Chapter 6: Dynamic ProgrammingEdit
The following codes are implementations of the Fibonacci-Numbers examples.
To calculate Fibonacci numbers negative values are not needed so we define an integer type which starts at 0. With the integer type defined you can calculate up until
Fib (88) will result in an
You might notice that there is not equivalence for the
assert (n >= 0) from the original example. Ada will test the correctness of the parameter before the function is called.
function Fib (n : Integer_Type) return Integer_Type is begin if n = 0 then return 0; elsif n = 1 then return 1; else return Fib (n - 1) + Fib (n - 2); end if; end Fib; ...
For this implementation we need a special cache type can also store a -1 as "not calculated" marker
The actual type for calculating the fibonacci numbers continues to start at 0. As it is a subtype of the cache type Ada will automatically convert between the two. (the conversion is - of course - checked for validity)
In order to know how large the cache need to be we first read the actual value from the command line.
Value : constant Integer_Type := Integer_Type'Value (Ada.Command_Line.Argument (1));
The Cache array starts with element 2 since Fib (0) and Fib (1) are constants and ends with the value we want to calculate.
The Cache is initialized to the first valid value of the cache type — this is
F : Cache_Array := (others => Cache_Type'First);
What follows is the actual algorithm.
function Fib (N : Integer_Type) return Integer_Type is begin if N = 0 or else N = 1 then return N; elsif F (N) /= Cache_Type'First then return F (N); else F (N) := Fib (N - 1) + Fib (N - 2); return F (N); end if; end Fib; ...
This implementation is faithful to the original from the Algorithms book. However, in Ada you would normally do it a little different:
when you use a slightly larger array which also stores the elements 0 and 1 and initializes them to the correct values
type Cache_Array is array (Integer_Type range 0 .. Value) of Cache_Type; F : Cache_Array := (0 => 0, 1 => 1, others => Cache_Type'First);
and then you can remove the first if path.
This will save about 45% of the execution-time (measured on Linux i686) while needing only two more elements in the cache array.
Memory Optimized ImplementationEdit
This version looks just like the original in WikiCode.
type Integer_Type is range 0 .. 999_999_999_999_999_999; function Fib (N : Integer_Type) return Integer_Type is U : Integer_Type := 0; V : Integer_Type := 1; begin for I in 2 .. N loop Calculate_Next : declare T : constant Integer_Type := U + V; begin U := V; V := T; end Calculate_Next; end loop; return V; end Fib;
No 64 bit integersEdit
Your Ada compiler does not support 64 bit integer numbers? Then you could try to use decimal numbers instead. Using decimal numbers results in a slower program (takes about three times as long) but the result will be the same.
You should know that floating point numbers are unsuitable for the calculation of fibonacci numbers. They will not report an error condition when the number calculated becomes too large — instead they will lose in precision which makes the result meaningless.