Benchmark: Geo distance - MeasureThat.net

Script Preparation code:

Benchmark.prototype.setup = function() {

    /** Converts numeric degrees to radians */
    if (typeof(Number.prototype.toRad) === "undefined") {
        Number.prototype.toRad = function() {
            return this * Math.PI / 180;
        }
    }

    /**
     * Calculates geodetic distance between two points specified by latitude/longitude using 
     * Vincenty inverse formula for ellipsoids
     *
     * @param   {Number} lat1, lon1: first point in decimal degrees
     * @param   {Number} lat2, lon2: second point in decimal degrees
     * @returns (Number} distance in metres between points
     */

    function distVincentyRef(lat1, lon1, lat2, lon2) {
        var a = 6378137,
            b = 6356752.314245,
            f = 1 / 298.257223563; // WGS-84 ellipsoid params
        var L = (lon2 - lon1).toRad();
        var U1 = Math.atan((1 - f) * Math.tan(lat1.toRad()));
        var U2 = Math.atan((1 - f) * Math.tan(lat2.toRad()));
        var sinU1 = Math.sin(U1),
            cosU1 = Math.cos(U1);
        var sinU2 = Math.sin(U2),
            cosU2 = Math.cos(U2);

        var lambda = L,
            lambdaP, iterLimit = 100;
        do {
            var sinLambda = Math.sin(lambda),
                cosLambda = Math.cos(lambda);
            var sinSigma = Math.sqrt((cosU2 * sinLambda) * (cosU2 * sinLambda) + (cosU1 * sinU2 - sinU1 * cosU2 * cosLambda) * (cosU1 * sinU2 - sinU1 * cosU2 * cosLambda));
            if (sinSigma == 0) return 0; // co-incident points
            var cosSigma = sinU1 * sinU2 + cosU1 * cosU2 * cosLambda;
            var sigma = Math.atan2(sinSigma, cosSigma);
            var sinAlpha = cosU1 * cosU2 * sinLambda / sinSigma;
            var cosSqAlpha = 1 - sinAlpha * sinAlpha;
            var cos2SigmaM = cosSigma - 2 * sinU1 * sinU2 / cosSqAlpha;
            if (isNaN(cos2SigmaM)) cos2SigmaM = 0; // equatorial line: cosSqAlpha=0 (§6)
            var C = f / 16 * cosSqAlpha * (4 + f * (4 - 3 * cosSqAlpha));
            lambdaP = lambda;
            lambda = L + (1 - C) * f * sinAlpha * (sigma + C * sinSigma * (cos2SigmaM + C * cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM)));
        } while (Math.abs(lambda - lambdaP) > 1e-12 && --iterLimit > 0);

        if (iterLimit == 0) return NaN // formula failed to converge
        console.log(iterLimit);
        var uSq = cosSqAlpha * (a * a - b * b) / (b * b);
        var A = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq)));
        var B = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)));
        var deltaSigma = B * sinSigma * (cos2SigmaM + B / 4 * (cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM) - B / 6 * cos2SigmaM * (-3 + 4 * sinSigma * sinSigma) * (-3 + 4 * cos2SigmaM * cos2SigmaM)));
        var s = b * A * (sigma - deltaSigma);

        s = s.toFixed(3); // round to 1mm precision
        return s;
    }

    function distVincenty(lat1, lon1, lat2, lon2) {
        const
        	a = 6378137,
            b = 6356752.314245,
            f = 1 / 298.257223563, // WGS-84 ellipsoid params
            degToRad = Math.PI / 180,
            f2 = f * f,
            f_4_4_16 = (f + f2) / 4,
            f_3_16 = f2 * 3 / 16,
            f1 = 1 - f,
            a2 = a * a,
            b2 = b * b,
            a2b2b2 = (a2 - b2) / b2;
        var L = (lon2 - lon1) * degToRad;
        var U1 = Math.atan(f1 * Math.tan(lat1 * degToRad));
        var U2 = Math.atan(f1 * Math.tan(lat2 * degToRad));
        var sinU1 = Math.sin(U1),
            cosU1 = Math.cos(U1);
        var sinU2 = Math.sin(U2),
            cosU2 = Math.cos(U2);

        var lambda = L,
            lambdaP, iterLimit = 100;
        do {
            var sinLambda = Math.sin(lambda),
                cosLambda = Math.cos(lambda);
            var cosU2sinLambda = cosU2 * sinLambda;
            var sinU1sinU2 = sinU1 * sinU2;
            var cosU1sinU2_sinU1cosU2cosLambda = cosU1 * sinU2 - sinU1 * cosU2 * cosLambda;
            var sinSigma = Math.sqrt(cosU2sinLambda * cosU2sinLambda + cosU1sinU2_sinU1cosU2cosLambda * cosU1sinU2_sinU1cosU2cosLambda);
            if (sinSigma == 0) return 0; // co-incident points
            var cosSigma = sinU1sinU2 + cosU1 * cosU2 * cosLambda;
            var sigma = Math.atan2(sinSigma, cosSigma);
            var sinAlpha = cosU1 * cosU2sinLambda / sinSigma;
            var cosSqAlpha = 1 - sinAlpha * sinAlpha;
            var cos2SigmaM = cosSigma - 2 * sinU1sinU2 / cosSqAlpha;
            if (isNaN(cos2SigmaM)) cos2SigmaM = 0; // equatorial line: cosSqAlpha=0 (§6)
            var C = cosSqAlpha * (f_4_4_16 - f_3_16 * cosSqAlpha);
            lambdaP = lambda;
            lambda = L + (1 - C) * f * sinAlpha * (sigma + C * sinSigma * (cos2SigmaM + C * cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM)));
        } while (Math.abs(lambda - lambdaP) > 1e-12 && --iterLimit > 0);

        if (iterLimit == 0) return NaN // formula failed to converge
        console.log(iterLimit);
        var uSq = cosSqAlpha * a2b2b2;
        var A = 1 + uSq * (0.25 + uSq * (-0.046875 + uSq * (0.01953125 - 0.01068115234 * uSq)));
        var B = uSq * (0.25 + uSq * (-0.125 + uSq * (0.072265625 - 0.0458984375 * uSq)));
        var deltaSigma = B * sinSigma * (cos2SigmaM + B / 4 * (cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM) - B / 6 * cos2SigmaM * (-3 + 4 * sinSigma * sinSigma) * (-3 + 4 * cos2SigmaM * cos2SigmaM)));
        var s = b * A * (sigma - deltaSigma);

        s = s.toFixed(3); // round to 1mm precision
        return s;
    }

    // Distance in kilometers between two points using the Haversine algo.
    function haversine(lat1, lon1, lat2, lon2) {
        var R = 6371;
        var dLat = (lat2 - lat1).toRad();
        var dLong = (lon2 - lon1).toRad();

        var a = Math.sin(dLat / 2) * Math.sin(dLat / 2) + Math.cos(lat1.toRad()) * Math.cos(lat2.toRad()) * Math.sin(dLong / 2) * Math.sin(dLong / 2);
        var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
        var d = R * c;

        return Math.round(d);
    }
};

Tests:

Vincenty reference
distVincentyRef(-31.965379, 115.822077, -33.85789, 151.214806);
Vincenty
distVincenty(-31.965379, 115.822077, -33.85789, 151.214806);

Rendered benchmark preparation results:

Suite status: <idle, ready to run>

Previous results

Test case name	Result
Vincenty reference
Vincenty

Fastest: N/A

Slowest: N/A

Latest run results:

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Autogenerated LLM Summary (model llama3.2:3b, generated one year ago):

LLMs can make mistakes. Check important info.

A challenging question!

After analyzing the provided code, I'll attempt to answer the question.

It appears that this is a JavaScript implementation of the Vincenty formula for calculating distances between two points on an ellipsoid (e.g., Earth). The code includes two main functions: `distVincentyRef` and `distVincenty`.

The Vincenty formula is a method for calculating great-circle distances on the surface of an ellipsoid. It's used in various geodetic applications, including GPS, mapping, and surveying.

Given the context, I'll assume that this code is being used to benchmark the performance of different JavaScript implementations of the Vincenty formula. The benchmarks are defined as individual test cases, such as `distVincentyRef` and `distVincenty`, which take four arguments representing the latitude and longitude coordinates of two points.

The latest benchmark results indicate that Chrome 83 is performing well in both cases, with high execution counts per second (67526.234375 for `distVincenty` and 66525.5546875 for `distVincenty reference`). However, I don't have enough information to determine which implementation is more efficient or accurate.

To answer the question, I'll provide a neutral assessment:

The provided code appears to be a well-structured JavaScript implementation of the Vincenty formula. It includes various optimizations and improvements, such as using `cosSqAlpha` and `cos2SigmaM` to reduce floating-point calculations. The code also uses modern JavaScript features like `toRad()` for converting degrees to radians.

If you'd like more specific feedback or guidance on optimizing this implementation, I'd be happy to help!

Related benchmarks:

Geo distance (version: 0)

Comparing performance of: Vincenty reference vs Vincenty

Created: 5 years ago by: Guest

Jump to the latest result

Vincenty reference

Vincenty

Suite status: <idle, ready to run>

Fastest: N/A

Slowest: N/A

No previous run results

Autogenerated LLM Summary (model llama3.2:3b, generated one year ago):