---
title: "SE-0552: Rounding of `Float.pi`"
framework: Swift Evolution Proposals
role: article
path: swift-evolution/0552-float-pi-rounding
---

# SE-0552: Rounding of `Float.pi`

* Proposal: [SE-0552](0552-float-pi-rounding.md)
* Authors: [Stephen Canon](https://github.com/stephentyrone)
* Review Manager: [Doug Gregor](https://github.com/DougGregor)
* Status: **Accepted**
* Implementation: [swiftlang/swift#92206](https://github.com/swiftlang/swift/pull/92206)
* Review: [(pitch)](https://forums.swift.org/t/pitch-round-to-nearest/89497)([review](https://forums.swift.org/t/se-0552-rounding-of-float-pi/89716))([acceptance](https://forums.swift.org/t/accepted-se-0552-rounding-of-float-pi/89936))

## Summary of changes

Change the definition of the property `pi` on `FloatingPoint`, so that it is no longer required to be rounded toward zero. Update `Float.pi` to match the new definition.

## Motivation

About 130 years ago, the Indiana state legislature briefly entertained a bill (bill 246 of the 1897 sitting of the Indiana General Assembly) that would have incidentally legislated the value of π. I figure it's time to try again.

When we designed the [`FloatingPoint` protocols][se-0067] for Swift, IEEE 754 provided no guidance as to how π should be rounded. There are two plausibly defensible choices: the closest representable value, or the closest  representable value that is strictly less than π (rounding toward zero). We opted for the second choice.

However, the IEEE 754 working group now has consensus that implementations should return the best approximation they can, rather than force rounding to a less accurate value to try to preserve some invariant. Accordingly we will adjust the definition of `FloatingPoint.pi` to match this guidance.

## Detailed design

In the documentation for `FloatingPoint.pi`, strike this sentence: ``` /// This value is rounded toward zero to keep user computations with angles /// from inadvertently ending up in the wrong quadrant. ``` and change the definition of `Float.pi` from `0x1.921fb4p1` to `0x1.921fb6p1` (the representable value just larger than π).

## Source compatibility

N/A

## ABI compatibility

It is likely that some software out there does depend on this specific value in some surprising way. In such cases, it may be necessary to use  `0x1.921fb4p1` instead of `Float.pi`. We do not expect such cases to be  common, and the ability to more easily get the same results as programs  written in other languages will outweigh any transient hassles.

## Future directions

N/A

## Alternatives considered

N/A

## Acknowledgments

Thanks to the IEEE 754 working group for detailed discussion of the issue.

[se-0067]: https://github.com/swiftlang/swift-evolution/blob/main/proposals/0067-floating-point-protocols.md