incrprod

Compute a product incrementally.

Usage

var incrprod = require( '@stdlib/math/stats/incr/prod' );

incrprod()

Returns an accumulator function which incrementally computes a product.

var accumulator = incrprod();

accumulator( [x] )

If provided an input value x, the accumulator function returns an updated product. If not provided an input value x, the accumulator function returns the current product.

var prod = accumulator( 2.0 );
// returns 2.0

prod = accumulator( 1.0 );
// returns 2.0

prod = accumulator( 3.0 );
// returns 6.0

prod = accumulator();
// returns 6.0

Under certain conditions, overflow may be transient.

// Large values:
var x = 5.0e+300;
var y = 1.0e+300;

// Tiny value:
var z = 2.0e-302;

// Initialize an accumulator:
var accumulator = incrprod();

var prod = accumulator( x );
// returns 5.0e+300

// Transient overflow:
prod = accumulator( y );
// returns Infinity

// Recover a finite result:
prod = accumulator( z );
// returns 1.0e+299

Similarly, under certain conditions, underflow may be transient.

// Tiny values:
var x = 4.0e-302;
var y = 9.0e-303;

// Large value:
var z = 2.0e+300;

// Initialize an accumulator:
var accumulator = incrprod();

var prod = accumulator( x );
// returns 4.0e-302

// Transient underflow:
prod = accumulator( y );
// returns 0.0

// Recover a non-zero result:
prod = accumulator( z );
// returns 7.2e-304

Notes

  • Input values are not type checked. If provided NaN or a value which, when used in computations, results in NaN, the accumulated value is NaN for all future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly before passing the value to the accumulator function.
  • For long running accumulations or accumulations of either large or small numbers, care should be taken to prevent overflow and underflow. Note, however, that overflow/underflow may be transient, as the accumulator does not use a double-precision floating-point number to store an accumulated product. Instead, the accumulator splits an accumulated product into a normalized fraction and exponent and updates each component separately. Doing so guards against a loss in precision.

Examples

var randu = require( '@stdlib/random/base/randu' );
var incrprod = require( '@stdlib/math/stats/incr/prod' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = incrprod();

// For each simulated value, update the product...
for ( i = 0; i < 100; i++ ) {
    v = randu() * 100.0;
    accumulator( v );
}
console.log( accumulator() );