	10,000 days
Floating point
FP19	71.2	71.3	71.3	71.3	71.3	71.3
ABDKMathQuad	33.8	33.6	34.0	33.6	33.6	33.3
Fixed point
FP127	38.6	38.6	38.6	38.5	38.0	37.1
ABDK 64.64	19.1	18.9	19.0	19.3	18.8	17.8
Solady	18.3	18.7	18.2	18.1	18.1	17.9
Solmate	18.3	18.7	18.2	18.1	18.1	17.9
PRBMath SD	18.3	17.9	17.7	18.1	17.7	17.7
PRBMath UD	18.3	17.9	17.7	18.1	17.7	17.7
snekmate	18.3	18.7	18.2	18.1	18.1	17.9
Balancer	18.3	18.7	18.2	18.1	18.1	17.9
Aave	16.8	12.8	8.8	6.6	4.8	1.2
Morpho	13.7	12.5	8.8	6.6	4.8	1.2

Twice the digits, and competitive on gas

FP127 carries twice the digits of every 18-decimal library and costs less than PRBMath's SD59x18 on add, mul, div, exp, ln, pow and sqrt. FP19 carries twice binary128's digits and costs less than ABDKMathQuad on add, mul, div, exp, ln and pow. Solady is cheaper than both, at 18 digits.

Each dot is a library: the digits its format holds at 1, against its gas as a multiple of FP127's over the ops both offer; hover for the range. Median of inline calls over random inputs that take no shortcut (^t). Aave, Morpho and Maker are formulas inside protocols, so they have no gas. Every op: per op; data: gas.json, fp19/gas.json.

Gas per call, 24 ops

	Floating point		Fixed point
op · gas per call	FP19	Quad	FP127	64.64	Solady	Solmate	PRB SD	PRB UD	snek	Balancer	OZ	Uniswap
digits at 1	71	34	38	19	18	18	18	18	18	18	18	18
`add`	662	765	128	162	3	—	189	150	—	—	—	—
`mul`	530	688	267	171	126	131	485	237	—	—	—	—
`div`	800	818	412	221	93	97	509	261	—	—	—	—
`expᵗ`	3,278	5,808	2,716	3,380	430	430	2,816	2,720	604	1,040	—	—
`lnᵗ`	3,043	16,335	1,944	7,080	556	632	7,083	6,474	1,226	1,091	—	—
`powᵗ`	5,901	23,597	3,317	—	1,279	1,355	10,065	9,544	—	2,223	—	—
`sqrtᵗ`	1,205	759	469	828	393	456	978	824	—	2,349	766	—
`avg`	663	—	114	31	60	—	154	105	113	—	318	—
`abs`	133	21	140	120	18	—	121	—	—	—	18	—
`divDown`	987	—	475	—	87	150	—	—	323	—	239	179
`divUp`	988	—	478	—	113	176	—	—	386	—	621	282
`inv`	747	1,259	242	202	93	—	177	94	—	—	—	—
`log2ᵗ`	2,822	15,553	1,723	6,990	—	—	6,724	6,402	—	1,908	—	—
`mulDown`	727	—	315	—	86	150	—	—	323	—	239	179
`mulUp`	728	—	337	—	110	176	—	—	386	—	621	282
`powuᵗ`	6,631	—	5,189	3,133	2,318	2,559	4,006	3,881	—	—	—	—
`sub`	745	1,236	140	162	3	—	187	150	—	—	—	—
`exp2ᵗ`	3,096	5,073	2,668	3,225	—	—	2,671	2,557	—	—	—	—
`gavg`	2,099	—	1,079	833	449	—	960	949	—	—	—	—
`cbrtᵗ`	2,734	—	1,936	—	619	—	—	—	1,424	2,311	—	—
`log10ᵗ`	3,038	—	1,934	—	—	—	8,618	8,233	—	1,891	—	—
`log2Up`	679	—	209	—	247	—	—	—	505	—	513	—
`neg`	127	9	116	76	—	—	134	—	—	—	—	—
`sign`	139	181	75	—	—	—	84	—	78	—	—	—

Correct to the last wei

BlockulatorWad keeps Solady's function names and returns the exact answer, rounded the way each function promises, on all 108,000 results we tested across 27 functions and rounding directions. The libraries it replaces are a wei off on up to 98% of their results for some functions.

Seeded inputs over each function's domain, including those whose exact value sits next to a wei boundary. Every library here is 18-decimal fixed point. Every library that offers them is exact on divWad, divWadUp, mulWad, mulWadUp, sDivWad, sMulWad, sqrtWad, sqrtWadUp. Counts: wad.md.

Share wrong, per function

	Fixed point
function · share wrong	BWad	Solady	Solmate	PRB SD	PRB UD	snek	OZ	Uniswap
`cbrtWad`	0 of 4,000	0	—	—	—	23%	—	—
`expWad`	0 of 3,995	48%	48%	72%	93%	48%	—	—
`lnWad`	0 of 3,998	24%	24%	98%	98%	24%	—	—
`log2Wad`	0 of 3,998	—	—	93%	90%	—	—	—
`log10Wad`	0 of 3,998	—	—	88%	90%	—	—	—
`powWad`	0 of 3,461	66%	66%	71%	85%	—	—	—
`lambertW0Wad`	0 of 3,999	28%	—	—	—	—	—	—
`mulWad`	0 of 3,720	0	0	0	—	0	0	0
`mulWadUp`	0 of 3,720	0	0	—	—	0	0	0
`divWad`	0 of 3,966	0	0	0	—	0	0	0
`divWadUp`	0 of 3,966	0	0	—	—	0	0	0
`sMulWad`	0 of 3,715	0	0	0	—	—	—	—
`sDivWad`	0 of 3,937	0	0	0	—	—	—	—
`sqrtWad`	0 of 4,000	0	0	0	—	—	0	—
`sqrtWadUp`	0 of 4,000	—	—	—	—	—	0	—

Everything else we measured

scenarios

The definitive source for precision.

38 digits fixed, 71 floating

Against 300-digit arithmetic

Deploy it or inline it

No owner, no upgrades

Leave a market alone and its interest goes wrong

Twice the digits, and competitive on gas

Correct to the last wei

Everything else we measured

14 real calculations, up to 10,000 steps

139 calls where formats break

Aave and Morpho as deployed

Four exploits, replayed

Use FP127 and FP19.