8000 round: add Round and RoundToEven pure Go implementations by soypat · Pull Request #31 · chewxy/math32 · GitHub
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round: add Round and RoundToEven pure Go implementations #31

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Merged
merged 1 commit into from
Nov 29, 2021
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round: add Round and RoundToEven pure Go implementations #31

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1 change: 1 addition & 0 deletions bits.go
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Original file line number Diff line number Diff line change
Expand Up @@ -3,6 +3,7 @@ package math32
const (
uvnan = 0x7FE00000
uvinf = 0x7F800000
uvone = 0x3f800000
uvneginf = 0xFF800000
mask = 0xFF
shift = 32 - 8 - 1
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75 changes: 72 additions & 3 deletions round.go
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Original file line number Diff line number Diff line change
@@ -1,7 +1,76 @@
package math32

import "math"
// Round returns the nearest integer, rounding half away from zero.
//
// Special cases are:
// Round(±0) = ±0
// Round(±Inf) = ±Inf
// Round(NaN) = NaN
func Round(x float32) float32 {
// Round is a faster implementation of:
//
// func Round(x float64) float64 {
// t := Trunc(x)
// if Abs(x-t) >= 0.5 {
// return t + Copysign(1, x)
// }
// return t
// }
bits := Float32bits(x)
e := uint(bits>>shift) & mask
if e < bias {
// Round abs(x) < 1 including denormals.
bits &= signMask // +-0
if e == bias-1 {
bits |= uvone // +-1
}
} else if e < bias+shift {
// Round any abs(x) >= 1 containing a fractional component [0,1).
//
// Numbers with larger exponents are returned unchanged since they
// must be either an integer, infinity, or NaN.
const half = 1 << (shift - 1)
e -= bias
bits += half >> e
bits &^= fracMask >> e
}
return Float32frombits(bits)
}

func Round(value float32) float32 {
return float32(math.Round(float64(value)))
// RoundToEven returns the nearest integer, rounding ties to even.
//
// Special cases are:
// RoundToEven(±0) = ±0
// RoundToEven(±Inf) = ±Inf
// RoundToEven(NaN) = NaN
func RoundToEven(x float32) float32 {
// RoundToEven is a faster implementation of:
//
// func RoundToEven(x float64) float64 {
// t := math.Trunc(x)
// odd := math.Remainder(t, 2) != 0
// if d := math.Abs(x - t); d > 0.5 || (d == 0.5 && odd) {
// return t + math.Copysign(1, x)
// }
// return t
// }
bits := Float32bits(x)
e := uint(bits>>shift) & mask
if e >= bias {
// Round abs(x) >= 1.
// - Large numbers without fractional components, infinity, and NaN are unchanged.
// - Add 0.499.. or 0.5 before truncating depending on whether the truncated
// number is even or odd (respectively).
const halfMinusULP = (1 << (shift - 1)) - 1
e -= bias
bits += (halfMinusULP + (bits>>(shift-e))&1) >> e
bits &^= fracMask >> e
} else if e == bias-1 && bits&fracMask != 0 {
// Round 0.5 < abs(x) < 1.
bits = bits&signMask | uvone // +-1
} else {
// Round abs(x) <= 0.5 including denormals.
bits &= signMask // +-0
}
return Float32frombits(bits)
}
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