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// `var` -> a variable
// `$var` -> the double precision approximation to `var`
// `_var` -> the absolute value of $var (a prefix underscore on a variable means absolute value)
// `var_` -> the error in var (a postfix underscore means error bound but should still be multiplied by 3*γ²)
// `_var_` -> means both absolute value and absolute error bound
// recall: `a*b`, where both `a` and `b` have errors |a| and |b| we get for the
//   * error bound of (a*b) === a_|b| + |a|b_ + |a*b|   (when either of a and b is double)
//   * error bound of (a*b) === a_|b| + |a|b_ + 2|a*b|  (when both a and b is double-double)
//   * error bound of (a+b) === a_ + b_ + |a+b|         (when a and/or b is double or double-double)
// * the returned errors need to be multiplied by 3γ² to get the true error
// * can use either `$var` or `var[var.length-1]` (the approx value) in error calculations
//   due to multiplication by 3*γ² and not 3*u²
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// examples: (all?)
// ----------------
// let qmd === ddMultDouble2, etc.
//
// ---------------
// 1. double-double X by double
// ---------------
// qmd(a,b);  // both `a` and `b` is error-free
// use: error bound of (a*b) === a_|b| + |a|b_ + |a*b| (by definition)
//                           === 0|b| + |a|0 + |a*b|
//                           === |a*b|
//
// ---------------
// 2a. double-double +/- double-double
// ---------------
// qdq(a,b);  // error in a === |a|, thus call the error _a_, same with b
// use: error bound of (a+b) === a_ + b_ + |a+b| (by definition)
//                           === _a_ + _b_ + |a+b|
//
// ---------------
// 2b. double-double +/- double-double
// ---------------
// qaq(a,b);  // error in a === 2|a|, thus the error is 2*_a, same with b
// use: error bound of (a+b) === a_ + b_ + |a+b| (by definition)
//                           === 2*_a + 2*_b + |a+b|
//                           === 2*(_a + _b) + |a+b| OR
//                           === a_ + b_ + |a+b|
//
// ---------------
// 3a. double-double X double-double
// ---------------
// qmq(a,b);  // both `a` and `b` error-free
// use: error bound of (a*b) === a_|b| + |a|b_ + |a*b| (by definition)
//                           === 0|b| + |a|0 + 2|a*b|
//                           === 2|a*b| 
//
// ---------------
// 3b. double-double X double-double
// ---------------
// qmq(a,b);  // both `a` and `b` not error-free
// use: error bound of (a*b) === a_|b| + |a|b_ + 2|a*b| (by definition)
//
// ---------------
// 3b. double-double X double-double
// ---------------
// qmq(a,b);  // both `a` not error-free and `b` error-free
// use: error bound of (a*b) === a_|b| + |a|b_ + 2|a*b| (by definition)
//                           === a_|b| + 2|a*b| 
//
// ---------------
// 4a. double-double +/- double
// ---------------
// qad(a,b);  // both `a` and `b` error-free
// use: error bound of (a+b) === a_ + b_ + |a+b| (by definition)
//                           === 0 + 0 + |a+b|
//                           === |a+b| 
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