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Last active August 29, 2015 14:27
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testing d3 v.4 range() method, wait ...
Raw
README.md

These are some tests to check behavior of the d3 range() method when it is used with fractional step sizes.

https://github.com/d3/d3-arrays has the candidate versions for a new release d3. The range() function below is copied over from there.

Raw
index.html
<html>
<body>
<p>
number of unexpected range(0, 1, step) lengths for steps 1/n with n = 1 to
<span id='result1'> </span>.
</p>
<p>with workaround</p>
<p>
number of unexpected range(0, 1-eps, step) lengths for eps=1e<sup>-17</sup> and steps 1/n with n = 1 to
<span id='result2'> </span>.
</p>
<p>
number of unexpected range(0, (1-eps)*max, step) lengths for steps max/n and max = 2<sup>m</sup> with n = 1 to
<span id='result3'> </span>.
</p>
<p>
number of unexpected range(offset, offset + (1-eps)*max, step) lengths for steps max/n, max = 2<sup>m</sup> and offset = 3<sup>m</sup> with n = 1 to
<span id='result4'> </span>.
</p>
number of unexpected range(0, 1-eps, step) lengths for eps=1e<sup>-16</sup> and steps 1/n with n = 1 to
<span id='result2b'> </span>.
</p>
<p>
number of unexpected range(0, (1-eps)*max, step) lengths for steps max/n and max = 2<sup>m</sup> with n = 1 to
<span id='result3b'> </span>.
</p>
<p>
number of unexpected range(offset, offset + (1-eps)*max, step) lengths for steps max/n, max = 2<sup>m</sup> and offset = 3<sup>m</sup> with n = 1 to
<span id='result4b'> </span>.
</p>
<p>
number of unexpected range((1-eps)*offset, (1-eps)*(offset + max), step) lengths for steps max/n, max = 2<sup>m</sup> and offset = 3<sup>m</sup> with n = 1 to
<span id='result4c'> </span>.
</p>
<p>
number of unexpected range((1-eps)*offset, (1-eps)*(offset + max), step) lengths for eps=1e<sup>-10</sup> and steps max/n, max = 2<sup>m</sup> and offset = 3<sup>m</sup> with n = 1 to
<span id='result4d'> </span>.
</p>
<script>
//this is the new range function
function range(start, stop, step) {
if ((n = arguments.length) < 3) {
step = 1;
if (n < 2) {
stop = start;
start = 0;
}
}
var i = -1,
n = Math.max(0, Math.ceil((stop - start) / step)) | 0,
k = scale(Math.abs(step)),
range = new Array(n);
start *= k;
step *= k;
while (++i < n) {
range[i] = (start + i * step) / k;
}
return range;
};
function scale(x) {
var k = 1;
while (x * k % 1) k *= 10;
return k;
};
//test
function collect_mismatches(max_d, eps, eps2, offset, max) {
var mismatches = [];
var max = max;
range(1, max_d).forEach(function(d) {
if (range(offset * (1-eps2), offset * (1-eps2) + max * (1-eps), max/d).length !== d)
{mismatches.push([offset, max, d]);}
});
return mismatches;
};
function mismatches_thru_domains(max_d, eps, eps2, minscale, max_e) {
var collected = [];
range(0, max_e).forEach(function(e) {
var max = Math.pow(2, e);
var min = Math.pow(3, e) * minscale;
collected = collected.concat(collect_mismatches(max_d, eps, eps2, min, max));
});
return collected;
};
var max_denominator = 1000;
var max_expo = 64;
var r1 = collect_mismatches(max_denominator, 0, 0, 0, 1).length;
var r2 = collect_mismatches(max_denominator, 1e-17, 0, 0, 1).length;
var r3 = mismatches_thru_domains(max_denominator, 1e-17, 0, 0, max_expo).length;
var r4 = mismatches_thru_domains(max_denominator, 1e-17, 0, 1, max_expo).length;
var r2b = collect_mismatches(max_denominator, 1e-16, 0, 0, 1).length;
var r3b = mismatches_thru_domains(max_denominator, 1e-16, 0, 0, max_expo).length;
var ar4b = mismatches_thru_domains(max_denominator, 1e-16, 0 , 1, max_expo);
var ar4c = mismatches_thru_domains(max_denominator, 1e-16, 1e-16, 1, max_expo);
var ar4d = mismatches_thru_domains(max_denominator, 1e-10, 1e-10, 1, max_expo);
document.getElementById('result1').textContent = max_denominator + " : " + r1;
document.getElementById('result2').textContent = max_denominator + " : " + r2;
document.getElementById('result3').textContent = max_denominator + " and m = 0 to " + max_expo + " : " + r3;
document.getElementById('result4').textContent = max_denominator + " and m = 0 to " + max_expo + " : " + r4;
document.getElementById('result2b').textContent = max_denominator + " : " + r2b;
document.getElementById('result3b').textContent = max_denominator + " and m = 0 to " + max_expo + " : " + r3b;
document.getElementById('result4b').textContent = max_denominator + " and m = 0 to " + max_expo + " : " + ar4b.length + " ; first: " + ar4b[0];
document.getElementById('result4c').textContent = max_denominator + " and m = 0 to " + max_expo + " : " + ar4c.length + " ; first: " + ar4c[0];
document.getElementById('result4d').textContent = max_denominator + " and m = 0 to " + max_expo + " : " + ar4d.length + " ; first: " + ar4d[0];
</script>
</body>
</html>
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