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