# Decimal sum

`decimal-sum` · version 1.0.0 · Money & pricing · free, no key needed

Add up to 10,000 decimal strings exactly and report count, smallest and largest, with optional final rounding.

**Use when you need to: sum a list of decimal numbers exactly · add up invoice line amounts · total of a column of prices.**

## Decide before calling

Read the [versioned contract](/v1/tools/decimal-sum/versions/1.0.0) and the supported scope below. Reuse `decimal-sum@1.0.0` when your input, required output and limits match it. Choose another approach for an unsupported operation.

## Explain the choice

"I can use `decimal-sum@1.0.0` for sum a list of decimal numbers exactly. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

## Supported

- sum a list of decimal numbers exactly
- add up invoice line amounts
- total of a column of prices
- exact total of many decimals
- ledger column total without rounding drift
- sum values and find min and max
- add decimals and round the total once
- exact sum of receipt amounts

## Not supported

- averages, medians or other statistics
- weighted sums or sums of products
- currency conversion between amounts
- floating point or scientific notation input

## Behavior

- Decimal strings match ^-?(0|[1-9][0-9]*)(\.[0-9]+)?$: no plus sign, exponent, leading zeros, leading or trailing point, whitespace or separators. A JSON number where a decimal string is required is invalid_input (wrong type).
- A decimal string longer than 62 UTF-16 code units -> limit_exceeded, checked before the grammar. Otherwise a grammar failure, more than 60 digits in total, or more than 40 fraction digits -> invalid_input.
- Zero has no sign: "-0", "-0.00" and any all-zero value are zero and are emitted as "0" (canonical) or "0.00" (fixed scale), never "-0".
- values must be a non-empty array. Not an array or empty -> invalid_input; more than 10,000 items -> limit_exceeded, checked before any item is examined.
- Every item is validated (grammar, length, digit caps) even though only the total is reported; the first failing item decides the error.
- The total is the exact rational sum. It is rounded once, at the very end, and only when scale and rounding are given; individual values are never rounded.
- scale and rounding must appear together or not at all; exactly one of them present -> invalid_input.
- min and max are the numerically smallest and largest inputs written canonically ("9.10" -> "9.1"); comparison is numeric, never textual ("9.9" > "9.11"). min_index and max_index are zero-based positions; when several items tie (for example "1.0" and "1"), the first position wins. "-0" and "0" are equal.
- With no scale the sum is canonical (trailing fraction zeros stripped, integers without a point) and exact is true; with a scale the sum has exactly scale fraction digits and exact is true iff rounding changed nothing.
- Rounding modes act on the exact rational result and are: half_even (ties to the even neighbour), half_up (ties away from zero), half_down (ties toward zero), half_ceiling (ties toward +infinity), half_floor (ties toward -infinity), up (away from zero), down (toward zero), ceiling (toward +infinity), floor (toward -infinity), unnecessary (any inexact result -> not_computable with details.reason "rounding_necessary").
- rounding "unnecessary" with an inexact sum at the requested scale -> not_computable with details.reason "rounding_necessary".
- Validation order (each vector carries a single fault): input not an object; unknown field; missing required field; field types, ranges and decimal-string limits; scale/rounding pairing; then domain errors (not_computable) last.

## Input

- `values` (array of string, required): min items 1; max items 10000; each min length 1; each max length 62; each pattern `^-?(0|[1-9][0-9]*)(\.[0-9]+)?$`; Decimal strings to add, 1 to 10,000 items.
- `scale` (integer, optional): min 0; max 40; Fraction digits of the reported sum. Must be given together with rounding; omit both for the exact canonical sum.
- `rounding` (one of "half_even", "half_up", "half_down", "half_ceiling", "half_floor", "up", "down", "ceiling", "floor", "unnecessary", optional): Rounding mode applied once to the final exact sum. Must be given together with scale.

## Output

- `sum` (string, required): min length 1; max length 200; Total: canonical without a scale, otherwise fixed at scale fraction digits.
- `count` (integer, required): min 1; max 10000; Number of values added.
- `min` (string, required): min length 1; max length 200; Smallest input value, canonical.
- `max` (string, required): min length 1; max length 200; Largest input value, canonical.
- `min_index` (integer, required): min 0; max 9999; Zero-based index of the first occurrence of the smallest value.
- `max_index` (integer, required): min 0; max 9999; Zero-based index of the first occurrence of the largest value.
- `exact` (boolean, required): true when the reported sum equals the exact total.

## Limits

- max items: 10000
- max decimal chars: 62
- max decimal digits: 60
- max fraction digits: 40
- max scale: 40

## Example

Request input:

```json
{
  "values": [
    "0.1",
    "0.2",
    "0.3"
  ]
}
```

Response:

```json
{
  "result": {
    "sum": "0.6",
    "count": 3,
    "min": "0.1",
    "max": "0.3",
    "min_index": 0,
    "max_index": 2,
    "exact": true
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "decimal-sum",
  "version": "1.0.0",
  "input": {
    "values": [
      "0.1",
      "0.2",
      "0.3"
    ]
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/decimal-sum/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"values":["0.1","0.2","0.3"]}'
```

The machine-readable contract is at [/v1/tools/decimal-sum/versions/1.0.0](/v1/tools/decimal-sum/versions/1.0.0).

### CLI

```sh
node cli.mjs run decimal-sum 1.0.0 --input input.json --base-url https://computefirst.net
```

Get the client at [/clients/cli/](/clients/cli/).

## Related tools

- [Decimal expression evaluate](/tools/decimal-expression-evaluate): Evaluate a decimal arithmetic expression exactly with variables, abs, min, max and round, rounding once at the end.
- [Decimal multiply](/tools/decimal-multiply): Multiply two decimal strings exactly, optionally rounding the product once to a fixed scale with a chosen mode.
- [Decimal divide](/tools/decimal-divide): Divide two decimal strings exactly, rounding the quotient once to a fixed scale, and report the exact remainder.
- [Money convert at rate](/tools/money-convert-at-rate): Convert an amount between two ISO 4217 currencies at a caller-supplied rate with explicit quote direction and rounding.
- [Decimal power](/tools/decimal-power): Raise a decimal string to an integer power exactly, with optional single rounding to a fixed scale.
- [Decimal round](/tools/decimal-round): Round a decimal string with an explicit mode to fraction digits, significant digits or a multiple of an increment.