From 7a28498753799b53ee811b1f7205352d2a2670bf Mon Sep 17 00:00:00 2001 From: Abhist17 Date: Fri, 2 Oct 2026 04:51:40 +0530 Subject: [PATCH 1/2] fix: avoid cancellation for small `p` in `stats/base/dists/geometric/cdf` `1 - p` rounds away the low-order bits of `p`, and `1 - (1-p)^(x+1)` then cancels. For `p < 2^-53` the function returned `0`. Use `-expm1( (x+1) * log1p(-p) )` and generate the fixtures from the textbook formula in extended precision. --- .../base/dists/geometric/cdf/lib/factory.js | 5 +++-- .../base/dists/geometric/cdf/lib/main.js | 5 +++-- .../base/dists/geometric/cdf/manifest.json | 9 +++++--- .../stats/base/dists/geometric/cdf/src/main.c | 5 +++-- .../geometric/cdf/test/fixtures/julia/REQUIRE | 1 - .../cdf/test/fixtures/julia/large_p.json | 2 +- .../cdf/test/fixtures/julia/runner.jl | 13 +++++++---- .../cdf/test/fixtures/julia/small_p.json | 2 +- .../cdf/test/fixtures/julia/tiny_p.json | 1 + .../base/dists/geometric/cdf/test/test.cdf.js | 20 ++++++++++++++++- .../dists/geometric/cdf/test/test.factory.js | 22 ++++++++++++++++++- .../dists/geometric/cdf/test/test.native.js | 20 ++++++++++++++++- 12 files changed, 86 insertions(+), 19 deletions(-) create mode 100644 lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/tiny_p.json diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/lib/factory.js index 920931c22fe0..bed54d01ab71 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/lib/factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/lib/factory.js @@ -23,7 +23,8 @@ var constantFunction = require( '@stdlib/utils/constant-function' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); var floor = require( '@stdlib/math/base/special/floor' ); -var pow = require( '@stdlib/math/base/special/pow' ); +var expm1 = require( '@stdlib/math/base/special/expm1' ); +var log1p = require( '@stdlib/math/base/special/log1p' ); var PINF = require( '@stdlib/constants/float64/pinf' ); @@ -71,7 +72,7 @@ function factory( p ) { return 1.0; } x = floor( x ); - return 1.0 - pow( 1.0 - p, x + 1.0 ); + return -expm1( ( x+1.0 ) * log1p( -p ) ); } } diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/lib/main.js index bec80fff33b8..b9576835a006 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/lib/main.js @@ -22,7 +22,8 @@ var isnan = require( '@stdlib/math/base/assert/is-nan' ); var floor = require( '@stdlib/math/base/special/floor' ); -var pow = require( '@stdlib/math/base/special/pow' ); +var expm1 = require( '@stdlib/math/base/special/expm1' ); +var log1p = require( '@stdlib/math/base/special/log1p' ); var PINF = require( '@stdlib/constants/float64/pinf' ); @@ -76,7 +77,7 @@ function cdf( x, p ) { return 1.0; } x = floor( x ); - return 1.0 - pow( 1.0 - p, x + 1.0 ); + return -expm1( ( x+1.0 ) * log1p( -p ) ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/manifest.json b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/manifest.json index 8de05b4fb95b..72eb427ef3b0 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/manifest.json +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/manifest.json @@ -42,7 +42,8 @@ "@stdlib/math/base/assert/is-nan", "@stdlib/constants/float64/pinf", "@stdlib/math/base/special/floor", - "@stdlib/math/base/special/pow" + "@stdlib/math/base/special/expm1", + "@stdlib/math/base/special/log1p" ] }, { @@ -61,7 +62,8 @@ "@stdlib/constants/float64/pinf", "@stdlib/math/base/special/floor", "@stdlib/constants/float64/eps", - "@stdlib/math/base/special/pow" + "@stdlib/math/base/special/expm1", + "@stdlib/math/base/special/log1p" ] }, { @@ -79,7 +81,8 @@ "@stdlib/math/base/assert/is-nan", "@stdlib/constants/float64/pinf", "@stdlib/math/base/special/floor", - "@stdlib/math/base/special/pow" + "@stdlib/math/base/special/expm1", + "@stdlib/math/base/special/log1p" ] } ] diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/src/main.c index 5e4d7c871dad..2d5793b9d693 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/src/main.c +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/src/main.c @@ -20,7 +20,8 @@ #include "stdlib/math/base/assert/is_nan.h" #include "stdlib/constants/float64/pinf.h" #include "stdlib/math/base/special/floor.h" -#include "stdlib/math/base/special/pow.h" +#include "stdlib/math/base/special/expm1.h" +#include "stdlib/math/base/special/log1p.h" /** * Evaluates the cumulative distribution function (CDF) for a geometric distribution with success probability `p` at a value `x`. @@ -48,5 +49,5 @@ double stdlib_base_dists_geometric_cdf( const double x, const double p ) { if ( x == STDLIB_CONSTANT_FLOAT64_PINF ) { return 1.0; } - return 1.0 - stdlib_base_pow( 1.0 - p, stdlib_base_floor( x ) + 1.0 ); + return -stdlib_base_expm1( ( stdlib_base_floor( x ) + 1.0 ) * stdlib_base_log1p( -p ) ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/REQUIRE index 98be20b58ed3..308c3be89c85 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/REQUIRE +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/REQUIRE @@ -1,3 +1,2 @@ -Distributions 0.23.8 julia 1.5 JSON 0.21 diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/large_p.json b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/large_p.json index 39f2ff816ad4..30f8298e3ca4 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/large_p.json +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/large_p.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/runner.jl index 5c659e6bd520..85aa1a2003be 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/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, Geometric import JSON """ @@ -24,6 +23,8 @@ import JSON Generate fixture data and write to file. +The CDF is evaluated in extended precision from the textbook formula `1 - (1-p)^(floor(x)+1)`, as forming `1-p` in double precision rounds away the low-order bits of `p` (all of them for `p < 2^-53`). + # Arguments * `x`: input value @@ -39,9 +40,8 @@ julia> gen( x, p, "data.json" ); ``` """ function gen( x, p, name ) - z = Array{Float64}( undef, length(x) ); - for i in eachindex(x) - z[ i ] = cdf( Geometric( p[i] ), x[i] ); + z = setprecision( BigFloat, 2048 ) do + Float64.( 1 .- ( 1 .- BigFloat.( p ) ) .^ ( floor.( x ) .+ 1 ) ) end # Store data to be written to file as a collection: @@ -76,3 +76,8 @@ gen( x, p, "large_p.json" ); x = rand( 1000 ) .* 10.0; p = rand( 1000 ) .* 0.5; gen( x, p, "small_p.json" ); + +# Tiny `p`: +x = rand( 1000 ) .* 100.0; +p = exp10.( range( -300.0, stop = -1.0, length = 1000 ) ); +gen( x, p, "tiny_p.json" ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/small_p.json b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/small_p.json index a21ce6f4192a..5c886e9392f0 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/small_p.json +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/small_p.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/tiny_p.json b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/tiny_p.json new file mode 100644 index 000000000000..1498a8d45b0d --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/tiny_p.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.cdf.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.cdf.js index 36fc1315b32f..da03c002c406 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.cdf.js +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.cdf.js @@ -31,6 +31,7 @@ var cdf = require( './../lib' ); // FIXTURES // var smallP = require( './fixtures/julia/small_p.json' ); +var tinyP = require( './fixtures/julia/tiny_p.json' ); var largeP = require( './fixtures/julia/large_p.json' ); @@ -99,7 +100,7 @@ tape( 'the function evaluates the cdf for `x` given small parameter `p`', functi p = smallP.p; for ( i = 0; i < x.length; i++ ) { y = cdf( x[i], p[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 20 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); } t.end(); }); @@ -120,3 +121,20 @@ tape( 'the function evaluates the cdf for `x` given large parameter `p`', functi } t.end(); }); + +tape( 'the function evaluates the cdf for `x` given tiny parameter `p`', function test( t ) { + var expected; + var x; + var p; + var y; + var i; + + expected = tinyP.expected; + x = tinyP.x; + p = tinyP.p; + for ( i = 0; i < x.length; i++ ) { + y = cdf( x[i], p[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + } + t.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.factory.js index 6365cb59dcf3..3b23823fe365 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.factory.js @@ -31,6 +31,7 @@ var factory = require( './../lib/factory.js' ); // FIXTURES // var smallP = require( './fixtures/julia/small_p.json' ); +var tinyP = require( './fixtures/julia/tiny_p.json' ); var largeP = require( './fixtures/julia/large_p.json' ); @@ -133,7 +134,7 @@ tape( 'the created function evaluates the cdf for `x` given small parameter `p`' for ( i = 0; i < x.length; i++ ) { cdf = factory( p[i] ); y = cdf( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 20 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); } t.end(); }); @@ -156,3 +157,22 @@ tape( 'the created function evaluates the cdf for `x` given large parameter `p`' } t.end(); }); + +tape( 'the created function evaluates the cdf for `x` given tiny parameter `p`', function test( t ) { + var expected; + var cdf; + var x; + var p; + var y; + var i; + + expected = tinyP.expected; + x = tinyP.x; + p = tinyP.p; + for ( i = 0; i < x.length; i++ ) { + cdf = factory( p[i] ); + y = cdf( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + } + t.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.native.js index ae93520693dc..828cbcfebe9c 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.native.js @@ -32,6 +32,7 @@ var tryRequire = require( '@stdlib/utils/try-require' ); // FIXTURES // var smallP = require( './fixtures/julia/small_p.json' ); +var tinyP = require( './fixtures/julia/tiny_p.json' ); var largeP = require( './fixtures/julia/large_p.json' ); @@ -108,7 +109,7 @@ tape( 'the function evaluates the cdf for `x` given small parameter `p`', opts, p = smallP.p; for ( i = 0; i < x.length; i++ ) { y = cdf( x[i], p[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 20 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); } t.end(); }); @@ -129,3 +130,20 @@ tape( 'the function evaluates the cdf for `x` given large parameter `p`', opts, } t.end(); }); + +tape( 'the function evaluates the cdf for `x` given tiny parameter `p`', opts, function test( t ) { + var expected; + var x; + var p; + var y; + var i; + + expected = tinyP.expected; + x = tinyP.x; + p = tinyP.p; + for ( i = 0; i < x.length; i++ ) { + y = cdf( x[i], p[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + } + t.end(); +}); From 9149c8bb90b467d48a7965530d26967d25842bb3 Mon Sep 17 00:00:00 2001 From: Abhist17 Date: Fri, 9 Oct 2026 04:00:06 +0530 Subject: [PATCH 2/2] test: cover tiny `p` with `x` near `1/p` in `stats/base/dists/geometric/cdf` Per review: every existing tiny-`p` case had a result below 1e-14, so CDF values of order 1 (`cdf( 1e20, 1e-20 ) = 0.632`; develop gives 0) weren't tested. Adds `tiny_p_large_x.json` with `x` up to `3/p`, at 1 ULP. --- .../cdf/test/fixtures/julia/runner.jl | 5 +++++ .../test/fixtures/julia/tiny_p_large_x.json | 1 + .../base/dists/geometric/cdf/test/test.cdf.js | 18 +++++++++++++++++ .../dists/geometric/cdf/test/test.factory.js | 20 +++++++++++++++++++ .../dists/geometric/cdf/test/test.native.js | 18 +++++++++++++++++ 5 files changed, 62 insertions(+) create mode 100644 lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/tiny_p_large_x.json diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/runner.jl index 85aa1a2003be..df09cefb96a5 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/runner.jl @@ -81,3 +81,8 @@ gen( x, p, "small_p.json" ); x = rand( 1000 ) .* 100.0; p = exp10.( range( -300.0, stop = -1.0, length = 1000 ) ); gen( x, p, "tiny_p.json" ); + +# Tiny `p` with `x` near `1/p`, where the CDF is of order `1`: +p = exp10.( range( -300.0, stop = -1.0, length = 1000 ) ); +x = floor.( rand( 1000 ) .* 3.0 ./ p ); +gen( x, p, "tiny_p_large_x.json" ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/tiny_p_large_x.json b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/tiny_p_large_x.json new file mode 100644 index 000000000000..aab29b938fd1 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/fixtures/julia/tiny_p_large_x.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.cdf.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.cdf.js index da03c002c406..b3717ac63181 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.cdf.js +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.cdf.js @@ -32,6 +32,7 @@ var cdf = require( './../lib' ); var smallP = require( './fixtures/julia/small_p.json' ); var tinyP = require( './fixtures/julia/tiny_p.json' ); +var tinyPLargeX = require( './fixtures/julia/tiny_p_large_x.json' ); var largeP = require( './fixtures/julia/large_p.json' ); @@ -138,3 +139,20 @@ tape( 'the function evaluates the cdf for `x` given tiny parameter `p`', functio } t.end(); }); + +tape( 'the function evaluates the cdf for `x` given tiny parameter `p` and `x` near `1/p`', function test( t ) { + var expected; + var x; + var p; + var y; + var i; + + expected = tinyPLargeX.expected; + x = tinyPLargeX.x; + p = tinyPLargeX.p; + for ( i = 0; i < x.length; i++ ) { + y = cdf( x[i], p[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + } + t.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.factory.js index 3b23823fe365..ceeba2238c7b 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.factory.js @@ -32,6 +32,7 @@ var factory = require( './../lib/factory.js' ); var smallP = require( './fixtures/julia/small_p.json' ); var tinyP = require( './fixtures/julia/tiny_p.json' ); +var tinyPLargeX = require( './fixtures/julia/tiny_p_large_x.json' ); var largeP = require( './fixtures/julia/large_p.json' ); @@ -176,3 +177,22 @@ tape( 'the created function evaluates the cdf for `x` given tiny parameter `p`', } t.end(); }); + +tape( 'the created function evaluates the cdf for `x` given tiny parameter `p` and `x` near `1/p`', function test( t ) { + var expected; + var cdf; + var x; + var p; + var y; + var i; + + expected = tinyPLargeX.expected; + x = tinyPLargeX.x; + p = tinyPLargeX.p; + for ( i = 0; i < x.length; i++ ) { + cdf = factory( p[i] ); + y = cdf( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + } + t.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.native.js index 828cbcfebe9c..fede016712fd 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/cdf/test/test.native.js @@ -33,6 +33,7 @@ var tryRequire = require( '@stdlib/utils/try-require' ); var smallP = require( './fixtures/julia/small_p.json' ); var tinyP = require( './fixtures/julia/tiny_p.json' ); +var tinyPLargeX = require( './fixtures/julia/tiny_p_large_x.json' ); var largeP = require( './fixtures/julia/large_p.json' ); @@ -147,3 +148,20 @@ tape( 'the function evaluates the cdf for `x` given tiny parameter `p`', opts, f } t.end(); }); + +tape( 'the function evaluates the cdf for `x` given tiny parameter `p` and `x` near `1/p`', opts, function test( t ) { + var expected; + var x; + var p; + var y; + var i; + + expected = tinyPLargeX.expected; + x = tinyPLargeX.x; + p = tinyPLargeX.p; + for ( i = 0; i < x.length; i++ ) { + y = cdf( x[i], p[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + } + t.end(); +});