expm1 — Compute exp(x)-1 element-wise with near-zero accuracy in MATLAB and RunMat.

Y = expm1(X) evaluates exp(X) - 1 element-wise with improved numerical accuracy near zero for real or complex single/double input. Sparse input remains sparse because implicit zeros remain zero, and table or timetable variables are mapped independently.

Syntax

Y = expm1(X)

Inputs

Returns

Errors

How expm1 works

• Dense single/double input preserves class and shape, including complex storage.
• Integer, logical, and character inputs are three independent RunMat-only extensions; each is rejected in MATLAB-compatible mode with its own RunMat:compatibility:*Extension identifier.
• The integer extension accepts all eight classes, returns double, and rejects values outside the inclusive exact binary64 interval [-2^53, 2^53] before conversion.
• Complex values follow MATLAB's definition by computing exp(z) - 1 using complex arithmetic.
• Sparse single/double input preserves sparse storage because expm1(0) = 0; table and timetable variables are mapped only when every variable supports expm1.
• GPU input returns to its original owning provider after direct execution or host fallback; complex-interleaved storage never enters a real unary provider hook.
• Fusion is disabled until the fusion ABI can use the precise expm1 helper instead of the inaccurate exp(x) - 1 expression.

Does RunMat run expm1 on the GPU?

RunMat Accelerate keeps real floating tensors resident through the precise unary_expm1 hook. An explicitly unsupported hook and complex input use an owner-preserving host fallback; other provider errors and malformed or hostile handles are reported as internal errors.

GPU memory and residency

In most workflows you do not need to call gpuArray manually. RunMat's auto-offload planner and fusion engine keep data on the GPU when beneficial. You can still call gpuArray to mirror MathWorks MATLAB workflows or to pin data on the device explicitly.

Examples

Maintaining precision for tiny growth rates

x = 1e-12;
y = expm1(x)

Expected output:

y = 1.0000000000005e-12

Applying expm1 to model percentage growth

rates = [-0.10 -0.05 0 0.05 0.10];
factors = expm1(rates)

Expected output:

factors = [-0.0952 -0.0488 0 0.0513 0.1052]

Running expm1 on GPU arrays

G = gpuArray(linspace(-1, 1, 5));
result = expm1(G);
out = gather(result)

Expected output:

out = [-0.6321 -0.3935 0 0.6487 1.7183]

Using expm1 with complex numbers

z = [1+1i, -1+pi*1i];
w = expm1(z)

Expected output:

w = [0.4687 + 2.2874i, -1.3679 + 0.0000i]

Computing exp(X)-1 from character codes

C = 'ABC';
Y = expm1(C)

Expected output:

Y = [1.6949e+28 4.6072e+28 1.2524e+29]

Using expm1 with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how expm1 changes the result.

FAQ

Related Math functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how expm1 is executed, line by line, in Rust.

• View the source for expm1 in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

About RunMat

RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.

• RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
• Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.

Getting started · Benchmarks · Pricing