The recently released Multiprecision Computing Toolbox version 3.3.2 introduces multiple new routines and features for advanced numerical computing in arbitrary precision.

• Matrix functions, including logarithm, square root, exponential, trigonometric, and a general matrix function

  funm	% Evaluate general matrix function	
  expm	% Matrix exponential					
  sqrtm	% Matrix square root					
  logm	% Matrix logarithm					
  sinm	% Matrix sine							
  cosm	% Matrix cosine						
  sinhm	% Matrix hyperbolic sine				
  coshm	% Matrix hyperbolic cosine

• Special cases of an “economy sized” SVD decomposition

  [U,S,V] = svd(X,0)
  [U,S,V] = svd(X,'econ')

• Kernel(null space) matrices, and matrices in Hessenberg form

  null	% Null space
  hess	% Hessenberg form of matrix

• The formatted conversion of multiprecision entities into a string, and to standard data types

  num2str	% Convert number to string
  cast	% Cast variable to different data type
  double	% Convert to double precision
  int16	% Convert to 16-bit signed integer
  int32	% Convert to 32-bit signed integer
  int64	% Convert to 64-bit signed integer
  int8	% Convert to 8-bit signed integer
  single	% Convert to single precision
  uint16	% Convert to 16-bit unsigned integer
  uint32	% Convert to 32-bit unsigned integer
  uint64	% Convert to 64-bit unsigned integer
  uint8	% Convert to 8-bit unsigned integer

• Logical Operations

  all	% Determine whether all array elements are nonzero or true
  any	% Determine whether any array elements are nonzero
  not	% Find logical NOT of array or scalar input
  xor	% Logical exclusive-OR

Examples:

>> mp.Digits(50);
 
% Matrix Logarithm
>> X = mp.rand(5);
>> norm(X - expm(logm(X)),1)
1.4833924403864679909085701388241692669212380232102e-54
 
% Null Space of Matrix
>> X = mp.rand(3,5);
>> norm(X*null(X),1)
8.6664199965605403870371093638563522224156087802478e-56
 
% Hessenberg Form of Matrix
>> X = mp.rand(10);
>> [P,H] = hess(X);
>> norm(X - P*H*P',1)
3.3951974810054822928039499037225474000757620280265e-54