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/**
* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var tape = require( 'tape' );
var isnan = require( './../../../../base/assert/is-nan' );
var abs = require( './../../../../base/special/abs' );
var max = require( './../../../../base/special/max' );
var ln = require( './../../../../base/special/ln' );
var pow = require( './../../../../base/special/pow' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var gammaln = require( './../lib' );
// FIXTURES //
var data1 = require( './fixtures/r/data1.json' );
var expected1 = require( './fixtures/r/expected1.json' );
var data2 = require( './fixtures/r/data2.json' );
var expected2 = require( './fixtures/r/expected2.json' );
// TESTS //
tape( 'main export is a function', function test( t ) {
t.ok( true, __filename );
t.equal( typeof gammaln, 'function', 'main export is a function' );
t.end();
});
tape( 'if provided `NaN`, the function returns `NaN`', function test( t ) {
var v = gammaln( NaN );
t.equal( isnan( v ), true, 'returns NaN when provided a NaN' );
t.end();
});
tape( 'the function returns `infinity` when provided `infinity`', function test( t ) {
var v = gammaln( PINF );
t.equal( v, PINF, 'returns +Inf when provided +Inf' );
v = gammaln( NINF );
t.equal( v, NINF, 'returns -Inf when provided -Inf' );
t.end();
});
tape( 'the function returns `+infinity` when provided `0`', function test( t ) {
var v = gammaln( 0.0 );
t.equal( v, PINF, 'returns +Inf when provided 0' );
t.end();
});
tape( 'the function returns `+infinity` for x smaller than `-2^52`', function test( t ) {
var v = gammaln( -pow( 2.0, 53 ) );
t.equal( v, PINF, 'returns +Inf when provided 2^53' );
t.end();
});
tape( 'the function returns `-ln(x)` for very small x', function test( t ) {
var x;
var v;
x = 2.0e-90;
v = gammaln( x );
t.equal( v, -ln( x ), 'equals -ln(x)' );
t.end();
});
tape( 'the function evaluates the natural logarithm of the gamma function (positive integers)', function test( t ) {
var delta;
var tol;
var v;
var i;
for ( i = 0; i < data1.length; i++ ) {
v = gammaln( data1[ i ] );
delta = abs( v - expected1[ i ] );
tol = 4.75e-15 * max( 1.0, abs( v ), abs( expected1[ i ] ) );
t.ok( delta <= tol, 'within tolerance. x: ' + data1[ i ] + '. Value: ' + v + '. Expected: ' + expected1[ i ] + '. Tolerance: ' + tol + '.' );
}
t.end();
});
tape( 'the function evaluates the natural logarithm of the gamma function (decimal values)', function test( t ) {
var delta;
var tol;
var v;
var i;
for ( i = 0; i < data2.length; i++ ) {
v = gammaln( data2[ i ] );
delta = abs( v - expected2[ i ] );
tol = 2.5e-12 * max( 1.0, abs( v ), abs( expected2[ i ] ) );
t.ok( delta <= tol, 'within tolerance. x: ' + data2[ i ] + '. Value: ' + v + '. Expected: ' + expected2[ i ] + '. Tolerance: ' + tol + '.' );
}
t.end();
});
tape( 'the function evaluates the natural logarithm of the gamma function for x > 2^58', function test( t ) {
var x;
var v;
x = pow( 2.0, 59 );
v = gammaln( x );
t.equal( v, x * (ln(x)-1.0), 'returns x*(ln(x)-1) for x>2^58' );
t.end();
});
tape( 'if provided a positive integer, the function returns the natural logarithm of the factorial of (n-1)', function test( t ) {
t.equal( gammaln( 4.0 ), ln(6.0), 'returns ln(6)' );
t.equal( gammaln( 5.0 ), ln(24.0), 'returns ln(24)' );
t.equal( gammaln( 6.0 ), ln(120.0), 'returns ln(120)' );
t.end();
});
tape( 'returns `+infinity` for `x=-2^51`', function test( t ) {
var v = gammaln( -pow( 2.0, 51 ) );
t.equal( v, PINF, 'returns +Infinity when provided x=-2^51' );
t.end();
});
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