README
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Float16 (Binary16) in Go/Golang
float16 package provides IEEE 754 half-precision floating-point format (binary16) 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.
Lowercase "float16" refers to IEEE 754 binary16. And capitalized "Float16" refers to exported Go data type provided by this library.
Features
Current features include:
- float16 to float32 conversions use lossless conversion.
- float32 to float16 conversions use IEEE 754-2008 "Round-to-Nearest RoundTiesToEven".
- conversions using pure Go take about 2.65 ns/op on a desktop amd64.
- unit tests provide 100% code coverage and check all possible 4+ billion conversions.
- other functions include: IsInf(), IsNaN(), IsNormal(), PrecisionFromfloat32(), String(), etc.
- 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. The version number < 1.0 indicates more functions and options are planned but not yet published.
Current status:
- core API is done and breaking API changes are unlikely.
- 100% of unit tests pass:
- short mode (
go test -short) tests around 65765 conversions in 0.005s. - normal mode (
go test) tests all possible 4+ billion conversions in about 95s.
- 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 functions for fast batch conversions leveraging SIMD when supported by hardware.
- 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 1-2 minutes to check all 4+ billion float32 input values and results for Fromfloat32(), FromNaN32ps(), and PrecisionFromfloat32().
Unit tests in short mode use a small subset (around 229 float32 inputs) and finish in under 0.01 second while still reaching 100% code coverage.
Usage
Install with go get github.com/x448/float16.
// Convert float32 to float16
pi := float32(math.Pi)
pi16 := float16.Fromfloat32(pi)
// Convert float16 to float32
pi32 := pi16.Float32()
// PrecisionFromfloat32() is faster than the overhead of calling a function.
// This example only converts if there's no data loss and input is not a subnormal.
if float16.PrecisionFromfloat32(pi) == float16.PrecisionExact {
pi16 := float16.Fromfloat32(pi)
}
Float16 Type and API
Float16 (capitalized) is a Go type with uint16 as the underlying state. There are 6 exported functions and 9 exported methods.
package float16 // import "github.com/x448/float16"
// Exported types and consts
type Float16 uint16
const ErrInvalidNaNValue = float16Error("float16: invalid NaN value, expected IEEE 754 NaN")
// Exported functions
Fromfloat32(f32 float32) Float16 // Float16 number converted from f32 using IEEE 754 default rounding
with identical results to AMD and Intel F16C hardware. NaN inputs
are converted with quiet bit always set on, to be like F16C.
FromNaN32ps(nan float32) (Float16, error) // Float16 NaN without modifying quiet bit.
// The "ps" suffix means "preserve signaling".
// Returns sNaN and ErrInvalidNaNValue if nan isn't a NaN.
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
PrecisionFromfloat32(f32 float32) Precision // quickly indicates exact, ..., overflow, underflow
// (inline and < 1 ns/op)
// 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) IsQuietNaN() bool // true if f is a quiet 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 -> float32 and float32 -> float16 on amd64. Speeds can vary depending on input value.
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 0.29ns ± 5% // speed using Frombits() to cast a uint16 to Float16
PrecisionFromFloat32-2 0.29ns ± 1% // speed using PrecisionFromfloat32() to check for overflows, etc.
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
¶
Index ¶
Constants ¶
const ErrInvalidNaNValue = float16Error("float16: invalid NaN value, expected IEEE 754 NaN")
ErrInvalidNaNValue indicates a NaN was not received.
Variables ¶
This section is empty.
Functions ¶
This section is empty.
Types ¶
type Float16 ¶
type Float16 uint16
Float16 represents IEEE 754 half-precision floating-point numbers (binary16).
func FromNaN32ps ¶
FromNaN32ps converts nan to IEEE binary16 NaN while preserving both signaling and payload. Unlike Fromfloat32(), which can only return qNaN because it sets quiet bit = 1, this can return both sNaN and qNaN. If the result is infinity (sNaN with empty payload), then the lowest bit of payload is set to make the result a NaN. Returns ErrInvalidNaNValue and 0x7c01 (sNaN) if nan isn't IEEE 754 NaN. This function was kept simple to be able to inline.
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 NaN ¶
func NaN() Float16
NaN returns a Float16 of IEEE 754 binary16 not-a-number (NaN). Returned NaN value 0x7e01 has all exponent bits = 1 with the first and last bits = 1 in the significand. This is consistent with Go's 64-bit math.NaN(). Canonical CBOR in RFC 7049 uses 0x7e00.
func (Float16) Bits ¶
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.
func (Float16) IsQuietNaN ¶
IsQuietNaN reports whether f is a quiet (non-signaling) IEEE 754 binary16 “not-a-number” value.
type Precision ¶
type Precision int
Precision indicates whether the conversion to Float16 is exact, subnormal without dropped bits, inexact, underflow, or overflow.
const ( // PrecisionExact is for non-subnormals that don't drop bits during conversion. // All of these can round-trip. Should always convert to float16. PrecisionExact Precision = iota // PrecisionUnknown is for subnormals that don't drop bits during conversion but // not all of these can round-trip so precision is unknown without more effort. // Only 2046 of these can round-trip and the rest cannot round-trip. PrecisionUnknown // PrecisionInexact is for dropped significand bits and cannot round-trip. // Some of these are subnormals. Cannot round-trip float32->float16->float32. PrecisionInexact // PrecisionUnderflow is for Underflows. Cannot round-trip float32->float16->float32. PrecisionUnderflow // PrecisionOverflow is for Overflows. Cannot round-trip float32->float16->float32. PrecisionOverflow )
func PrecisionFromfloat32 ¶
PrecisionFromfloat32 returns Precision without performing the conversion. Conversions from both Infinity and NaN values will always report PrecisionExact even if NaN payload or NaN-Quiet-Bit is lost. This function is kept simple to allow inlining and run < 0.5 ns/op, to serve as a fast filter.
Source Files