From ed35ab8ed0253d9ca0bd8bc668d2194dc4482600 Mon Sep 17 00:00:00 2001 From: Abhist17 Date: Mon, 28 Sep 2026 04:50:27 +0530 Subject: [PATCH 1/5] fix: avoid rounding `x + 1` for `-1 < x < 1` in `math/base/special/factorialln` `gammaln( x + 1.0 )` loses the low-order bits of `x` when forming `x + 1`, and all of them for `|x| < 2^-53`: `factorialln( 1e-20 )` returned `0` instead of `-5.77e-21`, and `factorialln( 1e-8 )` had 8 correct digits. For `-1 < x < 1`, evaluate `log1p( gamma1pm1( x ) )`, which never forms `x + 1`. Add a fixture for `x` in `(-1, 1)` generated in 2048-bit precision. --- .../math/base/special/factorialln/lib/main.js | 6 +++ .../base/special/factorialln/manifest.json | 6 +++ .../math/base/special/factorialln/src/main.c | 6 +++ .../test/fixtures/julia/fractional.json | 1 + .../factorialln/test/fixtures/julia/runner.jl | 38 +++++++++++++++++++ .../base/special/factorialln/test/test.js | 21 +++++++++- .../special/factorialln/test/test.native.js | 21 +++++++++- 7 files changed, 97 insertions(+), 2 deletions(-) create mode 100644 lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/fractional.json diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js b/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js index 192df90b8730..0ab7394cb556 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js @@ -21,7 +21,9 @@ // MODULES // var isNegativeInteger = require( '@stdlib/math/base/assert/is-negative-integer' ); +var gamma1pm1 = require( '@stdlib/math/base/special/gamma1pm1' ); var gammaln = require( '@stdlib/math/base/special/gammaln' ); +var log1p = require( '@stdlib/math/base/special/log1p' ); // MAIN // @@ -56,6 +58,10 @@ function factorialln( x ) { if ( isNegativeInteger( x ) ) { return NaN; } + // For `-1 < x < 1`, `x + 1` rounds away the low-order bits of `x` (all of them for `|x| < 2^-53`), so use `ln(1 + (Γ(x+1) - 1))` with `Γ(x+1) - 1` evaluated without forming `x + 1`: + if ( x > -1.0 && x < 1.0 ) { + return log1p( gamma1pm1( x ) ); + } return gammaln( x + 1.0 ); } diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/manifest.json b/lib/node_modules/@stdlib/math/base/special/factorialln/manifest.json index 48f9714d9802..a6688f495f10 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/manifest.json +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/manifest.json @@ -38,7 +38,9 @@ "dependencies": [ "@stdlib/math/base/napi/unary", "@stdlib/math/base/assert/is-negative-integer", + "@stdlib/math/base/special/gamma1pm1", "@stdlib/math/base/special/gammaln", + "@stdlib/math/base/special/log1p", "@stdlib/constants/float64/nan" ] }, @@ -54,7 +56,9 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/assert/is-negative-integer", + "@stdlib/math/base/special/gamma1pm1", "@stdlib/math/base/special/gammaln", + "@stdlib/math/base/special/log1p", "@stdlib/constants/float64/nan" ] }, @@ -70,7 +74,9 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/assert/is-negative-integer", + "@stdlib/math/base/special/gamma1pm1", "@stdlib/math/base/special/gammaln", + "@stdlib/math/base/special/log1p", "@stdlib/constants/float64/nan" ] } diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c b/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c index c8be4e611932..b267d96b73a5 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c @@ -19,7 +19,9 @@ #include "stdlib/math/base/special/factorialln.h" #include "stdlib/constants/float64/nan.h" #include "stdlib/math/base/assert/is_negative_integer.h" +#include "stdlib/math/base/special/gamma1pm1.h" #include "stdlib/math/base/special/gammaln.h" +#include "stdlib/math/base/special/log1p.h" /** * Evaluates the natural logarithm of the factorial of `x`. @@ -35,5 +37,9 @@ double stdlib_base_factorialln( const double x ) { if ( stdlib_base_is_negative_integer( x ) ) { return STDLIB_CONSTANT_FLOAT64_NAN; } + // For `-1 < x < 1`, `x + 1` rounds away the low-order bits of `x` (all of them for `|x| < 2^-53`), so use `ln(1 + (Γ(x+1) - 1))` with `Γ(x+1) - 1` evaluated without forming `x + 1`: + if ( x > -1.0 && x < 1.0 ) { + return stdlib_base_log1p( stdlib_base_gamma1pm1( x ) ); + } return stdlib_base_gammaln( x + 1.0 ); } diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/fractional.json b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/fractional.json new file mode 100644 index 000000000000..093de21bf5d0 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/fractional.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl index 0d280a26bb7c..5d388360855e 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl @@ -62,6 +62,40 @@ function gen( x, name ) close( outfile ); end +""" + gen_fractional( x, name ) + +Generate fixture data for `-1 < x < 1` in extended precision and write to file. In double precision, `x+1` rounds away the low-order bits of `x`, so the reference value is computed from `x` exactly. + +# Arguments + +* `x`: domain +* `name::AbstractString`: output filename +""" +function gen_fractional( x, name ) + y = Array{Float64}( undef, length( x ) ); + setprecision( BigFloat, 2048 ) do + for i in eachindex(x) + y[i] = Float64( loggamma( BigFloat( x[i] ) + 1 ) ); + end + end + + # Store data to be written to file as a collection: + data = Dict([ + ("x", x), + ("expected", y) + ]); + + # 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__; @@ -83,3 +117,7 @@ gen( x, "large_positive.json" ); # Very large positive values: x = collect( 5000:50:10000 ); gen( x, "very_large_positive.json" ); + +# Fractional values in (-1,1), including tiny magnitudes: +x = vcat( -exp10.( range( -300.0, stop = log10( 0.999 ), length = 500 ) ), exp10.( range( -300.0, stop = log10( 0.999 ), length = 500 ) ), collect( range( -0.999, stop = 0.999, length = 1000 ) ) ); +gen_fractional( x, "fractional.json" ); diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.js b/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.js index 283fca3452bb..c62e8d0eeab3 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.js @@ -36,6 +36,7 @@ var factorialln = require( './../lib' ); var veryLargePositive = require( './fixtures/julia/very_large_positive.json' ); var largePositive = require( './fixtures/julia/large_positive.json' ); var mediumPositive = require( './fixtures/julia/medium_positive.json' ); +var fractional = require( './fixtures/julia/fractional.json' ); var smallPositive = require( './fixtures/julia/small_positive.json' ); @@ -125,6 +126,22 @@ tape( 'the function evaluates the natural logarithm of the factorial of `x` (med t.end(); }); +tape( 'the function evaluates the natural logarithm of the factorial of `x` (`-1 < x < 1`)', function test( t ) { + var expected; + var x; + var y; + var i; + + expected = fractional.expected; + x = fractional.x; + + for ( i = 0; i < x.length; i++ ) { + y = factorialln( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); + } + t.end(); +}); + tape( 'the function evaluates the natural logarithm of the factorial of `x` (small positive values)', function test( t ) { var expected; var x; @@ -150,7 +167,9 @@ tape( 'the function returns a value almost equal to `ln( factorial( x )` for `x` for ( i = 0; i < values.length; i++ ) { v = factorialln( values[ i ] ); expected = ln( factorial( values[ i ] ) ); - t.strictEqual( isAlmostSameValue( v, expected, 6 ), true, 'returns expected value' ); + + // Note: `ln( factorial( 0.5 ) )` is itself 7 ULP from the correctly rounded value of `ln(Γ(1.5))`, which the function returns... + t.strictEqual( isAlmostSameValue( v, expected, 8 ), true, 'returns expected value' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.native.js index 6a82c22b0a3f..003d0c9e26c2 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.native.js @@ -37,6 +37,7 @@ var tryRequire = require( '@stdlib/utils/try-require' ); var veryLargePositive = require( './fixtures/julia/very_large_positive.json' ); var largePositive = require( './fixtures/julia/large_positive.json' ); var mediumPositive = require( './fixtures/julia/medium_positive.json' ); +var fractional = require( './fixtures/julia/fractional.json' ); var smallPositive = require( './fixtures/julia/small_positive.json' ); @@ -136,6 +137,22 @@ tape( 'the function evaluates the natural logarithm of the factorial of `x` (med t.end(); }); +tape( 'the function evaluates the natural logarithm of the factorial of `x` (`-1 < x < 1`)', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + expected = fractional.expected; + x = fractional.x; + + for ( i = 0; i < x.length; i++ ) { + y = factorialln( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); + } + t.end(); +}); + tape( 'the function evaluates the natural logarithm of the factorial of `x` (small positive values)', opts, function test( t ) { var expected; var x; @@ -161,7 +178,9 @@ tape( 'the function returns a value almost equal to `ln( factorial( x )` for `x` for ( i = 0; i < values.length; i++ ) { v = factorialln( values[ i ] ); expected = ln( factorial( values[ i ] ) ); - t.strictEqual( isAlmostSameValue( v, expected, 6 ), true, 'returns expected value' ); + + // Note: `ln( factorial( 0.5 ) )` is itself 7 ULP from the correctly rounded value of `ln(Γ(1.5))`, which the function returns... + t.strictEqual( isAlmostSameValue( v, expected, 8 ), true, 'returns expected value' ); } t.end(); }); From b780a232a69758c74139213931e85385a9dd451f Mon Sep 17 00:00:00 2001 From: Abhist17 Date: Mon, 28 Sep 2026 05:10:09 +0530 Subject: [PATCH 2/5] chore: use tab indentation in the `factorialln` fixture runner docstrings --- .../base/special/factorialln/test/fixtures/julia/runner.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl index 5d388360855e..33ee45784e37 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl @@ -20,7 +20,7 @@ import JSON using SpecialFunctions """ - gen( x, name ) + gen( x, name ) Generate fixture data and write to file. @@ -63,7 +63,7 @@ function gen( x, name ) end """ - gen_fractional( x, name ) + gen_fractional( x, name ) Generate fixture data for `-1 < x < 1` in extended precision and write to file. In double precision, `x+1` rounds away the low-order bits of `x`, so the reference value is computed from `x` exactly. From c84ca3fbb5d9257b7a094a3d2c86a4281dbd01f1 Mon Sep 17 00:00:00 2001 From: Abhist17 Date: Mon, 28 Sep 2026 09:34:33 +0530 Subject: [PATCH 3/5] docs: document the method in the JSDoc and C doc comments --- .../@stdlib/math/base/special/factorialln/lib/main.js | 11 ++++++++++- .../@stdlib/math/base/special/factorialln/src/main.c | 11 ++++++++++- 2 files changed, 20 insertions(+), 2 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js b/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js index 0ab7394cb556..451fb0e00f67 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js @@ -31,6 +31,16 @@ var log1p = require( '@stdlib/math/base/special/log1p' ); /** * Evaluates the natural logarithm of the factorial of `x`. * +* ## Method +* +* The function evaluates \\(\ln \Gamma(x+1)\\). For \\(-1 < x < 1\\), forming \\(x+1\\) in double precision rounds away the low-order bits of \\(x\\) (all of them for \\(|x| < 2^{-53}\\)), so the function instead evaluates +* +* ```tex +* \ln \Gamma(x+1) = \operatorname{log1p}\left( \Gamma(x+1) - 1 \right) +* ``` +* +* where \\(\Gamma(x+1) - 1\\) is computed directly from \\(x\\) (see `gamma1pm1`). +* * @param {number} x - input value * @returns {number} natural logarithm of factorial of `x` * @@ -58,7 +68,6 @@ function factorialln( x ) { if ( isNegativeInteger( x ) ) { return NaN; } - // For `-1 < x < 1`, `x + 1` rounds away the low-order bits of `x` (all of them for `|x| < 2^-53`), so use `ln(1 + (Γ(x+1) - 1))` with `Γ(x+1) - 1` evaluated without forming `x + 1`: if ( x > -1.0 && x < 1.0 ) { return log1p( gamma1pm1( x ) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c b/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c index b267d96b73a5..d8b44b550236 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c @@ -26,6 +26,16 @@ /** * Evaluates the natural logarithm of the factorial of `x`. * +* ## Method +* +* The function evaluates `\ln \Gamma(x+1)`. For `-1 < x < 1`, forming `x+1` in double precision rounds away the low-order bits of `x` (all of them for `|x| < 2^{-53}`), so the function instead evaluates +* +* ```tex +* \ln \Gamma(x+1) = \operatorname{log1p}\left( \Gamma(x+1) - 1 \right) +* ``` +* +* where `\Gamma(x+1) - 1` is computed directly from `x` (see `gamma1pm1`). +* * @param x input value * @return natural logarithm of factorial of `x` * @@ -37,7 +47,6 @@ double stdlib_base_factorialln( const double x ) { if ( stdlib_base_is_negative_integer( x ) ) { return STDLIB_CONSTANT_FLOAT64_NAN; } - // For `-1 < x < 1`, `x + 1` rounds away the low-order bits of `x` (all of them for `|x| < 2^-53`), so use `ln(1 + (Γ(x+1) - 1))` with `Γ(x+1) - 1` evaluated without forming `x + 1`: if ( x > -1.0 && x < 1.0 ) { return stdlib_base_log1p( stdlib_base_gamma1pm1( x ) ); } From 89e917582f1c97744d62daee53a373c2cefa02f5 Mon Sep 17 00:00:00 2001 From: Abhist17 Date: Tue, 29 Sep 2026 21:47:16 +0530 Subject: [PATCH 4/5] fix: extend the `log1p( gamma1pm1( x ) )` path to `x < 2` For `1 <= x < 2`, `ln(gamma(x+1))` passes through zero at `x = 1`, so the rounding error in forming `x+1` is large relative to the result (up to ~27,700 ULP just above `1`). `log1p( gamma1pm1( x ) )` stays within 3 ULP there. Regenerate `small_positive.json` in extended precision, as the double-precision `lgamma( x+1 )` values were themselves up to 869 ULP off, and add a fixture for `[1, 2)`. --- .../math/base/special/factorialln/lib/main.js | 4 ++-- .../math/base/special/factorialln/src/main.c | 4 ++-- .../test/fixtures/julia/one_to_two.json | 1 + .../factorialln/test/fixtures/julia/runner.jl | 6 +++++- .../test/fixtures/julia/small_positive.json | 2 +- .../base/special/factorialln/test/test.js | 19 ++++++++++++++++++- .../special/factorialln/test/test.native.js | 19 ++++++++++++++++++- 7 files changed, 47 insertions(+), 8 deletions(-) create mode 100644 lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/one_to_two.json diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js b/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js index 451fb0e00f67..ff48d5a1e3f0 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js @@ -33,7 +33,7 @@ var log1p = require( '@stdlib/math/base/special/log1p' ); * * ## Method * -* The function evaluates \\(\ln \Gamma(x+1)\\). For \\(-1 < x < 1\\), forming \\(x+1\\) in double precision rounds away the low-order bits of \\(x\\) (all of them for \\(|x| < 2^{-53}\\)), so the function instead evaluates +* The function evaluates \\(\ln \Gamma(x+1)\\). For \\(-1 < x < 1\\), forming \\(x+1\\) in double precision rounds away the low-order bits of \\(x\\) (all of them for \\(|x| < 2^{-53}\\)). For \\(1 \leq x < 2\\), \\(\ln \Gamma(x+1)\\) passes through zero at \\(x = 1\\), so the rounding error in \\(x+1\\) is large relative to the result. On \\(-1 < x < 2\\), the function instead evaluates * * ```tex * \ln \Gamma(x+1) = \operatorname{log1p}\left( \Gamma(x+1) - 1 \right) @@ -68,7 +68,7 @@ function factorialln( x ) { if ( isNegativeInteger( x ) ) { return NaN; } - if ( x > -1.0 && x < 1.0 ) { + if ( x > -1.0 && x < 2.0 ) { return log1p( gamma1pm1( x ) ); } return gammaln( x + 1.0 ); diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c b/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c index d8b44b550236..afd1fef5050c 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c @@ -28,7 +28,7 @@ * * ## Method * -* The function evaluates `\ln \Gamma(x+1)`. For `-1 < x < 1`, forming `x+1` in double precision rounds away the low-order bits of `x` (all of them for `|x| < 2^{-53}`), so the function instead evaluates +* The function evaluates `\ln \Gamma(x+1)`. For `-1 < x < 1`, forming `x+1` in double precision rounds away the low-order bits of `x` (all of them for `|x| < 2^{-53}`). For `1 \leq x < 2`, `\ln \Gamma(x+1)` passes through zero at `x = 1`, so the rounding error in `x+1` is large relative to the result. On `-1 < x < 2`, the function instead evaluates * * ```tex * \ln \Gamma(x+1) = \operatorname{log1p}\left( \Gamma(x+1) - 1 \right) @@ -47,7 +47,7 @@ double stdlib_base_factorialln( const double x ) { if ( stdlib_base_is_negative_integer( x ) ) { return STDLIB_CONSTANT_FLOAT64_NAN; } - if ( x > -1.0 && x < 1.0 ) { + if ( x > -1.0 && x < 2.0 ) { return stdlib_base_log1p( stdlib_base_gamma1pm1( x ) ); } return stdlib_base_gammaln( x + 1.0 ); diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/one_to_two.json b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/one_to_two.json new file mode 100644 index 000000000000..e2356f9509d0 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/one_to_two.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl index 33ee45784e37..2a0940aef7aa 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl @@ -104,7 +104,7 @@ dir = dirname( file ); # Positive small values: x = range( 1.0, stop = 3.0, length = 1001 ); -gen( x, "small_positive.json" ); +gen_fractional( x, "small_positive.json" ); # Positive medium values: x = range( 3.0, stop = 20.0, length = 1001 ); @@ -121,3 +121,7 @@ gen( x, "very_large_positive.json" ); # Fractional values in (-1,1), including tiny magnitudes: x = vcat( -exp10.( range( -300.0, stop = log10( 0.999 ), length = 500 ) ), exp10.( range( -300.0, stop = log10( 0.999 ), length = 500 ) ), collect( range( -0.999, stop = 0.999, length = 1000 ) ) ); gen_fractional( x, "fractional.json" ); + +# Values in [1,2), where `ln(gamma(x+1))` passes through zero at `x = 1`: +x = vcat( 1.0 .+ exp10.( range( -300.0, stop = log10( 0.999 ), length = 500 ) ), collect( range( 1.0, stop = 1.999, length = 500 ) ) ); +gen_fractional( x, "one_to_two.json" ); diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/small_positive.json b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/small_positive.json index 7cde790a1a04..33d10b720f5f 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/small_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/small_positive.json @@ -1 +1 @@ -{"expected":[0.0,0.0008468579998411857,0.0016962925076425244,0.0025483003023125724,0.003402878170606481,0.004260022907098346,0.0051197313141529335,0.005982000201897527,0.006846826388194666,0.007714206698615022,0.008584137966409635,0.009456617032482264,0.010331640745362651,0.0112092059611799,0.012089309543635214,0.012971948363974752,0.013857119300963382,0.014744819240858568,0.0156350450773836,0.016527793711700933,0.01742306205238642,0.018320847015403714,0.01922114552407795,0.02012395450906957,0.02102927090834905,0.021937091667171754,0.022847413738052096,0.02376023408073783,0.024675549662185253,0.02559335745653451,0.02651365444508423,0.027436437616266265,0.02836170396562134,0.029289450495774822,0.03021967421641183,0.031152372144252368,0.032087541303027454,0.03302517872345535,0.03396528144321707,0.03490784650693197,0.03585287096613432,0.03680035187924998,0.03775028631157228,0.03870267133523813,0.03965750402920492,0.040614781479227674,0.04157450077783539,0.04253665902430744,0.04350125332465105,0.04446828079157876,0.04543773854448518,0.046409623709423864,0.04738393341908512,0.04836066481277393,0.049339815036387104,0.05032138124239053,0.0513053605897974,0.05229175024414652,0.05328054737747987,0.05427174916832023,0.05526535280164979,0.0562613554688889,0.05725975436787393,0.05826054670283515,0.05926372968437676,0.060269300529453826,0.06127725646135254,0.06228759470966844,0.06330031251028481,0.06431540710535227,0.0653328757432682,0.06635271567865561,0.06737492417234196,0.06839949849133894,0.06942643590882247,0.07045573370411176,0.07148738916264859,0.07252139957597736,0.07355776224172557,0.0745964744635831,0.07563753355128187,0.07668093682057636,0.07772668159322423,0.07877476519696612,0.0798251849655056,0.08087793823848996,0.08193302236149128,0.08299043468598649,0.08405017256933767,0.08511223337477322,0.0861766144713692,0.0872433132340298,0.08831232704346781,0.08938365328618632,0.09045728935446024,0.09153323264631712,0.09261148056551806,0.09369203052153953,0.09477487992955536,0.09586002621041784,0.09694746679063887,0.09803719910237223,0.09912922058339575,0.10022352867709283,0.10132012083243383,0.10241899450395861,0.10352014715175915,0.10462357624146122,0.10572927924420614,0.10683725363663366,0.10794749690086476,0.10906000652448375,0.11017478000052028,0.11129181482743242,0.11241110850908993,0.11353265855475653,0.11465646247907214,0.1157825178020365,0.1169108220489924,0.11804137275060847,0.11917416744286168,0.12030920366702107,0.1214464789696315,0.12258599090249654,0.12372773702266135,0.1248717148923966,0.12601792207918258,0.12716635615569238,0.12831701469977483,0.12946989529443903,0.1306249955278385,0.13178231299325455,0.13294184528907985,0.1341035900188028,0.13526754479099215,0.1364337072192808,0.13760207492234924,0.1387726455239105,0.13994541665269497,0.14112038594243423,0.1422975510318451,0.14347690956461462,0.14465845918938508,0.14584219755973837,0.14702812233418,0.14821623117612437,0.14940652175388033,0.15059899174063537,0.15179363881444013,0.15299046065819394,0.15418945495963046,0.15539061941130228,0.1565939517105655,0.15779944955956568,0.15900711066522363,0.16021693273922022,0.16142891349798136,0.16264305066266388,0.16385934195914187,0.16507778511799157,0.16629837787447654,0.16752111796853394,0.1687460031447609,0.1699730311523998,0.17120219974532352,0.17243350668202215,0.17366694972558933,0.17490252664370792,0.17614023520863553,0.17738007319719123,0.17862203839074234,0.1798661285751902,0.1811123415409559,0.18236067508296727,0.18361112700064589,0.184863695097893,0.18611837718307556,0.1873751710690133,0.18863407457296613,0.1898950855166201,0.1911582017260737,0.19242342103182528,0.19369074126876037,0.19496016027613813,0.19623167589757776,0.19750528598104597,0.19878098837884484,0.2000587809475981,0.20133866154823774,0.20262062804599296,0.2039046783103754,0.20519081021516825,0.20647902163841297,0.207769310462396,0.2090616745736368,0.21035611186287606,0.2116526202250626,0.2129511975593404,0.2142518417690369,0.21555455076165125,0.21685932244884157,0.21816615474641202,0.21947504557430136,0.2207859928565714,0.22209899452139437,0.2234140485010403,0.2247311527318657,0.22605030515430213,0.2273715037128439,0.22869474635603548,0.23002003103646043,0.23134735571073023,0.23267671833947198,0.2340081168873162,0.2353415493228858,0.2366770136187851,0.2380145077515877,0.23935402970182448,0.24069557745397285,0.24203914899644574,0.2433847423215798,0.24473235542562355,0.24608198630872666,0.24743363297492932,0.2487872934321505,0.25014296569217626,0.2515006477706492,0.25286033768705807,0.25422203346472616,0.2555857331307997,0.2569514347162376,0.2583191362558012,0.25968883578804264,0.2610605313552937,0.26243422100365565,0.26380990278298877,0.2651875747469016,0.2665672349527392,0.26794888146157375,0.26933251233819383,0.2707181256510941,0.2721057194724636,0.2734952918781761,0.2748868409477806,0.27628036476448997,0.2776758614151702,0.27907332899033066,0.2804727655841145,0.2818741692942879,0.2832775382222291,0.2846828704729192,0.286090164154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diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.js b/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.js index c62e8d0eeab3..5a2568a93c9c 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.js @@ -37,6 +37,7 @@ var veryLargePositive = require( './fixtures/julia/very_large_positive.json' ); var largePositive = require( './fixtures/julia/large_positive.json' ); var mediumPositive = require( './fixtures/julia/medium_positive.json' ); var fractional = require( './fixtures/julia/fractional.json' ); +var oneToTwo = require( './fixtures/julia/one_to_two.json' ); var smallPositive = require( './fixtures/julia/small_positive.json' ); @@ -142,6 +143,22 @@ tape( 'the function evaluates the natural logarithm of the factorial of `x` (`-1 t.end(); }); +tape( 'the function evaluates the natural logarithm of the factorial of `x` (`1 <= x < 2`)', function test( t ) { + var expected; + var x; + var y; + var i; + + expected = oneToTwo.expected; + x = oneToTwo.x; + + for ( i = 0; i < x.length; i++ ) { + y = factorialln( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); + } + t.end(); +}); + tape( 'the function evaluates the natural logarithm of the factorial of `x` (small positive values)', function test( t ) { var expected; var x; @@ -152,7 +169,7 @@ tape( 'the function evaluates the natural logarithm of the factorial of `x` (sma x = smallPositive.x; for ( i = 0; i < x.length; i++ ) { y = factorialln( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.native.js index 003d0c9e26c2..33e7d9b7e34e 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.native.js @@ -38,6 +38,7 @@ var veryLargePositive = require( './fixtures/julia/very_large_positive.json' ); var largePositive = require( './fixtures/julia/large_positive.json' ); var mediumPositive = require( './fixtures/julia/medium_positive.json' ); var fractional = require( './fixtures/julia/fractional.json' ); +var oneToTwo = require( './fixtures/julia/one_to_two.json' ); var smallPositive = require( './fixtures/julia/small_positive.json' ); @@ -153,6 +154,22 @@ tape( 'the function evaluates the natural logarithm of the factorial of `x` (`-1 t.end(); }); +tape( 'the function evaluates the natural logarithm of the factorial of `x` (`1 <= x < 2`)', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + expected = oneToTwo.expected; + x = oneToTwo.x; + + for ( i = 0; i < x.length; i++ ) { + y = factorialln( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); + } + t.end(); +}); + tape( 'the function evaluates the natural logarithm of the factorial of `x` (small positive values)', opts, function test( t ) { var expected; var x; @@ -163,7 +180,7 @@ tape( 'the function evaluates the natural logarithm of the factorial of `x` (sma x = smallPositive.x; for ( i = 0; i < x.length; i++ ) { y = factorialln( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); } t.end(); }); From 63a5437918aee3e6e616feb1d3d624027b15481d Mon Sep 17 00:00:00 2001 From: Karan Anand Date: Tue, 29 Sep 2026 20:20:42 -0700 Subject: [PATCH 5/5] chore: clean-up - Shorten the `## Method` section and use the same text in JS and C. - Generate fixtures in extended precision with a single `gen`. - Replace `fractional.json` and `one_to_two.json` with `tiny_negative.json`, `tiny_positive.json`, `small_negative.json`, and `small_positive.json`. - Use the minimum passing tolerances. - Follow current test conventions. Co-Authored-By: Claude Opus 5.5 --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: na - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../math/base/special/factorialln/lib/main.js | 6 +- .../math/base/special/factorialln/src/main.c | 6 +- .../test/fixtures/julia/fractional.json | 1 - .../test/fixtures/julia/one_to_two.json | 1 - .../factorialln/test/fixtures/julia/runner.jl | 68 +++++------------- .../test/fixtures/julia/small_negative.json | 1 + .../test/fixtures/julia/small_positive.json | 2 +- .../test/fixtures/julia/tiny_negative.json | 1 + .../test/fixtures/julia/tiny_positive.json | 1 + .../base/special/factorialln/test/test.js | 70 +++++++++++-------- .../special/factorialln/test/test.native.js | 70 +++++++++++-------- 11 files changed, 105 insertions(+), 122 deletions(-) delete mode 100644 lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/fractional.json delete mode 100644 lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/one_to_two.json create mode 100644 lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/small_negative.json create mode 100644 lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/tiny_negative.json create mode 100644 lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/tiny_positive.json diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js b/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js index ff48d5a1e3f0..900805748c80 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js @@ -33,14 +33,12 @@ var log1p = require( '@stdlib/math/base/special/log1p' ); * * ## Method * -* The function evaluates \\(\ln \Gamma(x+1)\\). For \\(-1 < x < 1\\), forming \\(x+1\\) in double precision rounds away the low-order bits of \\(x\\) (all of them for \\(|x| < 2^{-53}\\)). For \\(1 \leq x < 2\\), \\(\ln \Gamma(x+1)\\) passes through zero at \\(x = 1\\), so the rounding error in \\(x+1\\) is large relative to the result. On \\(-1 < x < 2\\), the function instead evaluates +* For \\(-1 < x < 2\\), forming \\(x+1\\) can round away low-order bits of \\(x\\), which results in large relative errors near the zeros of \\(\ln \Gamma(x+1)\\) at \\(x = 0\\) and \\(x = 1\\). To avoid forming \\(x+1\\), we use the identity * * ```tex -* \ln \Gamma(x+1) = \operatorname{log1p}\left( \Gamma(x+1) - 1 \right) +* \ln \Gamma(x+1) = \operatorname{log1p}(\Gamma(x+1) - 1) = \operatorname{log1p}(\operatorname{gamma1pm1}(x)) * ``` * -* where \\(\Gamma(x+1) - 1\\) is computed directly from \\(x\\) (see `gamma1pm1`). -* * @param {number} x - input value * @returns {number} natural logarithm of factorial of `x` * diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c b/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c index afd1fef5050c..eb48c234675c 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c @@ -28,14 +28,12 @@ * * ## Method * -* The function evaluates `\ln \Gamma(x+1)`. For `-1 < x < 1`, forming `x+1` in double precision rounds away the low-order bits of `x` (all of them for `|x| < 2^{-53}`). For `1 \leq x < 2`, `\ln \Gamma(x+1)` passes through zero at `x = 1`, so the rounding error in `x+1` is large relative to the result. On `-1 < x < 2`, the function instead evaluates +* For \\(-1 < x < 2\\), forming \\(x+1\\) can round away low-order bits of \\(x\\), which results in large relative errors near the zeros of \\(\ln \Gamma(x+1)\\) at \\(x = 0\\) and \\(x = 1\\). To avoid forming \\(x+1\\), we use the identity * * ```tex -* \ln \Gamma(x+1) = \operatorname{log1p}\left( \Gamma(x+1) - 1 \right) +* \ln \Gamma(x+1) = \operatorname{log1p}(\Gamma(x+1) - 1) = \operatorname{log1p}(\operatorname{gamma1pm1}(x)) * ``` * -* where `\Gamma(x+1) - 1` is computed directly from `x` (see `gamma1pm1`). -* * @param x input value * @return natural logarithm of factorial of `x` * diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/fractional.json b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/fractional.json deleted file mode 100644 index 093de21bf5d0..000000000000 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/fractional.json +++ /dev/null @@ -1 +0,0 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/one_to_two.json b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/one_to_two.json deleted file mode 100644 index e2356f9509d0..000000000000 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/one_to_two.json +++ /dev/null @@ -1 +0,0 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl index 2a0940aef7aa..f9f9e961f39d 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl @@ -37,47 +37,9 @@ julia> gen( x, \"data.json\" ); ``` """ function gen( x, name ) - y = Array{Float64}( undef, length( x ) ); - for i in eachindex(x) - if isinteger( x[i] ) - y[i] = lfactorial( Int64( x[i] ) ); - else - y[i] = lgamma( x[i]+1 ); - end - end - - # Store data to be written to file as a collection: - data = Dict([ - ("x", x), - ("expected", y) - ]); - - # 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 - -""" - gen_fractional( x, name ) - -Generate fixture data for `-1 < x < 1` in extended precision and write to file. In double precision, `x+1` rounds away the low-order bits of `x`, so the reference value is computed from `x` exactly. - -# Arguments - -* `x`: domain -* `name::AbstractString`: output filename -""" -function gen_fractional( x, name ) - y = Array{Float64}( undef, length( x ) ); - setprecision( BigFloat, 2048 ) do - for i in eachindex(x) - y[i] = Float64( loggamma( BigFloat( x[i] ) + 1 ) ); - end + # Evaluate in extended precision, as forming `x+1` in double precision can round away the low-order bits of `x`: + y = setprecision( BigFloat, 2048 ) do + Float64.( loggamma.( BigFloat.( x ) .+ 1 ) ) end # Store data to be written to file as a collection: @@ -102,9 +64,21 @@ file = @__FILE__; # Extract the directory in which this file resides: dir = dirname( file ); +# Negative tiny values: +x = range( -1.0e-300, stop = -1.0e-308, length = 500 ); +gen( x, "tiny_negative.json" ); + +# Positive tiny values: +x = range( 1.0e-300, stop = 1.0e-308, length = 500 ); +gen( x, "tiny_positive.json" ); + +# Negative small values: +x = range( -0.999, stop = -0.001, length = 500 ); +gen( x, "small_negative.json" ); + # Positive small values: -x = range( 1.0, stop = 3.0, length = 1001 ); -gen_fractional( x, "small_positive.json" ); +x = range( 0.002, stop = 3.0, length = 1500 ); +gen( x, "small_positive.json" ); # Positive medium values: x = range( 3.0, stop = 20.0, length = 1001 ); @@ -117,11 +91,3 @@ gen( x, "large_positive.json" ); # Very large positive values: x = collect( 5000:50:10000 ); gen( x, "very_large_positive.json" ); - -# Fractional values in (-1,1), including tiny magnitudes: -x = vcat( -exp10.( range( -300.0, stop = log10( 0.999 ), length = 500 ) ), exp10.( range( -300.0, stop = log10( 0.999 ), length = 500 ) ), collect( range( -0.999, stop = 0.999, length = 1000 ) ) ); -gen_fractional( x, "fractional.json" ); - -# Values in [1,2), where `ln(gamma(x+1))` passes through zero at `x = 1`: -x = vcat( 1.0 .+ exp10.( range( -300.0, stop = log10( 0.999 ), length = 500 ) ), collect( range( 1.0, stop = 1.999, length = 500 ) ) ); -gen_fractional( x, "one_to_two.json" ); diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/small_negative.json b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/small_negative.json new file mode 100644 index 000000000000..5b9a78252dc9 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/small_negative.json @@ -0,0 +1 @@ +{"expected":[6.9071788853838525,5.807418734725977,5.295451799982127,4.957844784368176,4.7054020901548075,4.503609622996786,4.335440242151057,4.191230559217485,4.064965015335488,3.952643399235571,3.851470361297991,3.759415387088238,3.674956947385164,3.5969254226836873,3.524402304388072,3.456653086974839,3.3930811807180192,3.3331954073912837,3.276586541328727,3.222910033847072,3.1718730627935647,3.1232246695384775,3.076748140193624,3.032255044856693,2.9895805198908048,2.9485794945917863,2.909123644093329,2.871098906977536,2.834403446481069,2.7989459634470717,2.76464429062277,2.731424213811968,2.6992184773202705,2.667965940165458,2.6376108564325826,2.608102258480727,2.579393425851028,2.551441425971994,2.5242067153207235,2.4976527917352254,2.4717458902021603,2.446454715755348,2.42175020818161,2.3976053340942145,2.3739949026407587,2.350895401693265,2.3282848518481,2.30614267596149,2.2844495822781474,2.263187459488125,2.2423392822801476,2.2218890261562483,2.2018215904388594,2.1821227285426956,2.1627789847040684,2.143777636463035,2.1251066422818927,2.106754593759239,2.088710671964119,2.07096460747118,2.0535066437266893,2.036327503417712,2.0194183575537963,2.002770797002779,1.986376806250606,1.9702287391798505,1.954319296683377,1.938641505948793,1.9231887012662465,1.9079545062270862,1.8929328171941517,1.8781177879362239,1.8635038153296068,1.8490855260391232,1.8348577640991037,1.8208155793223624,1.806954216471784,1.7932691051350937,1.7797558502487132,1.7664102232213992,1.7532281536126797,1.7402057213249846,1.727339149271884,1.7146247964880101,1.7020591516491146,1.689638826973306,1.6773605524768742,1.6652211705602409,1.6532176309015325,1.641346985637029,1.6296063848093687,1.6179930720658466,1.6065043805905022,1.595137729254906,1.58389061897369,1.5727606292518854,1.5617454149120837,1.5508427029902945,1.5400502897901691,1.5293660380859986,1.518787874465552,1.5083137868044507,1.497941821864341,1.487670083007653,1.477496728022218,1.4674199670494679,1.4574380606103543,1.4475493177235046,1.4377520941104927,1.4280447904834295,1.4184258509103806,1.4088937612544064,1.3994470476822782,1.3900842752391753,1.3808040464858826,1.3716050001952358,1.3624858101047435,1.353445183722511,1.3444818611837488,1.335594614155321,1.3267822447859294,1.3180435846996699,1.3093774940308287,1.3007828604979073,1.2922585985149757,1.2838036483385669,1.2754169752484132,1.2670975687604333,1.2588444418704519,1.250656630327226,1.2425331919334257,1.2344732058732855,1.2264757720657187,1.2185400105417412,1.210665060845122,1.2028500814552223,1.1950942492310477,1.187396758875585,1.1797568224195385,1.1721736687236322,1.1646465429986796,1.1571747063426665,1.1497574352941258,1.1423940214011257,1.135083770805214,1.1278260038397048,1.1206200546417178,1.1134652707774046,1.1063610128798336,1.0993066542990182,1.0923015807636076,1.0853451900537725,1.0784368916848461,1.0715761066012988,1.0647622668806427,1.0579948154468835,1.0512732057931504,1.0445969017131538,1.0379653770411386,1.031378115400008,1.0248346099573133,1.0183343631888193,1.0118768866493595,1.0054617007507167,0.9990883345462722,0.9927563255221741,0.9864652193947925,0.980214569914234,0.9740039386737,0.9678328949244811,0.9617010153963875,0.9556078841234273,0.949553092274547,0.9435362379892602,0.9375569262179961,0.9316147685670046,0.9257093831476644,0.9198403944300432,0.9140074331005685,0.9082101359236702,0.9024481456072615,0.8967211106719343,0.8910286853237424,0.8853705293304581,0.8797463079011888,0.8741556915692409,0.8685983560781323,0.8630739822706475,0.8575822559808401,0.8521228679288901,0.8466955136187237,0.8412998932383107,0.8359357115625548,0.8306026778586973,0.8253005057941549,0.8200289133467181,0.8147876227170371,0.8095763602433264,0.80439485631822,0.7992428453077133,0.7941200654721277,0.7890262588890395,0.7839611713781132,0.7789245524277829,0.7739161551237298,0.7689357360790994,0.7639830553664106,0.7590578764511084,0.7541599661267085,0.7492890944514934,0.7444450346867116,0.7396275632362402,0.7348364595876671,0.7300715062547537,0.725332488721241,0.7206191953859583,0.7159314175092015,0.7112689491603443,0.7066315871666485,0.7020191310632413,0.697431383044226,0.6928681479148989,0.688329233045038,0.6838144483232381,0.6793236061122628,0.6748565212053868,0.6704130107837011,0.6659928943743585,0.6615959938097311,0.6572221331874578,0.6528711388313592,0.6485428392531958,0.644237065115249,0.6399536491937026,0.6356924263428055,0.6314532334597951,0.6272359094505608,0.6230402951960322,0.6188662335192696,0.6147135691532428,0.6105821487092784,0.6064718206461605,0.6023824352398679,0.598313844553933,0.5942659024104052,0.5902384643614065,0.5862313876612628,0.5822445312391981,0.5782777556725774,0.5743309231606863,0.5704038974990318,0.5664965440541545,0.5626087297389398,0.5587403229884136,0.5548911937360149,0.5510612133903311,0.5472502548122865,0.5434581922927735,0.5396849015307151,0.5359302596115506,0.532194144986133,0.5284764374500291,0.5247770181232141,0.5210957694301498,0.5174325750802402,0.5137873200486532,0.51015989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diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/small_positive.json b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/small_positive.json index 33d10b720f5f..9b458d336e03 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/small_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/small_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/tiny_negative.json b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/tiny_negative.json new file mode 100644 index 000000000000..45698875f505 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/tiny_negative.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/tiny_positive.json b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/tiny_positive.json new file mode 100644 index 000000000000..834b47900af6 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/tiny_positive.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.js b/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.js index 5a2568a93c9c..28e8b15facc0 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.js @@ -36,9 +36,10 @@ var factorialln = require( './../lib' ); var veryLargePositive = require( './fixtures/julia/very_large_positive.json' ); var largePositive = require( './fixtures/julia/large_positive.json' ); var mediumPositive = require( './fixtures/julia/medium_positive.json' ); -var fractional = require( './fixtures/julia/fractional.json' ); -var oneToTwo = require( './fixtures/julia/one_to_two.json' ); +var smallNegative = require( './fixtures/julia/small_negative.json' ); var smallPositive = require( './fixtures/julia/small_positive.json' ); +var tinyNegative = require( './fixtures/julia/tiny_negative.json' ); +var tinyPositive = require( './fixtures/julia/tiny_positive.json' ); // TESTS // @@ -57,26 +58,26 @@ tape( 'if provided a negative integer, the function returns `NaN`', function tes values = incrspace( -1.0, -500.0, -1.0 ); for ( i = 0; i < values.length; i++ ) { v = factorialln( values[ i ] ); - t.strictEqual( isnan( v ), true, 'returns NaN when provided ' + values[ i ] ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); } t.end(); }); tape( 'if provided negative infinity, the function returns `NaN`', function test( t ) { var v = factorialln( NINF ); - t.strictEqual( isnan( v ), true, 'returns NaN when provided negative infinity' ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); t.end(); }); tape( 'if provided positive infinity, the function returns `+infinity`', function test( t ) { var v = factorialln( PINF ); - t.ok( v, PINF, 'returns +infinity when provided +infinity' ); + t.strictEqual( v, PINF, 'returns expected value' ); t.end(); }); tape( 'if provided `NaN`, the function returns `NaN`', function test( t ) { var v = factorialln( NaN ); - t.strictEqual( isnan( v ), true, 'returns NaN when provided a NaN' ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); t.end(); }); @@ -88,9 +89,8 @@ tape( 'the function evaluates the natural logarithm of the factorial of `x` (ver expected = veryLargePositive.expected; x = veryLargePositive.x; - for ( i = 0; i < x.length; i++ ) { - y = factorialln( x[i] ); + y = factorialln( x[ i ] ); t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); } t.end(); @@ -104,9 +104,8 @@ tape( 'the function evaluates the natural logarithm of the factorial of `x` (lar expected = largePositive.expected; x = largePositive.x; - for ( i = 0; i < x.length; i++ ) { - y = factorialln( x[i] ); + y = factorialln( x[ i ] ); t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); } t.end(); @@ -121,60 +120,73 @@ tape( 'the function evaluates the natural logarithm of the factorial of `x` (med expected = mediumPositive.expected; x = mediumPositive.x; for ( i = 0; i < x.length; i++ ) { - y = factorialln( x[i] ); + y = factorialln( x[ i ] ); t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); } t.end(); }); -tape( 'the function evaluates the natural logarithm of the factorial of `x` (`-1 < x < 1`)', function test( t ) { +tape( 'the function evaluates the natural logarithm of the factorial of `x` (small negative values)', function test( t ) { var expected; var x; var y; var i; - expected = fractional.expected; - x = fractional.x; - + expected = smallNegative.expected; + x = smallNegative.x; for ( i = 0; i < x.length; i++ ) { - y = factorialln( x[i] ); + y = factorialln( x[ i ] ); t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); } t.end(); }); -tape( 'the function evaluates the natural logarithm of the factorial of `x` (`1 <= x < 2`)', function test( t ) { +tape( 'the function evaluates the natural logarithm of the factorial of `x` (small positive values)', function test( t ) { var expected; var x; var y; var i; - expected = oneToTwo.expected; - x = oneToTwo.x; + expected = smallPositive.expected; + x = smallPositive.x; + for ( i = 0; i < x.length; i++ ) { + y = factorialln( x[ i ] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' ); + } + t.end(); +}); +tape( 'the function evaluates the natural logarithm of the factorial of `x` (tiny negative values)', function test( t ) { + var expected; + var x; + var y; + var i; + + expected = tinyNegative.expected; + x = tinyNegative.x; for ( i = 0; i < x.length; i++ ) { - y = factorialln( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); + y = factorialln( x[ i ] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); } t.end(); }); -tape( 'the function evaluates the natural logarithm of the factorial of `x` (small positive values)', function test( t ) { +tape( 'the function evaluates the natural logarithm of the factorial of `x` (tiny positive values)', function test( t ) { var expected; var x; var y; var i; - expected = smallPositive.expected; - x = smallPositive.x; + expected = tinyPositive.expected; + x = tinyPositive.x; for ( i = 0; i < x.length; i++ ) { - y = factorialln( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); + y = factorialln( x[ i ] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); } t.end(); }); -tape( 'the function returns a value almost equal to `ln( factorial( x )` for `x` in `[0,171]', function test( t ) { +tape( 'the function returns a value almost equal to `ln( factorial( x ) )` for `x` in `[0,171]', function test( t ) { var expected; var values; var v; @@ -184,9 +196,7 @@ tape( 'the function returns a value almost equal to `ln( factorial( x )` for `x` for ( i = 0; i < values.length; i++ ) { v = factorialln( values[ i ] ); expected = ln( factorial( values[ i ] ) ); - - // Note: `ln( factorial( 0.5 ) )` is itself 7 ULP from the correctly rounded value of `ln(Γ(1.5))`, which the function returns... - t.strictEqual( isAlmostSameValue( v, expected, 8 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( v, expected, 7 ), true, 'returns expected value' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.native.js index 33e7d9b7e34e..ca86d2c13ede 100644 --- a/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/factorialln/test/test.native.js @@ -37,9 +37,10 @@ var tryRequire = require( '@stdlib/utils/try-require' ); var veryLargePositive = require( './fixtures/julia/very_large_positive.json' ); var largePositive = require( './fixtures/julia/large_positive.json' ); var mediumPositive = require( './fixtures/julia/medium_positive.json' ); -var fractional = require( './fixtures/julia/fractional.json' ); -var oneToTwo = require( './fixtures/julia/one_to_two.json' ); +var smallNegative = require( './fixtures/julia/small_negative.json' ); var smallPositive = require( './fixtures/julia/small_positive.json' ); +var tinyNegative = require( './fixtures/julia/tiny_negative.json' ); +var tinyPositive = require( './fixtures/julia/tiny_positive.json' ); // VARIABLES // @@ -66,26 +67,26 @@ tape( 'if provided a negative integer, the function returns `NaN`', opts, functi values = incrspace( -1.0, -500.0, -1.0 ); for ( i = 0; i < values.length; i++ ) { v = factorialln( values[ i ] ); - t.strictEqual( isnan( v ), true, 'returns expected value when provided ' + values[ i ] ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); } t.end(); }); tape( 'if provided negative infinity, the function returns `NaN`', opts, function test( t ) { var v = factorialln( NINF ); - t.strictEqual( isnan( v ), true, 'returns expected value when provided negative infinity' ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); t.end(); }); tape( 'if provided positive infinity, the function returns `+infinity`', opts, function test( t ) { var v = factorialln( PINF ); - t.ok( v, PINF, 'returns +infinity when provided +infinity' ); + t.strictEqual( v, PINF, 'returns expected value' ); t.end(); }); tape( 'if provided `NaN`, the function returns `NaN`', opts, function test( t ) { var v = factorialln( NaN ); - t.strictEqual( isnan( v ), true, 'returns expected value when provided a NaN' ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); t.end(); }); @@ -97,9 +98,8 @@ tape( 'the function evaluates the natural logarithm of the factorial of `x` (ver expected = veryLargePositive.expected; x = veryLargePositive.x; - for ( i = 0; i < x.length; i++ ) { - y = factorialln( x[i] ); + y = factorialln( x[ i ] ); t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); } t.end(); @@ -113,9 +113,8 @@ tape( 'the function evaluates the natural logarithm of the factorial of `x` (lar expected = largePositive.expected; x = largePositive.x; - for ( i = 0; i < x.length; i++ ) { - y = factorialln( x[i] ); + y = factorialln( x[ i ] ); t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); } t.end(); @@ -130,7 +129,7 @@ tape( 'the function evaluates the natural logarithm of the factorial of `x` (med expected = mediumPositive.expected; x = mediumPositive.x; for ( i = 0; i < x.length; i++ ) { - y = factorialln( x[i] ); + y = factorialln( x[ i ] ); // NOTE: the tolerance here is larger than for the JavaScript implementation due to compiler optimizations which may be performed resulting in result divergence. For discussion, see https://github.com/stdlib-js/stdlib/pull/2774#discussion_r1712904184 t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); @@ -138,54 +137,67 @@ tape( 'the function evaluates the natural logarithm of the factorial of `x` (med t.end(); }); -tape( 'the function evaluates the natural logarithm of the factorial of `x` (`-1 < x < 1`)', opts, function test( t ) { +tape( 'the function evaluates the natural logarithm of the factorial of `x` (small negative values)', opts, function test( t ) { var expected; var x; var y; var i; - expected = fractional.expected; - x = fractional.x; - + expected = smallNegative.expected; + x = smallNegative.x; for ( i = 0; i < x.length; i++ ) { - y = factorialln( x[i] ); + y = factorialln( x[ i ] ); t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); } t.end(); }); -tape( 'the function evaluates the natural logarithm of the factorial of `x` (`1 <= x < 2`)', opts, function test( t ) { +tape( 'the function evaluates the natural logarithm of the factorial of `x` (small positive values)', opts, function test( t ) { var expected; var x; var y; var i; - expected = oneToTwo.expected; - x = oneToTwo.x; + expected = smallPositive.expected; + x = smallPositive.x; + for ( i = 0; i < x.length; i++ ) { + y = factorialln( x[ i ] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' ); + } + t.end(); +}); +tape( 'the function evaluates the natural logarithm of the factorial of `x` (tiny negative values)', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + expected = tinyNegative.expected; + x = tinyNegative.x; for ( i = 0; i < x.length; i++ ) { - y = factorialln( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); + y = factorialln( x[ i ] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); } t.end(); }); -tape( 'the function evaluates the natural logarithm of the factorial of `x` (small positive values)', opts, function test( t ) { +tape( 'the function evaluates the natural logarithm of the factorial of `x` (tiny positive values)', opts, function test( t ) { var expected; var x; var y; var i; - expected = smallPositive.expected; - x = smallPositive.x; + expected = tinyPositive.expected; + x = tinyPositive.x; for ( i = 0; i < x.length; i++ ) { - y = factorialln( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); + y = factorialln( x[ i ] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); } t.end(); }); -tape( 'the function returns a value almost equal to `ln( factorial( x )` for `x` in `[0,171]', opts, function test( t ) { +tape( 'the function returns a value almost equal to `ln( factorial( x ) )` for `x` in `[0,171]', opts, function test( t ) { var expected; var values; var v; @@ -195,9 +207,7 @@ tape( 'the function returns a value almost equal to `ln( factorial( x )` for `x` for ( i = 0; i < values.length; i++ ) { v = factorialln( values[ i ] ); expected = ln( factorial( values[ i ] ) ); - - // Note: `ln( factorial( 0.5 ) )` is itself 7 ULP from the correctly rounded value of `ln(Γ(1.5))`, which the function returns... - t.strictEqual( isAlmostSameValue( v, expected, 8 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( v, expected, 7 ), true, 'returns expected value' ); } t.end(); });