From 716b8e9a3aadafd3b1e00f74177444256233c002 Mon Sep 17 00:00:00 2001 From: Abhist17 Date: Fri, 2 Oct 2026 05:01:02 +0530 Subject: [PATCH 1/2] fix: avoid cancellation in `stats/base/dists/kumaraswamy/logcdf` `ln( 1 - (1 - x^a)^b )` cancels twice: `1 - x^a` rounds away the low-order bits of a small `x^a`, and `1 - (1 - x^a)^b` loses the digits of a small CDF, as `ln` of a value close to `1` does for a CDF close to `1`. Evaluate `ln(1-x^a)` with `log1p` or `expm1`, depending on the size of `x^a`, and finish with `log1mexp`. Add fixtures generated from the textbook formula in extended precision. --- .../dists/kumaraswamy/logcdf/lib/factory.js | 14 +++- .../base/dists/kumaraswamy/logcdf/lib/main.js | 14 +++- .../dists/kumaraswamy/logcdf/manifest.json | 9 +++ .../base/dists/kumaraswamy/logcdf/src/main.c | 14 +++- .../logcdf/test/fixtures/julia/REQUIRE | 2 + .../logcdf/test/fixtures/julia/data.json | 1 + .../logcdf/test/fixtures/julia/large_x.json | 1 + .../logcdf/test/fixtures/julia/runner.jl | 80 +++++++++++++++++++ .../logcdf/test/fixtures/julia/small_x.json | 1 + .../kumaraswamy/logcdf/test/test.factory.js | 72 ++++++++++++++--- .../kumaraswamy/logcdf/test/test.logcdf.js | 66 ++++++++++++--- .../kumaraswamy/logcdf/test/test.native.js | 66 ++++++++++++--- 12 files changed, 303 insertions(+), 37 deletions(-) create mode 100644 lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/REQUIRE create mode 100644 lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/data.json create mode 100644 lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/large_x.json create mode 100644 lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/runner.jl create mode 100644 lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/small_x.json diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/factory.js index 416f508778e8..7978bc1c1908 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/factory.js @@ -23,6 +23,9 @@ var constantFunction = require( '@stdlib/utils/constant-function' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); var pow = require( '@stdlib/math/base/special/pow' ); +var log1mexp = require( '@stdlib/math/base/special/log1mexp' ); +var log1p = require( '@stdlib/math/base/special/log1p' ); +var expm1 = require( '@stdlib/math/base/special/expm1' ); var ln = require( '@stdlib/math/base/special/ln' ); var NINF = require( '@stdlib/constants/float64/ninf' ); @@ -68,6 +71,8 @@ function factory( a, b ) { * // returns */ function logcdf( x ) { + var u; + var v; if ( isnan( x ) ) { return NaN; } @@ -77,7 +82,14 @@ function factory( a, b ) { if ( x >= 1.0 ) { return 0.0; } - return ln( 1.0 - pow( 1.0 - pow( x, a ), b ) ); + // Evaluate `v = ln(1-x^a)` without forming `1-x^a`, which rounds away the low-order bits of a small `x^a` and, for `x^a` close to `1`, of `1-x^a` itself: + u = pow( x, a ); + if ( u < 0.5 ) { + v = log1p( -u ); + } else { + v = ln( -expm1( a * ln( x ) ) ); + } + return log1mexp( b * v ); } } diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/main.js index 5943ace09033..5b56e0e924de 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/main.js @@ -22,6 +22,9 @@ var isnan = require( '@stdlib/math/base/assert/is-nan' ); var pow = require( '@stdlib/math/base/special/pow' ); +var log1mexp = require( '@stdlib/math/base/special/log1mexp' ); +var log1p = require( '@stdlib/math/base/special/log1p' ); +var expm1 = require( '@stdlib/math/base/special/expm1' ); var ln = require( '@stdlib/math/base/special/ln' ); var NINF = require( '@stdlib/constants/float64/ninf' ); @@ -81,6 +84,8 @@ var NINF = require( '@stdlib/constants/float64/ninf' ); * // returns NaN */ function logcdf( x, a, b ) { + var u; + var v; if ( isnan( x ) || isnan( a ) || @@ -96,7 +101,14 @@ function logcdf( x, a, b ) { if ( x >= 1.0 ) { return 0.0; } - return ln( 1.0 - pow( 1.0 - pow( x, a ), b ) ); + // Evaluate `v = ln(1-x^a)` without forming `1-x^a`, which rounds away the low-order bits of a small `x^a` and, for `x^a` close to `1`, of `1-x^a` itself: + u = pow( x, a ); + if ( u < 0.5 ) { + v = log1p( -u ); + } else { + v = ln( -expm1( a * ln( x ) ) ); + } + return log1mexp( b * v ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/manifest.json b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/manifest.json index b302141e0a29..20e9f978ffc8 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/manifest.json +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/manifest.json @@ -41,6 +41,9 @@ "@stdlib/math/base/napi/ternary", "@stdlib/math/base/assert/is-nan", "@stdlib/math/base/special/pow", + "@stdlib/math/base/special/log1mexp", + "@stdlib/math/base/special/log1p", + "@stdlib/math/base/special/expm1", "@stdlib/math/base/special/ln", "@stdlib/constants/float64/ninf" ] @@ -59,6 +62,9 @@ "dependencies": [ "@stdlib/math/base/assert/is-nan", "@stdlib/math/base/special/pow", + "@stdlib/math/base/special/log1mexp", + "@stdlib/math/base/special/log1p", + "@stdlib/math/base/special/expm1", "@stdlib/math/base/special/ln", "@stdlib/constants/float64/ninf" ] @@ -77,6 +83,9 @@ "dependencies": [ "@stdlib/math/base/assert/is-nan", "@stdlib/math/base/special/pow", + "@stdlib/math/base/special/log1mexp", + "@stdlib/math/base/special/log1p", + "@stdlib/math/base/special/expm1", "@stdlib/math/base/special/ln", "@stdlib/constants/float64/ninf" ] diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/src/main.c index f6f23ead8607..1ad9c8b3d185 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/src/main.c +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/src/main.c @@ -19,6 +19,9 @@ #include "stdlib/stats/base/dists/kumaraswamy/logcdf.h" #include "stdlib/math/base/assert/is_nan.h" #include "stdlib/math/base/special/pow.h" +#include "stdlib/math/base/special/log1mexp.h" +#include "stdlib/math/base/special/log1p.h" +#include "stdlib/math/base/special/expm1.h" #include "stdlib/math/base/special/ln.h" #include "stdlib/constants/float64/ninf.h" @@ -35,6 +38,8 @@ * // returns ~-0.693 */ double stdlib_base_dists_kumaraswamy_logcdf( const double x, const double a, const double b ) { + double u; + double v; if ( stdlib_base_is_nan( x ) || stdlib_base_is_nan( a ) || @@ -50,5 +55,12 @@ double stdlib_base_dists_kumaraswamy_logcdf( const double x, const double a, con if ( x >= 1.0 ) { return 0.0; } - return stdlib_base_ln( 1.0 - stdlib_base_pow( 1.0 - stdlib_base_pow( x, a ), b ) ); + // Evaluate `v = ln(1-x^a)` without forming `1-x^a`, which rounds away the low-order bits of a small `x^a` and, for `x^a` close to `1`, of `1-x^a` itself: + u = stdlib_base_pow( x, a ); + if ( u < 0.5 ) { + v = stdlib_base_log1p( -u ); + } else { + v = stdlib_base_ln( -stdlib_base_expm1( a * stdlib_base_ln( x ) ) ); + } + return stdlib_base_log1mexp( b * v ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/REQUIRE new file mode 100644 index 000000000000..308c3be89c85 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/REQUIRE @@ -0,0 +1,2 @@ +julia 1.5 +JSON 0.21 diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/data.json b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/data.json new file mode 100644 index 000000000000..2cb82ea526a8 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/data.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/large_x.json b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/large_x.json new file mode 100644 index 000000000000..b0ab06409d5f --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/large_x.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/runner.jl new file mode 100644 index 000000000000..94f284d43bc0 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/runner.jl @@ -0,0 +1,80 @@ +#!/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( x, a, b, name ) + +Generate fixture data and write to file. + +The logarithm of the CDF is evaluated in extended precision from the textbook formula `ln(1 - (1 - x^a)^b)`, as forming `1 - x^a` in double precision rounds away the low-order bits of `x^a` (all of them for `x^a < 2^-53`). + +# Arguments + +* `x`: input value +* `a`: first shape parameter +* `b`: second shape parameter +* `name::AbstractString`: output filename +""" +function gen( x, a, b, name ) + z = setprecision( BigFloat, 2048 ) do + Float64.( log.( 1 .- ( 1 .- BigFloat.( x ) .^ BigFloat.( a ) ) .^ BigFloat.( b ) ) ) + end + + # Store data to be written to file as a collection: + data = Dict([ + ("x", x), + ("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: +x = rand( 1000 ); +a = ( rand( 1000 ) .* 5.0 ) .+ 0.5; +b = ( rand( 1000 ) .* 5.0 ) .+ 0.5; +gen( x, a, b, "data.json" ); + +# Small `x` (with `a` small enough that `x^a` does not underflow): +x = exp10.( range( -100.0, stop = -1.0, length = 1000 ) ); +a = ( rand( 1000 ) .* 2.5 ) .+ 0.5; +b = ( rand( 1000 ) .* 5.0 ) .+ 0.5; +gen( x, a, b, "small_x.json" ); + +# `x` close to `1`: +x = 1.0 .- exp10.( range( -15.0, stop = -1.0, length = 1000 ) ); +a = ( rand( 1000 ) .* 5.0 ) .+ 0.5; +b = ( rand( 1000 ) .* 5.0 ) .+ 0.5; +gen( x, a, b, "large_x.json" ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/small_x.json b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/small_x.json new file mode 100644 index 000000000000..dc76fd19940a --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/small_x.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.factory.js index 29910a003d05..31129a6e126e 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.factory.js @@ -21,15 +21,20 @@ // 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 smallX = require( './fixtures/julia/small_x.json' ); +var largeX = require( './fixtures/julia/large_x.json' ); + + // TESTS // tape( 'main export is a function', function test( t ) { @@ -186,22 +191,65 @@ tape( 'if provided a nonpositive `a`, the created function always returns `NaN`' t.end(); }); -tape( 'the returned function evaluates the logcdf of a Kumaraswamy\'s double bounded distribution', function test( t ) { +tape( 'the created function evaluates the logcdf for random `x`, `a` and `b`', function test( t ) { + var expected; var logcdf; var a; var b; + var i; var x; var y; + + expected = data.expected; + x = data.x; + a = data.a; + b = data.b; + for ( i = 0; i < expected.length; i++ ) { + logcdf = factory( a[i], b[i] ); + y = logcdf( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 25 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the created function evaluates the logcdf for small `x`', function test( t ) { + var expected; + var logcdf; + var a; + var b; var i; + var x; + var y; + + expected = smallX.expected; + x = smallX.x; + a = smallX.a; + b = smallX.b; + for ( i = 0; i < expected.length; i++ ) { + logcdf = factory( a[i], b[i] ); + y = logcdf( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the created function evaluates the logcdf for `x` close to `1`', function test( t ) { + var expected; + var logcdf; + var a; + var b; + var i; + var x; + var y; - // TODO: Add fixtures - a = ( randu()*5.0 ) + EPS; - b = ( randu()*5.0 ) + EPS; - logcdf = factory( a, b ); - for ( i = 0; i < 100; i++ ) { - x = randu(); - y = logcdf( x, a, b ); - t.strictEqual( isNumber( y ), true, 'returns expected value' ); + expected = largeX.expected; + x = largeX.x; + a = largeX.a; + b = largeX.b; + for ( i = 0; i < expected.length; i++ ) { + logcdf = factory( a[i], b[i] ); + y = logcdf( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 148 ), true, 'returns expected value' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.logcdf.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.logcdf.js index 01c7712b251e..06c21915fe84 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.logcdf.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.logcdf.js @@ -21,15 +21,20 @@ // 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 logcdf = require( './../lib' ); +// FIXTURES // + +var data = require( './fixtures/julia/data.json' ); +var smallX = require( './fixtures/julia/small_x.json' ); +var largeX = require( './fixtures/julia/large_x.json' ); + + // TESTS // tape( 'main export is a function', function test( t ) { @@ -134,20 +139,59 @@ tape( 'if provided a nonpositive `b`, the function returns `NaN`', function test t.end(); }); -tape( 'the function evaluates the logcdf of a Kumaraswamy\'s double bounded distribution', function test( t ) { +tape( 'the function evaluates the logcdf for random `x`, `a` and `b`', function test( t ) { + var expected; var a; var b; + var i; var x; var y; + + expected = data.expected; + x = data.x; + a = data.a; + b = data.b; + for ( i = 0; i < expected.length; i++ ) { + y = logcdf( x[i], a[i], b[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 25 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the logcdf for small `x`', function test( t ) { + var expected; + var a; + var b; var i; + var x; + var y; + + expected = smallX.expected; + x = smallX.x; + a = smallX.a; + b = smallX.b; + for ( i = 0; i < expected.length; i++ ) { + y = logcdf( x[i], a[i], b[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the logcdf for `x` close to `1`', function test( t ) { + var expected; + var a; + var b; + var i; + var x; + var y; - // TODO: Add fixtures - for ( i = 0; i < 100; i++ ) { - x = randu(); - a = ( randu()*5.0 ) + EPS; - b = ( randu()*5.0 ) + EPS; - y = logcdf( x, a, b ); - t.strictEqual( isNumber( y ), true, 'returns expected value' ); + expected = largeX.expected; + x = largeX.x; + a = largeX.a; + b = largeX.b; + for ( i = 0; i < expected.length; i++ ) { + y = logcdf( x[i], a[i], b[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 148 ), true, 'returns expected value' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.native.js index 0ac6174fb072..959f4e35af9e 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.native.js @@ -23,12 +23,17 @@ 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 smallX = require( './fixtures/julia/small_x.json' ); +var largeX = require( './fixtures/julia/large_x.json' ); // VARIABLES // @@ -143,20 +148,59 @@ tape( 'if provided a nonpositive `b`, the function returns `NaN`', opts, functio t.end(); }); -tape( 'the function evaluates the logcdf of a Kumaraswamy\'s double bounded distribution', opts, function test( t ) { +tape( 'the function evaluates the logcdf for random `x`, `a` and `b`', opts, function test( t ) { + var expected; var a; var b; + var i; var x; var y; + + expected = data.expected; + x = data.x; + a = data.a; + b = data.b; + for ( i = 0; i < expected.length; i++ ) { + y = logcdf( x[i], a[i], b[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 25 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the logcdf for small `x`', opts, function test( t ) { + var expected; + var a; + var b; var i; + var x; + var y; + + expected = smallX.expected; + x = smallX.x; + a = smallX.a; + b = smallX.b; + for ( i = 0; i < expected.length; i++ ) { + y = logcdf( x[i], a[i], b[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the logcdf for `x` close to `1`', opts, function test( t ) { + var expected; + var a; + var b; + var i; + var x; + var y; - // TODO: Add fixtures - for ( i = 0; i < 100; i++ ) { - x = randu(); - a = ( randu()*5.0 ) + EPS; - b = ( randu()*5.0 ) + EPS; - y = logcdf( x, a, b ); - t.strictEqual( isNumber( y ), true, 'returns expected value' ); + expected = largeX.expected; + x = largeX.x; + a = largeX.a; + b = largeX.b; + for ( i = 0; i < expected.length; i++ ) { + y = logcdf( x[i], a[i], b[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 148 ), true, 'returns expected value' ); } t.end(); }); From c83cde08a7fc5ad728a860717492be45cf9df4c7 Mon Sep 17 00:00:00 2001 From: Abhist17 Date: Fri, 9 Oct 2026 03:55:39 +0530 Subject: [PATCH 2/2] fix: handle underflow of `x^a` and `b*v` in `stats/base/dists/kumaraswamy/logcdf` Per review: when `x^a` is subnormal the log-CDF is `ln(b) + a*ln(x)`, and when `b*v` underflows it is `ln(b) + ln(-v)`. `logcdf( 1e-200, 3, 2 )`, `logcdf( 0.9, 1e5, 2 )` and `logcdf( 1e-100, 2, 1e-200 )` returned -Infinity. The small-`x` fixture now reaches `1e-300` with `a` up to 5.5, evaluated at 8192 bits, at 2 ULP. --- .../base/dists/kumaraswamy/logcdf/lib/factory.js | 12 +++++++++++- .../stats/base/dists/kumaraswamy/logcdf/lib/main.js | 12 +++++++++++- .../base/dists/kumaraswamy/logcdf/manifest.json | 9 ++++++--- .../stats/base/dists/kumaraswamy/logcdf/src/main.c | 12 +++++++++++- .../kumaraswamy/logcdf/test/fixtures/julia/runner.jl | 8 ++++---- .../logcdf/test/fixtures/julia/small_x.json | 2 +- .../dists/kumaraswamy/logcdf/test/test.factory.js | 2 +- .../dists/kumaraswamy/logcdf/test/test.logcdf.js | 2 +- .../dists/kumaraswamy/logcdf/test/test.native.js | 2 +- 9 files changed, 47 insertions(+), 14 deletions(-) diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/factory.js index 7978bc1c1908..eec289018dd5 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/factory.js @@ -28,6 +28,7 @@ var log1p = require( '@stdlib/math/base/special/log1p' ); var expm1 = require( '@stdlib/math/base/special/expm1' ); var ln = require( '@stdlib/math/base/special/ln' ); var NINF = require( '@stdlib/constants/float64/ninf' ); +var FLOAT64_SMALLEST_NORMAL = require( '@stdlib/constants/float64/smallest-normal' ); // MAIN // @@ -73,6 +74,7 @@ function factory( a, b ) { function logcdf( x ) { var u; var v; + var t; if ( isnan( x ) ) { return NaN; } @@ -84,12 +86,20 @@ function factory( a, b ) { } // Evaluate `v = ln(1-x^a)` without forming `1-x^a`, which rounds away the low-order bits of a small `x^a` and, for `x^a` close to `1`, of `1-x^a` itself: u = pow( x, a ); + if ( u < FLOAT64_SMALLEST_NORMAL ) { + // `x^a` is subnormal or underflows, so `ln(1-(1-x^a)^b) = ln(b) + a*ln(x)`: + return ln( b ) + ( a * ln( x ) ); + } if ( u < 0.5 ) { v = log1p( -u ); } else { v = ln( -expm1( a * ln( x ) ) ); } - return log1mexp( b * v ); + t = b * v; + if ( t > -FLOAT64_SMALLEST_NORMAL ) { + return ln( b ) + ln( -v ); + } + return log1mexp( t ); } } diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/main.js index 5b56e0e924de..355a88d282ef 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/lib/main.js @@ -27,6 +27,7 @@ var log1p = require( '@stdlib/math/base/special/log1p' ); var expm1 = require( '@stdlib/math/base/special/expm1' ); var ln = require( '@stdlib/math/base/special/ln' ); var NINF = require( '@stdlib/constants/float64/ninf' ); +var FLOAT64_SMALLEST_NORMAL = require( '@stdlib/constants/float64/smallest-normal' ); // MAIN // @@ -86,6 +87,7 @@ var NINF = require( '@stdlib/constants/float64/ninf' ); function logcdf( x, a, b ) { var u; var v; + var t; if ( isnan( x ) || isnan( a ) || @@ -103,12 +105,20 @@ function logcdf( x, a, b ) { } // Evaluate `v = ln(1-x^a)` without forming `1-x^a`, which rounds away the low-order bits of a small `x^a` and, for `x^a` close to `1`, of `1-x^a` itself: u = pow( x, a ); + if ( u < FLOAT64_SMALLEST_NORMAL ) { + // `x^a` is subnormal or underflows, so `ln(1-(1-x^a)^b) = ln(b) + a*ln(x)`: + return ln( b ) + ( a * ln( x ) ); + } if ( u < 0.5 ) { v = log1p( -u ); } else { v = ln( -expm1( a * ln( x ) ) ); } - return log1mexp( b * v ); + t = b * v; + if ( t > -FLOAT64_SMALLEST_NORMAL ) { + return ln( b ) + ln( -v ); + } + return log1mexp( t ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/manifest.json b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/manifest.json index 20e9f978ffc8..83413db0ef69 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/manifest.json +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/manifest.json @@ -45,7 +45,8 @@ "@stdlib/math/base/special/log1p", "@stdlib/math/base/special/expm1", "@stdlib/math/base/special/ln", - "@stdlib/constants/float64/ninf" + "@stdlib/constants/float64/ninf", + "@stdlib/constants/float64/smallest-normal" ] }, { @@ -66,7 +67,8 @@ "@stdlib/math/base/special/log1p", "@stdlib/math/base/special/expm1", "@stdlib/math/base/special/ln", - "@stdlib/constants/float64/ninf" + "@stdlib/constants/float64/ninf", + "@stdlib/constants/float64/smallest-normal" ] }, { @@ -87,7 +89,8 @@ "@stdlib/math/base/special/log1p", "@stdlib/math/base/special/expm1", "@stdlib/math/base/special/ln", - "@stdlib/constants/float64/ninf" + "@stdlib/constants/float64/ninf", + "@stdlib/constants/float64/smallest-normal" ] } ] diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/src/main.c index 1ad9c8b3d185..999dbc5cb981 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/src/main.c +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/src/main.c @@ -24,6 +24,7 @@ #include "stdlib/math/base/special/expm1.h" #include "stdlib/math/base/special/ln.h" #include "stdlib/constants/float64/ninf.h" +#include "stdlib/constants/float64/smallest_normal.h" /** * Evaluates the natural logarithm of the cumulative distribution function (CDF) for a Kumaraswamy's double bounded distribution with first shape parameter `a` and second shape parameter `b` at a value `x`. @@ -40,6 +41,7 @@ double stdlib_base_dists_kumaraswamy_logcdf( const double x, const double a, const double b ) { double u; double v; + double t; if ( stdlib_base_is_nan( x ) || stdlib_base_is_nan( a ) || @@ -57,10 +59,18 @@ double stdlib_base_dists_kumaraswamy_logcdf( const double x, const double a, con } // Evaluate `v = ln(1-x^a)` without forming `1-x^a`, which rounds away the low-order bits of a small `x^a` and, for `x^a` close to `1`, of `1-x^a` itself: u = stdlib_base_pow( x, a ); + if ( u < STDLIB_CONSTANT_FLOAT64_SMALLEST_NORMAL ) { + // `x^a` is subnormal or underflows, so `ln(1-(1-x^a)^b) = ln(b) + a*ln(x)`: + return stdlib_base_ln( b ) + ( a * stdlib_base_ln( x ) ); + } if ( u < 0.5 ) { v = stdlib_base_log1p( -u ); } else { v = stdlib_base_ln( -stdlib_base_expm1( a * stdlib_base_ln( x ) ) ); } - return stdlib_base_log1mexp( b * v ); + t = b * v; + if ( t > -STDLIB_CONSTANT_FLOAT64_SMALLEST_NORMAL ) { + return stdlib_base_ln( b ) + stdlib_base_ln( -v ); + } + return stdlib_base_log1mexp( t ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/runner.jl index 94f284d43bc0..bdcfde50d747 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/runner.jl @@ -33,7 +33,7 @@ The logarithm of the CDF is evaluated in extended precision from the textbook fo * `name::AbstractString`: output filename """ function gen( x, a, b, name ) - z = setprecision( BigFloat, 2048 ) do + z = setprecision( BigFloat, 8192 ) do Float64.( log.( 1 .- ( 1 .- BigFloat.( x ) .^ BigFloat.( a ) ) .^ BigFloat.( b ) ) ) end @@ -67,9 +67,9 @@ a = ( rand( 1000 ) .* 5.0 ) .+ 0.5; b = ( rand( 1000 ) .* 5.0 ) .+ 0.5; gen( x, a, b, "data.json" ); -# Small `x` (with `a` small enough that `x^a` does not underflow): -x = exp10.( range( -100.0, stop = -1.0, length = 1000 ) ); -a = ( rand( 1000 ) .* 2.5 ) .+ 0.5; +# Small `x`: +x = exp10.( range( -300.0, stop = -1.0, length = 1000 ) ); +a = ( rand( 1000 ) .* 5.0 ) .+ 0.5; b = ( rand( 1000 ) .* 5.0 ) .+ 0.5; gen( x, a, b, "small_x.json" ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/small_x.json b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/small_x.json index dc76fd19940a..7bc07025ca21 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/small_x.json +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/fixtures/julia/small_x.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.factory.js index 31129a6e126e..642dacc5a4e9 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.factory.js @@ -228,7 +228,7 @@ tape( 'the created function evaluates the logcdf for small `x`', function test( for ( i = 0; i < expected.length; i++ ) { logcdf = factory( a[i], b[i] ); y = logcdf( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.logcdf.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.logcdf.js index 06c21915fe84..7008f291af86 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.logcdf.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.logcdf.js @@ -172,7 +172,7 @@ tape( 'the function evaluates the logcdf for small `x`', function test( t ) { b = smallX.b; for ( i = 0; i < expected.length; i++ ) { y = logcdf( x[i], a[i], b[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.native.js index 959f4e35af9e..f5fffbb71b63 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/logcdf/test/test.native.js @@ -181,7 +181,7 @@ tape( 'the function evaluates the logcdf for small `x`', opts, function test( t b = smallX.b; for ( i = 0; i < expected.length; i++ ) { y = logcdf( x[i], a[i], b[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); });