{ "category": "Operators", "display_name": "Multiplication (*)", "entry_kind": "built_in_operator", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.OP_MULTIPLY", "implementation_state": { "answer_bank": null, "detail": "Recorded: 5,661 workbook cells.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "matches", "state_label": "Matches every recorded Excel answer", "summary": "Matches all 5,661 recorded answers", "workbook_corpus": { "cells": 5664, "matched": 5661, "pending": 3, "worst_ulp": 0 } }, "implementations": [ { "commit": "9e1884369a678158dd82d3d74188daf986995e87", "flavour": "excel-compatibility-candidate", "language": "Rust", "name": "CalcFunc", "own_code": [ "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/arithmetic.rs#L40-L40", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/arithmetic.rs#L63-L68" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/arithmetic::flushed", "catalogue/arithmetic::binary", "catalogue/arithmetic::operands" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/arithmetic.rs#L40-L40", "state": "matches", "suite": null, "summary": "Matches all 5,661 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.OP_MULTIPLY.json", "name": "OP_MULTIPLY", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n### Relationships\n\n\n- [`FUNC.OP_DIVIDE`](FUNC.OP_DIVIDE.md) — the inverse operation, and the one that adds an\n error lane (`#DIV/0!`) `*` does not have.\n- [`FUNC.OP_POWER`](FUNC.OP_POWER.md) — repeated multiplication when the exponent is an exact\n integer; see that page for the publication subtlety.\n- `PRODUCT` — the aggregate. As with `SUM` versus `+`, `PRODUCT` scans ranges under an\n aggregate policy and is not `*` folded over a list.\n- `SUMPRODUCT`, `MMULT` — elementwise-then-sum and matrix product. `MMULT` is emphatically\n not `*`: `*` on two arrays broadcasts elementwise, `MMULT` contracts an index.\n- `IMPRODUCT` — complex multiplication over text-encoded complex numbers.\n\n\n", "how-to-implement": "\n### Notes for implementers\n\n\n- The elementwise-versus-matrix distinction is the single most common user-facing confusion\n on this row. An implementation that \"helpfully\" contracts conformable arrays is wrong;\n `*` broadcasts.\n- Do not fuse. A fused multiply-add (`a*b+c` computed with one rounding) gives a different,\n usually more accurate, result than Excel's two-rounding sequence. For the\n `excel-bitexact` flavour, fusion must be disabled explicitly — many compilers will\n introduce it at higher optimization levels without asking.\n- Guard the array orientation before the kernel. Broadcast shape selection belongs in the\n shared lift layer so that `*`, `+`, `-`, `/` and `^` cannot drift apart.\n\n\n", "quirks": "\n### Result and edge cases\n\n- **Text and logical operands.** Shared to-number rules; `*` adds nothing of its own.\n- **Zero times anything finite** is zero, with the sign given by the operand signs. The\n Handbook has not recorded whether the sign of that zero is observable in a published Excel\n result.\n- **Empty and omitted operands.** Per-family policy under chapter 02; unrecorded here.\n- **Overflow and underflow.** The recorded real-result policy is `non_finite=allow`, and the\n entry marks that axis `default-unexamined`. Overflow of a product is easy to reach\n (`1E300 * 1E300`), so this is not a hypothetical lane; it is simply unrecorded.\n\n\n", "sources": "- `data/presence/FUNC.OP_MULTIPLY.json` — implementing module\n `earlier-implementation/operator_arithmetic_family.rs`.\n- Handbook `content/model/01-value-universe.md`, `02-coercion-and-lifting.md`,\n `03-call-pipeline.md`.\n\n\n", "version-differences": "No comparison between specific Excel builds is recorded here yet. This does not establish that all builds behave alike.", "what-it-does": "\n`A * B` converts each operand to a number and returns the IEEE-754 binary64 product, rounded\nonce to nearest with ties to even.\n\nThree properties that matter in practice:\n\n1. **One rounding, not two.** The exact product of two doubles generally needs about twice\n the significand; the operation rounds it once. That single rounding is what makes\n `a*b` reproducible across conforming platforms, and what makes `(a*b)*c ≠ a*(b*c)` in\n general — multiplication is commutative but not associative in binary64.\n2. **Underflow is gradual, then total.** A product whose magnitude falls below the smallest\n normal double becomes subnormal and loses significand bits; below the smallest subnormal\n it becomes zero. The zero is signed, and the sign is the XOR of the operand signs.\n3. **The coercion is doing most of the work in real workbooks.** `=(A1>5)*(B1<3)` multiplies\n two logicals — the classic array-formula spelling of AND — and depends entirely on the\n shared to-logical-to-number rule (TRUE→1, FALSE→0) of\n [coercion and lifting](../model/02-coercion-and-lifting.md), not on anything specific to\n `*`.\n\n\n\n### Arguments\n\n\n| Position | Name | Meaning |\n|---|---|---|\n| 0 | `A` | Left factor. Required. |\n| 1 | `B` | Right factor. Required. |\n\nArity is exactly 2; no optional arguments, no defaults. Multiplication is commutative on\nfinite numbers, so operand order does not change the value — but it does change the\nbroadcast orientation when the operands are arrays of different shapes, so the positions are\nnot interchangeable in the array case.\n\n\n" }, "signature": { "display": "number1 * number2", "parameters": [ { "description": null, "name": "number1", "optional": false, "repeats": false }, { "description": null, "name": "number2", "optional": false, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 2, "min": 2 }, "category": "Operators", "classification": { "arg_preparation_profile": "ValuesOnlyPreAdapter", "coercion_lift_profile": "Custom", "determinism_class": "Deterministic", "error_collapse_profile": "None", "fec_dependency_profile": "None", "host_interaction_class": "None", "kernel_signature_class": "NumsToNum", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "RefOnly", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": null, "short_source": "no-short-description" }, "docs": null, "entry_kind": "built_in_operator", "localized_family_names": null, "localized_names": [], "signature": { "display": "number1 * number2", "parameters": [ { "description": null, "name": "number1", "optional": false, "repeats": false }, { "description": null, "name": "number2", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "OP_MULTIPLY", "version_marker": null, "xlcall": null }, "microsoft": null }, "try_it": { "formula": "=3*4" }, "url": "https://handbook.dnacalc.com/functions/OP_MULTIPLY.html", "variants": [], "versions": [] }