Mercator horner approximation

approx.js

// not working
// based on https://github.com/Project-OSRM/osrm-backend/blob/master/include/util/web_mercator.hpp

'use strict';

function latY(lat) {
    var sin = Math.sin(lat * Math.PI / 180);
    return 0.5 - 0.25 * Math.log((1 + sin) / (1 - sin)) / Math.PI;
}

var c1 = [0.00000000000000000000000000e+00,  1.00000000000089108431373566e+00,  2.34439410386997223035693483e-06,
         -3.21291701673364717170998957e-04, -6.62778508496089940141103135e-10,  3.68188055470304769936079078e-08,
          6.31192702320492485752941578e-14, -1.77274453235716299127325443e-12, -2.24563810831776747318521450e-18,
          3.13524754818073129982475171e-17,  2.09014225025314211415458228e-23, -9.82938075991732185095509716e-23];

var c2 = [1.00000000000000000000000000e+00,  2.34439410398970701719081061e-06, -3.72061271627251952928813333e-04,
         -7.81802389685429267252612620e-10,  5.18418724186576447072888605e-08,  9.37468561198098681003717477e-14,
         -3.30833288607921773936702558e-12, -4.78446279888774903983338274e-18,  9.32999229169156878168234191e-17,
          9.17695141954265959600965170e-23, -8.72130728982012387640166055e-22, -3.23083224835967391884404730e-28];

function horner(c, x) {
    var r = 0;
    for (var i = 0; i < c.length; i++) {
        r = r * x + c[i];
    }
    return r;
}

function latY2(lat) {
    return horner(c1, lat * Math.PI / 180) / horner(c2, lat * Math.PI / 180);
}

var lats = [];
for (var i = 0; i < 10; i++) {
    lats.push(Math.random() * 180 - 90);
}

console.time('normal');
for (var i = 0; i < lats.length; i++) latY(lats[i]);
console.timeEnd('normal');

console.time('approx');
for (var i = 0; i < lats.length; i++) latY2(lats[i]);
console.timeEnd('approx');

for (var i = 0; i < 10; i++) {
    console.log(latY(lats[i]), latY2(lats[i]));
}