tile38/cmd/tile38-benchmark/main.go

635 lines
20 KiB
Go

package main
import (
"fmt"
"math"
"math/rand"
"net"
"os"
"strconv"
"strings"
"sync/atomic"
"time"
"github.com/tidwall/redbench"
"github.com/tidwall/tile38/core"
)
var (
hostname = "127.0.0.1"
port = 9851
clients = 50
requests = 100000
quiet = false
pipeline = 1
csv = false
json = false
tests = "PING,SET,GET,INTERSECTS,WITHIN,NEARBY,EVAL"
redis = false
)
var addr string
func showHelp() bool {
gitsha := ""
if core.GitSHA == "" || core.GitSHA == "0000000" {
gitsha = ""
} else {
gitsha = " (git:" + core.GitSHA + ")"
}
fmt.Fprintf(os.Stdout, "tile38-benchmark %s%s\n\n", core.Version, gitsha)
fmt.Fprintf(os.Stdout, "Usage: tile38-benchmark [-h <host>] [-p <port>] [-c <clients>] [-n <requests>]\n")
fmt.Fprintf(os.Stdout, " -h <hostname> Server hostname (default: %s)\n", hostname)
fmt.Fprintf(os.Stdout, " -p <port> Server port (default: %d)\n", port)
fmt.Fprintf(os.Stdout, " -c <clients> Number of parallel connections (default %d)\n", clients)
fmt.Fprintf(os.Stdout, " -n <requests> Total number or requests (default %d)\n", requests)
fmt.Fprintf(os.Stdout, " -q Quiet. Just show query/sec values\n")
fmt.Fprintf(os.Stdout, " -P <numreq> Pipeline <numreq> requests. Default 1 (no pipeline).\n")
fmt.Fprintf(os.Stdout, " -t <tests> Only run the comma separated list of tests. The test\n")
fmt.Fprintf(os.Stdout, " names are the same as the ones produced as output.\n")
fmt.Fprintf(os.Stdout, " --csv Output in CSV format.\n")
fmt.Fprintf(os.Stdout, " --json Request JSON responses (default is RESP output)\n")
fmt.Fprintf(os.Stdout, " --redis Runs against a Redis server\n")
fmt.Fprintf(os.Stdout, "\n")
return false
}
func parseArgs() bool {
defer func() {
if v := recover(); v != nil {
if v, ok := v.(string); ok && v == "bad arg" {
showHelp()
}
}
}()
args := os.Args[1:]
readArg := func(arg string) string {
if len(args) == 0 {
panic("bad arg")
}
var narg = args[0]
args = args[1:]
return narg
}
readIntArg := func(arg string) int {
n, err := strconv.ParseUint(readArg(arg), 10, 64)
if err != nil {
panic("bad arg")
}
return int(n)
}
badArg := func(arg string) bool {
fmt.Fprintf(os.Stderr, "Unrecognized option or bad number of args for: '%s'\n", arg)
return false
}
for len(args) > 0 {
arg := readArg("")
if arg == "--help" || arg == "-?" {
return showHelp()
}
if !strings.HasPrefix(arg, "-") {
args = append([]string{arg}, args...)
break
}
switch arg {
default:
return badArg(arg)
case "-h":
hostname = readArg(arg)
case "-p":
port = readIntArg(arg)
case "-c":
clients = readIntArg(arg)
if clients <= 0 {
clients = 1
}
case "-n":
requests = readIntArg(arg)
if requests <= 0 {
requests = 0
}
case "-q":
quiet = true
case "-P":
pipeline = readIntArg(arg)
if pipeline <= 0 {
pipeline = 1
}
case "-t":
tests = readArg(arg)
case "--csv":
csv = true
case "--json":
json = true
case "--redis":
redis = true
}
}
return true
}
func fillOpts() *redbench.Options {
opts := *redbench.DefaultOptions
opts.CSV = csv
opts.Clients = clients
opts.Pipeline = pipeline
opts.Quiet = quiet
opts.Requests = requests
opts.Stderr = os.Stderr
opts.Stdout = os.Stdout
return &opts
}
func randPoint() (lat, lon float64) {
return rand.Float64()*180 - 90, rand.Float64()*360 - 180
}
func isValidRect(minlat, minlon, maxlat, maxlon float64) bool {
return minlat > -90 && maxlat < 90 && minlon > -180 && maxlon < 180
}
func randRect(meters float64) (minlat, minlon, maxlat, maxlon float64) {
for {
lat, lon := randPoint()
maxlat, _ = destinationPoint(lat, lon, meters, 0)
_, maxlon = destinationPoint(lat, lon, meters, 90)
minlat, _ = destinationPoint(lat, lon, meters, 180)
_, minlon = destinationPoint(lat, lon, meters, 270)
if isValidRect(minlat, minlon, maxlat, maxlon) {
return
}
}
}
func prepFn(conn net.Conn) bool {
if json {
conn.Write([]byte("output json\r\n"))
resp := make([]byte, 100)
conn.Read(resp)
}
return true
}
func main() {
rand.Seed(time.Now().UnixNano())
if !parseArgs() {
return
}
opts := fillOpts()
addr = fmt.Sprintf("%s:%d", hostname, port)
for _, test := range strings.Split(tests, ",") {
switch strings.ToUpper(strings.TrimSpace(test)) {
case "PING":
redbench.Bench("PING", addr, opts, prepFn,
func(buf []byte) []byte {
return redbench.AppendCommand(buf, "PING")
},
)
case "GEOADD":
//GEOADD key longitude latitude member
if redis {
var i int64
redbench.Bench("GEOADD", addr, opts, prepFn,
func(buf []byte) []byte {
i := atomic.AddInt64(&i, 1)
lat, lon := randPoint()
return redbench.AppendCommand(buf, "GEOADD", "key:bench",
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
"id:"+strconv.FormatInt(i, 10),
)
},
)
}
case "SET", "SET-POINT", "SET-RECT", "SET-STRING":
if redis {
redbench.Bench("SET", addr, opts, prepFn,
func(buf []byte) []byte {
return redbench.AppendCommand(buf, "SET", "key:__rand_int__", "xxx")
},
)
} else {
var i int64
switch strings.ToUpper(strings.TrimSpace(test)) {
case "SET", "SET-POINT":
redbench.Bench("SET (point)", addr, opts, prepFn,
func(buf []byte) []byte {
i := atomic.AddInt64(&i, 1)
lat, lon := randPoint()
return redbench.AppendCommand(buf, "SET", "key:bench", "id:"+strconv.FormatInt(i, 10), "POINT",
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
)
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "SET", "SET-RECT":
redbench.Bench("SET (rect)", addr, opts, prepFn,
func(buf []byte) []byte {
i := atomic.AddInt64(&i, 1)
minlat, minlon, maxlat, maxlon := randRect(10000)
return redbench.AppendCommand(buf, "SET", "key:bench", "id:"+strconv.FormatInt(i, 10), "BOUNDS",
strconv.FormatFloat(minlat, 'f', 5, 64),
strconv.FormatFloat(minlon, 'f', 5, 64),
strconv.FormatFloat(maxlat, 'f', 5, 64),
strconv.FormatFloat(maxlon, 'f', 5, 64),
)
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "SET", "SET-STRING":
redbench.Bench("SET (string)", addr, opts, prepFn,
func(buf []byte) []byte {
i := atomic.AddInt64(&i, 1)
return redbench.AppendCommand(buf, "SET", "key:bench", "id:"+strconv.FormatInt(i, 10), "STRING", "xxx")
},
)
}
}
case "GET":
if redis {
redbench.Bench("GET", addr, opts, prepFn,
func(buf []byte) []byte {
return redbench.AppendCommand(buf, "GET", "key:__rand_int__")
},
)
} else {
var i int64
redbench.Bench("GET (point)", addr, opts, prepFn,
func(buf []byte) []byte {
i := atomic.AddInt64(&i, 1)
return redbench.AppendCommand(buf, "GET", "key:bench", "id:"+strconv.FormatInt(i, 10), "POINT")
},
)
redbench.Bench("GET (rect)", addr, opts, prepFn,
func(buf []byte) []byte {
i := atomic.AddInt64(&i, 1)
return redbench.AppendCommand(buf, "GET", "key:bench", "id:"+strconv.FormatInt(i, 10), "BOUNDS")
},
)
redbench.Bench("GET (string)", addr, opts, prepFn,
func(buf []byte) []byte {
i := atomic.AddInt64(&i, 1)
return redbench.AppendCommand(buf, "GET", "key:bench", "id:"+strconv.FormatInt(i, 10), "OBJECT")
},
)
}
case "INTERSECTS",
"INTERSECTS-RECT", "INTERSECTS-RECT-1000", "INTERSECTS-RECT-10000", "INTERSECTS-RECT-100000",
"INTERSECTS-CIRCLE", "INTERSECTS-CIRCLE-1000", "INTERSECTS-CIRCLE-10000", "INTERSECTS-CIRCLE-100000":
if redis {
break
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "INTERSECTS", "INTERSECTS-CIRCLE", "INTERSECTS-CIRCLE-1000":
redbench.Bench("INTERSECTS (intersects-circle 1km)", addr, opts, prepFn,
func(buf []byte) []byte {
lat, lon := randPoint()
return redbench.AppendCommand(buf,
"INTERSECTS", "key:bench", "COUNT", "CIRCLE",
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
"1000")
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "INTERSECTS", "INTERSECTS-CIRCLE", "INTERSECTS-CIRCLE-10000":
redbench.Bench("INTERSECTS (intersects-circle 10km)", addr, opts, prepFn,
func(buf []byte) []byte {
lat, lon := randPoint()
return redbench.AppendCommand(buf,
"INTERSECTS", "key:bench", "COUNT", "CIRCLE",
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
"10000")
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "INTERSECTS", "INTERSECTS-CIRCLE", "INTERSECTS-CIRCLE-100000":
redbench.Bench("INTERSECTS (intersects-circle 100km)", addr, opts, prepFn,
func(buf []byte) []byte {
lat, lon := randPoint()
return redbench.AppendCommand(buf,
"INTERSECTS", "key:bench", "COUNT", "CIRCLE",
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
"100000")
},
)
}
// INTERSECTS-BOUNDS
switch strings.ToUpper(strings.TrimSpace(test)) {
case "INTERSECTS", "INTERSECTS-BOUNDS", "INTERSECTS-BOUNDS-1000":
minlat, minlon, maxlat, maxlon := randRect(1000)
redbench.Bench("INTERSECTS (intersects-bounds 1km)", addr, opts, prepFn,
func(buf []byte) []byte {
return redbench.AppendCommand(buf,
"INTERSECTS", "key:bench", "COUNT", "BOUNDS",
strconv.FormatFloat(minlat, 'f', 5, 64),
strconv.FormatFloat(minlon, 'f', 5, 64),
strconv.FormatFloat(maxlat, 'f', 5, 64),
strconv.FormatFloat(maxlon, 'f', 5, 64))
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "INTERSECTS", "INTERSECTS-BOUNDS", "INTERSECTS-BOUNDS-10000":
minlat, minlon, maxlat, maxlon := randRect(10000)
redbench.Bench("INTERSECTS (intersects-bounds 10km)", addr, opts, prepFn,
func(buf []byte) []byte {
return redbench.AppendCommand(buf,
"INTERSECTS", "key:bench", "COUNT", "BOUNDS",
strconv.FormatFloat(minlat, 'f', 5, 64),
strconv.FormatFloat(minlon, 'f', 5, 64),
strconv.FormatFloat(maxlat, 'f', 5, 64),
strconv.FormatFloat(maxlon, 'f', 5, 64))
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "INTERSECTS", "INTERSECTS-BOUNDS", "INTERSECTS-BOUNDS-100000":
minlat, minlon, maxlat, maxlon := randRect(10000)
redbench.Bench("INTERSECTS (intersects-bounds 100km)", addr, opts, prepFn,
func(buf []byte) []byte {
return redbench.AppendCommand(buf,
"INTERSECTS", "key:bench", "COUNT", "BOUNDS",
strconv.FormatFloat(minlat, 'f', 5, 64),
strconv.FormatFloat(minlon, 'f', 5, 64),
strconv.FormatFloat(maxlat, 'f', 5, 64),
strconv.FormatFloat(maxlon, 'f', 5, 64))
},
)
}
case "WITHIN",
"WITHIN-RECT", "WITHIN-RECT-1000", "WITHIN-RECT-10000", "WITHIN-RECT-100000",
"WITHIN-CIRCLE", "WITHIN-CIRCLE-1000", "WITHIN-CIRCLE-10000", "WITHIN-CIRCLE-100000":
if redis {
break
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "WITHIN", "WITHIN-CIRCLE", "WITHIN-CIRCLE-1000":
redbench.Bench("WITHIN (within-circle 1km)", addr, opts, prepFn,
func(buf []byte) []byte {
lat, lon := randPoint()
return redbench.AppendCommand(buf,
"WITHIN", "key:bench", "COUNT", "CIRCLE",
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
"1000")
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "WITHIN", "WITHIN-CIRCLE", "WITHIN-CIRCLE-10000":
redbench.Bench("WITHIN (within-circle 10km)", addr, opts, prepFn,
func(buf []byte) []byte {
lat, lon := randPoint()
return redbench.AppendCommand(buf,
"WITHIN", "key:bench", "COUNT", "CIRCLE",
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
"10000")
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "WITHIN", "WITHIN-CIRCLE", "WITHIN-CIRCLE-100000":
redbench.Bench("WITHIN (within-circle 100km)", addr, opts, prepFn,
func(buf []byte) []byte {
lat, lon := randPoint()
return redbench.AppendCommand(buf,
"WITHIN", "key:bench", "COUNT", "CIRCLE",
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
"100000")
},
)
}
// WITHIN-BOUNDS
switch strings.ToUpper(strings.TrimSpace(test)) {
case "WITHIN", "WITHIN-BOUNDS", "WITHIN-BOUNDS-1000":
minlat, minlon, maxlat, maxlon := randRect(1000)
redbench.Bench("WITHIN (within-bounds 1km)", addr, opts, prepFn,
func(buf []byte) []byte {
return redbench.AppendCommand(buf,
"WITHIN", "key:bench", "COUNT", "BOUNDS",
strconv.FormatFloat(minlat, 'f', 5, 64),
strconv.FormatFloat(minlon, 'f', 5, 64),
strconv.FormatFloat(maxlat, 'f', 5, 64),
strconv.FormatFloat(maxlon, 'f', 5, 64))
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "WITHIN", "WITHIN-BOUNDS", "WITHIN-BOUNDS-10000":
minlat, minlon, maxlat, maxlon := randRect(10000)
redbench.Bench("WITHIN (within-bounds 10km)", addr, opts, prepFn,
func(buf []byte) []byte {
return redbench.AppendCommand(buf,
"WITHIN", "key:bench", "COUNT", "BOUNDS",
strconv.FormatFloat(minlat, 'f', 5, 64),
strconv.FormatFloat(minlon, 'f', 5, 64),
strconv.FormatFloat(maxlat, 'f', 5, 64),
strconv.FormatFloat(maxlon, 'f', 5, 64))
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "WITHIN", "WITHIN-BOUNDS", "WITHIN-BOUNDS-100000":
minlat, minlon, maxlat, maxlon := randRect(10000)
redbench.Bench("WITHIN (within-bounds 100km)", addr, opts, prepFn,
func(buf []byte) []byte {
return redbench.AppendCommand(buf,
"WITHIN", "key:bench", "COUNT", "BOUNDS",
strconv.FormatFloat(minlat, 'f', 5, 64),
strconv.FormatFloat(minlon, 'f', 5, 64),
strconv.FormatFloat(maxlat, 'f', 5, 64),
strconv.FormatFloat(maxlon, 'f', 5, 64))
},
)
}
case "NEARBY",
"NEARBY-KNN", "NEARBY-KNN-1", "NEARBY-KNN-10", "NEARBY-KNN-100",
"NEARBY-POINT", "NEARBY-POINT-1000", "NEARBY-POINT-10000", "NEARBY-POINT-100000":
if redis {
break
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "NEARBY", "NEARBY-KNN", "NEARBY-KNN-1":
redbench.Bench("NEARBY (limit 1)", addr, opts, prepFn,
func(buf []byte) []byte {
lat, lon := randPoint()
return redbench.AppendCommand(buf,
"NEARBY", "key:bench", "LIMIT", "1", "COUNT", "POINT",
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
)
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "NEARBY", "NEARBY-KNN", "NEARBY-KNN-10":
redbench.Bench("NEARBY (limit 10)", addr, opts, prepFn,
func(buf []byte) []byte {
lat, lon := randPoint()
return redbench.AppendCommand(buf,
"NEARBY", "key:bench", "LIMIT", "10", "COUNT", "POINT",
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
)
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "NEARBY", "NEARBY-KNN", "NEARBY-KNN-100":
redbench.Bench("NEARBY (limit 100)", addr, opts, prepFn,
func(buf []byte) []byte {
lat, lon := randPoint()
return redbench.AppendCommand(buf,
"NEARBY", "key:bench", "LIMIT", "100", "COUNT", "POINT",
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
)
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "NEARBY", "NEARBY-POINT", "NEARBY-POINT-1000":
redbench.Bench("NEARBY (point 1km)", addr, opts, prepFn,
func(buf []byte) []byte {
lat, lon := randPoint()
return redbench.AppendCommand(buf,
"NEARBY", "key:bench", "COUNT", "POINT",
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
"1000",
)
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "NEARBY", "NEARBY-POINT", "NEARBY-POINT-10000":
redbench.Bench("NEARBY (point 10km)", addr, opts, prepFn,
func(buf []byte) []byte {
lat, lon := randPoint()
return redbench.AppendCommand(buf,
"NEARBY", "key:bench", "COUNT", "POINT",
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
"10000",
)
},
)
}
switch strings.ToUpper(strings.TrimSpace(test)) {
case "NEARBY", "NEARBY-POINT", "NEARBY-POINT-100000":
redbench.Bench("NEARBY (point 100km)", addr, opts, prepFn,
func(buf []byte) []byte {
lat, lon := randPoint()
return redbench.AppendCommand(buf,
"NEARBY", "key:bench", "COUNT", "POINT",
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
"100000",
)
},
)
}
case "EVAL":
if !redis {
var i int64
get_script := "return tile38.call('GET', KEYS[1], ARGV[1], 'point')"
get4_script :=
"a = tile38.call('GET', KEYS[1], ARGV[1], 'point');" +
"b = tile38.call('GET', KEYS[1], ARGV[2], 'point');" +
"c = tile38.call('GET', KEYS[1], ARGV[3], 'point');" +
"d = tile38.call('GET', KEYS[1], ARGV[4], 'point');" +
"return d"
set_script := "return tile38.call('SET', KEYS[1], ARGV[1], 'point', ARGV[2], ARGV[3])"
if !opts.Quiet {
fmt.Println("Scripts to run:")
fmt.Println("GET SCRIPT: " + get_script)
fmt.Println("GET FOUR SCRIPT: " + get4_script)
fmt.Println("SET SCRIPT: " + set_script)
}
redbench.Bench("EVAL (set point)", addr, opts, prepFn,
func(buf []byte) []byte {
i := atomic.AddInt64(&i, 1)
lat, lon := randPoint()
return redbench.AppendCommand(buf, "EVAL", set_script, "1",
"key:bench",
"id:"+strconv.FormatInt(i, 10),
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
)
},
)
redbench.Bench("EVALNA (set point)", addr, opts, prepFn,
func(buf []byte) []byte {
i := atomic.AddInt64(&i, 1)
lat, lon := randPoint()
return redbench.AppendCommand(buf, "EVALNA", set_script, "1",
"key:bench",
"id:"+strconv.FormatInt(i, 10),
strconv.FormatFloat(lat, 'f', 5, 64),
strconv.FormatFloat(lon, 'f', 5, 64),
)
},
)
redbench.Bench("EVALRO (get point)", addr, opts, prepFn,
func(buf []byte) []byte {
i := atomic.AddInt64(&i, 1)
return redbench.AppendCommand(buf, "EVALRO", get_script, "1", "key:bench", "id:"+strconv.FormatInt(i, 10))
},
)
redbench.Bench("EVALRO (get 4 points)", addr, opts, prepFn,
func(buf []byte) []byte {
i := atomic.AddInt64(&i, 1)
return redbench.AppendCommand(buf, "EVALRO", get4_script, "1",
"key:bench",
"id:"+strconv.FormatInt(i, 10),
"id:"+strconv.FormatInt(i+1, 10),
"id:"+strconv.FormatInt(i+2, 10),
"id:"+strconv.FormatInt(i+3, 10),
)
},
)
redbench.Bench("EVALNA (get point)", addr, opts, prepFn,
func(buf []byte) []byte {
i := atomic.AddInt64(&i, 1)
return redbench.AppendCommand(buf, "EVALNA", get_script, "1", "key:bench", "id:"+strconv.FormatInt(i, 10))
},
)
}
}
}
}
const earthRadius = 6371e3
func toRadians(deg float64) float64 { return deg * math.Pi / 180 }
func toDegrees(rad float64) float64 { return rad * 180 / math.Pi }
// destinationPoint return the destination from a point based on a distance and bearing.
func destinationPoint(lat, lon, meters, bearingDegrees float64) (destLat, destLon float64) {
// see http://williams.best.vwh.net/avform.htm#LL
δ := meters / earthRadius // angular distance in radians
θ := toRadians(bearingDegrees)
φ1 := toRadians(lat)
λ1 := toRadians(lon)
φ2 := math.Asin(math.Sin(φ1)*math.Cos(δ) + math.Cos(φ1)*math.Sin(δ)*math.Cos(θ))
λ2 := λ1 + math.Atan2(math.Sin(θ)*math.Sin(δ)*math.Cos(φ1), math.Cos(δ)-math.Sin(φ1)*math.Sin(φ2))
λ2 = math.Mod(λ2+3*math.Pi, 2*math.Pi) - math.Pi // normalise to -180..+180°
return toDegrees(φ2), toDegrees(λ2)
}