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+# Float16 (Binary16) in Go/Golang
+[![Build Status](https://travis-ci.org/x448/float16.svg?branch=master)](https://travis-ci.org/x448/float16)
+[![codecov](https://codecov.io/gh/x448/float16/branch/master/graph/badge.svg?v=4)](https://codecov.io/gh/x448/float16)
+[![Go Report Card](https://goreportcard.com/badge/github.com/x448/float16)](https://goreportcard.com/report/github.com/x448/float16)
+[![Release](https://img.shields.io/github/release/x448/float16.svg?style=flat-square)](https://github.com/x448/float16/releases)
+[![License](http://img.shields.io/badge/license-mit-blue.svg?style=flat-square)](https://raw.githubusercontent.com/x448/float16/master/LICENSE)
+
+`float16` package provides [IEEE 754 half-precision floating-point format (binary16)](https://en.wikipedia.org/wiki/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.
+
+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](https://github.com/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.  
+* 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](https://godoc.org/github.com/x448/float16) 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](https://github.com/starkat99/half-rs), a very nice rust implementation of float16.
+
+## License
+Copyright (c) 2019 Montgomery Edwards⁴⁴⁸ and Faye Amacker
+
+Licensed under [MIT License](LICENSE)