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IBM

MCP Math Server

by IBM

digit_count

Count digits in numbers for any base. Use this tool to determine digit count in arithmetic operations across different numeral systems.

Instructions

Count the number of digits in a number for given base. (Domain: arithmetic, Category: digital_operations)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
baseNo
Behavior2/5

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool counts digits, but does not mention any behavioral traits such as error handling (e.g., for negative bases or invalid inputs), performance characteristics, or output format. This leaves significant gaps for a tool with parameters.

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?

The description is very concise—a single sentence that directly states the tool's purpose, followed by domain/category tags. There is no wasted verbiage, and the core function is front-loaded. However, the domain/category tags add little value and could be considered slightly redundant if the sibling list already implies this context.

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

Completeness2/5

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

Given the lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not address key contextual aspects such as parameter details, behavioral constraints, or return values. For a tool with two parameters and mathematical operations, more information is needed to ensure correct usage.

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

Parameters2/5

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

The schema description coverage is 0%, meaning parameters 'n' and 'base' are undocumented in the schema. The description only mentions 'a number' and 'given base', which adds minimal semantic context. It does not explain what 'n' represents (e.g., integer input), the valid range for 'base', or the default value of 10 for 'base', failing to compensate for the low coverage.

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?

The description clearly states the tool's purpose: 'Count the number of digits in a number for given base.' It specifies the verb ('Count'), resource ('digits in a number'), and scope ('for given base'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'digit_frequency' or 'digit_sum', which prevents a perfect score.

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

Usage Guidelines2/5

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

The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('digital_operations'), but this is too vague to help an agent choose between similar tools like 'digit_frequency' or 'digit_sum'. No explicit when/when-not instructions or named alternatives are provided.

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

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