atan2 — Quadrant-aware inverse tangent atan2(y, x) in MATLAB and RunMat.

theta = atan2(y, x) computes the four-quadrant inverse tangent of point (x, y). The result is in radians over (-pi, pi], with element-wise scalar expansion behavior that matches MATLAB and RunMat.

Syntax

Z = atan2(Y, X)

Inputs

Returns

Errors

How atan2 works

• Documented inputs are real single or double scalars, vectors, matrices, and N-D arrays. MATLAB-style implicit expansion applies when every paired dimension is equal or one dimension is singleton.
• atan2 treats y as the numerator and x as the denominator: atan2(Y, X) equals atan(Y ./ X) but keeps the correct quadrant and handles zero denominators.
• RunMat can additionally accept all eight real integer classes, logical arrays, and character arrays when RunMat extensions are enabled. These are classified extensions, not MATLAB-compatible forms; integer storage remains authoritative until one explicit binary64 computation boundary.
• Complex inputs are not supported; MATLAB raises an error and RunMat matches that behaviour.
• MATLAB deliberately differs from IEEE 754 for a negative-zero denominator: both atan2(0,-0) and atan2(-0,-0) return positive zero. RunMat applies that rule on host, provider, and fused execution paths while preserving the negative-zero result of atan2(-0,0).
• atan2(NaN, x) or atan2(y, NaN) returns NaN; inputs containing Inf combinations follow IEEE-754 quadrant semantics exactly like MATLAB.
• The output has the broadcasted input size. Double inputs return double; single inputs return single; a mixed single/double call computes with double operands and casts the result to single.

Does RunMat run atan2 on the GPU?

When both operands already reside on the GPU and the active provider implements the elem_atan2 hook, RunMat executes the operation entirely on the device without reformatting buffers.

If shapes require implicit expansion or the provider lacks elem_atan2, RunMat transparently gathers both tensors to the host, computes the result with the reference CPU implementation, and restores it to the first resident input's owning provider.

Native single storage remains single. Mixed single/double inputs compute in double and return single, matching the documented MATLAB binary element-wise rule.

Fusion-aware expressions (for example, sin(atan2(y, x))) can still emit a combined WGSL kernel; the emitted expression includes MATLAB's positive-zero override for a negative-zero denominator.

GPU memory and residency

RunMat's planner keeps tensors on the GPU whenever profitable. Explicit gpuArray calls are optional—use them only when you need to control residency for interoperability. When elem_atan2 is unavailable, broadcasting is required, or an admitted extension uses typed integer/logical storage, RunMat gathers through the owning provider, computes on the CPU, and restores the result to that provider.

Examples

Computing the polar angle of a point

theta = atan2(4, 3)

Expected output:

theta = 0.9273

Determining quadrants for a vector of coordinates

Y = [-1 0 1];
X = [-1 -1 -1];
angles = atan2(Y, X)

Expected output:

angles = [-2.3562 3.1416 2.3562]

Broadcasting a scalar denominator across a matrix

A = [1 2 3; 4 5 6];
angles = atan2(A, 2)

Expected output:

angles =
    0.4636    0.7854    0.9828
    1.1071    1.1903    1.2490

Handling zero numerators and signed zeros

theta = atan2([0 -0], [-2 0])

Expected output:

theta = [pi 0]

Executing atan2 on the GPU

Gy = gpuArray([1 1; -1 -1]);
Gx = gpuArray([1 -1; 1 -1]);
angles_gpu = atan2(Gy, Gx);
angles = gather(angles_gpu)

Expected output:

angles =
    0.7854    2.3562
   -0.7854   -2.3562

Computing four-quadrant angles from character codes

theta = atan2('A', 100)

Expected output:

theta = 0.5764

Using atan2 with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how atan2 changes the result.

FAQ

Related Math functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how atan2 is executed, line by line, in Rust.

• View the source for atan2 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