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proof-pile / formal /afp /Affine_Arithmetic /Ex_Affine_Approximation.thy
Zhangir Azerbayev
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section \<open>Examples\<close>
theory Ex_Affine_Approximation
imports
Affine_Code
Print
Float_Real
begin
context includes floatarith_notation begin
definition "rotate_fas =
[Cos (Rad_of (Var 2)) * Var 0 - Sin (Rad_of (Var 2)) * Var 1,
Sin (Rad_of (Var 2)) * Var 0 + Cos (Rad_of (Var 2)) * Var 1]"
definition "rotate_slp = slp_of_fas rotate_fas"
definition "approx_rotate p t X = approx_slp_outer p 3 rotate_slp X"
fun rotate_aform where
"rotate_aform x i = (let r = (((the o (\<lambda>x. approx_rotate 30 (FloatR 1 (-3)) x))^^i) x) in
(r ! 0) \<times>\<^sub>a (r ! 1) \<times>\<^sub>a (r ! 2))"
value [code] "rotate_aform (aforms_of_ivls [2, 1, 45] [3, 5, 45]) 70"
definition "translate_slp = slp_of_fas [Var 0 + Var 2, Var 1 + Var 2]"
fun translatei where "translatei x i = (((the o (\<lambda>x. approx_slp_outer 7 3 translate_slp x))^^i) x)"
value "translatei (aforms_of_ivls [2, 1, 512] [3, 5, 512]) 50"
end
hide_const rotate_fas rotate_slp approx_rotate rotate_aform translate_slp translatei
end