Add notes from Mar 2021 API review.

Design/meetings/2021/api-design-2021-03-04.md

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+# Q# API Design Meeting / 4 March 2021
+
+Attendees (in order by username): @bettinaheim, @cgranade, @guenp, @msoeken.
+
+## Agenda
+
+- https://github.com/microsoft/QuantumLibraries/issues/408
+- https://github.com/microsoft/QuantumLibraries/issues/413
+- https://github.com/microsoft/QuantumLibraries/issues/424
+- https://github.com/microsoft/QuantumLibraries/issues/418
+- https://github.com/microsoft/QuantumLibraries/issues/405
+- Preliminary discussion of https://github.com/microsoft/QuantumLibraries/issues/419
+
+## Discussion
+
+### Library support for multidimensional arrays (microsoft/qsharp-language#49)
+
+**Proposal**: https://github.com/microsoft/QuantumLibraries/issues/408
+
+**Discussion**:
+
+- Previous consensus: Defer until next review, read in detail and discuss async until then.
+- Good to take inspiration from other high-level multidimensional array APIs like NumPy.
+  - Some differences reflecting different terminology in Q# from Python (e.g.: "size" vs "shape").
+  - **Action item**: Rename "reshape" → "resize" for consistency with QEP 3.
+- Not specific to this proposal, but lack of overloading can make names confusing.
+- Selection of different functions and operations makes sense.
+- Nice to provide guidance on how users can write their own.
+- Perhaps reasonable to schedule out-of-band review to do deeper dive.
+- Good to have consensus by approximately July.
+- Add application-driven examples (e.g.: BSM).
+
+**Consensus**: Defer until out-of-band review, revise in the meantime.
+
+<!--  -->
+
+### Additions to Microsoft.Quantum.Math for floating point support
+
+**Proposal**: https://github.com/microsoft/QuantumLibraries/issues/413
+
+**Discussion**:
+
+- Tense of `FiniteFact` may not match `EqualityFact`; perhaps `FinitenessFact`?
+  - "Finite" is a synonym of "finiteness," such that a slight inconsistency in tense may be reasonable here for the sake of brevity.
+
+**Consensus**: Approve as-is.
+
+<!--  -->
+
+### Autoemulation attribute
+
+**Proposal**: https://github.com/microsoft/QuantumLibraries/issues/424
+
+**Discussion**:
+
+- "Emulate with" is a verb phrase.
+- "Emulatable with" may make clear that the attribute isn't doing the substitution, but is providing metadata to the relevant rewrite step.
+- "Emulation" may not be the right root either; one way to use it, but functionality is more general: target-specific substitution. Simulators are one specific kind of target.
+  - Alternatively, can narrow definition of attribute; e.g.: "simulator specific implementation."
+  - Only supported on C# runtime for now, but keep more general in case other runtimes support it eventually?
+- Microsoft.Quantum.Targeting as namespace instead of Microsoft.Quantum.Core?
+- **Action item**: Modify to `Microsoft.Quantum.Targeting.SubstitutableOnTarget("Alternative", "TargetName")`.
+
+**Consensus**: Approved with modification above.
+
+<!--  -->
+
+### Deprecate Microsoft.Quantum.Environment operations
+
+**Proposal**: https://github.com/microsoft/QuantumLibraries/issues/418
+
+**Discussion**:
+
+- Long-term goal would be to do qubit allocation statically, would be very difficult to do dynamically with this API.
+- May not be usecases for this feature; need other ways of exposing width–depth tradeoffs to static analysis.
+- Dynamic qubit management would require JIT anyway.
+
+**Consensus**: Approved as-is.
+
+<!--  -->
+
+### DoubleAsInt
+
+**Proposal**: https://github.com/microsoft/QuantumLibraries/issues/405
+
+**Discussion**:
+
+- Previous consensus: Introduce `DoubleAsInt`, effectively as an alias for `Truncate`.
+- Revisiting due to additional feedback from @bettinaheim.
+- **Action item**: Duplicate table of different truncate/round/ceil/floor outputs in each different function.
+
+**Consensus**: Resolve with additional API documentation to clarify.
+
+<!--  -->
+
+
+### Formatting functions
+
+**Proposal**: https://github.com/microsoft/QuantumLibraries/issues/419
+
+**Administrative note**: Proposal still in draft, but request to consider deprecating previous functions immediately.
+
+**Consensus**: Deprecate formatting functions immediately.
+