{"id":"integer-sqrt","version":"1.0.0","description":"Compute the exact floor of the square root of a non-negative integer string.","supported_operations":["integer sqrt","integer square root","floor square root"],"unsupported_operations":["negative square root","floating-point square root","nth root"],"semantics":["value is a canonical non-negative integer string: 0 or a non-zero leading digit followed by digits, at most 1000 digits.","Negative values are rejected.","The result is floor(sqrt(value)), computed exactly by integer Newton iteration (no floating point).","is_perfect_square is true exactly when result * result equals value.","The result may have up to 500 digits."],"limits":{"max_digits":1000},"pricing":{"status":"unpriced","charge_usd":null},"input_schema":{"type":"object","additionalProperties":false,"required":["value"],"properties":{"value":{"type":"string","pattern":"^(0|[1-9][0-9]*)$","maxLength":1000}}},"output_schema":{"type":"object","additionalProperties":false,"required":["result","is_perfect_square"],"properties":{"result":{"type":"string"},"is_perfect_square":{"type":"boolean"}}},"examples":[{"input":{"value":"17"},"output":{"result":"4","is_perfect_square":false}}],"execute_url":"/v1/tools/integer-sqrt/versions/1.0.0/execute"}