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	13.1x
`*`	2 ns	0 ns	41 ns	4.9x	24.4x
`/`	2 ns	1 ns	64 ns	3.1x	29.8x
`sqrt`	1 ns	1 ns	131 ns	1.0x	124.3x
`abs`	0 ns	0 ns	18 ns	1.1x	50.4x
`fma`	6 ns	0 ns	59 ns	17.3x	10.0x

Elementary Functions

function	Double64	Float64	BigFloat	D64/F64	Big/D64
`exp`	73 ns	2 ns	1.41 µs	43.2x	19.2x
`log`	54 ns	3 ns	2.49 µs	16.7x	46.3x
`sin`	80 ns	3 ns	1.32 µs	30.0x	16.6x
`cos`	80 ns	3 ns	973 ns	28.3x	12.1x
`tan`	135 ns	4 ns	1.48 µs	33.7x	10.9x
`atan`	148 ns	3 ns	6.15 µs	45.1x	41.5x
`sinh`	94 ns	3 ns	1.58 µs	36.3x	16.7x
`tanh`	90 ns	3 ns	1.65 µs	30.9x	18.3x
`asinh`	100 ns	7 ns	2.81 µs	13.4x	28.2x
`x^y`	140 ns	14 ns	4.21 µs	10.1x	30.1x

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)`	406 ns	87 ns	5.17 µs	4.6x	12.7x
`A * B (n=8)`	4.26 µs	132 ns	35.40 µs	32.3x	8.3x
`A * B (n=16)`	4.14 µs	307 ns	264.57 µs	13.5x	63.9x
`A * B (n=32)`	24.16 µs	1.90 µs	1.95 ms	12.7x	80.9x
`A * B (n=64)`	136.20 µs	15.62 µs	15.49 ms	8.7x	113.8x
`lu(A)`	61.75 µs	5.03 µs	796.37 µs	12.3x	12.9x
`qr(A)`	150.86 µs	16.48 µs	1.65 ms	9.2x	11.0x
`A \ b`	59.28 µs	5.55 µs	1.21 ms	10.7x	20.5x
`eigen(S) symmetric`	860.22 µs	50.46 µs	missing	17.0x	—
`eigen(A) general`	4.22 ms	131.64 µs	missing	32.1x	—
`svd(A)`	458.27 µs	26.57 µs	missing	17.2x	—

Matrix Functions (n = 8)

operation	Double64	Float64	BigFloat	D64/F64	Big/D64
`exp(A)`	51.09 µs	2.23 µs	missing	23.0x	—
`exp(P) spd`	24.16 µs	6.63 µs	missing	3.6x	—
`sqrt(P) spd`	22.96 µs	6.50 µs	missing	3.5x	—
`log(P) spd`	23.30 µs	5.79 µs	missing	4.0x	—
`cosh(A)`	36.94 µs	4.72 µs	missing	7.8x	—
`cosh(P) spd`	24.31 µs	6.46 µs	missing	3.8x	—
`sylvester(A, B, S)`	660.35 µs	14.76 µs	missing	44.7x	—

spd = symmetric positive definite

Matrix Functions (n = 16)

operation	Double64	Float64	BigFloat	D64/F64	Big/D64
`exp(A)`	98.74 µs	5.96 µs	missing	16.6x	—
`exp(P) spd`	153.30 µs	15.58 µs	missing	9.8x	—
`sqrt(P) spd`	147.38 µs	15.82 µs	missing	9.3x	—
`log(P) spd`	144.34 µs	15.65 µs	missing	9.2x	—
`cosh(A)`	64.75 µs	12.39 µs	missing	5.2x	—
`cosh(P) spd`	148.98 µs	15.64 µs	missing	9.5x	—
`sylvester(A, B, S)`	3.97 ms	59.09 µs	missing	67.2x	—

spd = symmetric positive definite

Matrix Functions (n = 64)

operation	Double64	Float64	BigFloat	D64/F64	Big/D64
`exp(A)`	2.48 ms	126.02 µs	missing	19.7x	—
`exp(P) spd`	8.07 ms	229.45 µs	missing	35.2x	—
`sqrt(P) spd`	7.62 ms	222.10 µs	missing	34.3x	—
`log(P) spd`	7.48 ms	223.22 µs	missing	33.5x	—
`cosh(A)`	1.93 ms	258.16 µs	missing	7.5x	—
`cosh(P) spd`	7.58 ms	224.60 µs	missing	33.8x	—
`sylvester(A, B, S)`	200.88 ms	1.53 ms	missing	131.1x	—

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	31 ns	6.8x	12.1x
`*`	2 ns	0 ns	41 ns	4.1x	26.4x
`/`	2 ns	1 ns	65 ns	4.3x	27.2x
`sqrt`	1 ns	1 ns	130 ns	2.2x	112.5x
`abs`	1 ns	0 ns	17 ns	2.1x	24.7x
`fma`	4 ns	0 ns	59 ns	10.7x	14.2x

Elementary Functions

function	Double32	Float32	BigFloat	D32/F32	Big/D32
`exp`	79 ns	2 ns	1.40 µs	35.5x	17.7x
`log`	59 ns	3 ns	2.48 µs	16.9x	42.1x
`sin`	85 ns	2 ns	1.32 µs	37.8x	15.5x
`cos`	86 ns	2 ns	952 ns	36.7x	11.1x
`tan`	140 ns	3 ns	1.49 µs	53.4x	10.7x
`atan`	154 ns	3 ns	6.16 µs	61.4x	40.1x
`sinh`	101 ns	1 ns	1.58 µs	70.3x	15.6x
`tanh`	99 ns	3 ns	1.63 µs	33.5x	16.4x
`asinh`	106 ns	7 ns	2.81 µs	15.2x	26.4x
`x^y`	153 ns	13 ns	4.20 µs	12.2x	27.6x

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)`	365 ns	67 ns	5.13 µs	5.5x	14.0x
`A * B (n=8)`	3.13 µs	136 ns	35.27 µs	23.0x	11.3x
`A * B (n=16)`	18.10 µs	210 ns	259.57 µs	86.2x	14.3x
`A * B (n=32)`	139.26 µs	1.10 µs	1.97 ms	126.7x	14.1x
`A * B (n=64)`	1.08 ms	7.23 µs	16.66 ms	148.9x	15.5x
`lu(A)`	54.71 µs	3.29 µs	806.39 µs	16.6x	14.7x
`qr(A)`	127.89 µs	16.26 µs	1.65 ms	7.9x	12.9x
`A \ b`	52.06 µs	4.07 µs	921.27 µs	12.8x	17.7x
`eigen(S) symmetric`	686.83 µs	46.01 µs	missing	14.9x	—
`eigen(A) general`	2.97 ms	106.43 µs	missing	27.9x	—
`svd(A)`	363.99 µs	25.27 µs	missing	14.4x	—

Matrix Functions (n = 8)

operation	Double32	Float32	BigFloat	D32/F32	Big/D32
`exp(A)`	199.33 µs	2.08 µs	missing	96.0x	—
`exp(P) spd`	19.66 µs	5.36 µs	missing	3.7x	—
`sqrt(P) spd`	19.05 µs	5.38 µs	missing	3.5x	—
`log(P) spd`	19.64 µs	5.33 µs	missing	3.7x	—
`cosh(A)`	107.75 µs	4.37 µs	missing	24.7x	—
`cosh(P) spd`	19.78 µs	5.37 µs	missing	3.7x	—
`sylvester(A, B, S)`	332.10 µs	12.12 µs	missing	27.4x	—

spd = symmetric positive definite

Matrix Functions (n = 16)

operation	Double32	Float32	BigFloat	D32/F32	Big/D32
`exp(A)`	1.34 ms	4.96 µs	missing	270.7x	—
`exp(P) spd`	114.20 µs	13.27 µs	missing	8.6x	—
`sqrt(P) spd`	112.69 µs	13.07 µs	missing	8.6x	—
`log(P) spd`	113.61 µs	12.96 µs	missing	8.8x	—
`cosh(A)`	821.90 µs	10.07 µs	missing	81.6x	—
`cosh(P) spd`	113.92 µs	13.07 µs	missing	8.7x	—
`sylvester(A, B, S)`	2.14 ms	48.52 µs	missing	44.2x	—

spd = symmetric positive definite

Matrix Functions (n = 64)

operation	Double32	Float32	BigFloat	D32/F32	Big/D32
`exp(A)`	80.08 ms	78.75 µs	missing	1016.9x	—
`exp(P) spd`	5.70 ms	217.07 µs	missing	26.2x	—
`sqrt(P) spd`	5.67 ms	218.18 µs	missing	26.0x	—
`log(P) spd`	5.68 ms	215.54 µs	missing	26.4x	—
`cosh(A)`	67.63 ms	159.03 µs	missing	425.2x	—
`cosh(P) spd`	5.67 ms	214.26 µs	missing	26.5x	—
`sylvester(A, B, S)`	120.53 ms	1.20 ms	missing	100.4x	—

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).