fix: avoid cancellation for small p in stats/base/dists/kumaraswamy/quantile

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/quantile/lib/factory.js

@@ -22,6 +22,8 @@
 
 var constantFunction = require( '@stdlib/utils/constant-function' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var expm1 = require( '@stdlib/math/base/special/expm1' );
+var log1p = require( '@stdlib/math/base/special/log1p' );
 var pow = require( '@stdlib/math/base/special/pow' );
 
 
@@ -69,7 +71,7 @@ function factory( a, b ) {
 		if ( isnan( p ) || p < 0.0 || p > 1.0 ) {
 			return NaN;
 		}
-		return pow( 1.0 - pow( 1.0-p, 1.0/b ), 1.0/a );
+		return pow( -expm1( log1p( -p ) / b ), 1.0/a );
 	}
 }
 

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/quantile/lib/main.js

@@ -21,6 +21,8 @@
 // MODULES //
 
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var expm1 = require( '@stdlib/math/base/special/expm1' );
+var log1p = require( '@stdlib/math/base/special/log1p' );
 var pow = require( '@stdlib/math/base/special/pow' );
 
 
@@ -86,7 +88,7 @@ function quantile( p, a, b ) {
 	) {
 		return NaN;
 	}
-	return pow( 1.0 - pow( 1.0-p, 1.0/b ), 1.0/a );
+	return pow( -expm1( log1p( -p ) / b ), 1.0/a );
 }
 
 

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/quantile/manifest.json

@@ -40,6 +40,8 @@
       "dependencies": [
         "@stdlib/math/base/napi/ternary",
         "@stdlib/math/base/assert/is-nan",
+        "@stdlib/math/base/special/expm1",
+        "@stdlib/math/base/special/log1p",
         "@stdlib/math/base/special/pow"
       ]
     },
@@ -56,6 +58,8 @@
       "libpath": [],
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
+        "@stdlib/math/base/special/expm1",
+        "@stdlib/math/base/special/log1p",
         "@stdlib/math/base/special/pow",
         "@stdlib/constants/float64/eps"
       ]
@@ -73,6 +77,8 @@
       "libpath": [],
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
+        "@stdlib/math/base/special/expm1",
+        "@stdlib/math/base/special/log1p",
         "@stdlib/math/base/special/pow",
         "@stdlib/constants/float64/eps"
       ]

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/quantile/src/main.c

@@ -18,6 +18,8 @@
 
 #include "stdlib/stats/base/dists/kumaraswamy/quantile.h"
 #include "stdlib/math/base/assert/is_nan.h"
+#include "stdlib/math/base/special/expm1.h"
+#include "stdlib/math/base/special/log1p.h"
 #include "stdlib/math/base/special/pow.h"
 
 /**
@@ -44,5 +46,5 @@ double stdlib_base_dists_kumaraswamy_quantile( const double p, const double a, c
 	) {
 		return 0.0/0.0; // NaN
 	}
-	return stdlib_base_pow( 1.0 - stdlib_base_pow( 1.0-p, 1.0/b ), 1.0/a );
+	return stdlib_base_pow( -stdlib_base_expm1( stdlib_base_log1p( -p ) / b ), 1.0/a );
 }

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/quantile/test/fixtures/julia/REQUIRE

@@ -0,0 +1,2 @@
+julia 1.5
+JSON 0.21

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/quantile/test/fixtures/julia/runner.jl

@@ -0,0 +1,74 @@
+#!/usr/bin/env julia
+#
+# @license Apache-2.0
+#
+# Copyright (c) 2026 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.
+
+import JSON
+
+"""
+	gen( p, a, b, name )
+
+Generate fixture data and write to file.
+
+The quantile is evaluated in extended precision from the textbook formula `(1 - (1-p)^(1/b))^(1/a)`, as forming `1-p` in double precision rounds away the low-order bits of `p` (all of them for `p < 2^-53`).
+
+# Arguments
+
+* `p`: input probability
+* `a`: first shape parameter
+* `b`: second shape parameter
+* `name::AbstractString`: output filename
+"""
+function gen( p, a, b, name )
+	z = setprecision( BigFloat, 2048 ) do
+		Float64.( ( 1 .- ( 1 .- BigFloat.( p ) ) .^ ( 1 ./ BigFloat.( b ) ) ) .^ ( 1 ./ BigFloat.( a ) ) )
+	end
+
+	# Store data to be written to file as a collection:
+	data = Dict([
+		("p", p),
+		("a", a),
+		("b", b),
+		("expected", z)
+	]);
+
+	# Based on the script directory, create an output filepath:
+	filepath = joinpath( dir, name );
+
+	# Write the data to the output filepath as JSON:
+	outfile = open( filepath, "w" );
+	write( outfile, JSON.json(data) );
+	write( outfile, "\n" );
+	close( outfile );
+end
+
+# Get the filename:
+file = @__FILE__;
+
+# Extract the directory in which this file resides:
+dir = dirname( file );
+
+# Random values:
+p = rand( 1000 );
+a = ( rand( 1000 ) .* 5.0 ) .+ 0.5;
+b = ( rand( 1000 ) .* 5.0 ) .+ 0.5;
+gen( p, a, b, "data.json" );
+
+# Small `p` (`a` is a power of two, so that `1/a` is exact and the test measures the error from `1-p`):
+p = exp10.( range( -300.0, stop = -1.0, length = 1000 ) );
+a = repeat( [ 1.0, 2.0, 4.0, 8.0 ], 250 );
+b = ( rand( 1000 ) .* 5.0 ) .+ 0.5;
+gen( p, a, b, "small_p.json" );

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/quantile/test/test.factory.js

@@ -21,15 +21,19 @@
 // MODULES //
 
 var tape = require( 'tape' );
-var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive;
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var randu = require( '@stdlib/random/base/randu' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
-var EPS = require( '@stdlib/constants/float64/eps' );
 var factory = require( './../lib/factory.js' );
 
 
+// FIXTURES //
+
+var data = require( './fixtures/julia/data.json' );
+var smallP = require( './fixtures/julia/small_p.json' );
+
+
 // TESTS //
 
 tape( 'main export is a function', function test( t ) {
@@ -143,22 +147,44 @@ tape( 'if provided a nonpositive `a`, the created function always returns `NaN`'
 	t.end();
 });
 
-tape( 'the returned function evaluates the quantile function of a Kumaraswamy\'s double bounded distribution', function test( t ) {
+tape( 'the created function evaluates the quantile for random `p`, `a` and `b`', function test( t ) {
+	var expected;
 	var quantile;
 	var a;
 	var b;
+	var i;
 	var p;
 	var y;
+
+	expected = data.expected;
+	p = data.p;
+	a = data.a;
+	b = data.b;
+	for ( i = 0; i < expected.length; i++ ) {
+		quantile = factory( a[i], b[i] );
+		y = quantile( p[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' );
+	}
+	t.end();
+});
+
+tape( 'the created function evaluates the quantile for small `p`', function test( t ) {
+	var expected;
+	var quantile;
+	var a;
+	var b;
 	var i;
+	var p;
+	var y;
 
-	// TODO: Add fixtures
-	a = ( randu()*5.0 ) + EPS;
-	b = ( randu()*5.0 ) + EPS;
-	quantile = factory( a, b );
-	for ( i = 0; i < 100; i++ ) {
-		p = randu();
-		y = quantile( p, a, b );
-		t.strictEqual( isNumber( y ), true, 'returns expected value' );
+	expected = smallP.expected;
+	p = smallP.p;
+	a = smallP.a;
+	b = smallP.b;
+	for ( i = 0; i < expected.length; i++ ) {
+		quantile = factory( a[i], b[i] );
+		y = quantile( p[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/quantile/test/test.native.js

@@ -23,12 +23,16 @@
 var resolve = require( 'path' ).resolve;
 var tape = require( 'tape' );
 var tryRequire = require( '@stdlib/utils/try-require' );
-var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive;
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var randu = require( '@stdlib/random/base/randu' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
-var EPS = require( '@stdlib/constants/float64/eps' );
+
+
+// FIXTURES //
+
+var data = require( './fixtures/julia/data.json' );
+var smallP = require( './fixtures/julia/small_p.json' );
 
 
 // VARIABLES //
@@ -119,20 +123,40 @@ tape( 'if provided a nonpositive `b`, the function returns `NaN`', opts, functio
 	t.end();
 });
 
-tape( 'the function evaluates the quantile function of a Kumaraswamy\'s double bounded distribution', opts, function test( t ) {
+tape( 'the function evaluates the quantile for random `p`, `a` and `b`', opts, function test( t ) {
+	var expected;
 	var a;
 	var b;
+	var i;
 	var p;
 	var y;
+
+	expected = data.expected;
+	p = data.p;
+	a = data.a;
+	b = data.b;
+	for ( i = 0; i < expected.length; i++ ) {
+		y = quantile( p[i], a[i], b[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' );
+	}
+	t.end();
+});
+
+tape( 'the function evaluates the quantile for small `p`', opts, function test( t ) {
+	var expected;
+	var a;
+	var b;
 	var i;
+	var p;
+	var y;
 
-	// TODO: Add fixtures
-	for ( i = 0; i < 100; i++ ) {
-		p = randu();
-		a = ( randu()*5.0 ) + EPS;
-		b = ( randu()*5.0 ) + EPS;
-		y = quantile( p, a, b );
-		t.strictEqual( isNumber( y ), true, 'returns expected value' );
+	expected = smallP.expected;
+	p = smallP.p;
+	a = smallP.a;
+	b = smallP.b;
+	for ( i = 0; i < expected.length; i++ ) {
+		y = quantile( p[i], a[i], b[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/quantile/test/test.quantile.js

@@ -21,15 +21,19 @@
 // MODULES //
 
 var tape = require( 'tape' );
-var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive;
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var randu = require( '@stdlib/random/base/randu' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
-var EPS = require( '@stdlib/constants/float64/eps' );
 var quantile = require( './../lib' );
 
 
+// FIXTURES //
+
+var data = require( './fixtures/julia/data.json' );
+var smallP = require( './fixtures/julia/small_p.json' );
+
+
 // TESTS //
 
 tape( 'main export is a function', function test( t ) {
@@ -110,20 +114,40 @@ tape( 'if provided a nonpositive `b`, the function returns `NaN`', function test
 	t.end();
 });
 
-tape( 'the function evaluates the quantile function of a Kumaraswamy\'s double bounded distribution', function test( t ) {
+tape( 'the function evaluates the quantile for random `p`, `a` and `b`', function test( t ) {
+	var expected;
 	var a;
 	var b;
+	var i;
 	var p;
 	var y;
+
+	expected = data.expected;
+	p = data.p;
+	a = data.a;
+	b = data.b;
+	for ( i = 0; i < expected.length; i++ ) {
+		y = quantile( p[i], a[i], b[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' );
+	}
+	t.end();
+});
+
+tape( 'the function evaluates the quantile for small `p`', function test( t ) {
+	var expected;
+	var a;
+	var b;
 	var i;
+	var p;
+	var y;
 
-	// TODO: Add fixtures
-	for ( i = 0; i < 100; i++ ) {
-		p = randu();
-		a = ( randu()*5.0 ) + EPS;
-		b = ( randu()*5.0 ) + EPS;
-		y = quantile( p, a, b );
-		t.strictEqual( isNumber( y ), true, 'returns expected value' );
+	expected = smallP.expected;
+	p = smallP.p;
+	a = smallP.a;
+	b = smallP.b;
+	for ( i = 0; i < expected.length; i++ ) {
+		y = quantile( p[i], a[i], b[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });