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fix: improve numerical accuracy for -1 < x < 2 in math/base/special/factorialln #15610

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fix: improve numerical accuracy for -1 < x < 2 in math/base/special/factorialln #15610

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ed35ab8
fix: avoid rounding `x + 1` for `-1 < x < 1` in `math/base/special/fa…
Abhist17 Sep 27, 2026
b780a23
chore: use tab indentation in the `factorialln` fixture runner docstr…
Abhist17 Sep 27, 2026
c84ca3f
docs: document the method in the JSDoc and C doc comments
Abhist17 Sep 28, 2026
89e9175
fix: extend the `log1p( gamma1pm1( x ) )` path to `x < 2`
Abhist17 Sep 29, 2026
824fc40
Merge branch 'develop' into fix/factorialln-small-x
anandkaranubc Sep 30, 2026
63a5437
chore: clean-up
anandkaranubc Sep 30, 2026
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13 changes: 13 additions & 0 deletions lib/node_modules/@stdlib/math/base/special/factorialln/lib/main.js
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Original file line number Diff line number Diff line change
Expand Up @@ -21,14 +21,24 @@
// 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 //

/**
* Evaluates the natural logarithm of the factorial of `x`.
*
* ## Method
*
* 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}(\Gamma(x+1) - 1) = \operatorname{log1p}(\operatorname{gamma1pm1}(x))
* ```
*
* @param {number} x - input value
* @returns {number} natural logarithm of factorial of `x`
*
Expand Down Expand Up @@ -56,6 +66,9 @@ function factorialln( x ) {
if ( isNegativeInteger( x ) ) {
return NaN;
}
if ( x > -1.0 && x < 2.0 ) {
return log1p( gamma1pm1( x ) );
}
return gammaln( x + 1.0 );
}

Expand Down
6 changes: 6 additions & 0 deletions lib/node_modules/@stdlib/math/base/special/factorialln/manifest.json
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Expand Up @@ -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"
]
},
Expand All @@ -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"
]
},
Expand All @@ -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"
]
}
Expand Down
13 changes: 13 additions & 0 deletions lib/node_modules/@stdlib/math/base/special/factorialln/src/main.c
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Expand Up @@ -19,11 +19,21 @@
#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`.
*
* ## Method
*
* 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}(\Gamma(x+1) - 1) = \operatorname{log1p}(\operatorname{gamma1pm1}(x))
* ```
*
* @param x input value
* @return natural logarithm of factorial of `x`
*
Expand All @@ -35,5 +45,8 @@ double stdlib_base_factorialln( const double x ) {
if ( stdlib_base_is_negative_integer( x ) ) {
return STDLIB_CONSTANT_FLOAT64_NAN;
}
if ( x > -1.0 && x < 2.0 ) {
return stdlib_base_log1p( stdlib_base_gamma1pm1( x ) );
}
return stdlib_base_gammaln( x + 1.0 );
}
26 changes: 17 additions & 9 deletions lib/node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/runner.jl
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Expand Up @@ -20,7 +20,7 @@ import JSON
using SpecialFunctions

"""
gen( x, name )
gen( x, name )

Generate fixture data and write to file.

Expand All @@ -37,13 +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
# 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:
Expand All @@ -68,8 +64,20 @@ 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 );
x = range( 0.002, stop = 3.0, length = 1500 );
gen( x, "small_positive.json" );

# Positive medium values:
Expand Down
1 change: 1 addition & 0 deletions ...ode_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/small_negative.json
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@@ -0,0 +1 @@
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2 changes: 1 addition & 1 deletion ...ode_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/small_positive.json
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1 change: 1 addition & 0 deletions ...node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/tiny_negative.json
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1 change: 1 addition & 0 deletions ...node_modules/@stdlib/math/base/special/factorialln/test/fixtures/julia/tiny_positive.json
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