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square() for arithmetic types: multiply instead of calling std::pow(x, 2) #3368

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square() for arithmetic types: multiply instead of calling std::pow(x, 2) #3368

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7 changes: 6 additions & 1 deletion stan/math/prim/fun/square.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -25,7 +25,12 @@ namespace math {
*/
template <typename T, require_arithmetic_t<T>* = nullptr>
inline double square(const T x) {
return std::pow(x, 2);
// widen to double first, then multiply: identical to the previous
// std::pow(x, 2) (a correctly-rounded square equals the rounded
// product), including the promoted-to-double semantics for integral
// arguments (where x * x could overflow), without the libm call.
const double x_d = x;
return x_d * x_d;
}

/**
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16 changes: 8 additions & 8 deletions stan/math/rev/fun/squared_distance.hpp
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Expand Up @@ -21,11 +21,11 @@ namespace math {
inline var squared_distance(const var& a, const var& b) {
check_finite("squared_distance", "a", a);
check_finite("squared_distance", "b", b);
return make_callback_vari(std::pow(a.val() - b.val(), 2),
[a, b](const auto& vi) mutable {
const double diff = 2.0 * (a.val() - b.val());
a.adj() += vi.adj_ * diff;
b.adj() -= vi.adj_ * diff;
const double diff = a.val() - b.val();
return make_callback_vari(diff * diff, [a, b, diff](const auto& vi) mutable {
const double adj_diff = 2.0 * diff;
a.adj() += vi.adj_ * adj_diff;
b.adj() -= vi.adj_ * adj_diff;
});
}

Expand All @@ -35,9 +35,9 @@ inline var squared_distance(const var& a, const var& b) {
inline var squared_distance(const var& a, double b) {
check_finite("squared_distance", "a", a);
check_finite("squared_distance", "b", b);
return make_callback_vari(std::pow(a.val() - b, 2),
[a, b](const auto& vi) mutable {
a.adj() += vi.adj_ * 2.0 * (a.val() - b);
const double diff = a.val() - b;
return make_callback_vari(diff * diff, [a, b, diff](const auto& vi) mutable {
a.adj() += vi.adj_ * 2.0 * diff;
});
}

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