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// 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)
}
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