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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 isNegativeZero = require( './../../../../base/assert/is-negative-zero' );
var isPositiveZero = require( './../../../../base/assert/is-positive-zero' );
var abs = require( './../../../../base/special/abs' );
var pow = require( './../../../../base/special/pow' );
var exp = require( './../../../../base/special/exp' );
var incrspace = require( '@stdlib/array/incrspace' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var EPS = require( '@stdlib/constants/float64/eps' );
var expm1 = require( './../lib' );
// FIXTURES //
var cppMediumPositive = require( './fixtures/cpp/medium_positive.json' );
var cppMediumNegative = require( './fixtures/cpp/medium_negative.json' );
var mediumNegative = require( './fixtures/julia/medium_negative.json' );
var mediumPositive = require( './fixtures/julia/medium_positive.json' );
var smallNegative = require( './fixtures/julia/small_negative.json' );
var smallPositive = require( './fixtures/julia/small_positive.json' );
var tiny = require( './fixtures/julia/tiny.json' );
// TESTS //
tape( 'main export is a function', function test( t ) {
t.ok( true, __filename );
t.equal( typeof expm1, 'function', 'main export is a function' );
t.end();
});
tape( 'the function agrees with `exp(x) - 1` for most `x`', function test( t ) {
var expected;
var delta;
var val;
var tol;
var x;
var y;
var i;
x = incrspace( -10.0, 50.0, 0.5 );
for ( i = 0; i < x.length; i++ ) {
val = x[ i ];
y = expm1( val );
expected = exp( val ) - 1.0;
delta = abs( y - expected );
tol = 1e-12 * abs( expected );
t.ok( delta <= tol, 'within tolerance. x: '+x+'. y: '+y+'. Δ: '+delta+'. E: '+ expected+'. tol: '+tol+'.' );
}
t.end();
});
tape( 'the function accurately computes `exp(x) - 1` for negative medium numbers', function test( t ) {
var expected;
var delta;
var tol;
var x;
var v;
var i;
x = mediumNegative.x;
expected = mediumNegative.expected;
for ( i = 0; i < x.length; i++ ) {
v = expm1( x[ i ] );
delta = abs( v - expected[ i ] );
tol = EPS * abs( expected[ i ] );
t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+v+'. E: '+ expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}
t.end();
});
tape( 'the function accurately computes `exp(x) - 1` for negative medium numbers (tested against the Boost C++ library)', function test( t ) {
var expected;
var delta;
var tol;
var x;
var v;
var i;
x = cppMediumNegative.x;
expected = cppMediumNegative.expected;
for ( i = 0; i < x.length; i++ ) {
v = expm1( x[ i ] );
delta = abs( v - expected[ i ] );
tol = EPS * abs( expected[ i ] );
t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+v+'. E: '+ expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}
t.end();
});
tape( 'the function accurately computes `exp(x) - 1` for positive medium numbers', function test( t ) {
var expected;
var delta;
var tol;
var x;
var v;
var i;
x = mediumPositive.x;
expected = mediumPositive.expected;
for ( i = 0; i < x.length; i++ ) {
v = expm1( x[ i ] );
delta = abs( v - expected[ i ] );
tol = EPS * abs( expected[ i ] );
t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+v+'. E: '+ expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}
t.end();
});
tape( 'the function accurately computes `exp(x) - 1` for positive medium numbers (tested against the Boost C++ library)', function test( t ) {
var expected;
var delta;
var tol;
var x;
var v;
var i;
x = cppMediumPositive.x;
expected = cppMediumPositive.expected;
for ( i = 0; i < x.length; i++ ) {
v = expm1( x[ i ] );
delta = abs( v - expected[ i ] );
tol = EPS * abs( expected[ i ] );
t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+v+'. E: '+ expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}
t.end();
});
tape( 'the function accurately computes `exp(x) - 1` for negative small numbers', function test( t ) {
var expected;
var delta;
var tol;
var x;
var v;
var i;
x = smallNegative.x;
expected = smallNegative.expected;
for ( i = 0; i < x.length; i++ ) {
v = expm1( x[ i ] );
delta = abs( v - expected[ i ] );
tol = EPS * abs( expected[ i ] );
t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+v+'. E: '+ expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}
t.end();
});
tape( 'the function accurately computes `exp(x) - 1` for positive small numbers', function test( t ) {
var expected;
var delta;
var tol;
var x;
var v;
var i;
x = smallPositive.x;
expected = smallPositive.expected;
for ( i = 0; i < x.length; i++ ) {
v = expm1( x[ i ] );
delta = abs( v - expected[ i ] );
tol = EPS * abs( expected[ i ] );
t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+v+'. E: '+ expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}
t.end();
});
tape( 'the function accurately computes `exp(x) - 1` for very small `x`', function test( t ) {
var expected;
var delta;
var tol;
var x;
var v;
var i;
x = tiny.x;
expected = tiny.expected;
for ( i = 0; i < x.length; i++ ) {
v = expm1( x[ i ] );
delta = abs( v - expected[ i ] );
tol = EPS * abs( expected[ i ] );
t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+v+'. E: '+ expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}
t.end();
});
tape( 'the function returns `+infinity` for very large `x`', function test( t ) {
t.equal( expm1( 800.0 ), PINF, 'equals +infinity' );
t.equal( expm1( 900.0 ), PINF, 'equals +infinity' );
t.equal( expm1( 1000.0 ), PINF, 'equals +infinity' );
t.end();
});
tape( 'the function returns `-1` for negative large `x`', function test( t ) {
t.equal( expm1( -800.0 ), -1.0, 'equals -1' );
t.equal( expm1( -900.0 ), -1.0, 'equals -1' );
t.equal( expm1( -1000.0 ), -1.0, 'equals -1' );
t.end();
});
tape( 'the function returns `x` for `x` smaller than `2**-54`', function test( t ) {
var val = pow( 2.0, -80 );
t.equal( expm1( val ), val, 'equals input value' );
val = pow( 2.0, -55 );
t.equal( expm1( val ), val, 'equals input value' );
val = pow( 2.0, -60 );
t.equal( expm1( val ), val, 'equals input value' );
t.end();
});
tape( 'the function returns `-1` if provided `-infinity`', function test( t ) {
t.equal( expm1( NINF ), -1.0, 'equals -1' );
t.end();
});
tape( 'the function returns `+infinity` if provided `+infinity`', function test( t ) {
t.equal( expm1( PINF ), PINF, 'equals +infinity' );
t.end();
});
tape( 'the function returns `0` if provided `0`', function test( t ) {
var v = expm1( 0.0 );
t.equal( isPositiveZero( v ), true, 'equals 0' );
t.end();
});
tape( 'the function returns `-0` if provided `-0` (IEEE 754-2008)', function test( t ) {
var v = expm1( -0.0 );
t.equal( isNegativeZero( v ), true, 'equals -0' );
t.end();
});
tape( 'the function returns `NaN` if provided `NaN`', function test( t ) {
var val = expm1( NaN );
t.equal( isnan( val ), true, 'equals NaN' );
t.end();
});
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