fix: use expm1 in stats/base/dists/rayleigh/cdf

lib/node_modules/@stdlib/stats/base/dists/rayleigh/cdf/lib/factory.js

@@ -23,7 +23,7 @@
 var constantFunction = require( '@stdlib/utils/constant-function' );
 var degenerate = require( '@stdlib/stats/base/dists/degenerate/cdf' ).factory;
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var exp = require( '@stdlib/math/base/special/exp' );
+var expm1 = require( '@stdlib/math/base/special/expm1' );
 var pow = require( '@stdlib/math/base/special/pow' );
 
 
@@ -44,14 +44,12 @@ var pow = require( '@stdlib/math/base/special/pow' );
 * // returns ~0.118
 */
 function factory( sigma ) {
-	var s2;
 	if ( isnan( sigma ) || sigma < 0.0 ) {
 		return constantFunction( NaN );
 	}
 	if ( sigma === 0.0 ) {
 		return degenerate( 0.0 );
 	}
-	s2 = pow( sigma, 2.0 );
 	return cdf;
 
 	/**
@@ -72,7 +70,7 @@ function factory( sigma ) {
 		if ( x < 0.0 ) {
 			return 0.0;
 		}
-		return 1.0 - exp( -pow( x, 2.0 ) / ( 2.0 * s2 ) );
+		return -expm1( -0.5 * pow( x / sigma, 2.0 ) );
 	}
 }
 

lib/node_modules/@stdlib/stats/base/dists/rayleigh/cdf/lib/main.js

@@ -21,7 +21,7 @@
 // MODULES //
 
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var exp = require( '@stdlib/math/base/special/exp' );
+var expm1 = require( '@stdlib/math/base/special/expm1' );
 var pow = require( '@stdlib/math/base/special/pow' );
 
 
@@ -60,7 +60,6 @@ var pow = require( '@stdlib/math/base/special/pow' );
 * // returns NaN
 */
 function cdf( x, sigma ) {
-	var s2;
 	if (
 		isnan( x ) ||
 		isnan( sigma ) ||
@@ -74,8 +73,7 @@ function cdf( x, sigma ) {
 	if ( x < 0.0 ) {
 		return 0.0;
 	}
-	s2 = pow( sigma, 2.0 );
-	return 1.0 - exp( -pow( x, 2.0 ) / ( 2.0 * s2 ) );
+	return -expm1( -0.5 * pow( x / sigma, 2.0 ) );
 }
 
 

lib/node_modules/@stdlib/stats/base/dists/rayleigh/cdf/manifest.json

@@ -40,7 +40,7 @@
       "dependencies": [
         "@stdlib/math/base/napi/binary",
         "@stdlib/math/base/assert/is-nan",
-        "@stdlib/math/base/special/exp",
+        "@stdlib/math/base/special/expm1",
         "@stdlib/math/base/special/pow"
       ]
     },
@@ -57,7 +57,7 @@
       "libpath": [],
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
-        "@stdlib/math/base/special/exp",
+        "@stdlib/math/base/special/expm1",
         "@stdlib/constants/float64/eps",
         "@stdlib/math/base/special/pow"
       ]
@@ -75,7 +75,7 @@
       "libpath": [],
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
-        "@stdlib/math/base/special/exp",
+        "@stdlib/math/base/special/expm1",
         "@stdlib/math/base/special/pow"
       ]
     }

lib/node_modules/@stdlib/stats/base/dists/rayleigh/cdf/src/main.c

@@ -18,7 +18,7 @@
 
 #include "stdlib/stats/base/dists/rayleigh/cdf.h"
 #include "stdlib/math/base/assert/is_nan.h"
-#include "stdlib/math/base/special/exp.h"
+#include "stdlib/math/base/special/expm1.h"
 #include "stdlib/math/base/special/pow.h"
 
 /**
@@ -33,7 +33,6 @@
 * // returns ~0.199
 */
 double stdlib_base_dists_rayleigh_cdf( const double x, const double sigma ) {
-	double s2;
 	if (
 		stdlib_base_is_nan( x ) ||
 		stdlib_base_is_nan( sigma ) ||
@@ -47,6 +46,5 @@ double stdlib_base_dists_rayleigh_cdf( const double x, const double sigma ) {
 	if ( x < 0.0 ) {
 		return 0.0;
 	}
-	s2 = stdlib_base_pow( sigma, 2.0 );
-	return 1.0 - stdlib_base_exp( -stdlib_base_pow( x, 2.0 ) / ( 2.0 * s2 ) );
+	return -stdlib_base_expm1( -0.5 * stdlib_base_pow( x / sigma, 2.0 ) );
 }

lib/node_modules/@stdlib/stats/base/dists/rayleigh/cdf/test/fixtures/julia/REQUIRE

@@ -1,3 +1,2 @@
-Distributions 0.23.8
 julia 1.5
 JSON 0.21

lib/node_modules/@stdlib/stats/base/dists/rayleigh/cdf/test/fixtures/julia/runner.jl

@@ -16,7 +16,6 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-import Distributions: cdf, Rayleigh
 import JSON
 
 """
@@ -39,9 +38,9 @@ julia> gen( x, sigma, \"data.json\" );
 ```
 """
 function gen( x, sigma, name )
-	z = Array{Float64}( undef, length(x) );
-	for i in eachindex(x)
-		z[ i ] = cdf( Rayleigh( sigma[i] ), x[i] );
+	# The CDF is evaluated in extended precision using the textbook formula `1 - exp(-x^2 / (2*sigma^2))`, as subtracting the exponential from `1` in double precision cancels for small `x/sigma`...
+	z = setprecision( BigFloat, 2048 ) do
+		Float64.( 1 .- exp.( .-( BigFloat.( x ) .^ 2 ) ./ ( 2 .* BigFloat.( sigma ) .^ 2 ) ) );
 	end
 
 	# Store data to be written to file as a collection:
@@ -81,3 +80,8 @@ gen( x, sigma, "medium_scale.json" );
 x = rand( 1000 ) .* 20.0;
 sigma = rand( 1000 ) .* 5.0;
 gen( x, sigma, "small_scale.json" );
+
+# Small `x`:
+sigma = exp10.( ( rand( 1000 ) .* 400.0 ) .- 200.0 );
+x = sigma .* exp10.( range( -150.0, stop = -1.0, length = 1000 ) );
+gen( x, sigma, "small_x.json" );

lib/node_modules/@stdlib/stats/base/dists/rayleigh/cdf/test/test.cdf.js

@@ -33,6 +33,7 @@ var cdf = require( './../lib' );
 var smallScale = require( './fixtures/julia/small_scale.json' );
 var mediumScale = require( './fixtures/julia/medium_scale.json' );
 var largeScale = require( './fixtures/julia/large_scale.json' );
+var smallX = require( './fixtures/julia/small_x.json' );
 
 
 // TESTS //
@@ -102,7 +103,7 @@ tape( 'the function evaluates the cdf for `x` given small scale parameter `sigma
 	sigma = smallScale.sigma;
 	for ( i = 0; i < x.length; i++ ) {
 		y = cdf( x[i], sigma[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
 	}
 	t.end();
 });
@@ -119,7 +120,7 @@ tape( 'the function evaluates the cdf for `x` given medium scale parameter `sigm
 	sigma = mediumScale.sigma;
 	for ( i = 0; i < x.length; i++ ) {
 		y = cdf( x[i], sigma[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
 	}
 	t.end();
 });
@@ -136,7 +137,24 @@ tape( 'the function evaluates the cdf for `x` given large scale parameter `sigma
 	sigma = largeScale.sigma;
 	for ( i = 0; i < x.length; i++ ) {
 		y = cdf( x[i], sigma[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
+	}
+	t.end();
+});
+
+tape( 'the function evaluates the cdf for small `x`', function test( t ) {
+	var expected;
+	var sigma;
+	var i;
+	var x;
+	var y;
+
+	expected = smallX.expected;
+	x = smallX.x;
+	sigma = smallX.sigma;
+	for ( i = 0; i < expected.length; i++ ) {
+		y = cdf( x[i], sigma[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
 	}
 	t.end();
 });

lib/node_modules/@stdlib/stats/base/dists/rayleigh/cdf/test/test.factory.js

@@ -33,6 +33,7 @@ var factory = require( './../lib/factory.js' );
 var smallScale = require( './fixtures/julia/small_scale.json' );
 var mediumScale = require( './fixtures/julia/medium_scale.json' );
 var largeScale = require( './fixtures/julia/large_scale.json' );
+var smallX = require( './fixtures/julia/small_x.json' );
 
 
 // TESTS //
@@ -137,7 +138,7 @@ tape( 'the created function evaluates the cdf for `x` given small scale paramete
 	for ( i = 0; i < x.length; i++ ) {
 		cdf = factory( sigma[i] );
 		y = cdf( x[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
 	}
 	t.end();
 });
@@ -156,7 +157,7 @@ tape( 'the created function evaluates the cdf for `x` given medium scale paramet
 	for ( i = 0; i < x.length; i++ ) {
 		cdf = factory( sigma[i] );
 		y = cdf( x[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
 	}
 	t.end();
 });
@@ -175,7 +176,26 @@ tape( 'the created function evaluates the cdf for `x` given large scale paramete
 	for ( i = 0; i < x.length; i++ ) {
 		cdf = factory( sigma[i] );
 		y = cdf( x[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
+	}
+	t.end();
+});
+
+tape( 'the created function evaluates the cdf for small `x`', function test( t ) {
+	var expected;
+	var sigma;
+	var cdf;
+	var i;
+	var x;
+	var y;
+
+	expected = smallX.expected;
+	x = smallX.x;
+	sigma = smallX.sigma;
+	for ( i = 0; i < expected.length; i++ ) {
+		cdf = factory( sigma[i] );
+		y = cdf( x[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
 	}
 	t.end();
 });

lib/node_modules/@stdlib/stats/base/dists/rayleigh/cdf/test/test.native.js

@@ -34,6 +34,7 @@ var NINF = require( '@stdlib/constants/float64/ninf' );
 var smallScale = require( './fixtures/julia/small_scale.json' );
 var mediumScale = require( './fixtures/julia/medium_scale.json' );
 var largeScale = require( './fixtures/julia/large_scale.json' );
+var smallX = require( './fixtures/julia/small_x.json' );
 
 
 // VARIABLES //
@@ -111,7 +112,7 @@ tape( 'the function evaluates the cdf for `x` given small scale parameter `sigma
 	sigma = smallScale.sigma;
 	for ( i = 0; i < x.length; i++ ) {
 		y = cdf( x[i], sigma[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
 	}
 	t.end();
 });
@@ -128,7 +129,7 @@ tape( 'the function evaluates the cdf for `x` given medium scale parameter `sigm
 	sigma = mediumScale.sigma;
 	for ( i = 0; i < x.length; i++ ) {
 		y = cdf( x[i], sigma[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
 	}
 	t.end();
 });
@@ -145,7 +146,24 @@ tape( 'the function evaluates the cdf for `x` given large scale parameter `sigma
 	sigma = largeScale.sigma;
 	for ( i = 0; i < x.length; i++ ) {
 		y = cdf( x[i], sigma[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
+	}
+	t.end();
+});
+
+tape( 'the function evaluates the cdf for small `x`', opts, function test( t ) {
+	var expected;
+	var sigma;
+	var i;
+	var x;
+	var y;
+
+	expected = smallX.expected;
+	x = smallX.x;
+	sigma = smallX.sigma;
+	for ( i = 0; i < expected.length; i++ ) {
+		y = cdf( x[i], sigma[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
 	}
 	t.end();
 });