{ "category": "Operators", "display_name": "Exponentiation (^)", "entry_kind": "built_in_operator", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.OP_POWER", "implementation_state": { "answer_bank": null, "detail": "Recorded: 42 workbook cells.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "matches", "state_label": "Matches every recorded Excel answer", "summary": "Matches all 42 recorded answers", "workbook_corpus": { "cells": 42, "matched": 42, "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#L42-L42", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/arithmetic.rs#L83-L89" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/arithmetic::power_value", "catalogue/arithmetic::operands", "catalogue/arithmetic::raise", "catalogue/arithmetic::power_algorithm", "ported/excel_numeric::backend::sqrt", "ported/excel_numeric::binary_with", "ported/excel_numeric::excel_pow_positive", "ported/excel_numeric::excel_pow_chain", "ported/excel_numeric::excel_x87_mul", "ported/excel_numeric::excel_x87_recip", "ported/excel_numeric/x87::mul", "ported/excel_numeric/x87::recip", "ported/excel_numeric/x87_chains::pow2_positive", "ported/excel_numeric/x87_chains::pow2", "ported/excel_numeric/x87_chains::exp_ext", "ported/excel_numeric/x87_chains::exp_with", "ported/excel_numeric/x87_chains::excel_exp", "ported/excel_numeric/x87_chains::log_with", "ported/excel_numeric/x87_chains::excel_log", "ported/power_fn::exact_integer_magnitude", "ported/power_fn::accept_negative_base_odd_root", "ported/power_fn::binexp_positive", "ported/power_fn::power_kernel" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/arithmetic.rs#L42-L42", "state": "matches", "suite": null, "summary": "Matches all 42 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.OP_POWER.json", "name": "OP_POWER", "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- `EXP`, `LN`, `LOG`, `LOG10` — the transcendental path `^` is documented *not* to take for\n integer exponents.\n- `SQRT` — `x^0.5` and `SQRT(x)` are different implementations of the same mathematical\n function. `SQRT` is a correctly-rounded IEEE primitive; a general power path usually is\n not. Prefer `SQRT` where you can.\n- `IMPOWER` — complex powers over text-encoded complex numbers, which *does* return a\n negative real base's fractional power as a complex value.\n- [`FUNC.OP_MULTIPLY`](FUNC.OP_MULTIPLY.md) — what the integer-exponent path reduces to.\n\n\n", "how-to-implement": "\n### Notes for implementers\n\n\n- Implement two paths deliberately: an exact-integer-exponent path by binary exponentiation\n and a general path, and make the integer test exact (the exponent must be an integer *as a\n double*, not merely close to one). This is the difference chapter 03 records as\n observable.\n- Binary exponentiation is not associativity-free either. `x^10` computed as\n `((x^2)^2 · x)^2` and as `x·x·…·x` differ in the last bits; a compatibility implementation\n must pin the exact multiplication schedule, not merely \"repeated multiplication\".\n- Route the domain checks before the kernel, in this order: error operands, coercion\n failures, zero-base cases, negative-base-non-integer-exponent, then the arithmetic.\n Reordering these changes which error a doubly-bad operand pair produces.\n- Never let a library `pow` return an infinity or NaN to the publication layer. The worksheet\n value universe has no such values (chapter 01); every non-finite must be mapped to an error\n or a documented saturation before it reaches a cell.\n\n\n", "quirks": "\n### Result and edge cases\n\n- **Negative base, integer exponent.** Real and well defined; the sign alternates with the\n parity of the exponent.\n- **Zero base.** Positive exponent gives zero; negative exponent is recorded as `#DIV/0!`;\n zero exponent is recorded as `#NUM!` (see above).\n- **Base 1 and exponent 0** are the usual identities, with the `0^0` exception above the only\n interesting corner.\n- **Text and logical operands.** Shared to-number rules from\n [coercion and lifting](../model/02-coercion-and-lifting.md).\n\n\n", "sources": "- `data/functions/FUNC.POWER.json` — the named function's\n `precision_rounding_profile: integer_exponent_publication`, the other half of the\n disagreement, and the Microsoft URL for the *function* form:\n .\n- `data/presence/FUNC.OP_POWER.json` — implementing module\n `earlier-implementation/operator_arithmetic_family.rs`.\n- Handbook `content/model/03-call-pipeline.md` — the `IntegerExponentPublication` axis, its\n `POWER(1.05, 10)` worked example, and the statement that `^` carries it.\n- Handbook `content/model/01-value-universe.md`, `02-coercion-and-lifting.md`.\n\n\n", "version-differences": "The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.\n\n| Excel 16.0 build | Platform and CPU | Captured inputs |\n|---|---|---:|\n\nThe record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.\n\n[Recorded environments and comparison details](https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.OP_POWER.json).", "what-it-does": "\n`A ^ B` converts both operands to numbers and returns `A` raised to the power `B`, as a real\nvalue.\n\nThe word \"real\" is the entire specification. Unlike IEEE-754's `pow`, which is defined over\nextended reals and returns infinities and NaN, the worksheet's `^` is a *real-valued* power\nwith three consequences:\n\n3. **Zero to the zero is refused.** The same record observes `=0^0` and `=POWER(0,0)` as\n `#NUM!` on the replayed baseline (Excel 16.0 build 19929, replay dated 2026-04-29 in that\n record). This is the single most surprising fact on this page: mathematics conventionally\n defines `0^0 = 1`, C's `pow(0,0)` returns `1`, and Excel — on that observation — does not.\n The Handbook reports the record; it has not re-measured it.\n\nThe second specification-level fact is *how* the power is computed. Chapter 03 describes a\ndeclared publication axis, `PrecisionRoundingProfile::IntegerExponentPublication`: when the\nexponent is an exact integer, Excel computes the power by repeated multiplication (binary\nexponentiation) rather than by the transcendental `exp(b·ln a)` path, and the two disagree in\nthe last bits. Chapter 03 names `POWER` and the `^` operator as the carriers of that axis and\ngives a worked `POWER(1.05, 10)` example.\n\n\n### Arguments\n\n\n| Position | Name | Meaning |\n|---|---|---|\n| 0 | `A` | Base. Required. |\n| 1 | `B` | Exponent. Required. |\n\nArity is exactly 2; no optional arguments, no defaults. Order is emphatically load-bearing.\n\nThe exponent's *exactness as an integer* is a semantic input, not a formatting detail: on the\ninteger-exponent publication rule, `x^3` and `x^3.0000000000000004` may take different\ncomputation paths, and a spreadsheet that computes its exponent rather than typing it can\nland on either side of that boundary without the author noticing.\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_POWER", "version_marker": null, "xlcall": null }, "microsoft": null }, "try_it": { "formula": "=2^3" }, "url": "https://handbook.dnacalc.com/functions/OP_POWER.html", "variants": [], "versions": [] }