DoubleFloats Benchmark Report

Generated by docs/reports/benchmarks.jl on Julia 1.12.6.

This report covers a representative sample of operations; it does not cover all available functions. Timings are best-of-trials amortized averages on the machine that ran the script — treat them as indicative magnitudes, not precise measurements.

Double64

Double64 carries ~32 significant decimal digits. Float64 is the native baseline; BigFloat timings use the default 256-bit precision.

Scalar Arithmetic

operation	Double64	Float64	BigFloat	D64/F64	Big/D64
`+`	2 ns	0 ns	31 ns	6.9x	13.2x
`*`	2 ns	0 ns	41 ns	4.9x	24.7x
`/`	2 ns	1 ns	64 ns	3.1x	29.8x
`sqrt`	1 ns	1 ns	121 ns	1.0x	114.8x
`abs`	0 ns	0 ns	31 ns	1.1x	88.8x
`fma`	6 ns	0 ns	58 ns	16.0x	9.9x

Elementary Functions

function	Double64	Float64	BigFloat	D64/F64	Big/D64
`exp`	32 ns	2 ns	1.40 µs	19.0x	43.5x
`log`	29 ns	3 ns	2.48 µs	9.1x	85.1x
`sin`	64 ns	4 ns	1.32 µs	18.2x	20.5x
`cos`	65 ns	3 ns	963 ns	22.0x	14.9x
`tan`	119 ns	4 ns	1.47 µs	30.3x	12.4x
`atan`	145 ns	3 ns	6.11 µs	43.8x	42.3x
`sinh`	68 ns	3 ns	1.58 µs	26.3x	23.2x
`tanh`	61 ns	3 ns	1.64 µs	20.6x	27.0x
`asinh`	73 ns	7 ns	2.81 µs	10.2x	38.4x
`x^y`	88 ns	14 ns	4.20 µs	6.3x	48.0x

Linear Algebra

Float64 timings use LAPACK/BLAS; Double64 uses pure-Julia generic algorithms (GenericLinearAlgebra / GenericSchur), so these ratios combine the precision cost with the loss of BLAS blocking and SIMD. Matrix multiplication is measured at several square sizes; the remaining operations use n = 32.

operation	Double64	Float64	BigFloat	D64/F64	Big/D64
`A * B (n=4)`	407 ns	88 ns	5.13 µs	4.6x	12.6x
`A * B (n=8)`	4.27 µs	138 ns	35.05 µs	30.9x	8.2x
`A * B (n=16)`	4.18 µs	309 ns	257.77 µs	13.5x	61.6x
`A * B (n=32)`	23.10 µs	1.71 µs	1.94 ms	13.5x	84.2x
`A * B (n=64)`	136.47 µs	15.07 µs	15.80 ms	9.1x	115.8x
`lu(A)`	61.55 µs	4.73 µs	800.53 µs	13.0x	13.0x
`qr(A)`	151.01 µs	16.66 µs	1.63 ms	9.1x	10.8x
`A \ b`	59.26 µs	5.15 µs	862.26 µs	11.5x	14.5x
`eigen(S) symmetric`	860.32 µs	50.05 µs	missing	17.2x	—
`eigen(A) general`	4.20 ms	130.25 µs	missing	32.3x	—
`svd(A)`	457.76 µs	26.51 µs	missing	17.3x	—

Matrix Functions (n = 8)

operation	Double64	Float64	BigFloat	D64/F64	Big/D64
`exp(A)`	62.72 µs	2.26 µs	missing	27.8x	—
`exp(P) spd`	23.16 µs	6.52 µs	missing	3.6x	—
`sqrt(P) spd`	23.19 µs	6.45 µs	missing	3.6x	—
`log(P) spd`	23.30 µs	5.23 µs	missing	4.5x	—
`cosh(A)`	37.37 µs	4.64 µs	missing	8.0x	—
`cosh(P) spd`	24.37 µs	6.38 µs	missing	3.8x	—
`sylvester(A, B, S)`	646.22 µs	14.73 µs	missing	43.9x	—

spd = symmetric positive definite

Matrix Functions (n = 16)

operation	Double64	Float64	BigFloat	D64/F64	Big/D64
`exp(A)`	104.13 µs	6.23 µs	missing	16.7x	—
`exp(P) spd`	145.50 µs	15.99 µs	missing	9.1x	—
`sqrt(P) spd`	145.18 µs	15.73 µs	missing	9.2x	—
`log(P) spd`	142.26 µs	15.83 µs	missing	9.0x	—
`cosh(A)`	67.91 µs	12.33 µs	missing	5.5x	—
`cosh(P) spd`	147.20 µs	15.91 µs	missing	9.3x	—
`sylvester(A, B, S)`	3.85 ms	58.21 µs	missing	66.2x	—

spd = symmetric positive definite

Matrix Functions (n = 64)

operation	Double64	Float64	BigFloat	D64/F64	Big/D64
`exp(A)`	2.47 ms	124.91 µs	missing	19.7x	—
`exp(P) spd`	7.57 ms	225.51 µs	missing	33.6x	—
`sqrt(P) spd`	7.52 ms	225.01 µs	missing	33.4x	—
`log(P) spd`	7.40 ms	219.91 µs	missing	33.6x	—
`cosh(A)`	1.86 ms	252.40 µs	missing	7.4x	—
`cosh(P) spd`	7.55 ms	222.09 µs	missing	34.0x	—
`sylvester(A, B, S)`	195.13 ms	1.51 ms	missing	128.9x	—

spd = symmetric positive definite

Double32

Double32 carries ~14 significant decimal digits. Float32 is the native baseline; BigFloat timings use the default 256-bit precision.

Scalar Arithmetic

operation	Double32	Float32	BigFloat	D32/F32	Big/D32
`+`	3 ns	0 ns	30 ns	6.5x	11.7x
`*`	2 ns	0 ns	41 ns	4.0x	26.2x
`/`	2 ns	1 ns	65 ns	4.2x	27.4x
`sqrt`	1 ns	1 ns	122 ns	2.2x	105.2x
`abs`	1 ns	0 ns	18 ns	2.1x	25.3x
`fma`	4 ns	0 ns	59 ns	11.0x	14.1x

Elementary Functions

function	Double32	Float32	BigFloat	D32/F32	Big/D32
`exp`	39 ns	2 ns	1.41 µs	17.6x	35.9x
`log`	36 ns	3 ns	2.48 µs	10.3x	69.0x
`sin`	70 ns	2 ns	1.32 µs	30.8x	18.9x
`cos`	70 ns	2 ns	961 ns	30.1x	13.7x
`tan`	125 ns	3 ns	1.47 µs	47.4x	11.8x
`atan`	152 ns	3 ns	6.15 µs	60.6x	40.6x
`sinh`	76 ns	1 ns	1.59 µs	52.5x	21.1x
`tanh`	71 ns	3 ns	1.64 µs	23.8x	23.0x
`asinh`	83 ns	7 ns	2.82 µs	11.8x	34.1x
`x^y`	103 ns	13 ns	4.20 µs	8.2x	40.9x

Linear Algebra

Float32 timings use LAPACK/BLAS; Double32 uses pure-Julia generic algorithms (GenericLinearAlgebra / GenericSchur), so these ratios combine the precision cost with the loss of BLAS blocking and SIMD. Matrix multiplication is measured at several square sizes; the remaining operations use n = 32.

operation	Double32	Float32	BigFloat	D32/F32	Big/D32
`A * B (n=4)`	367 ns	75 ns	6.25 µs	4.9x	17.0x
`A * B (n=8)`	2.46 µs	101 ns	34.05 µs	24.5x	13.8x
`A * B (n=16)`	18.04 µs	207 ns	256.99 µs	87.3x	14.2x
`A * B (n=32)`	139.20 µs	1.17 µs	1.96 ms	119.2x	14.1x
`A * B (n=64)`	1.07 ms	6.92 µs	16.04 ms	155.1x	14.9x
`lu(A)`	54.86 µs	3.28 µs	804.32 µs	16.7x	14.7x
`qr(A)`	128.02 µs	16.79 µs	1.66 ms	7.6x	12.9x
`A \ b`	52.27 µs	3.97 µs	868.48 µs	13.2x	16.6x
`eigen(S) symmetric`	687.29 µs	45.88 µs	missing	15.0x	—
`eigen(A) general`	2.98 ms	106.33 µs	missing	28.0x	—
`svd(A)`	365.66 µs	25.55 µs	missing	14.3x	—

Matrix Functions (n = 8)

operation	Double32	Float32	BigFloat	D32/F32	Big/D32
`exp(A)`	199.63 µs	2.15 µs	missing	92.7x	—
`exp(P) spd`	19.70 µs	5.50 µs	missing	3.6x	—
`sqrt(P) spd`	20.42 µs	5.41 µs	missing	3.8x	—
`log(P) spd`	19.74 µs	5.39 µs	missing	3.7x	—
`cosh(A)`	107.80 µs	4.44 µs	missing	24.3x	—
`cosh(P) spd`	20.49 µs	5.43 µs	missing	3.8x	—
`sylvester(A, B, S)`	331.57 µs	12.01 µs	missing	27.6x	—

spd = symmetric positive definite

Matrix Functions (n = 16)

operation	Double32	Float32	BigFloat	D32/F32	Big/D32
`exp(A)`	1.34 ms	4.98 µs	missing	268.9x	—
`exp(P) spd`	113.55 µs	13.18 µs	missing	8.6x	—
`sqrt(P) spd`	112.83 µs	13.04 µs	missing	8.7x	—
`log(P) spd`	113.19 µs	13.15 µs	missing	8.6x	—
`cosh(A)`	821.02 µs	9.52 µs	missing	86.2x	—
`cosh(P) spd`	113.37 µs	13.07 µs	missing	8.7x	—
`sylvester(A, B, S)`	2.14 ms	48.29 µs	missing	44.3x	—

spd = symmetric positive definite

Matrix Functions (n = 64)

operation	Double32	Float32	BigFloat	D32/F32	Big/D32
`exp(A)`	80.02 ms	78.68 µs	missing	1017.0x	—
`exp(P) spd`	5.65 ms	215.49 µs	missing	26.2x	—
`sqrt(P) spd`	5.65 ms	211.57 µs	missing	26.7x	—
`log(P) spd`	5.66 ms	213.29 µs	missing	26.5x	—
`cosh(A)`	67.59 ms	160.11 µs	missing	422.1x	—
`cosh(P) spd`	5.66 ms	217.18 µs	missing	26.0x	—
`sylvester(A, B, S)`	120.23 ms	1.19 ms	missing	101.3x	—

spd = symmetric positive definite

Notes

Entries below ~10 ns are at the resolution of the timing loop; treat them (and their ratios) as "too fast to matter" rather than exact.
Double64 and Double32 values are immutable bitstypes; vectors of them are stored inline, which is where much of the advantage over BigFloat comes from.
Matrix-function timings include the full dense algorithm (scaling-and-squaring for exp, Schur-based methods for sqrt/log).
missing BigFloat entries mark operations with no BigFloat method to benchmark against (generic eigen/svd and the dense matrix functions).