mirror of https://github.com/k3s-io/k3s
934 lines
22 KiB
Go
934 lines
22 KiB
Go
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// Copyright ©2013 The Gonum Authors. All rights reserved.
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// Use of this 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 floats
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import (
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"errors"
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"math"
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"sort"
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"strconv"
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"gonum.org/v1/gonum/internal/asm/f64"
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)
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// Add adds, element-wise, the elements of s and dst, and stores in dst.
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// Panics if the lengths of dst and s do not match.
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func Add(dst, s []float64) {
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if len(dst) != len(s) {
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panic("floats: length of the slices do not match")
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}
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f64.AxpyUnitaryTo(dst, 1, s, dst)
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}
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// AddTo adds, element-wise, the elements of s and t and
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// stores the result in dst. Panics if the lengths of s, t and dst do not match.
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func AddTo(dst, s, t []float64) []float64 {
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if len(s) != len(t) {
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panic("floats: length of adders do not match")
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}
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if len(dst) != len(s) {
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panic("floats: length of destination does not match length of adder")
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}
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f64.AxpyUnitaryTo(dst, 1, s, t)
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return dst
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}
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// AddConst adds the scalar c to all of the values in dst.
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func AddConst(c float64, dst []float64) {
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f64.AddConst(c, dst)
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}
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// AddScaled performs dst = dst + alpha * s.
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// It panics if the lengths of dst and s are not equal.
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func AddScaled(dst []float64, alpha float64, s []float64) {
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if len(dst) != len(s) {
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panic("floats: length of destination and source to not match")
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}
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f64.AxpyUnitaryTo(dst, alpha, s, dst)
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}
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// AddScaledTo performs dst = y + alpha * s, where alpha is a scalar,
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// and dst, y and s are all slices.
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// It panics if the lengths of dst, y, and s are not equal.
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//
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// At the return of the function, dst[i] = y[i] + alpha * s[i]
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func AddScaledTo(dst, y []float64, alpha float64, s []float64) []float64 {
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if len(dst) != len(s) || len(dst) != len(y) {
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panic("floats: lengths of slices do not match")
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}
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f64.AxpyUnitaryTo(dst, alpha, s, y)
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return dst
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}
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// argsort is a helper that implements sort.Interface, as used by
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// Argsort.
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type argsort struct {
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s []float64
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inds []int
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}
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func (a argsort) Len() int {
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return len(a.s)
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}
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func (a argsort) Less(i, j int) bool {
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return a.s[i] < a.s[j]
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}
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func (a argsort) Swap(i, j int) {
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a.s[i], a.s[j] = a.s[j], a.s[i]
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a.inds[i], a.inds[j] = a.inds[j], a.inds[i]
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}
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// Argsort sorts the elements of dst while tracking their original order.
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// At the conclusion of Argsort, dst will contain the original elements of dst
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// but sorted in increasing order, and inds will contain the original position
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// of the elements in the slice such that dst[i] = origDst[inds[i]].
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// It panics if the lengths of dst and inds do not match.
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func Argsort(dst []float64, inds []int) {
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if len(dst) != len(inds) {
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panic("floats: length of inds does not match length of slice")
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}
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for i := range dst {
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inds[i] = i
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}
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a := argsort{s: dst, inds: inds}
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sort.Sort(a)
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}
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// Count applies the function f to every element of s and returns the number
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// of times the function returned true.
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func Count(f func(float64) bool, s []float64) int {
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var n int
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for _, val := range s {
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if f(val) {
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n++
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}
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}
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return n
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}
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// CumProd finds the cumulative product of the first i elements in
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// s and puts them in place into the ith element of the
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// destination dst. A panic will occur if the lengths of arguments
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// do not match.
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//
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// At the return of the function, dst[i] = s[i] * s[i-1] * s[i-2] * ...
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func CumProd(dst, s []float64) []float64 {
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if len(dst) != len(s) {
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panic("floats: length of destination does not match length of the source")
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}
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if len(dst) == 0 {
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return dst
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}
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return f64.CumProd(dst, s)
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}
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// CumSum finds the cumulative sum of the first i elements in
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// s and puts them in place into the ith element of the
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// destination dst. A panic will occur if the lengths of arguments
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// do not match.
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//
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// At the return of the function, dst[i] = s[i] + s[i-1] + s[i-2] + ...
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func CumSum(dst, s []float64) []float64 {
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if len(dst) != len(s) {
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panic("floats: length of destination does not match length of the source")
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}
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if len(dst) == 0 {
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return dst
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}
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return f64.CumSum(dst, s)
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}
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// Distance computes the L-norm of s - t. See Norm for special cases.
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// A panic will occur if the lengths of s and t do not match.
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func Distance(s, t []float64, L float64) float64 {
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if len(s) != len(t) {
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panic("floats: slice lengths do not match")
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}
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if len(s) == 0 {
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return 0
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}
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var norm float64
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if L == 2 {
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for i, v := range s {
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diff := t[i] - v
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norm = math.Hypot(norm, diff)
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}
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return norm
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}
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if L == 1 {
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for i, v := range s {
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norm += math.Abs(t[i] - v)
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}
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return norm
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}
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if math.IsInf(L, 1) {
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for i, v := range s {
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absDiff := math.Abs(t[i] - v)
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if absDiff > norm {
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norm = absDiff
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}
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}
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return norm
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}
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for i, v := range s {
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norm += math.Pow(math.Abs(t[i]-v), L)
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}
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return math.Pow(norm, 1/L)
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}
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// Div performs element-wise division dst / s
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// and stores the value in dst. It panics if the
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// lengths of s and t are not equal.
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func Div(dst, s []float64) {
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if len(dst) != len(s) {
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panic("floats: slice lengths do not match")
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}
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f64.Div(dst, s)
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}
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// DivTo performs element-wise division s / t
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// and stores the value in dst. It panics if the
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// lengths of s, t, and dst are not equal.
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func DivTo(dst, s, t []float64) []float64 {
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if len(s) != len(t) || len(dst) != len(t) {
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panic("floats: slice lengths do not match")
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}
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return f64.DivTo(dst, s, t)
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}
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// Dot computes the dot product of s1 and s2, i.e.
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// sum_{i = 1}^N s1[i]*s2[i].
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// A panic will occur if lengths of arguments do not match.
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func Dot(s1, s2 []float64) float64 {
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if len(s1) != len(s2) {
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panic("floats: lengths of the slices do not match")
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}
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return f64.DotUnitary(s1, s2)
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}
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// Equal returns true if the slices have equal lengths and
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// all elements are numerically identical.
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func Equal(s1, s2 []float64) bool {
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if len(s1) != len(s2) {
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return false
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}
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for i, val := range s1 {
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if s2[i] != val {
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return false
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}
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}
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return true
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}
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// EqualApprox returns true if the slices have equal lengths and
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// all element pairs have an absolute tolerance less than tol or a
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// relative tolerance less than tol.
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func EqualApprox(s1, s2 []float64, tol float64) bool {
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if len(s1) != len(s2) {
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return false
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}
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for i, a := range s1 {
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if !EqualWithinAbsOrRel(a, s2[i], tol, tol) {
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return false
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}
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}
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return true
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}
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// EqualFunc returns true if the slices have the same lengths
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// and the function returns true for all element pairs.
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func EqualFunc(s1, s2 []float64, f func(float64, float64) bool) bool {
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if len(s1) != len(s2) {
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return false
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}
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for i, val := range s1 {
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if !f(val, s2[i]) {
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return false
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}
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}
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return true
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}
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// EqualWithinAbs returns true if a and b have an absolute
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// difference of less than tol.
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func EqualWithinAbs(a, b, tol float64) bool {
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return a == b || math.Abs(a-b) <= tol
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}
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const minNormalFloat64 = 2.2250738585072014e-308
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// EqualWithinRel returns true if the difference between a and b
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// is not greater than tol times the greater value.
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func EqualWithinRel(a, b, tol float64) bool {
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if a == b {
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return true
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}
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delta := math.Abs(a - b)
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if delta <= minNormalFloat64 {
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return delta <= tol*minNormalFloat64
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}
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// We depend on the division in this relationship to identify
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// infinities (we rely on the NaN to fail the test) otherwise
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// we compare Infs of the same sign and evaluate Infs as equal
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// independent of sign.
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return delta/math.Max(math.Abs(a), math.Abs(b)) <= tol
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}
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// EqualWithinAbsOrRel returns true if a and b are equal to within
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// the absolute tolerance.
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func EqualWithinAbsOrRel(a, b, absTol, relTol float64) bool {
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if EqualWithinAbs(a, b, absTol) {
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return true
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}
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return EqualWithinRel(a, b, relTol)
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}
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// EqualWithinULP returns true if a and b are equal to within
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// the specified number of floating point units in the last place.
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func EqualWithinULP(a, b float64, ulp uint) bool {
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if a == b {
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return true
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}
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if math.IsNaN(a) || math.IsNaN(b) {
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return false
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}
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if math.Signbit(a) != math.Signbit(b) {
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return math.Float64bits(math.Abs(a))+math.Float64bits(math.Abs(b)) <= uint64(ulp)
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}
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return ulpDiff(math.Float64bits(a), math.Float64bits(b)) <= uint64(ulp)
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}
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func ulpDiff(a, b uint64) uint64 {
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if a > b {
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return a - b
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}
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return b - a
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}
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// EqualLengths returns true if all of the slices have equal length,
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// and false otherwise. Returns true if there are no input slices.
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func EqualLengths(slices ...[]float64) bool {
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// This length check is needed: http://play.golang.org/p/sdty6YiLhM
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if len(slices) == 0 {
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return true
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}
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l := len(slices[0])
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for i := 1; i < len(slices); i++ {
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if len(slices[i]) != l {
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return false
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}
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}
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return true
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}
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// Find applies f to every element of s and returns the indices of the first
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// k elements for which the f returns true, or all such elements
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// if k < 0.
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// Find will reslice inds to have 0 length, and will append
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// found indices to inds.
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// If k > 0 and there are fewer than k elements in s satisfying f,
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// all of the found elements will be returned along with an error.
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// At the return of the function, the input inds will be in an undetermined state.
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func Find(inds []int, f func(float64) bool, s []float64, k int) ([]int, error) {
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// inds is also returned to allow for calling with nil
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// Reslice inds to have zero length
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inds = inds[:0]
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// If zero elements requested, can just return
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if k == 0 {
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return inds, nil
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}
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// If k < 0, return all of the found indices
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if k < 0 {
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for i, val := range s {
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if f(val) {
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inds = append(inds, i)
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}
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}
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return inds, nil
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}
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// Otherwise, find the first k elements
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nFound := 0
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for i, val := range s {
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if f(val) {
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inds = append(inds, i)
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nFound++
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if nFound == k {
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return inds, nil
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}
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}
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}
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// Finished iterating over the loop, which means k elements were not found
|
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return inds, errors.New("floats: insufficient elements found")
|
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}
|
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|
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// HasNaN returns true if the slice s has any values that are NaN and false
|
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// otherwise.
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func HasNaN(s []float64) bool {
|
||
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for _, v := range s {
|
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if math.IsNaN(v) {
|
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return true
|
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}
|
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}
|
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return false
|
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}
|
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|
|
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// LogSpan returns a set of n equally spaced points in log space between,
|
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// l and u where N is equal to len(dst). The first element of the
|
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// resulting dst will be l and the final element of dst will be u.
|
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// Panics if len(dst) < 2
|
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// Note that this call will return NaNs if either l or u are negative, and
|
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// will return all zeros if l or u is zero.
|
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// Also returns the mutated slice dst, so that it can be used in range, like:
|
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//
|
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// for i, x := range LogSpan(dst, l, u) { ... }
|
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func LogSpan(dst []float64, l, u float64) []float64 {
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Span(dst, math.Log(l), math.Log(u))
|
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for i := range dst {
|
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dst[i] = math.Exp(dst[i])
|
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}
|
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|
return dst
|
||
|
}
|
||
|
|
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// LogSumExp returns the log of the sum of the exponentials of the values in s.
|
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|
// Panics if s is an empty slice.
|
||
|
func LogSumExp(s []float64) float64 {
|
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|
// Want to do this in a numerically stable way which avoids
|
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// overflow and underflow
|
||
|
// First, find the maximum value in the slice.
|
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maxval := Max(s)
|
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|
if math.IsInf(maxval, 0) {
|
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|
// If it's infinity either way, the logsumexp will be infinity as well
|
||
|
// returning now avoids NaNs
|
||
|
return maxval
|
||
|
}
|
||
|
var lse float64
|
||
|
// Compute the sumexp part
|
||
|
for _, val := range s {
|
||
|
lse += math.Exp(val - maxval)
|
||
|
}
|
||
|
// Take the log and add back on the constant taken out
|
||
|
return math.Log(lse) + maxval
|
||
|
}
|
||
|
|
||
|
// Max returns the maximum value in the input slice. If the slice is empty, Max will panic.
|
||
|
func Max(s []float64) float64 {
|
||
|
return s[MaxIdx(s)]
|
||
|
}
|
||
|
|
||
|
// MaxIdx returns the index of the maximum value in the input slice. If several
|
||
|
// entries have the maximum value, the first such index is returned. If the slice
|
||
|
// is empty, MaxIdx will panic.
|
||
|
func MaxIdx(s []float64) int {
|
||
|
if len(s) == 0 {
|
||
|
panic("floats: zero slice length")
|
||
|
}
|
||
|
max := math.NaN()
|
||
|
var ind int
|
||
|
for i, v := range s {
|
||
|
if math.IsNaN(v) {
|
||
|
continue
|
||
|
}
|
||
|
if v > max || math.IsNaN(max) {
|
||
|
max = v
|
||
|
ind = i
|
||
|
}
|
||
|
}
|
||
|
return ind
|
||
|
}
|
||
|
|
||
|
// Min returns the maximum value in the input slice. If the slice is empty, Min will panic.
|
||
|
func Min(s []float64) float64 {
|
||
|
return s[MinIdx(s)]
|
||
|
}
|
||
|
|
||
|
// MinIdx returns the index of the minimum value in the input slice. If several
|
||
|
// entries have the maximum value, the first such index is returned. If the slice
|
||
|
// is empty, MinIdx will panic.
|
||
|
func MinIdx(s []float64) int {
|
||
|
if len(s) == 0 {
|
||
|
panic("floats: zero slice length")
|
||
|
}
|
||
|
min := math.NaN()
|
||
|
var ind int
|
||
|
for i, v := range s {
|
||
|
if math.IsNaN(v) {
|
||
|
continue
|
||
|
}
|
||
|
if v < min || math.IsNaN(min) {
|
||
|
min = v
|
||
|
ind = i
|
||
|
}
|
||
|
}
|
||
|
return ind
|
||
|
}
|
||
|
|
||
|
// Mul performs element-wise multiplication between dst
|
||
|
// and s and stores the value in dst. Panics if the
|
||
|
// lengths of s and t are not equal.
|
||
|
func Mul(dst, s []float64) {
|
||
|
if len(dst) != len(s) {
|
||
|
panic("floats: slice lengths do not match")
|
||
|
}
|
||
|
for i, val := range s {
|
||
|
dst[i] *= val
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// MulTo performs element-wise multiplication between s
|
||
|
// and t and stores the value in dst. Panics if the
|
||
|
// lengths of s, t, and dst are not equal.
|
||
|
func MulTo(dst, s, t []float64) []float64 {
|
||
|
if len(s) != len(t) || len(dst) != len(t) {
|
||
|
panic("floats: slice lengths do not match")
|
||
|
}
|
||
|
for i, val := range t {
|
||
|
dst[i] = val * s[i]
|
||
|
}
|
||
|
return dst
|
||
|
}
|
||
|
|
||
|
const (
|
||
|
nanBits = 0x7ff8000000000000
|
||
|
nanMask = 0xfff8000000000000
|
||
|
)
|
||
|
|
||
|
// NaNWith returns an IEEE 754 "quiet not-a-number" value with the
|
||
|
// payload specified in the low 51 bits of payload.
|
||
|
// The NaN returned by math.NaN has a bit pattern equal to NaNWith(1).
|
||
|
func NaNWith(payload uint64) float64 {
|
||
|
return math.Float64frombits(nanBits | (payload &^ nanMask))
|
||
|
}
|
||
|
|
||
|
// NaNPayload returns the lowest 51 bits payload of an IEEE 754 "quiet
|
||
|
// not-a-number". For values of f other than quiet-NaN, NaNPayload
|
||
|
// returns zero and false.
|
||
|
func NaNPayload(f float64) (payload uint64, ok bool) {
|
||
|
b := math.Float64bits(f)
|
||
|
if b&nanBits != nanBits {
|
||
|
return 0, false
|
||
|
}
|
||
|
return b &^ nanMask, true
|
||
|
}
|
||
|
|
||
|
// NearestIdx returns the index of the element in s
|
||
|
// whose value is nearest to v. If several such
|
||
|
// elements exist, the lowest index is returned.
|
||
|
// NearestIdx panics if len(s) == 0.
|
||
|
func NearestIdx(s []float64, v float64) int {
|
||
|
if len(s) == 0 {
|
||
|
panic("floats: zero length slice")
|
||
|
}
|
||
|
switch {
|
||
|
case math.IsNaN(v):
|
||
|
return 0
|
||
|
case math.IsInf(v, 1):
|
||
|
return MaxIdx(s)
|
||
|
case math.IsInf(v, -1):
|
||
|
return MinIdx(s)
|
||
|
}
|
||
|
var ind int
|
||
|
dist := math.NaN()
|
||
|
for i, val := range s {
|
||
|
newDist := math.Abs(v - val)
|
||
|
// A NaN distance will not be closer.
|
||
|
if math.IsNaN(newDist) {
|
||
|
continue
|
||
|
}
|
||
|
if newDist < dist || math.IsNaN(dist) {
|
||
|
dist = newDist
|
||
|
ind = i
|
||
|
}
|
||
|
}
|
||
|
return ind
|
||
|
}
|
||
|
|
||
|
// NearestIdxForSpan return the index of a hypothetical vector created
|
||
|
// by Span with length n and bounds l and u whose value is closest
|
||
|
// to v. That is, NearestIdxForSpan(n, l, u, v) is equivalent to
|
||
|
// Nearest(Span(make([]float64, n),l,u),v) without an allocation.
|
||
|
// NearestIdxForSpan panics if n is less than two.
|
||
|
func NearestIdxForSpan(n int, l, u float64, v float64) int {
|
||
|
if n <= 1 {
|
||
|
panic("floats: span must have length >1")
|
||
|
}
|
||
|
if math.IsNaN(v) {
|
||
|
return 0
|
||
|
}
|
||
|
|
||
|
// Special cases for Inf and NaN.
|
||
|
switch {
|
||
|
case math.IsNaN(l) && !math.IsNaN(u):
|
||
|
return n - 1
|
||
|
case math.IsNaN(u):
|
||
|
return 0
|
||
|
case math.IsInf(l, 0) && math.IsInf(u, 0):
|
||
|
if l == u {
|
||
|
return 0
|
||
|
}
|
||
|
if n%2 == 1 {
|
||
|
if !math.IsInf(v, 0) {
|
||
|
return n / 2
|
||
|
}
|
||
|
if math.Copysign(1, v) == math.Copysign(1, l) {
|
||
|
return 0
|
||
|
}
|
||
|
return n/2 + 1
|
||
|
}
|
||
|
if math.Copysign(1, v) == math.Copysign(1, l) {
|
||
|
return 0
|
||
|
}
|
||
|
return n / 2
|
||
|
case math.IsInf(l, 0):
|
||
|
if v == l {
|
||
|
return 0
|
||
|
}
|
||
|
return n - 1
|
||
|
case math.IsInf(u, 0):
|
||
|
if v == u {
|
||
|
return n - 1
|
||
|
}
|
||
|
return 0
|
||
|
case math.IsInf(v, -1):
|
||
|
if l <= u {
|
||
|
return 0
|
||
|
}
|
||
|
return n - 1
|
||
|
case math.IsInf(v, 1):
|
||
|
if u <= l {
|
||
|
return 0
|
||
|
}
|
||
|
return n - 1
|
||
|
}
|
||
|
|
||
|
// Special cases for v outside (l, u) and (u, l).
|
||
|
switch {
|
||
|
case l < u:
|
||
|
if v <= l {
|
||
|
return 0
|
||
|
}
|
||
|
if v >= u {
|
||
|
return n - 1
|
||
|
}
|
||
|
case l > u:
|
||
|
if v >= l {
|
||
|
return 0
|
||
|
}
|
||
|
if v <= u {
|
||
|
return n - 1
|
||
|
}
|
||
|
default:
|
||
|
return 0
|
||
|
}
|
||
|
|
||
|
// Can't guarantee anything about exactly halfway between
|
||
|
// because of floating point weirdness.
|
||
|
return int((float64(n)-1)/(u-l)*(v-l) + 0.5)
|
||
|
}
|
||
|
|
||
|
// Norm returns the L norm of the slice S, defined as
|
||
|
// (sum_{i=1}^N s[i]^L)^{1/L}
|
||
|
// Special cases:
|
||
|
// L = math.Inf(1) gives the maximum absolute value.
|
||
|
// Does not correctly compute the zero norm (use Count).
|
||
|
func Norm(s []float64, L float64) float64 {
|
||
|
// Should this complain if L is not positive?
|
||
|
// Should this be done in log space for better numerical stability?
|
||
|
// would be more cost
|
||
|
// maybe only if L is high?
|
||
|
if len(s) == 0 {
|
||
|
return 0
|
||
|
}
|
||
|
if L == 2 {
|
||
|
twoNorm := math.Abs(s[0])
|
||
|
for i := 1; i < len(s); i++ {
|
||
|
twoNorm = math.Hypot(twoNorm, s[i])
|
||
|
}
|
||
|
return twoNorm
|
||
|
}
|
||
|
var norm float64
|
||
|
if L == 1 {
|
||
|
for _, val := range s {
|
||
|
norm += math.Abs(val)
|
||
|
}
|
||
|
return norm
|
||
|
}
|
||
|
if math.IsInf(L, 1) {
|
||
|
for _, val := range s {
|
||
|
norm = math.Max(norm, math.Abs(val))
|
||
|
}
|
||
|
return norm
|
||
|
}
|
||
|
for _, val := range s {
|
||
|
norm += math.Pow(math.Abs(val), L)
|
||
|
}
|
||
|
return math.Pow(norm, 1/L)
|
||
|
}
|
||
|
|
||
|
// ParseWithNA converts the string s to a float64 in v.
|
||
|
// If s equals missing, w is returned as 0, otherwise 1.
|
||
|
func ParseWithNA(s, missing string) (v, w float64, err error) {
|
||
|
if s == missing {
|
||
|
return 0, 0, nil
|
||
|
}
|
||
|
v, err = strconv.ParseFloat(s, 64)
|
||
|
if err == nil {
|
||
|
w = 1
|
||
|
}
|
||
|
return v, w, err
|
||
|
}
|
||
|
|
||
|
// Prod returns the product of the elements of the slice.
|
||
|
// Returns 1 if len(s) = 0.
|
||
|
func Prod(s []float64) float64 {
|
||
|
prod := 1.0
|
||
|
for _, val := range s {
|
||
|
prod *= val
|
||
|
}
|
||
|
return prod
|
||
|
}
|
||
|
|
||
|
// Reverse reverses the order of elements in the slice.
|
||
|
func Reverse(s []float64) {
|
||
|
for i, j := 0, len(s)-1; i < j; i, j = i+1, j-1 {
|
||
|
s[i], s[j] = s[j], s[i]
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// Round returns the half away from zero rounded value of x with prec precision.
|
||
|
//
|
||
|
// Special cases are:
|
||
|
// Round(±0) = +0
|
||
|
// Round(±Inf) = ±Inf
|
||
|
// Round(NaN) = NaN
|
||
|
func Round(x float64, prec int) float64 {
|
||
|
if x == 0 {
|
||
|
// Make sure zero is returned
|
||
|
// without the negative bit set.
|
||
|
return 0
|
||
|
}
|
||
|
// Fast path for positive precision on integers.
|
||
|
if prec >= 0 && x == math.Trunc(x) {
|
||
|
return x
|
||
|
}
|
||
|
pow := math.Pow10(prec)
|
||
|
intermed := x * pow
|
||
|
if math.IsInf(intermed, 0) {
|
||
|
return x
|
||
|
}
|
||
|
if x < 0 {
|
||
|
x = math.Ceil(intermed - 0.5)
|
||
|
} else {
|
||
|
x = math.Floor(intermed + 0.5)
|
||
|
}
|
||
|
|
||
|
if x == 0 {
|
||
|
return 0
|
||
|
}
|
||
|
|
||
|
return x / pow
|
||
|
}
|
||
|
|
||
|
// RoundEven returns the half even rounded value of x with prec precision.
|
||
|
//
|
||
|
// Special cases are:
|
||
|
// RoundEven(±0) = +0
|
||
|
// RoundEven(±Inf) = ±Inf
|
||
|
// RoundEven(NaN) = NaN
|
||
|
func RoundEven(x float64, prec int) float64 {
|
||
|
if x == 0 {
|
||
|
// Make sure zero is returned
|
||
|
// without the negative bit set.
|
||
|
return 0
|
||
|
}
|
||
|
// Fast path for positive precision on integers.
|
||
|
if prec >= 0 && x == math.Trunc(x) {
|
||
|
return x
|
||
|
}
|
||
|
pow := math.Pow10(prec)
|
||
|
intermed := x * pow
|
||
|
if math.IsInf(intermed, 0) {
|
||
|
return x
|
||
|
}
|
||
|
if isHalfway(intermed) {
|
||
|
correction, _ := math.Modf(math.Mod(intermed, 2))
|
||
|
intermed += correction
|
||
|
if intermed > 0 {
|
||
|
x = math.Floor(intermed)
|
||
|
} else {
|
||
|
x = math.Ceil(intermed)
|
||
|
}
|
||
|
} else {
|
||
|
if x < 0 {
|
||
|
x = math.Ceil(intermed - 0.5)
|
||
|
} else {
|
||
|
x = math.Floor(intermed + 0.5)
|
||
|
}
|
||
|
}
|
||
|
|
||
|
if x == 0 {
|
||
|
return 0
|
||
|
}
|
||
|
|
||
|
return x / pow
|
||
|
}
|
||
|
|
||
|
func isHalfway(x float64) bool {
|
||
|
_, frac := math.Modf(x)
|
||
|
frac = math.Abs(frac)
|
||
|
return frac == 0.5 || (math.Nextafter(frac, math.Inf(-1)) < 0.5 && math.Nextafter(frac, math.Inf(1)) > 0.5)
|
||
|
}
|
||
|
|
||
|
// Same returns true if the input slices have the same length and the all elements
|
||
|
// have the same value with NaN treated as the same.
|
||
|
func Same(s, t []float64) bool {
|
||
|
if len(s) != len(t) {
|
||
|
return false
|
||
|
}
|
||
|
for i, v := range s {
|
||
|
w := t[i]
|
||
|
if v != w && !(math.IsNaN(v) && math.IsNaN(w)) {
|
||
|
return false
|
||
|
}
|
||
|
}
|
||
|
return true
|
||
|
}
|
||
|
|
||
|
// Scale multiplies every element in dst by the scalar c.
|
||
|
func Scale(c float64, dst []float64) {
|
||
|
if len(dst) > 0 {
|
||
|
f64.ScalUnitary(c, dst)
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// ScaleTo multiplies the elements in s by c and stores the result in dst.
|
||
|
func ScaleTo(dst []float64, c float64, s []float64) []float64 {
|
||
|
if len(dst) != len(s) {
|
||
|
panic("floats: lengths of slices do not match")
|
||
|
}
|
||
|
if len(dst) > 0 {
|
||
|
f64.ScalUnitaryTo(dst, c, s)
|
||
|
}
|
||
|
return dst
|
||
|
}
|
||
|
|
||
|
// Span returns a set of N equally spaced points between l and u, where N
|
||
|
// is equal to the length of the destination. The first element of the destination
|
||
|
// is l, the final element of the destination is u.
|
||
|
//
|
||
|
// Panics if len(dst) < 2.
|
||
|
//
|
||
|
// Span also returns the mutated slice dst, so that it can be used in range expressions,
|
||
|
// like:
|
||
|
//
|
||
|
// for i, x := range Span(dst, l, u) { ... }
|
||
|
func Span(dst []float64, l, u float64) []float64 {
|
||
|
n := len(dst)
|
||
|
if n < 2 {
|
||
|
panic("floats: destination must have length >1")
|
||
|
}
|
||
|
|
||
|
// Special cases for Inf and NaN.
|
||
|
switch {
|
||
|
case math.IsNaN(l):
|
||
|
for i := range dst[:len(dst)-1] {
|
||
|
dst[i] = math.NaN()
|
||
|
}
|
||
|
dst[len(dst)-1] = u
|
||
|
return dst
|
||
|
case math.IsNaN(u):
|
||
|
for i := range dst[1:] {
|
||
|
dst[i+1] = math.NaN()
|
||
|
}
|
||
|
dst[0] = l
|
||
|
return dst
|
||
|
case math.IsInf(l, 0) && math.IsInf(u, 0):
|
||
|
for i := range dst[:len(dst)/2] {
|
||
|
dst[i] = l
|
||
|
dst[len(dst)-i-1] = u
|
||
|
}
|
||
|
if len(dst)%2 == 1 {
|
||
|
if l != u {
|
||
|
dst[len(dst)/2] = 0
|
||
|
} else {
|
||
|
dst[len(dst)/2] = l
|
||
|
}
|
||
|
}
|
||
|
return dst
|
||
|
case math.IsInf(l, 0):
|
||
|
for i := range dst[:len(dst)-1] {
|
||
|
dst[i] = l
|
||
|
}
|
||
|
dst[len(dst)-1] = u
|
||
|
return dst
|
||
|
case math.IsInf(u, 0):
|
||
|
for i := range dst[1:] {
|
||
|
dst[i+1] = u
|
||
|
}
|
||
|
dst[0] = l
|
||
|
return dst
|
||
|
}
|
||
|
|
||
|
step := (u - l) / float64(n-1)
|
||
|
for i := range dst {
|
||
|
dst[i] = l + step*float64(i)
|
||
|
}
|
||
|
return dst
|
||
|
}
|
||
|
|
||
|
// Sub subtracts, element-wise, the elements of s from dst. Panics if
|
||
|
// the lengths of dst and s do not match.
|
||
|
func Sub(dst, s []float64) {
|
||
|
if len(dst) != len(s) {
|
||
|
panic("floats: length of the slices do not match")
|
||
|
}
|
||
|
f64.AxpyUnitaryTo(dst, -1, s, dst)
|
||
|
}
|
||
|
|
||
|
// SubTo subtracts, element-wise, the elements of t from s and
|
||
|
// stores the result in dst. Panics if the lengths of s, t and dst do not match.
|
||
|
func SubTo(dst, s, t []float64) []float64 {
|
||
|
if len(s) != len(t) {
|
||
|
panic("floats: length of subtractor and subtractee do not match")
|
||
|
}
|
||
|
if len(dst) != len(s) {
|
||
|
panic("floats: length of destination does not match length of subtractor")
|
||
|
}
|
||
|
f64.AxpyUnitaryTo(dst, -1, t, s)
|
||
|
return dst
|
||
|
}
|
||
|
|
||
|
// Sum returns the sum of the elements of the slice.
|
||
|
func Sum(s []float64) float64 {
|
||
|
return f64.Sum(s)
|
||
|
}
|
||
|
|
||
|
// Within returns the first index i where s[i] <= v < s[i+1]. Within panics if:
|
||
|
// - len(s) < 2
|
||
|
// - s is not sorted
|
||
|
func Within(s []float64, v float64) int {
|
||
|
if len(s) < 2 {
|
||
|
panic("floats: slice length less than 2")
|
||
|
}
|
||
|
if !sort.Float64sAreSorted(s) {
|
||
|
panic("floats: input slice not sorted")
|
||
|
}
|
||
|
if v < s[0] || v >= s[len(s)-1] || math.IsNaN(v) {
|
||
|
return -1
|
||
|
}
|
||
|
for i, f := range s[1:] {
|
||
|
if v < f {
|
||
|
return i
|
||
|
}
|
||
|
}
|
||
|
return -1
|
||
|
}
|