vendor: fetch the dependencies

1 files changed, 302 insertions, 0 deletions

diff --git a/vendor/github.com/x448/float16/float16.go b/vendor/github.com/x448/float16/float16.go
new file mode 100644
index 000000000..1a0e6dad0
--- /dev/null
+++ b/vendor/github.com/x448/float16/float16.go
@@ -0,0 +1,302 @@
+// Copyright 2019 Montgomery Edwards⁴⁴⁸ and Faye Amacker
+//
+// Special thanks to Kathryn Long for her Rust implementation
+// of float16 at github.com/starkat99/half-rs (MIT license)
+
+package float16
+
+import (
+	"math"
+	"strconv"
+)
+
+// Float16 represents IEEE 754 half-precision floating-point numbers (binary16).
+type Float16 uint16
+
+// Precision indicates whether the conversion to Float16 is
+// exact, subnormal without dropped bits, inexact, underflow, or overflow.
+type Precision int
+
+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
+)
+
+// 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.
+func PrecisionFromfloat32(f32 float32) Precision {
+	u32 := math.Float32bits(f32)
+
+	if u32 == 0 || u32 == 0x80000000 {
+		// +- zero will always be exact conversion
+		return PrecisionExact
+	}
+
+	const COEFMASK uint32 = 0x7fffff // 23 least significant bits
+	const EXPSHIFT uint32 = 23
+	const EXPBIAS uint32 = 127
+	const EXPMASK uint32 = uint32(0xff) << EXPSHIFT
+	const DROPMASK uint32 = COEFMASK >> 10
+
+	exp := int32(((u32 & EXPMASK) >> EXPSHIFT) - EXPBIAS)
+	coef := u32 & COEFMASK
+
+	if exp == 128 {
+		// +- infinity or NaN
+		// apps may want to do extra checks for NaN separately
+		return PrecisionExact
+	}
+
+	// https://en.wikipedia.org/wiki/Half-precision_floating-point_format says,
+	// "Decimals between 2^−24 (minimum positive subnormal) and 2^−14 (maximum subnormal): fixed interval 2^−24"
+	if exp < -24 {
+		return PrecisionUnderflow
+	}
+	if exp > 15 {
+		return PrecisionOverflow
+	}
+	if (coef & DROPMASK) != uint32(0) {
+		// these include subnormals and non-subnormals that dropped bits
+		return PrecisionInexact
+	}
+
+	if exp < -14 {
+		// Subnormals. Caller may want to test these further.
+		// There are 2046 subnormals that can successfully round-trip f32->f16->f32
+		// and 20 of those 2046 have 32-bit input coef == 0.
+		// RFC 7049 and 7049bis Draft 12 don't precisely define "preserves value"
+		// so some protocols and libraries will choose to handle subnormals differently
+		// when deciding to encode them to CBOR float32 vs float16.
+		return PrecisionUnknown
+	}
+
+	return PrecisionExact
+}
+
+// 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 Frombits(u16 uint16) Float16 {
+	return Float16(u16)
+}
+
+// Fromfloat32 returns a Float16 value converted from f32. Conversion uses
+// IEEE default rounding (nearest int, with ties to even).
+func Fromfloat32(f32 float32) Float16 {
+	return Float16(f32bitsToF16bits(math.Float32bits(f32)))
+}
+
+// ErrInvalidNaNValue indicates a NaN was not received.
+const ErrInvalidNaNValue = float16Error("float16: invalid NaN value, expected IEEE 754 NaN")
+
+type float16Error string
+
+func (e float16Error) Error() string { return string(e) }
+
+// 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 FromNaN32ps(nan float32) (Float16, error) {
+	const SNAN = Float16(uint16(0x7c01)) // signalling NaN
+
+	u32 := math.Float32bits(nan)
+	sign := u32 & 0x80000000
+	exp := u32 & 0x7f800000
+	coef := u32 & 0x007fffff
+
+	if (exp != 0x7f800000) || (coef == 0) {
+		return SNAN, ErrInvalidNaNValue
+	}
+
+	u16 := uint16((sign >> 16) | uint32(0x7c00) | (coef >> 13))
+
+	if (u16 & 0x03ff) == 0 {
+		// result became infinity, make it NaN by setting lowest bit in payload
+		u16 = u16 | 0x0001
+	}
+
+	return Float16(u16), nil
+}
+
+// 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 NaN() Float16 {
+	return Float16(0x7e01)
+}
+
+// Inf returns a Float16 with an infinity value with the specified sign.
+// A sign >= returns positive infinity.
+// A sign < 0 returns negative infinity.
+func Inf(sign int) Float16 {
+	if sign >= 0 {
+		return Float16(0x7c00)
+	}
+	return Float16(0x8000 | 0x7c00)
+}
+
+// Float32 returns a float32 converted from f (Float16).
+// This is a lossless conversion.
+func (f Float16) Float32() float32 {
+	u32 := f16bitsToF32bits(uint16(f))
+	return math.Float32frombits(u32)
+}
+
+// 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 (f Float16) Bits() uint16 {
+	return uint16(f)
+}
+
+// IsNaN reports whether f is an IEEE 754 binary16 “not-a-number” value.
+func (f Float16) IsNaN() bool {
+	return (f&0x7c00 == 0x7c00) && (f&0x03ff != 0)
+}
+
+// IsQuietNaN reports whether f is a quiet (non-signaling) IEEE 754 binary16
+// “not-a-number” value.
+func (f Float16) IsQuietNaN() bool {
+	return (f&0x7c00 == 0x7c00) && (f&0x03ff != 0) && (f&0x0200 != 0)
+}
+
+// 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 (f Float16) IsInf(sign int) bool {
+	return ((f == 0x7c00) && sign >= 0) ||
+		(f == 0xfc00 && sign <= 0)
+}
+
+// IsFinite returns true if f is neither infinite nor NaN.
+func (f Float16) IsFinite() bool {
+	return (uint16(f) & uint16(0x7c00)) != uint16(0x7c00)
+}
+
+// IsNormal returns true if f is neither zero, infinite, subnormal, or NaN.
+func (f Float16) IsNormal() bool {
+	exp := uint16(f) & uint16(0x7c00)
+	return (exp != uint16(0x7c00)) && (exp != 0)
+}
+
+// Signbit reports whether f is negative or negative zero.
+func (f Float16) Signbit() bool {
+	return (uint16(f) & uint16(0x8000)) != 0
+}
+
+// String satisfies the fmt.Stringer interface.
+func (f Float16) String() string {
+	return strconv.FormatFloat(float64(f.Float32()), 'f', -1, 32)
+}
+
+// f16bitsToF32bits returns uint32 (float32 bits) converted from specified uint16.
+func f16bitsToF32bits(in uint16) uint32 {
+	// All 65536 conversions with this were confirmed to be correct
+	// by Montgomery Edwards⁴⁴⁸ (github.com/x448).
+
+	sign := uint32(in&0x8000) << 16 // sign for 32-bit
+	exp := uint32(in&0x7c00) >> 10  // exponenent for 16-bit
+	coef := uint32(in&0x03ff) << 13 // significand for 32-bit
+
+	if exp == 0x1f {
+		if coef == 0 {
+			// infinity
+			return sign | 0x7f800000 | coef
+		}
+		// NaN
+		return sign | 0x7fc00000 | coef
+	}
+
+	if exp == 0 {
+		if coef == 0 {
+			// zero
+			return sign
+		}
+
+		// normalize subnormal numbers
+		exp++
+		for coef&0x7f800000 == 0 {
+			coef <<= 1
+			exp--
+		}
+		coef &= 0x007fffff
+	}
+
+	return sign | ((exp + (0x7f - 0xf)) << 23) | coef
+}
+
+// f32bitsToF16bits returns uint16 (Float16 bits) converted from the specified float32.
+// Conversion rounds to nearest integer with ties to even.
+func f32bitsToF16bits(u32 uint32) uint16 {
+	// Translated from Rust to Go by Montgomery Edwards⁴⁴⁸ (github.com/x448).
+	// All 4294967296 conversions with this were confirmed to be correct by x448.
+	// Original Rust implementation is by Kathryn Long (github.com/starkat99) with MIT license.
+
+	sign := u32 & 0x80000000
+	exp := u32 & 0x7f800000
+	coef := u32 & 0x007fffff
+
+	if exp == 0x7f800000 {
+		// NaN or Infinity
+		nanBit := uint32(0)
+		if coef != 0 {
+			nanBit = uint32(0x0200)
+		}
+		return uint16((sign >> 16) | uint32(0x7c00) | nanBit | (coef >> 13))
+	}
+
+	halfSign := sign >> 16
+
+	unbiasedExp := int32(exp>>23) - 127
+	halfExp := unbiasedExp + 15
+
+	if halfExp >= 0x1f {
+		return uint16(halfSign | uint32(0x7c00))
+	}
+
+	if halfExp <= 0 {
+		if 14-halfExp > 24 {
+			return uint16(halfSign)
+		}
+		coef := coef | uint32(0x00800000)
+		halfCoef := coef >> uint32(14-halfExp)
+		roundBit := uint32(1) << uint32(13-halfExp)
+		if (coef&roundBit) != 0 && (coef&(3*roundBit-1)) != 0 {
+			halfCoef++
+		}
+		return uint16(halfSign | halfCoef)
+	}
+
+	uHalfExp := uint32(halfExp) << 10
+	halfCoef := coef >> 13
+	roundBit := uint32(0x00001000)
+	if (coef&roundBit) != 0 && (coef&(3*roundBit-1)) != 0 {
+		return uint16((halfSign | uHalfExp | halfCoef) + 1)
+	}
+	return uint16(halfSign | uHalfExp | halfCoef)
+}