soumyakanti3578 commented on code in PR #6036:
URL: https://github.com/apache/hive/pull/6036#discussion_r2285881539
##########
ql/src/test/org/apache/hadoop/hive/ql/exec/vector/aggregation/TestVectorAggregation.java:
##########
@@ -314,19 +306,35 @@ private boolean checkDecimal64(boolean tryDecimal64,
TypeInfo typeInfo) {
return result;
}
+ /**
+ * Generate a random number according to a distribution with the following
properties:
+ *
+ * <ul>
+ * <li>the probability decreases linearly from 1 (most probable) to
<code>maxSize</code> (least probable)</li>
+ * <li>1 is <emph>maxSize</emph>-times more likely than
<code>maxSize</code></li>
+ * </ul>
+ *
+ * @return a number from 1 to <code>maxSize</code> (both inclusive)
+ */
public static int getLinearRandomNumber(Random random, int maxSize) {
- //Get a linearly multiplied random number
- int randomMultiplier = maxSize * (maxSize + 1) / 2;
- int randomInt = random.nextInt(randomMultiplier);
-
- //Linearly iterate through the possible values to find the correct one
- int linearRandomNumber = 0;
- for(int i=maxSize; randomInt >= 0; i--){
- randomInt -= i;
- linearRandomNumber++;
- }
-
- return linearRandomNumber;
+ // Explanatory example: maxSize is 4, then the numbers 1 to 4 are
distributed according to
+ // 1:****, 2:***, 3:**, 4:*
+ // The number of stars is a triangular number, so 10 in the example
+ int triangularNumber = maxSize * (maxSize + 1) / 2;
+ // Pick a random star
+ int randomInt = random.nextInt(triangularNumber);
+
+ // Invert the problem: 1:*, 2:**, 3:***, 4:****
+ // So in the example, star index 0 becomes index 9 and vice versa
+ randomInt = triangularNumber - randomInt - 1;
+ // Use the formula for triangular numbers to convert from the star index
to the number
+ // n*(n+1)/2 = s
+ // n*n + n - 2s = 0
+ // then use the greater solution of the quadratic formula
+ // n = ( -1 + sqrt(1-4*1*(-2s)) )/2
+ int n = (int)(-1 + Math.sqrt(1+8* (randomInt)))/2;
Review Comment:
nit: formatting is inconsistent inside `sqrt`; could change to `sqrt(1 + 8 *
randomInt)`
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