Big floating point numbers

 

In Macsyma

For comparison with other CAS choose from: Axiom Derive Maple Mathematica Reduce

inputs outputs

    rn: - 1027/1410;

                                  1027
                                - ----
                                  1410

    cn: (167*i + 241)/5;

                             167 %i + 241
                             ------------
                                   5

• computation with floating point numbers

      bfloat(rn);
  
  

                        - 7.2836879432624113475b-1

      bfloat(cn);
  
  

                            3.34b1 %i + 4.82b1

      bfloat(%pi);
  

                         3.1415926535897932385b0

      cos(bfloat(%pi));
  

                                 - 1.0b0

  
      sin(1.0b0);
  

                         8.4147098480789650665b-1

• computation with an arbitrary number of digits

      fpprec: 50$
  
      bfloat(%pi);
  

          3.1415926535897932384626433832795028841971693993751b0

      cos(bfloat(%pi));
  

                                 - 1.0b0

• should be cos(pi/6) = sqrt(3)/2

      cos(bfloat(%pi/6));
  

          8.6602540378443864676372317075293618347140262690519b-1

      %^2;
  

                                  7.5b-1

      fpprec: 20$
  
   

• with normal defaults, underflows are converted to 0

      exp(-100000.1**2);
  

                                   0.0

• complex functions

      bfloat(rectform(tan(1.0b0 + 1.0b0*%i)));
  

          1.0839233273386945435b0 %i + 2.7175258531951171653b-1

      bfloat(log(1.0b0 + 1.0b0*%i));
  

          7.8539816339744830962b-1 %i + 3.4657359027997265471b-1