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section \<open>Optimizations for Code Integer\<close>
theory Optimize_Integer
imports
Complex_Main
"HOL-Library.Code_Target_Numeral"
begin
text \<open>shallowly embed log and power\<close>
definition log2::"int \<Rightarrow> int"
where "log2 a = floor (log 2 (of_int a))"
context includes integer.lifting begin
lift_definition log2_integer :: "integer \<Rightarrow> integer"
is "log2 :: int \<Rightarrow> int"
.
end
lemma [code]: "log2 (int_of_integer a) = int_of_integer (log2_integer a)"
by (simp add: log2_integer.rep_eq)
code_printing
constant "log2_integer :: integer \<Rightarrow> _" \<rightharpoonup>
(SML) "IntInf.log2"
definition power_int::"int \<Rightarrow> int \<Rightarrow> int"
where "power_int a b = a ^ (nat b)"
context includes integer.lifting begin
lift_definition power_integer :: "integer \<Rightarrow> integer \<Rightarrow> integer"
is "power_int :: int \<Rightarrow> int \<Rightarrow> int"
.
end
code_printing
constant "power_integer :: integer \<Rightarrow> _ \<Rightarrow> _" \<rightharpoonup>
(SML) "IntInf.pow ((_), (_))"
lemma [code]: "power_int (int_of_integer a) (int_of_integer b) = int_of_integer (power_integer a b)"
by (simp add: power_integer.rep_eq)
end
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