The D Programming Language's Unofficial Docs
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The D Programming Language's Unofficial Docs
beta
No-seed version. The first element of r is used as the seed's value. For each function f in fun, the corresponding seed type S is Unqual!(typeof(f(e, e))), where e is an element of r: ElementType!R. Once S has been determined, then S s = e; and s = f(s, e); must both be legal.
Seed version. The seed should be a single value if fun is a single function. If fun is multiple functions, then seed should be a std.typecons.Tuple, with one field per function in f. For convenience, if the seed is const, or has qualified fields, then cumulativeFold will operate on an unqualified copy. If this happens then the returned type will not perfectly match S.
one or more functions to use as fold operation
The function returns a range containing the consecutive reduced values. If there is more than one fun, the element type will be std.typecons.Tuple containing one element for each fun.
1 import std.algorithm.comparison : max, min; 2 import std.array : array; 3 import std.math : approxEqual; 4 import std.range : chain; 5 6 int[] arr = [1, 2, 3, 4, 5]; 7 // Partial sum of all elements 8 auto sum = cumulativeFold!((a, b) => a + b)(arr, 0); 9 assert(sum.array == [1, 3, 6, 10, 15]); 10 11 // Partial sum again, using a string predicate with "a" and "b" 12 auto sum2 = cumulativeFold!"a + b"(arr, 0); 13 assert(sum2.array == [1, 3, 6, 10, 15]); 14 15 // Compute the partial maximum of all elements 16 auto largest = cumulativeFold!max(arr); 17 assert(largest.array == [1, 2, 3, 4, 5]); 18 19 // Partial max again, but with Uniform Function Call Syntax (UFCS) 20 largest = arr.cumulativeFold!max; 21 assert(largest.array == [1, 2, 3, 4, 5]); 22 23 // Partial count of odd elements 24 auto odds = arr.cumulativeFold!((a, b) => a + (b & 1))(0); 25 assert(odds.array == [1, 1, 2, 2, 3]); 26 27 // Compute the partial sum of squares 28 auto ssquares = arr.cumulativeFold!((a, b) => a + b * b)(0); 29 assert(ssquares.array == [1, 5, 14, 30, 55]); 30 31 // Chain multiple ranges into seed 32 int[] a = [3, 4]; 33 int[] b = [100]; 34 auto r = cumulativeFold!"a + b"(chain(a, b)); 35 assert(r.array == [3, 7, 107]); 36 37 // Mixing convertible types is fair game, too 38 double[] c = [2.5, 3.0]; 39 auto r1 = cumulativeFold!"a + b"(chain(a, b, c)); 40 assert(approxEqual(r1, [3, 7, 107, 109.5, 112.5])); 41 42 // To minimize nesting of parentheses, Uniform Function Call Syntax can be used 43 auto r2 = chain(a, b, c).cumulativeFold!"a + b"; 44 assert(approxEqual(r2, [3, 7, 107, 109.5, 112.5]));
Sometimes it is very useful to compute multiple aggregates in one pass. One advantage is that the computation is faster because the looping overhead is shared. That's why cumulativeFold accepts multiple functions. If two or more functions are passed, cumulativeFold returns a std.typecons.Tuple object with one member per passed-in function. The number of seeds must be correspondingly increased.
1 import std.algorithm.comparison : max, min; 2 import std.algorithm.iteration : map; 3 import std.math : approxEqual; 4 import std.typecons : tuple; 5 6 double[] a = [3.0, 4, 7, 11, 3, 2, 5]; 7 // Compute minimum and maximum in one pass 8 auto r = a.cumulativeFold!(min, max); 9 // The type of r is Tuple!(int, int) 10 assert(approxEqual(r.map!"a[0]", [3, 3, 3, 3, 3, 2, 2])); // minimum 11 assert(approxEqual(r.map!"a[1]", [3, 4, 7, 11, 11, 11, 11])); // maximum 12 13 // Compute sum and sum of squares in one pass 14 auto r2 = a.cumulativeFold!("a + b", "a + b * b")(tuple(0.0, 0.0)); 15 assert(approxEqual(r2.map!"a[0]", [3, 7, 14, 25, 28, 30, 35])); // sum 16 assert(approxEqual(r2.map!"a[1]", [9, 25, 74, 195, 204, 208, 233])); // sum of squares
Note:
In functional programming languages this is typically called scan, scanl, scanLeft or reductions.
Similar to fold, but returns a range containing the successive reduced values. The call cumulativeFold!(fun)(range, seed) first assigns seed to an internal variable result, also called the accumulator. The returned range contains the values result = fun(result, x) lazily evaluated for each element x in range. Finally, the last element has the same value as fold!(fun)(seed, range). The one-argument version cumulativeFold!(fun)(range) works similarly, but it returns the first element unchanged and uses it as seed for the next elements. This function is also known as partial_sum, accumulate, scan, Cumulative Sum.