prevent unnecessary repeated squaring calculation (#58720)

(cherry picked from commit f61c640)

Author: nsajko

base/intfuncs.jl

@@ -335,11 +335,6 @@ function invmod(n::T) where {T<:BitInteger}
 end
 
 # ^ for any x supporting *
-function to_power_type(x::Number)
-    T = promote_type(typeof(x), typeof(x*x))
-    convert(T, x)
-end
-to_power_type(x) = oftype(x*x, x)
 @noinline throw_domerr_powbysq(::Any, p) = throw(DomainError(p, LazyString(
     "Cannot raise an integer x to a negative power ", p, ".",
     "\nConvert input to float.")))
@@ -355,12 +350,23 @@ to_power_type(x) = oftype(x*x, x)
     "or write float(x)^", p, " or Rational.(x)^", p, ".")))
 # The * keyword supports `*=checked_mul` for `checked_pow`
 @assume_effects :terminates_locally function power_by_squaring(x_, p::Integer; mul=*)
-    x = to_power_type(x_)
+    x_squared_ = x_ * x_
+    x_squared_type = typeof(x_squared_)
+    T = if x_ isa Number
+        promote_type(typeof(x_), x_squared_type)
+    else
+        x_squared_type
+    end
+    x = convert(T, x_)
+    square_is_useful = mul === *
     if p == 1
         return copy(x)
     elseif p == 0
         return one(x)
     elseif p == 2
+        if square_is_useful  # avoid performing the same multiplication a second time when possible
+            return convert(T, x_squared_)
+        end
         return mul(x, x)
     elseif p < 0
         isone(x) && return copy(x)
@@ -369,6 +375,11 @@ to_power_type(x) = oftype(x*x, x)
     end
     t = trailing_zeros(p) + 1
     p >>= t
+    if square_is_useful  # avoid performing the same multiplication a second time when possible
+        if (t -= 1) > 0
+            x = convert(T, x_squared_)
+        end
+    end
     while (t -= 1) > 0
         x = mul(x, x)
     end