Upgrade blevesearch dependency to v2.0.1 (#14346)

* Upgrade blevesearch dependency to v2.0.1

* Update rupture to v1.0.0

* Fix test

vendor/github.com/blevesearch/bleve/v2/geo/README.md

@@ -0,0 +1,9 @@
+# geo support in bleve
+
+First, all of this geo code is a Go adaptation of the [Lucene 5.3.2 sandbox geo support](https://lucene.apache.org/core/5_3_2/sandbox/org/apache/lucene/util/package-summary.html).
+
+## Notes
+
+- All of the APIs will use float64 for lon/lat values.
+- When describing a point in function arguments or return values, we always use the order lon, lat.
+- High level APIs will use TopLeft and BottomRight to describe bounding boxes.  This may not map cleanly to min/max lon/lat when crossing the dateline.  The lower level APIs will use min/max lon/lat and require the higher-level code to split boxes accordingly.

vendor/github.com/blevesearch/bleve/v2/geo/geo.go

@@ -0,0 +1,210 @@
+//  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 (
+	"fmt"
+	"math"
+
+	"github.com/blevesearch/bleve/v2/numeric"
+)
+
+// GeoBits is the number of bits used for a single geo point
+// Currently this is 32bits for lon and 32bits for lat
+var GeoBits uint = 32
+
+var minLon = -180.0
+var minLat = -90.0
+var maxLon = 180.0
+var maxLat = 90.0
+var minLonRad = minLon * degreesToRadian
+var minLatRad = minLat * degreesToRadian
+var maxLonRad = maxLon * degreesToRadian
+var maxLatRad = maxLat * degreesToRadian
+var geoTolerance = 1e-6
+var lonScale = float64((uint64(0x1)<<GeoBits)-1) / 360.0
+var latScale = float64((uint64(0x1)<<GeoBits)-1) / 180.0
+
+var geoHashMaxLength = 12
+
+// Point represents a geo point.
+type Point struct {
+	Lon float64 `json:"lon"`
+	Lat float64 `json:"lat"`
+}
+
+// MortonHash computes the morton hash value for the provided geo point
+// This point is ordered as lon, lat.
+func MortonHash(lon, lat float64) uint64 {
+	return numeric.Interleave(scaleLon(lon), scaleLat(lat))
+}
+
+func scaleLon(lon float64) uint64 {
+	rv := uint64((lon - minLon) * lonScale)
+	return rv
+}
+
+func scaleLat(lat float64) uint64 {
+	rv := uint64((lat - minLat) * latScale)
+	return rv
+}
+
+// MortonUnhashLon extracts the longitude value from the provided morton hash.
+func MortonUnhashLon(hash uint64) float64 {
+	return unscaleLon(numeric.Deinterleave(hash))
+}
+
+// MortonUnhashLat extracts the latitude value from the provided morton hash.
+func MortonUnhashLat(hash uint64) float64 {
+	return unscaleLat(numeric.Deinterleave(hash >> 1))
+}
+
+func unscaleLon(lon uint64) float64 {
+	return (float64(lon) / lonScale) + minLon
+}
+
+func unscaleLat(lat uint64) float64 {
+	return (float64(lat) / latScale) + minLat
+}
+
+// compareGeo will compare two float values and see if they are the same
+// taking into consideration a known geo tolerance.
+func compareGeo(a, b float64) float64 {
+	compare := a - b
+	if math.Abs(compare) <= geoTolerance {
+		return 0
+	}
+	return compare
+}
+
+// RectIntersects checks whether rectangles a and b intersect
+func RectIntersects(aMinX, aMinY, aMaxX, aMaxY, bMinX, bMinY, bMaxX, bMaxY float64) bool {
+	return !(aMaxX < bMinX || aMinX > bMaxX || aMaxY < bMinY || aMinY > bMaxY)
+}
+
+// RectWithin checks whether box a is within box b
+func RectWithin(aMinX, aMinY, aMaxX, aMaxY, bMinX, bMinY, bMaxX, bMaxY float64) bool {
+	rv := !(aMinX < bMinX || aMinY < bMinY || aMaxX > bMaxX || aMaxY > bMaxY)
+	return rv
+}
+
+// BoundingBoxContains checks whether the lon/lat point is within the box
+func BoundingBoxContains(lon, lat, minLon, minLat, maxLon, maxLat float64) bool {
+	return compareGeo(lon, minLon) >= 0 && compareGeo(lon, maxLon) <= 0 &&
+		compareGeo(lat, minLat) >= 0 && compareGeo(lat, maxLat) <= 0
+}
+
+const degreesToRadian = math.Pi / 180
+const radiansToDegrees = 180 / math.Pi
+
+// DegreesToRadians converts an angle in degrees to radians
+func DegreesToRadians(d float64) float64 {
+	return d * degreesToRadian
+}
+
+// RadiansToDegrees converts an angle in radians to degress
+func RadiansToDegrees(r float64) float64 {
+	return r * radiansToDegrees
+}
+
+var earthMeanRadiusMeters = 6371008.7714
+
+func RectFromPointDistance(lon, lat, dist float64) (float64, float64, float64, float64, error) {
+	err := checkLongitude(lon)
+	if err != nil {
+		return 0, 0, 0, 0, err
+	}
+	err = checkLatitude(lat)
+	if err != nil {
+		return 0, 0, 0, 0, err
+	}
+	radLon := DegreesToRadians(lon)
+	radLat := DegreesToRadians(lat)
+	radDistance := (dist + 7e-2) / earthMeanRadiusMeters
+
+	minLatL := radLat - radDistance
+	maxLatL := radLat + radDistance
+
+	var minLonL, maxLonL float64
+	if minLatL > minLatRad && maxLatL < maxLatRad {
+		deltaLon := asin(sin(radDistance) / cos(radLat))
+		minLonL = radLon - deltaLon
+		if minLonL < minLonRad {
+			minLonL += 2 * math.Pi
+		}
+		maxLonL = radLon + deltaLon
+		if maxLonL > maxLonRad {
+			maxLonL -= 2 * math.Pi
+		}
+	} else {
+		// pole is inside distance
+		minLatL = math.Max(minLatL, minLatRad)
+		maxLatL = math.Min(maxLatL, maxLatRad)
+		minLonL = minLonRad
+		maxLonL = maxLonRad
+	}
+
+	return RadiansToDegrees(minLonL),
+		RadiansToDegrees(maxLatL),
+		RadiansToDegrees(maxLonL),
+		RadiansToDegrees(minLatL),
+		nil
+}
+
+func checkLatitude(latitude float64) error {
+	if math.IsNaN(latitude) || latitude < minLat || latitude > maxLat {
+		return fmt.Errorf("invalid latitude %f; must be between %f and %f", latitude, minLat, maxLat)
+	}
+	return nil
+}
+
+func checkLongitude(longitude float64) error {
+	if math.IsNaN(longitude) || longitude < minLon || longitude > maxLon {
+		return fmt.Errorf("invalid longitude %f; must be between %f and %f", longitude, minLon, maxLon)
+	}
+	return nil
+}
+
+func BoundingRectangleForPolygon(polygon []Point) (
+	float64, float64, float64, float64, error) {
+	err := checkLongitude(polygon[0].Lon)
+	if err != nil {
+		return 0, 0, 0, 0, err
+	}
+	err = checkLatitude(polygon[0].Lat)
+	if err != nil {
+		return 0, 0, 0, 0, err
+	}
+	maxY, minY := polygon[0].Lat, polygon[0].Lat
+	maxX, minX := polygon[0].Lon, polygon[0].Lon
+	for i := 1; i < len(polygon); i++ {
+		err := checkLongitude(polygon[i].Lon)
+		if err != nil {
+			return 0, 0, 0, 0, err
+		}
+		err = checkLatitude(polygon[i].Lat)
+		if err != nil {
+			return 0, 0, 0, 0, err
+		}
+
+		maxY = math.Max(maxY, polygon[i].Lat)
+		minY = math.Min(minY, polygon[i].Lat)
+
+		maxX = math.Max(maxX, polygon[i].Lon)
+		minX = math.Min(minX, polygon[i].Lon)
+	}
+
+	return minX, maxY, maxX, minY, nil
+}

vendor/github.com/blevesearch/bleve/v2/geo/geo_dist.go

@@ -0,0 +1,98 @@
+//  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 (
+	"fmt"
+	"math"
+	"strconv"
+	"strings"
+)
+
+type distanceUnit struct {
+	conv     float64
+	suffixes []string
+}
+
+var inch = distanceUnit{0.0254, []string{"in", "inch"}}
+var yard = distanceUnit{0.9144, []string{"yd", "yards"}}
+var feet = distanceUnit{0.3048, []string{"ft", "feet"}}
+var kilom = distanceUnit{1000, []string{"km", "kilometers"}}
+var nauticalm = distanceUnit{1852.0, []string{"nm", "nauticalmiles"}}
+var millim = distanceUnit{0.001, []string{"mm", "millimeters"}}
+var centim = distanceUnit{0.01, []string{"cm", "centimeters"}}
+var miles = distanceUnit{1609.344, []string{"mi", "miles"}}
+var meters = distanceUnit{1, []string{"m", "meters"}}
+
+var distanceUnits = []*distanceUnit{
+	&inch, &yard, &feet, &kilom, &nauticalm, &millim, &centim, &miles, &meters,
+}
+
+// ParseDistance attempts to parse a distance string and return distance in
+// meters.  Example formats supported:
+// "5in" "5inch" "7yd" "7yards" "9ft" "9feet" "11km" "11kilometers"
+// "3nm" "3nauticalmiles" "13mm" "13millimeters" "15cm" "15centimeters"
+// "17mi" "17miles" "19m" "19meters"
+// If the unit cannot be determined, the entire string is parsed and the
+// unit of meters is assumed.
+// If the number portion cannot be parsed, 0 and the parse error are returned.
+func ParseDistance(d string) (float64, error) {
+	for _, unit := range distanceUnits {
+		for _, unitSuffix := range unit.suffixes {
+			if strings.HasSuffix(d, unitSuffix) {
+				parsedNum, err := strconv.ParseFloat(d[0:len(d)-len(unitSuffix)], 64)
+				if err != nil {
+					return 0, err
+				}
+				return parsedNum * unit.conv, nil
+			}
+		}
+	}
+	// no unit matched, try assuming meters?
+	parsedNum, err := strconv.ParseFloat(d, 64)
+	if err != nil {
+		return 0, err
+	}
+	return parsedNum, nil
+}
+
+// ParseDistanceUnit attempts to parse a distance unit and return the
+// multiplier for converting this to meters.  If the unit cannot be parsed
+// then 0 and the error message is returned.
+func ParseDistanceUnit(u string) (float64, error) {
+	for _, unit := range distanceUnits {
+		for _, unitSuffix := range unit.suffixes {
+			if u == unitSuffix {
+				return unit.conv, nil
+			}
+		}
+	}
+	return 0, fmt.Errorf("unknown distance unit: %s", u)
+}
+
+// Haversin computes the distance between two points.
+// This implemenation uses the sloppy math implemenations which trade off
+// accuracy for performance.  The distance returned is in kilometers.
+func Haversin(lon1, lat1, lon2, lat2 float64) float64 {
+	x1 := lat1 * degreesToRadian
+	x2 := lat2 * degreesToRadian
+	h1 := 1 - cos(x1-x2)
+	h2 := 1 - cos((lon1-lon2)*degreesToRadian)
+	h := (h1 + cos(x1)*cos(x2)*h2) / 2
+	avgLat := (x1 + x2) / 2
+	diameter := earthDiameter(avgLat)
+
+	return diameter * asin(math.Min(1, math.Sqrt(h)))
+}

vendor/github.com/blevesearch/bleve/v2/geo/geohash.go

@@ -0,0 +1,111 @@
+//  Copyright (c) 2019 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.
+// This implementation is inspired from the geohash-js
+// ref: https://github.com/davetroy/geohash-js
+
+package geo
+
+// encoding encapsulates an encoding defined by a given base32 alphabet.
+type encoding struct {
+	enc string
+	dec [256]byte
+}
+
+// newEncoding constructs a new encoding defined by the given alphabet,
+// which must be a 32-byte string.
+func newEncoding(encoder string) *encoding {
+	e := new(encoding)
+	e.enc = encoder
+	for i := 0; i < len(e.dec); i++ {
+		e.dec[i] = 0xff
+	}
+	for i := 0; i < len(encoder); i++ {
+		e.dec[encoder[i]] = byte(i)
+	}
+	return e
+}
+
+// base32encoding with the Geohash alphabet.
+var base32encoding = newEncoding("0123456789bcdefghjkmnpqrstuvwxyz")
+
+var masks = []uint64{16, 8, 4, 2, 1}
+
+// DecodeGeoHash decodes the string geohash faster with
+// higher precision. This api is in experimental phase.
+func DecodeGeoHash(geoHash string) (float64, float64) {
+	even := true
+	lat := []float64{-90.0, 90.0}
+	lon := []float64{-180.0, 180.0}
+
+	for i := 0; i < len(geoHash); i++ {
+		cd := uint64(base32encoding.dec[geoHash[i]])
+		for j := 0; j < 5; j++ {
+			if even {
+				if cd&masks[j] > 0 {
+					lon[0] = (lon[0] + lon[1]) / 2
+				} else {
+					lon[1] = (lon[0] + lon[1]) / 2
+				}
+			} else {
+				if cd&masks[j] > 0 {
+					lat[0] = (lat[0] + lat[1]) / 2
+				} else {
+					lat[1] = (lat[0] + lat[1]) / 2
+				}
+			}
+			even = !even
+		}
+	}
+
+	return (lat[0] + lat[1]) / 2, (lon[0] + lon[1]) / 2
+}
+
+func EncodeGeoHash(lat, lon float64) string {
+	even := true
+	lats := []float64{-90.0, 90.0}
+	lons := []float64{-180.0, 180.0}
+	precision := 12
+	var ch, bit uint64
+	var geoHash string
+
+	for len(geoHash) < precision {
+		if even {
+			mid := (lons[0] + lons[1]) / 2
+			if lon > mid {
+				ch |= masks[bit]
+				lons[0] = mid
+			} else {
+				lons[1] = mid
+			}
+		} else {
+			mid := (lats[0] + lats[1]) / 2
+			if lat > mid {
+				ch |= masks[bit]
+				lats[0] = mid
+			} else {
+				lats[1] = mid
+			}
+		}
+		even = !even
+		if bit < 4 {
+			bit++
+		} else {
+			geoHash += string(base32encoding.enc[ch])
+			ch = 0
+			bit = 0
+		}
+	}
+
+	return geoHash
+}

vendor/github.com/blevesearch/bleve/v2/geo/parse.go

@@ -0,0 +1,181 @@
+//  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 (
+	"reflect"
+	"strconv"
+	"strings"
+)
+
+// ExtractGeoPoint takes an arbitrary interface{} and tries it's best to
+// interpret it is as geo point.  Supported formats:
+// Container:
+// slice length 2 (GeoJSON)
+//  first element lon, second element lat
+// string (coordinates separated by comma, or a geohash)
+//  first element lat, second element lon
+// map[string]interface{}
+//  exact keys lat and lon or lng
+// struct
+//  w/exported fields case-insensitive match on lat and lon or lng
+// struct
+//  satisfying Later and Loner or Lnger interfaces
+//
+// in all cases values must be some sort of numeric-like thing: int/uint/float
+func ExtractGeoPoint(thing interface{}) (lon, lat float64, success bool) {
+	var foundLon, foundLat bool
+
+	thingVal := reflect.ValueOf(thing)
+	if !thingVal.IsValid() {
+		return lon, lat, false
+	}
+
+	thingTyp := thingVal.Type()
+
+	// is it a slice
+	if thingVal.Kind() == reflect.Slice {
+		// must be length 2
+		if thingVal.Len() == 2 {
+			first := thingVal.Index(0)
+			if first.CanInterface() {
+				firstVal := first.Interface()
+				lon, foundLon = extractNumericVal(firstVal)
+			}
+			second := thingVal.Index(1)
+			if second.CanInterface() {
+				secondVal := second.Interface()
+				lat, foundLat = extractNumericVal(secondVal)
+			}
+		}
+	}
+
+	// is it a string
+	if thingVal.Kind() == reflect.String {
+		geoStr := thingVal.Interface().(string)
+		if strings.Contains(geoStr, ",") {
+			// geo point with coordinates split by comma
+			points := strings.Split(geoStr, ",")
+			for i, point := range points {
+				// trim any leading or trailing white spaces
+				points[i] = strings.TrimSpace(point)
+			}
+			if len(points) == 2 {
+				var err error
+				lat, err = strconv.ParseFloat(points[0], 64)
+				if err == nil {
+					foundLat = true
+				}
+				lon, err = strconv.ParseFloat(points[1], 64)
+				if err == nil {
+					foundLon = true
+				}
+			}
+		} else {
+			// geohash
+			if len(geoStr) <= geoHashMaxLength {
+				lat, lon = DecodeGeoHash(geoStr)
+				foundLat = true
+				foundLon = true
+			}
+		}
+	}
+
+	// is it a map
+	if l, ok := thing.(map[string]interface{}); ok {
+		if lval, ok := l["lon"]; ok {
+			lon, foundLon = extractNumericVal(lval)
+		} else if lval, ok := l["lng"]; ok {
+			lon, foundLon = extractNumericVal(lval)
+		}
+		if lval, ok := l["lat"]; ok {
+			lat, foundLat = extractNumericVal(lval)
+		}
+	}
+
+	// now try reflection on struct fields
+	if thingVal.Kind() == reflect.Struct {
+		for i := 0; i < thingVal.NumField(); i++ {
+			fieldName := thingTyp.Field(i).Name
+			if strings.HasPrefix(strings.ToLower(fieldName), "lon") {
+				if thingVal.Field(i).CanInterface() {
+					fieldVal := thingVal.Field(i).Interface()
+					lon, foundLon = extractNumericVal(fieldVal)
+				}
+			}
+			if strings.HasPrefix(strings.ToLower(fieldName), "lng") {
+				if thingVal.Field(i).CanInterface() {
+					fieldVal := thingVal.Field(i).Interface()
+					lon, foundLon = extractNumericVal(fieldVal)
+				}
+			}
+			if strings.HasPrefix(strings.ToLower(fieldName), "lat") {
+				if thingVal.Field(i).CanInterface() {
+					fieldVal := thingVal.Field(i).Interface()
+					lat, foundLat = extractNumericVal(fieldVal)
+				}
+			}
+		}
+	}
+
+	// last hope, some interfaces
+	// lon
+	if l, ok := thing.(loner); ok {
+		lon = l.Lon()
+		foundLon = true
+	} else if l, ok := thing.(lnger); ok {
+		lon = l.Lng()
+		foundLon = true
+	}
+	// lat
+	if l, ok := thing.(later); ok {
+		lat = l.Lat()
+		foundLat = true
+	}
+
+	return lon, lat, foundLon && foundLat
+}
+
+// extract numeric value (if possible) and returns a float64
+func extractNumericVal(v interface{}) (float64, bool) {
+	val := reflect.ValueOf(v)
+	if !val.IsValid() {
+		return 0, false
+	}
+	typ := val.Type()
+	switch typ.Kind() {
+	case reflect.Float32, reflect.Float64:
+		return val.Float(), true
+	case reflect.Int, reflect.Int8, reflect.Int16, reflect.Int32, reflect.Int64:
+		return float64(val.Int()), true
+	case reflect.Uint, reflect.Uint8, reflect.Uint16, reflect.Uint32, reflect.Uint64:
+		return float64(val.Uint()), true
+	}
+
+	return 0, false
+}
+
+// various support interfaces which can be used to find lat/lon
+type loner interface {
+	Lon() float64
+}
+
+type later interface {
+	Lat() float64
+}
+
+type lnger interface {
+	Lng() float64
+}

vendor/github.com/blevesearch/bleve/v2/geo/sloppy.go

@@ -0,0 +1,212 @@
+//  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()
+}