149 lines
3.3 KiB
Go
149 lines
3.3 KiB
Go
// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package math
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// Floor returns the greatest integer value less than or equal to x.
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//
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// Special cases are:
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// Floor(±0) = ±0
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// Floor(±Inf) = ±Inf
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// Floor(NaN) = NaN
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//extern floor
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func libc_floor(float64) float64
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func Floor(x float64) float64 {
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return libc_floor(x)
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}
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func floor(x float64) float64 {
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if x == 0 || IsNaN(x) || IsInf(x, 0) {
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return x
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}
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if x < 0 {
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d, fract := Modf(-x)
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if fract != 0.0 {
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d = d + 1
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}
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return -d
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}
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d, _ := Modf(x)
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return d
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}
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// Ceil returns the least integer value greater than or equal to x.
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//
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// Special cases are:
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// Ceil(±0) = ±0
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// Ceil(±Inf) = ±Inf
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// Ceil(NaN) = NaN
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//extern ceil
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func libc_ceil(float64) float64
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func Ceil(x float64) float64 {
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return libc_ceil(x)
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}
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func ceil(x float64) float64 {
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return -Floor(-x)
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}
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// Trunc returns the integer value of x.
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//
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// Special cases are:
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// Trunc(±0) = ±0
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// Trunc(±Inf) = ±Inf
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// Trunc(NaN) = NaN
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func Trunc(x float64) float64 {
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if haveArchTrunc {
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return archTrunc(x)
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}
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return trunc(x)
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}
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func trunc(x float64) float64 {
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if x == 0 || IsNaN(x) || IsInf(x, 0) {
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return x
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}
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d, _ := Modf(x)
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return d
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}
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// Round returns the nearest integer, rounding half away from zero.
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//
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// Special cases are:
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// Round(±0) = ±0
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// Round(±Inf) = ±Inf
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// Round(NaN) = NaN
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func Round(x float64) float64 {
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// Round is a faster implementation of:
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//
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// func Round(x float64) float64 {
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// t := Trunc(x)
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// if Abs(x-t) >= 0.5 {
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// return t + Copysign(1, x)
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// }
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// return t
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// }
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bits := Float64bits(x)
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e := uint(bits>>shift) & mask
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if e < bias {
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// Round abs(x) < 1 including denormals.
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bits &= signMask // +-0
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if e == bias-1 {
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bits |= uvone // +-1
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}
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} else if e < bias+shift {
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// Round any abs(x) >= 1 containing a fractional component [0,1).
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//
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// Numbers with larger exponents are returned unchanged since they
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// must be either an integer, infinity, or NaN.
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const half = 1 << (shift - 1)
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e -= bias
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bits += half >> e
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bits &^= fracMask >> e
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}
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return Float64frombits(bits)
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}
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// RoundToEven returns the nearest integer, rounding ties to even.
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//
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// Special cases are:
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// RoundToEven(±0) = ±0
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// RoundToEven(±Inf) = ±Inf
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// RoundToEven(NaN) = NaN
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func RoundToEven(x float64) float64 {
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// RoundToEven is a faster implementation of:
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//
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// func RoundToEven(x float64) float64 {
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// t := math.Trunc(x)
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// odd := math.Remainder(t, 2) != 0
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// if d := math.Abs(x - t); d > 0.5 || (d == 0.5 && odd) {
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// return t + math.Copysign(1, x)
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// }
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// return t
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// }
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bits := Float64bits(x)
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e := uint(bits>>shift) & mask
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if e >= bias {
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// Round abs(x) >= 1.
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// - Large numbers without fractional components, infinity, and NaN are unchanged.
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// - Add 0.499.. or 0.5 before truncating depending on whether the truncated
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// number is even or odd (respectively).
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const halfMinusULP = (1 << (shift - 1)) - 1
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e -= bias
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bits += (halfMinusULP + (bits>>(shift-e))&1) >> e
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bits &^= fracMask >> e
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} else if e == bias-1 && bits&fracMask != 0 {
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// Round 0.5 < abs(x) < 1.
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bits = bits&signMask | uvone // +-1
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} else {
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// Round abs(x) <= 0.5 including denormals.
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bits &= signMask // +-0
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}
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return Float64frombits(bits)
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}
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