Singularis

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Fast Fourier transform

singularis_fft

Idempotent

Compute forward or inverse FFTs of 1D signals or 2D fields for spectra, convolution, filtering, and circulant systems; returns real/imaginary parts and a Parseval energy check.

Instructions

Fast Fourier transform (or inverse) of a 1D signal or 2D field of any size: spectra, convolution, circulant systems, filtering. Inputs: x inline or path; inverse flag; optional im, the imaginary part of a complex input, same shape as x. Returns the transform as separate real and imaginary parts plus a Parseval energy check. To invert a transform, pass its real part as x and its imaginary part as im with inverse=true -- a complex signal round-trips exactly, imaginary part intact. Cost scales with N log N.

Input Schema

Name	Required	Description	Default
`x`	No
`im`	No
`path`	No
`inverse`	No

Output Schema

Name	Required	Description	Default
No arguments

Schema Changelog

Changes observed during successful MCP inspections.

Changed1 schema field changedv0.1.11Oct 19, 2026

addedInput schema / properties / im

Added value: +{
+  "anyOf": [
+    {
+      "items": {
+        "type": "number"
+      },
+      "type": "array"
+    },
+    {
+      "items": {
+        "items": {
+          "type": "number"
+        },
+        "type": "array"
+      },
+      "type": "array"
+    },
+    {
+      "type": "null"
+    }
+  ],
+  "default": null,
+  "title": "Im"
+}

First observedv0.1.3Oct 15, 2026

TDQS

A3.9/5.0

Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations declare the safety profile (idempotent, non-destructive, open-world), and the description adds traits beyond that: a Parseval energy check is returned, a complex signal round-trips exactly, and cost scales as N log N. These are genuine behavioral disclosures not present in the annotations or schema.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loads the operation, then inputs, returns, inversion recipe, and cost. Sentences are dense and mostly earn their place; the return-format sentence is slightly redundant given an output schema exists, but the structure is clean.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With an output schema present, return-value explanation is not required, yet the description still covers all four parameters, the inversion workflow, and performance characteristics. Nothing an agent needs to call it correctly is missing, other than sibling routing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description carries the burden and largely does: x is 'inline or path', im is 'the imaginary part of a complex input, same shape as x', and inverse's meaning plus the x/im pairing is spelled out. This compensates well for the undocumented schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb+resource (Fast Fourier transform of a 1D signal or 2D field) and enumerates concrete applications (spectra, convolution, circulant systems, filtering). It never distinguishes itself from the sibling singularis_fft2, and '1D or 2D of any size' arguably overlaps that sibling's territory, so an agent cannot route confidently between them.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Gives explicit instructions for the inverse path (pass real part as x, imaginary part as im, inverse=true), which is real usage guidance. However it offers no when-to-use/when-not versus singularis_fft2 or any other sibling, so alternative selection is left to inference.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.