213 lines
7.3 KiB
Go
Vendored
213 lines
7.3 KiB
Go
Vendored
// Copyright (c) 2017 Couchbase, Inc.
|
|
//
|
|
// Licensed under the Apache License, Version 2.0 (the "License");
|
|
// you may not use this file except in compliance with the License.
|
|
// You may obtain a copy of the License at
|
|
//
|
|
// http://www.apache.org/licenses/LICENSE-2.0
|
|
//
|
|
// Unless required by applicable law or agreed to in writing, software
|
|
// distributed under the License is distributed on an "AS IS" BASIS,
|
|
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
// See the License for the specific language governing permissions and
|
|
// limitations under the License.
|
|
|
|
package geo
|
|
|
|
import (
|
|
"math"
|
|
)
|
|
|
|
var earthDiameterPerLatitude []float64
|
|
var sinTab []float64
|
|
var cosTab []float64
|
|
var asinTab []float64
|
|
var asinDer1DivF1Tab []float64
|
|
var asinDer2DivF2Tab []float64
|
|
var asinDer3DivF3Tab []float64
|
|
var asinDer4DivF4Tab []float64
|
|
|
|
const radiusTabsSize = (1 << 10) + 1
|
|
const radiusDelta = (math.Pi / 2) / (radiusTabsSize - 1)
|
|
const radiusIndexer = 1 / radiusDelta
|
|
const sinCosTabsSize = (1 << 11) + 1
|
|
const asinTabsSize = (1 << 13) + 1
|
|
const oneDivF2 = 1 / 2.0
|
|
const oneDivF3 = 1 / 6.0
|
|
const oneDivF4 = 1 / 24.0
|
|
|
|
// 1.57079632673412561417e+00 first 33 bits of pi/2
|
|
var pio2Hi = math.Float64frombits(0x3FF921FB54400000)
|
|
|
|
// 6.07710050650619224932e-11 pi/2 - PIO2_HI
|
|
var pio2Lo = math.Float64frombits(0x3DD0B4611A626331)
|
|
|
|
var asinPio2Hi = math.Float64frombits(0x3FF921FB54442D18) // 1.57079632679489655800e+00
|
|
var asinPio2Lo = math.Float64frombits(0x3C91A62633145C07) // 6.12323399573676603587e-17
|
|
var asinPs0 = math.Float64frombits(0x3fc5555555555555) // 1.66666666666666657415e-01
|
|
var asinPs1 = math.Float64frombits(0xbfd4d61203eb6f7d) // -3.25565818622400915405e-01
|
|
var asinPs2 = math.Float64frombits(0x3fc9c1550e884455) // 2.01212532134862925881e-01
|
|
var asinPs3 = math.Float64frombits(0xbfa48228b5688f3b) // -4.00555345006794114027e-02
|
|
var asinPs4 = math.Float64frombits(0x3f49efe07501b288) // 7.91534994289814532176e-04
|
|
var asinPs5 = math.Float64frombits(0x3f023de10dfdf709) // 3.47933107596021167570e-05
|
|
var asinQs1 = math.Float64frombits(0xc0033a271c8a2d4b) // -2.40339491173441421878e+00
|
|
var asinQs2 = math.Float64frombits(0x40002ae59c598ac8) // 2.02094576023350569471e+00
|
|
var asinQs3 = math.Float64frombits(0xbfe6066c1b8d0159) // -6.88283971605453293030e-01
|
|
var asinQs4 = math.Float64frombits(0x3fb3b8c5b12e9282) // 7.70381505559019352791e-02
|
|
|
|
var twoPiHi = 4 * pio2Hi
|
|
var twoPiLo = 4 * pio2Lo
|
|
var sinCosDeltaHi = twoPiHi/sinCosTabsSize - 1
|
|
var sinCosDeltaLo = twoPiLo/sinCosTabsSize - 1
|
|
var sinCosIndexer = 1 / (sinCosDeltaHi + sinCosDeltaLo)
|
|
var sinCosMaxValueForIntModulo = ((math.MaxInt64 >> 9) / sinCosIndexer) * 0.99
|
|
var asinMaxValueForTabs = math.Sin(73.0 * degreesToRadian)
|
|
|
|
var asinDelta = asinMaxValueForTabs / (asinTabsSize - 1)
|
|
var asinIndexer = 1 / asinDelta
|
|
|
|
func init() {
|
|
// initializes the tables used for the sloppy math functions
|
|
|
|
// sin and cos
|
|
sinTab = make([]float64, sinCosTabsSize)
|
|
cosTab = make([]float64, sinCosTabsSize)
|
|
sinCosPiIndex := (sinCosTabsSize - 1) / 2
|
|
sinCosPiMul2Index := 2 * sinCosPiIndex
|
|
sinCosPiMul05Index := sinCosPiIndex / 2
|
|
sinCosPiMul15Index := 3 * sinCosPiIndex / 2
|
|
for i := 0; i < sinCosTabsSize; i++ {
|
|
// angle: in [0,2*PI].
|
|
angle := float64(i)*sinCosDeltaHi + float64(i)*sinCosDeltaLo
|
|
sinAngle := math.Sin(angle)
|
|
cosAngle := math.Cos(angle)
|
|
// For indexes corresponding to null cosine or sine, we make sure the value is zero
|
|
// and not an epsilon. This allows for a much better accuracy for results close to zero.
|
|
if i == sinCosPiIndex {
|
|
sinAngle = 0.0
|
|
} else if i == sinCosPiMul2Index {
|
|
sinAngle = 0.0
|
|
} else if i == sinCosPiMul05Index {
|
|
sinAngle = 0.0
|
|
} else if i == sinCosPiMul15Index {
|
|
sinAngle = 0.0
|
|
}
|
|
sinTab[i] = sinAngle
|
|
cosTab[i] = cosAngle
|
|
}
|
|
|
|
// asin
|
|
asinTab = make([]float64, asinTabsSize)
|
|
asinDer1DivF1Tab = make([]float64, asinTabsSize)
|
|
asinDer2DivF2Tab = make([]float64, asinTabsSize)
|
|
asinDer3DivF3Tab = make([]float64, asinTabsSize)
|
|
asinDer4DivF4Tab = make([]float64, asinTabsSize)
|
|
for i := 0; i < asinTabsSize; i++ {
|
|
// x: in [0,ASIN_MAX_VALUE_FOR_TABS].
|
|
x := float64(i) * asinDelta
|
|
asinTab[i] = math.Asin(x)
|
|
oneMinusXSqInv := 1.0 / (1 - x*x)
|
|
oneMinusXSqInv05 := math.Sqrt(oneMinusXSqInv)
|
|
oneMinusXSqInv15 := oneMinusXSqInv05 * oneMinusXSqInv
|
|
oneMinusXSqInv25 := oneMinusXSqInv15 * oneMinusXSqInv
|
|
oneMinusXSqInv35 := oneMinusXSqInv25 * oneMinusXSqInv
|
|
asinDer1DivF1Tab[i] = oneMinusXSqInv05
|
|
asinDer2DivF2Tab[i] = (x * oneMinusXSqInv15) * oneDivF2
|
|
asinDer3DivF3Tab[i] = ((1 + 2*x*x) * oneMinusXSqInv25) * oneDivF3
|
|
asinDer4DivF4Tab[i] = ((5 + 2*x*(2+x*(5-2*x))) * oneMinusXSqInv35) * oneDivF4
|
|
}
|
|
|
|
// earth radius
|
|
a := 6378137.0
|
|
b := 6356752.31420
|
|
a2 := a * a
|
|
b2 := b * b
|
|
earthDiameterPerLatitude = make([]float64, radiusTabsSize)
|
|
earthDiameterPerLatitude[0] = 2.0 * a / 1000
|
|
earthDiameterPerLatitude[radiusTabsSize-1] = 2.0 * b / 1000
|
|
for i := 1; i < radiusTabsSize-1; i++ {
|
|
lat := math.Pi * float64(i) / (2*radiusTabsSize - 1)
|
|
one := math.Pow(a2*math.Cos(lat), 2)
|
|
two := math.Pow(b2*math.Sin(lat), 2)
|
|
three := math.Pow(float64(a)*math.Cos(lat), 2)
|
|
four := math.Pow(b*math.Sin(lat), 2)
|
|
radius := math.Sqrt((one + two) / (three + four))
|
|
earthDiameterPerLatitude[i] = 2 * radius / 1000
|
|
}
|
|
}
|
|
|
|
// earthDiameter returns an estimation of the earth's diameter at the specified
|
|
// latitude in kilometers
|
|
func earthDiameter(lat float64) float64 {
|
|
index := math.Mod(math.Abs(lat)*radiusIndexer+0.5, float64(len(earthDiameterPerLatitude)))
|
|
if math.IsNaN(index) {
|
|
return 0
|
|
}
|
|
return earthDiameterPerLatitude[int(index)]
|
|
}
|
|
|
|
var pio2 = math.Pi / 2
|
|
|
|
func sin(a float64) float64 {
|
|
return cos(a - pio2)
|
|
}
|
|
|
|
// cos is a sloppy math (faster) implementation of math.Cos
|
|
func cos(a float64) float64 {
|
|
if a < 0.0 {
|
|
a = -a
|
|
}
|
|
if a > sinCosMaxValueForIntModulo {
|
|
return math.Cos(a)
|
|
}
|
|
// index: possibly outside tables range.
|
|
index := int(a*sinCosIndexer + 0.5)
|
|
delta := (a - float64(index)*sinCosDeltaHi) - float64(index)*sinCosDeltaLo
|
|
// Making sure index is within tables range.
|
|
// Last value of each table is the same than first, so we ignore it (tabs size minus one) for modulo.
|
|
index &= (sinCosTabsSize - 2) // index % (SIN_COS_TABS_SIZE-1)
|
|
indexCos := cosTab[index]
|
|
indexSin := sinTab[index]
|
|
return indexCos + delta*(-indexSin+delta*(-indexCos*oneDivF2+delta*(indexSin*oneDivF3+delta*indexCos*oneDivF4)))
|
|
}
|
|
|
|
// asin is a sloppy math (faster) implementation of math.Asin
|
|
func asin(a float64) float64 {
|
|
var negateResult bool
|
|
if a < 0 {
|
|
a = -a
|
|
negateResult = true
|
|
}
|
|
if a <= asinMaxValueForTabs {
|
|
index := int(a*asinIndexer + 0.5)
|
|
delta := a - float64(index)*asinDelta
|
|
result := asinTab[index] + delta*(asinDer1DivF1Tab[index]+delta*(asinDer2DivF2Tab[index]+delta*(asinDer3DivF3Tab[index]+delta*asinDer4DivF4Tab[index])))
|
|
if negateResult {
|
|
return -result
|
|
}
|
|
return result
|
|
}
|
|
// value > ASIN_MAX_VALUE_FOR_TABS, or value is NaN
|
|
// This part is derived from fdlibm.
|
|
if a < 1 {
|
|
t := (1.0 - a) * 0.5
|
|
p := t * (asinPs0 + t*(asinPs1+t*(asinPs2+t*(asinPs3+t*(asinPs4+t+asinPs5)))))
|
|
q := 1.0 + t*(asinQs1+t*(asinQs2+t*(asinQs3+t*asinQs4)))
|
|
s := math.Sqrt(t)
|
|
z := s + s*(p/q)
|
|
result := asinPio2Hi - ((z + z) - asinPio2Lo)
|
|
if negateResult {
|
|
return -result
|
|
}
|
|
return result
|
|
}
|
|
// value >= 1.0, or value is NaN
|
|
if a == 1.0 {
|
|
if negateResult {
|
|
return -math.Pi / 2
|
|
}
|
|
return math.Pi / 2
|
|
}
|
|
return math.NaN()
|
|
}
|