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# Source file src/math/floor.go

## Documentation: math

```  // Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style

package math

// Floor returns the greatest integer value less than or equal to x.
//
// Special cases are:
//	Floor(±0) = ±0
//	Floor(±Inf) = ±Inf
//	Floor(NaN) = NaN
func Floor(x float64) float64

func floor(x float64) float64 {
if x == 0 || IsNaN(x) || IsInf(x, 0) {
return x
}
if x < 0 {
d, fract := Modf(-x)
if fract != 0.0 {
d = d + 1
}
return -d
}
d, _ := Modf(x)
return d
}

// Ceil returns the least integer value greater than or equal to x.
//
// Special cases are:
//	Ceil(±0) = ±0
//	Ceil(±Inf) = ±Inf
//	Ceil(NaN) = NaN
func Ceil(x float64) float64

func ceil(x float64) float64 {
return -Floor(-x)
}

// Trunc returns the integer value of x.
//
// Special cases are:
//	Trunc(±0) = ±0
//	Trunc(±Inf) = ±Inf
//	Trunc(NaN) = NaN
func Trunc(x float64) float64

func trunc(x float64) float64 {
if x == 0 || IsNaN(x) || IsInf(x, 0) {
return x
}
d, _ := Modf(x)
return d
}

// 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 float64) float64 {
// 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 := Float64bits(x)
if e < bias {
// Round abs(x) < 1 including denormals.
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
}
return Float64frombits(bits)
}

// RoundToEven returns the nearest integer, rounding ties to even.
//
// Special cases are:
//	RoundToEven(±0) = ±0
//	RoundToEven(±Inf) = ±Inf
//	RoundToEven(NaN) = NaN
func RoundToEven(x float64) float64 {
// 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 := Float64bits(x)
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