README
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Float16 (Binary16) in Go/Golang
float16 package provides IEEE 754 half-precision floating-point format with IEEE 754 default rounding for conversions. IEEE 754-2008 refers to this 16-bit floating-point format as binary16.
IEEE 754 default rounding ("Round-to-Nearest RoundTiesToEven") is considered the most accurate and statistically unbiased estimate of the true result.
All possible 4+ billion floating-point conversions with this library are verified to be correct.
Features
Current features include:
- float16 to float32 conversions use lossless conversion.
- float32 to float16 conversions use IEEE 754-2008 "Round-to-Nearest RoundTiesToEven".
- conversions use zero allocs and are about 2.65 ns/op (in pure Go) on a desktop amd64.
- unit tests provide 100% code coverage and check all possible 4+ billion conversions.
- other functions include: IsFinite(), IsInf(), IsNaN(), IsNormal(), Signbit(), and String().
- all functions in this library use zero allocs except String().
Status
This library is used by fxamacker/cbor and is ready for production use on supported platforms.
Current status:
- core API is done and breaking API changes are unlikely.
- 100% of unit tests pass:
- short mode (
go test -short) tests around 65763 conversions in 0.005s. - normal mode (
go test) tests all possible 4+ billion conversions in about 45s.
- short mode (
- 100% code coverage with both short mode and normal mode.
- tested on amd64 but it should work on all little-endian platforms supported by Go.
Roadmap:
- add a function to both convert and report precision issues in one call.
- add functions for fast batch conversions.
- speed up unit test when verifying all possible 4+ billion conversions.
- test on additional platforms.
Float16 to Float32 Conversion
Conversions from float16 to float32 are lossless conversions. All 65536 possible float16 to float32 conversions (in pure Go) are confirmed to be correct.
Unit tests take a fraction of a second to check all 65536 expected values for float16 to float32 conversions.
Float32 to Float16 Conversion
Conversions from float32 to float16 use IEEE 754 default rounding ("Round-to-Nearest RoundTiesToEven"). All 4294967296 possible float32 to float16 conversions (in pure Go) are confirmed to be correct.
Unit tests in normal mode take about 35-55 seconds to check all 4+ billion expected values for float32 to float16 conversions.
Unit tests in short mode use a small subset (65763) of expected values and finish in under 1 second while still reaching 100% code coverage.
Usage
Install with go get github.com/cbor-go/float16.
// Convert float32 to float16
pi := float32(math.Pi)
pi16 := float16.Fromfloat32(pi)
// Convert float16 to float32
pi32 := pi16.Float32()
Float16 Type and API
Float16 (capitalized) is a Go type with uint16 as the underlying state. There are 4 exported functions and 7 exported methods.
package float16 // import "github.com/cbor-go/float16"
// Exported types
type Float16 uint16
// Exported functions
Fromfloat32(f32 float32) Float16 // Float16 number converted from f32 using IEEE 754 default rounding
Frombits(b16 uint16) Float16 // Float16 number corresponding to b16 (IEEE 754 binary16 rep.)
NaN() Float16 // Float16 of IEEE 754 binary16 not-a-number
Inf(sign int) Float16 // Float16 of IEEE 754 binary16 infinity according to sign
// Exported methods
(f Float16) Float32() float32 // float32 number converted from f16 using lossless conversion
(f Float16) Bits() uint16 // the IEEE 754 binary16 representation of f
(f Float16) IsNaN() bool // true if f is not-a-number (NaN)
(f Float16) IsInf(sign int) bool // true if f is infinite based on sign (-1=NegInf, 0=any, 1=PosInf)
(f Float16) IsFinite() bool // true if f is not infinite or NaN
(f Float16) IsNormal() bool // true if f is not zero, infinite, subnormal, or NaN.
(f Float16) Signbit() bool // true if f is negative or negative zero
(f Float16) String() string // string representation of f to satisfy fmt.Stringer interface
See API at godoc.org for more info.
Benchmarks
Conversions (in pure Go) are around 2.65 ns/op for float16 to Float32 as well as Float32 to float16 on amd64.
Frombits is included as a canary to catch overoptimized benchmarks. Frombits should be faster than all other functions.
All functions have zero allocations except float16.String().
FromFloat32pi-2 2.59ns ± 0% // speed using Fromfloat32() to convert a float32 of math.Pi to Float16
ToFloat32pi-2 2.69ns ± 0% // speed using Float32() to convert a float16 of math.Pi to float32
Frombits-2 0.36ns ± 8% // speed using Frombits() to cast a uint16 to Float16
System Requirements
- Tested on Go 1.11, 1.12, and 1.13 but it should also work with older versions.
- Tested on amd64 but it should also work on all little-endian platforms supported by Go.
Special Thanks
Special thanks to Kathryn Long (starkat99) for creating half-rs, a very nice rust implementation of float16.
License
Copyright (c) 2019 Montgomery Edwards⁴⁴⁸ and Faye Amacker
Licensed under MIT License
Documentation
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Index ¶
Constants ¶
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Variables ¶
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Functions ¶
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Types ¶
type Float16 ¶
type Float16 uint16
Float16 represents IEEE 754 half-precision floating-point numbers (binary16).
func Frombits ¶
Frombits returns the float16 number corresponding to the IEEE 754 binary16 representation u16, with the sign bit of u16 and the result in the same bit position. Frombits(Bits(x)) == x.
func Fromfloat32 ¶
Fromfloat32 returns a Float16 value converted from f32. Conversion uses IEEE default rounding (nearest int, with ties to even).
func Inf ¶
Inf returns a Float16 with an infinity value with the specified sign. A sign >= returns positive infinity. A sign < 0 returns negative infinity.
func (Float16) Bits ¶ added in v0.7.0
Bits returns the IEEE 754 binary16 representation of f, with the sign bit of f and the result in the same bit position. Bits(Frombits(x)) == x.
func (Float16) Float32 ¶
Float32 returns a float32 converted from f (Float16). This is a lossless conversion.
func (Float16) IsInf ¶
IsInf reports whether f is an infinity (inf). A sign > 0 reports whether f is positive inf. A sign < 0 reports whether f is negative inf. A sign == 0 reports whether f is either inf.
Source Files