5 Numerical Libraries

Ada features a strong predefined standard library covering a variety of disciplines. In particular the numerical libraries are a solid foundation for scientific and engineering computations. Combined with a comprehensive set of data structures lead to reliable applications.

In this chapter numerical libraries are surveyed.

5.1 Learning Objectives

Creating text files in comma (or :) separated format
Elementary numerical function library
Interfacing with a plotting tool through files

5.2 Sinusoid

Basic sinusoids are supported directly by the library.

Code Fragment

~/bin/codemd ../Prj/dtypes/src/curves.adb -x DegRad -l

0039 |    function Radians (d : Integer) return Float is
0040 |    begin
0041 |       return 2.0 * Ada.Numerics.Pi * Float (d) / 360.0;
0042 |    end Radians;
0043 |    function Degrees (r : Float) return Integer is
0044 |    begin
0045 |       return Integer (r * 360.0 / (2.0 * Ada.Numerics.Pi));
0046 |    end Degrees;

Functions as defined above leverage the basic constants such as pi and e defined in the libraries.

~/bin/codemd ../Prj/dtypes/src/curves.adb -x Trig -l

0060 |       CreateOutputFile (myname, outfile);
0061 |       for deg in 0 .. 360 loop
0062 |          Put (Float'(Radians (deg))'Image);
0063 |          Put (" ; ");
0064 |          Put (Float'(Elementary_Functions.Sin (Radians (deg)))'Image);
0065 |          Put (" ; ");
0066 |          Put (Float'(Elementary_Functions.Cos (Radians (deg)))'Image);
0067 |          Put (" ; ");
0068 |          Put (Float'(Elementary_Functions.Tan (Radians (deg)))'Image);
0069 |          New_Line;
0070 |       end loop;
0071 |       Close (outfile);

which produces a CSV file in several columns :

~/bin/curves trig
sed -n "10,20p" curves.Trigonometric.csv

curves curves.adb Compiled Jan 21 2025 07:20:27
curves.Trigonometric
 1.57080E-01 ;  1.56434E-01 ;  9.87688E-01 ;  1.58384E-01
 1.74533E-01 ;  1.73648E-01 ;  9.84808E-01 ;  1.76327E-01
 1.91986E-01 ;  1.90809E-01 ;  9.81627E-01 ;  1.94380E-01
 2.09440E-01 ;  2.07912E-01 ;  9.78148E-01 ;  2.12557E-01
 2.26893E-01 ;  2.24951E-01 ;  9.74370E-01 ;  2.30868E-01
 2.44346E-01 ;  2.41922E-01 ;  9.70296E-01 ;  2.49328E-01
 2.61799E-01 ;  2.58819E-01 ;  9.65926E-01 ;  2.67949E-01
 2.79253E-01 ;  2.75637E-01 ;  9.61262E-01 ;  2.86745E-01
 2.96706E-01 ;  2.92372E-01 ;  9.56305E-01 ;  3.05731E-01
 3.14159E-01 ;  3.09017E-01 ;  9.51057E-01 ;  3.24920E-01
 3.31613E-01 ;  3.25568E-01 ;  9.45519E-01 ;  3.44328E-01

which can be plotted using Julia

using CSV
using DataFrames
using Plots

df=DataFrames.DataFrame(CSV.File("curves.Trigonometric.csv",delim=";",header=false));
plot(df.Column1 , [df.Column2,df.Column3] ,
                  label=["Sine" "Cosine"] ,
                  title="Trignometric Functions" , show=true)

5.3 Hyperbolic

The numerical library supports hyperbolic functions as well:

~/bin/codemd ../Prj/dtypes/src/curves.adb -x Hyper -l

0087 |       CreateOutputFile (myname, outfile);
0088 |       for d in 0 .. 40 loop
0089 |          x := Float (d) * 0.1 - 2.0;
0090 |          Put (x'Image);
0091 |          Put (" ; ");
0092 |          Put (Elementary_Functions.Sinh (x), Fore => 3, Aft => 3, Exp => 0);
0093 |          Put (" ; ");
0094 |          Put (Elementary_Functions.Cosh (x), Fore => 3, Aft => 3, Exp => 0);
0095 |          Put (" ; ");
0096 |          Put (Elementary_Functions.Tanh (x), Fore => 3, Aft => 3, Exp => 0);
0097 |          Put (" ; ");
0098 |          New_Line;
0099 |       end loop;
0100 |       Close (outfile);
0101 |       Set_Output (Standard_Output);

In this fragment, it can be seen that the floating point variables are directly printed instead of using the built in Image attribute. Direct print then affords the control over the format of the print out. The output generated by the above fragment illustrates this:

~/bin/curves hyper
sed -n "10,20p" curves.Hyperbolic.csv

curves curves.adb Compiled Jan 21 2025 07:20:27
curves.Hyperbolic
-1.10000E+00 ;  -1.336 ;   1.669 ;  -0.800 ; 
-1.00000E+00 ;  -1.175 ;   1.543 ;  -0.762 ; 
-9.00000E-01 ;  -1.027 ;   1.433 ;  -0.716 ; 
-8.00000E-01 ;  -0.888 ;   1.337 ;  -0.664 ; 
-7.00000E-01 ;  -0.759 ;   1.255 ;  -0.604 ; 
-6.00000E-01 ;  -0.637 ;   1.185 ;  -0.537 ; 
-5.00000E-01 ;  -0.521 ;   1.128 ;  -0.462 ; 
-4.00000E-01 ;  -0.411 ;   1.081 ;  -0.380 ; 
-3.00000E-01 ;  -0.305 ;   1.045 ;  -0.291 ; 
-2.00000E-01 ;  -0.201 ;   1.020 ;  -0.197 ; 
-1.00000E-01 ;  -0.100 ;   1.005 ;  -0.100 ;

using CSV
using DataFrames
using Plots

df=DataFrames.DataFrame(CSV.File("curves.Hyperbolic.csv",delim=";",header=false));
plot(df.Column1 , [df.Column2,df.Column3,df.Column4] ,
                  label=["Sinh" "Cosh" "Tanh"] ,
                  title="Hyperbolic Functions" , show=false)

5.4 Hypotrochoid

The curve hypotrochoid and its parameteric equations are found in Wikipedia