All Numeric Algorithms

Accumulation and reduction

• std::accumulate
• std::reduce
• std::transform_reduce

Prefix and suffix style scans

• std::inclusive_scan
• std::exclusive_scan
• std::transform_inclusive_scan
• std::transform_exclusive_scan

Differences and products

• std::adjacent_difference
• std::inner_product

Integer and ratio helpers

• std::gcd
• std::lcm
• midpoint-like helpers live elsewhere rather than in <numeric>

Common use guidance

• Use accumulate for ordered left folds when sequencing matters.
• Use reduce when parallel-friendly reduction semantics are acceptable.
• Use scan algorithms when each output element depends on prior accumulated state.
• Prefer named standard algorithms over handwritten loops when the operation matches directly.

Small worked example

#include <numeric>
#include <vector>

int main() {
	std::vector<int> values{5, 7, 2, 4};
	std::vector<int> prefix(values.size());
	std::inclusive_scan(values.begin(), values.end(), prefix.begin());
	return prefix.back();
}

Scan algorithms are the right tool when each output depends on all earlier input, such as running totals, partial sums, or progressive limits.

Decision guide

• use accumulate when left-to-right order matters or the operation is not safely reorderable
• use reduce when the operation is associative enough for parallel-friendly reduction semantics
• use transform_reduce when mapping and combining belong in one pass
• use scans when you need all intermediate accumulated results instead of only the final total

Related pages

• Header reference: <numeric>
• C++ algorithms and ranges
• C++ numerics and time