Source File
	floor.go

Belonging Package
	math

// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

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)
	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 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)
	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 Float64frombits(bits)
}