项目作者: x448

项目描述 :
float16 provides IEEE 754 half-precision format (binary16) with correct conversions to/from float32
高级语言: Go
项目地址: git://github.com/x448/float16.git
创建时间: 2019-12-28T21:09:45Z
项目社区:https://github.com/x448/float16

开源协议:MIT License

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Float16 (Binary16) in Go/Golang




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x448/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.

This library started as a contribution to fxamacker/cbor and became a standalone library to allow use by other software.

Software using this library include cbor and ollama.

[!NOTE]
This float16 library is extremely well-tested:

  • 100% code coverage for both go test and go test -short.
  • All 4294967296 possible float32 to float16 conversions (in pure Go) are confirmed to be correct.
  • All 65536 possible float16 to float32 conversions (in pure Go) are confirmed 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 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 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.
  • 100% code coverage with both short mode and normal mode.
  • Tested on amd64, arm64, ppc64le, and s390x.

Roadmap:

  • Add functions for fast batch conversions leveraging SIMD when supported by hardware.
  • Speed up unit test when verifying all possible 4+ billion conversions.

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.

  1. // Convert float32 to float16
  2. pi := float32(math.Pi)
  3. pi16 := float16.Fromfloat32(pi)
  4. // Convert float16 to float32
  5. pi32 := pi16.Float32()
  6. // PrecisionFromfloat32() is faster than the overhead of calling a function.
  7. // This example only converts if there's no data loss and input is not a subnormal.
  8. if float16.PrecisionFromfloat32(pi) == float16.PrecisionExact {
  9. pi16 := float16.Fromfloat32(pi)
  10. }

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.

  1. package float16 // import "github.com/x448/float16"
  2. // Exported types and consts
  3. type Float16 uint16
  4. const ErrInvalidNaNValue = float16Error("float16: invalid NaN value, expected IEEE 754 NaN")
  5. // Exported functions
  6. Fromfloat32(f32 float32) Float16 // Float16 number converted from f32 using IEEE 754 default rounding
  7. with identical results to AMD and Intel F16C hardware. NaN inputs
  8. are converted with quiet bit always set on, to be like F16C.
  9. FromNaN32ps(nan float32) (Float16, error) // Float16 NaN without modifying quiet bit.
  10. // The "ps" suffix means "preserve signaling".
  11. // Returns sNaN and ErrInvalidNaNValue if nan isn't a NaN.
  12. Frombits(b16 uint16) Float16 // Float16 number corresponding to b16 (IEEE 754 binary16 rep.)
  13. NaN() Float16 // Float16 of IEEE 754 binary16 not-a-number
  14. Inf(sign int) Float16 // Float16 of IEEE 754 binary16 infinity according to sign
  15. PrecisionFromfloat32(f32 float32) Precision // quickly indicates exact, ..., overflow, underflow
  16. // (inline and < 1 ns/op)
  17. // Exported methods
  18. (f Float16) Float32() float32 // float32 number converted from f16 using lossless conversion
  19. (f Float16) Bits() uint16 // the IEEE 754 binary16 representation of f
  20. (f Float16) IsNaN() bool // true if f is not-a-number (NaN)
  21. (f Float16) IsQuietNaN() bool // true if f is a quiet not-a-number (NaN)
  22. (f Float16) IsInf(sign int) bool // true if f is infinite based on sign (-1=NegInf, 0=any, 1=PosInf)
  23. (f Float16) IsFinite() bool // true if f is not infinite or NaN
  24. (f Float16) IsNormal() bool // true if f is not zero, infinite, subnormal, or NaN.
  25. (f Float16) Signbit() bool // true if f is negative or negative zero
  26. (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.

  1. All functions have zero allocations except float16.String().
  2. FromFloat32pi-2 2.59ns ± 0% // speed using Fromfloat32() to convert a float32 of math.Pi to Float16
  3. ToFloat32pi-2 2.69ns ± 0% // speed using Float32() to convert a float16 of math.Pi to float32
  4. Frombits-2 0.29ns ± 5% // speed using Frombits() to cast a uint16 to Float16
  5. PrecisionFromFloat32-2 0.29ns ± 1% // speed using PrecisionFromfloat32() to check for overflows, etc.

System Requirements

  • Go 1.12 (or newer).
  • amd64, arm64, ppc64le, or s390x.

Other architectures and Go versions may work, but are not tested regularly.

Special Thanks

Special thanks to Kathryn Long (starkat99) for creating half-rs, a very nice rust implementation of float16.

License

Copyright © 2019-present Montgomery Edwards⁴⁴⁸ and Faye Amacker.

x448/float16 is licensed under the MIT License. See LICENSE for the full license text.