diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/README.md b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/README.md
new file mode 100644
index 000000000000..a16464f61057
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/README.md
@@ -0,0 +1,224 @@
+
+
+# logGradient
+
+> Compute the [log loss gradient][log-loss-gradient] with respect to a model parameter.
+
+
+
+The [log loss gradient][log-loss-gradient] is defined as
+
+
+
+```math
+\frac{\partial \ell}{\partial w} = -\frac{y}{1+e^{yp}}x
+```
+
+
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var logGradient = require( '@stdlib/ml/base/loss/float64/log-gradient' );
+```
+
+#### logGradient( x, y, p )
+
+Computes the [log loss gradient][log-loss-gradient] with respect to a model parameter.
+
+```javascript
+var v = logGradient( 2.3, 1.0, 0.782 );
+// returns ~-0.722
+
+v = logGradient( 1.0, 1.0, -0.999 );
+// returns ~-0.731
+```
+
+The function accepts the following arguments:
+
+- **x**: input value.
+- **y**: true target value.
+- **p**: predicted value.
+
+If any argument is `NaN`, the function returns `NaN`.
+
+```javascript
+var v = logGradient( 1.0, NaN, 0.782 );
+// returns NaN
+
+v = logGradient( 3.0, 1.0, NaN );
+// returns NaN
+```
+
+If `y` is not +1 or -1, the function returns `NaN`.
+
+```javascript
+var v = logGradient( 3.4, -0.9, 2.0 );
+// returns NaN
+
+v = logGradient( 0.453, 0.76, 2.0 );
+// returns NaN
+```
+
+
+
+
+
+
+
+## Examples
+
+
+
+```javascript
+var uniform = require( '@stdlib/random/array/uniform' );
+var sample = require( '@stdlib/random/sample' );
+var logEachMap = require( '@stdlib/console/log-each-map' );
+var logGradient = require( '@stdlib/ml/base/loss/float64/log-gradient' );
+
+var opts = {
+ 'dtype': 'float64'
+};
+var x = uniform( 100, -10.0, 10.0, opts );
+var y = sample( [ -1.0, 1.0 ], {
+ 'size': 100
+});
+var p = uniform( 100, -5.0, 5.0, opts );
+
+logEachMap( 'logGradient(%0.4f, %0.4f, %0.4f) = %0.4f', x, y, p, logGradient );
+```
+
+
+
+
+
+
+
+* * *
+
+
+
+## C APIs
+
+
+
+
+
+
+
+
+
+
+
+### Usage
+
+```c
+#include "stdlib/ml/base/loss/float64/log_gradient.h"
+```
+
+#### stdlib_base_float64_log_gradient( x, y, p )
+
+Computes the [log loss gradient][log-loss-gradient] with respect to a model parameter.
+
+```c
+double out = stdlib_base_float64_log_gradient( 2.3, 1.0, 0.782 );
+// returns ~-0.722
+```
+
+The function accepts the following arguments:
+
+- **x**: `[in] double` input value.
+- **y**: `[in] double` true target value.
+- **p**: `[in] double` predicted value.
+
+```c
+double stdlib_base_float64_log_gradient( const double x, const double y, const double p );
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+### Examples
+
+```c
+#include "stdlib/ml/base/loss/float64/log_gradient.h"
+#include
+
+int main( void ) {
+ const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0 };
+ const double y[] = { -1.0, -1.0, -1.0, -1.0, -1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };
+ const double p[] = { -5.0, -3.89, -2.78, -1.67, -0.56, 0.56, 1.67, 2.78, 3.89, 5.0 };
+
+ double v;
+ int i;
+ for ( i = 0; i < 10; i++ ) {
+ v = stdlib_base_float64_log_gradient( x[ i ], y[ i ], p[ i ] );
+ printf( "logGradient(%lf, %lf, %lf) = %lf\n", x[ i ], y[ i ], p[ i ], v );
+ }
+}
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[log-loss-gradient]: https://en.wikipedia.org/wiki/Cross-entropy#Relation_to_linear_regression
+
+
+
+
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/benchmark/benchmark.js b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/benchmark/benchmark.js
new file mode 100644
index 000000000000..0e734a53e993
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/benchmark/benchmark.js
@@ -0,0 +1,61 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var sample = require( '@stdlib/random/sample' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var logGradient = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+ var len;
+ var x;
+ var y;
+ var p;
+ var v;
+ var i;
+
+ len = 100;
+ x = uniform( len, -10.0, 10.0 );
+ y = sample( [ -1.0, 1.0 ], {
+ 'size': len
+ });
+ p = uniform( len, -2.0, 2.0 );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ v = logGradient( x[ i%x.length ], y[ i%y.length ], p[ i%p.length ] );
+ if ( isnan( v ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnan( v ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+});
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/benchmark/benchmark.native.js
new file mode 100644
index 000000000000..955f73a5dbef
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/benchmark/benchmark.native.js
@@ -0,0 +1,71 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var resolve = require( 'path' ).resolve;
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var sample = require( '@stdlib/random/sample' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var logGradient = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+ 'skip': ( logGradient instanceof Error )
+};
+
+
+// MAIN //
+
+bench( format( '%s::native', pkg ), opts, function benchmark( b ) {
+ var len;
+ var x;
+ var y;
+ var p;
+ var v;
+ var i;
+
+ len = 100;
+ x = uniform( len, -10.0, 10.0 );
+ y = sample( [ -1.0, 1.0 ], {
+ 'size': len
+ });
+ p = uniform( len, -2.0, 2.0 );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ v = logGradient( x[ i%x.length ], y[ i%y.length ], p[ i%p.length ] );
+ if ( isnan( v ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnan( v ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+});
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/benchmark/c/native/Makefile
new file mode 100644
index 000000000000..979768abbcec
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/benchmark/c/native/Makefile
@@ -0,0 +1,146 @@
+#/
+# @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.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+ QUIET := @
+else
+ QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+ OS := WINNT
+endif
+endif
+endif
+endif
+
+# Define the program used for compiling C source files:
+ifdef C_COMPILER
+ CC := $(C_COMPILER)
+else
+ CC := gcc
+endif
+
+# Define the command-line options when compiling C files:
+CFLAGS ?= \
+ -std=c99 \
+ -O3 \
+ -Wall \
+ -pedantic
+
+# Determine whether to generate position independent code ([1][1], [2][2]).
+#
+# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
+# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
+ifeq ($(OS), WINNT)
+ fPIC ?=
+else
+ fPIC ?= -fPIC
+endif
+
+# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`):
+INCLUDE ?=
+
+# List of source files:
+SOURCE_FILES ?=
+
+# List of libraries (e.g., `-lopenblas -lpthread`):
+LIBRARIES ?=
+
+# List of library paths (e.g., `-L /foo/bar -L /beep/boop`):
+LIBPATH ?=
+
+# List of C targets:
+c_targets := benchmark.out
+
+
+# RULES #
+
+#/
+# Compiles source files.
+#
+# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`)
+# @param {string} [CFLAGS] - C compiler options
+# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`)
+# @param {string} [SOURCE_FILES] - list of source files
+# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`)
+# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`)
+#
+# @example
+# make
+#
+# @example
+# make all
+#/
+all: $(c_targets)
+
+.PHONY: all
+
+#/
+# Compiles C source files.
+#
+# @private
+# @param {string} CC - C compiler (e.g., `gcc`)
+# @param {string} CFLAGS - C compiler options
+# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`)
+# @param {string} SOURCE_FILES - list of source files
+# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`)
+# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`)
+#/
+$(c_targets): %.out: %.c
+ $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES)
+
+#/
+# Runs compiled benchmarks.
+#
+# @example
+# make run
+#/
+run: $(c_targets)
+ $(QUIET) ./$<
+
+.PHONY: run
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean:
+ $(QUIET) -rm -f *.o *.out
+
+.PHONY: clean
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/benchmark/c/native/benchmark.c
new file mode 100644
index 000000000000..2feeb94b5572
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/benchmark/c/native/benchmark.c
@@ -0,0 +1,161 @@
+/**
+* @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.
+*/
+
+#include "stdlib/ml/base/loss/float64/log_gradient.h"
+#include
+#include
+#include
+#include
+#include
+
+#define NAME "log_gradient"
+#define ITERATIONS 1000000
+#define REPEATS 3
+
+/**
+* Prints the TAP version.
+*/
+static void print_version( void ) {
+ printf( "TAP version 13\n" );
+}
+
+/**
+* Prints the TAP summary.
+*
+* @param total total number of tests
+* @param passing total number of passing tests
+*/
+static void print_summary( int total, int passing ) {
+ printf( "#\n" );
+ printf( "1..%d\n", total ); // TAP plan
+ printf( "# total %d\n", total );
+ printf( "# pass %d\n", passing );
+ printf( "#\n" );
+ printf( "# ok\n" );
+}
+
+/**
+* Prints benchmarks results.
+*
+* @param elapsed elapsed time in seconds
+*/
+static void print_results( double elapsed ) {
+ double rate = (double)ITERATIONS / elapsed;
+ printf( " ---\n" );
+ printf( " iterations: %d\n", ITERATIONS );
+ printf( " elapsed: %0.9f\n", elapsed );
+ printf( " rate: %0.9f\n", rate );
+ printf( " ...\n" );
+}
+
+/**
+* Returns a clock time.
+*
+* @return clock time
+*/
+static double tic( void ) {
+ struct timeval now;
+ gettimeofday( &now, NULL );
+ return (double)now.tv_sec + (double)now.tv_usec/1.0e6;
+}
+
+/**
+* Generates a random number on the interval [min,max).
+*
+* @param min minimum value (inclusive)
+* @param max maximum value (exclusive)
+* @return random number
+*/
+static double random_uniform( const double min, const double max ) {
+ double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
+ return min + ( v*(max-min) );
+}
+
+/**
+* Randomly samples either +1 or -1.
+*
+* @return randomly sampled value (+1 or -1)
+*/
+static double random_sample( void ) {
+ double v = (double)rand() / ( (double)RAND_MAX );
+ if ( v >= 0.5 ) {
+ return 1.0;
+ }
+ return -1.0;
+}
+
+/**
+* Runs a benchmark.
+*
+* @return elapsed time in seconds
+*/
+static double benchmark( void ) {
+ double elapsed;
+ double *x;
+ double *p;
+ double *y;
+ double v;
+ double t;
+ int i;
+
+ x = (double *) malloc( 100 * sizeof( double ) );
+ y = (double *) malloc( 100 * sizeof( double ) );
+ p = (double *) malloc( 100 * sizeof( double ) );
+ for ( i = 0; i < 100; i++ ) {
+ y[ i ] = random_sample();
+ x[ i ] = random_uniform( -10.0, 10.0 );
+ p[ i ] = random_uniform( -2.0, 2.0 );
+ }
+
+ t = tic();
+ for ( i = 0; i < ITERATIONS; i++ ) {
+ v = stdlib_base_float64_log_gradient( x[ i % 100 ], y[ i % 100 ], p[ i % 100 ] );
+ if ( v != v ) {
+ printf( "should not return NaN\n" );
+ break;
+ }
+ }
+ elapsed = tic() - t;
+ if ( v != v ) {
+ printf( "should not return NaN\n" );
+ }
+ free( x );
+ free( y );
+ free( p );
+ return elapsed;
+}
+
+/**
+* Main execution sequence.
+*/
+int main( void ) {
+ double elapsed;
+ int i;
+
+ // Use the current time to seed the random number generator:
+ srand( time( NULL ) );
+
+ print_version();
+ for ( i = 0; i < REPEATS; i++ ) {
+ printf( "# c::native::%s\n", NAME );
+ elapsed = benchmark();
+ print_results( elapsed );
+ printf( "ok %d benchmark finished\n", i+1 );
+ }
+ print_summary( REPEATS, REPEATS );
+}
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/binding.gyp b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/binding.gyp
new file mode 100644
index 000000000000..0d6508a12e99
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/binding.gyp
@@ -0,0 +1,170 @@
+# @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.
+
+# A `.gyp` file for building a Node.js native add-on.
+#
+# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md
+# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md
+{
+ # List of files to include in this file:
+ 'includes': [
+ './include.gypi',
+ ],
+
+ # Define variables to be used throughout the configuration for all targets:
+ 'variables': {
+ # Target name should match the add-on export name:
+ 'addon_target_name%': 'addon',
+
+ # Set variables based on the host OS:
+ 'conditions': [
+ [
+ 'OS=="win"',
+ {
+ # Define the object file suffix:
+ 'obj': 'obj',
+ },
+ {
+ # Define the object file suffix:
+ 'obj': 'o',
+ }
+ ], # end condition (OS=="win")
+ ], # end conditions
+ }, # end variables
+
+ # Define compile targets:
+ 'targets': [
+
+ # Target to generate an add-on:
+ {
+ # The target name should match the add-on export name:
+ 'target_name': '<(addon_target_name)',
+
+ # Define dependencies:
+ 'dependencies': [],
+
+ # Define directories which contain relevant include headers:
+ 'include_dirs': [
+ # Local include directory:
+ '<@(include_dirs)',
+ ],
+
+ # List of source files:
+ 'sources': [
+ '<@(src_files)',
+ ],
+
+ # Settings which should be applied when a target's object files are used as linker input:
+ 'link_settings': {
+ # Define libraries:
+ 'libraries': [
+ '<@(libraries)',
+ ],
+
+ # Define library directories:
+ 'library_dirs': [
+ '<@(library_dirs)',
+ ],
+ },
+
+ # C/C++ compiler flags:
+ 'cflags': [
+ # Enable commonly used warning options:
+ '-Wall',
+
+ # Aggressive optimization:
+ '-O3',
+ ],
+
+ # C specific compiler flags:
+ 'cflags_c': [
+ # Specify the C standard to which a program is expected to conform:
+ '-std=c99',
+ ],
+
+ # C++ specific compiler flags:
+ 'cflags_cpp': [
+ # Specify the C++ standard to which a program is expected to conform:
+ '-std=c++11',
+ ],
+
+ # Linker flags:
+ 'ldflags': [],
+
+ # Apply conditions based on the host OS:
+ 'conditions': [
+ [
+ 'OS=="mac"',
+ {
+ # Linker flags:
+ 'ldflags': [
+ '-undefined dynamic_lookup',
+ '-Wl,-no-pie',
+ '-Wl,-search_paths_first',
+ ],
+ },
+ ], # end condition (OS=="mac")
+ [
+ 'OS!="win"',
+ {
+ # C/C++ flags:
+ 'cflags': [
+ # Generate platform-independent code:
+ '-fPIC',
+ ],
+ },
+ ], # end condition (OS!="win")
+ ], # end conditions
+ }, # end target <(addon_target_name)
+
+ # Target to copy a generated add-on to a standard location:
+ {
+ 'target_name': 'copy_addon',
+
+ # Declare that the output of this target is not linked:
+ 'type': 'none',
+
+ # Define dependencies:
+ 'dependencies': [
+ # Require that the add-on be generated before building this target:
+ '<(addon_target_name)',
+ ],
+
+ # Define a list of actions:
+ 'actions': [
+ {
+ 'action_name': 'copy_addon',
+ 'message': 'Copying addon...',
+
+ # Explicitly list the inputs in the command-line invocation below:
+ 'inputs': [],
+
+ # Declare the expected outputs:
+ 'outputs': [
+ '<(addon_output_dir)/<(addon_target_name).node',
+ ],
+
+ # Define the command-line invocation:
+ 'action': [
+ 'cp',
+ '<(PRODUCT_DIR)/<(addon_target_name).node',
+ '<(addon_output_dir)/<(addon_target_name).node',
+ ],
+ },
+ ], # end actions
+ }, # end target copy_addon
+ ], # end targets
+}
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/docs/repl.txt b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/docs/repl.txt
new file mode 100644
index 000000000000..3c3ff9099a47
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/docs/repl.txt
@@ -0,0 +1,40 @@
+
+{{alias}}( x, y, p )
+ Computes the log loss gradient with respect to a model parameter.
+
+ If any argument is `NaN`, the function returns `NaN`.
+
+ If `y` is not +1 or -1, the function returns `NaN`.
+
+ Parameters
+ ----------
+ x: number
+ Input value.
+
+ y: number
+ True target value.
+
+ p: number
+ Predicted value.
+
+ Returns
+ -------
+ v: number
+ Log loss gradient.
+
+ Examples
+ --------
+ > var v = {{alias}}( 2.3, 1.0, 0.782 )
+ ~-0.722
+ > v = {{alias}}( 1.4, 1.0, 0.202 )
+ ~-0.63
+ > v = {{alias}}( 1.0, 1.0, -0.999 )
+ ~-0.731
+ > v = {{alias}}( -3.2, -1.0, 0.2 )
+ ~-1.759
+ > v = {{alias}}( 1.0, NaN, 0.987 )
+ NaN
+
+ See Also
+ --------
+
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/docs/types/index.d.ts b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/docs/types/index.d.ts
new file mode 100644
index 000000000000..04062582e5cc
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/docs/types/index.d.ts
@@ -0,0 +1,62 @@
+/*
+* @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.
+*/
+
+// TypeScript Version: 4.1
+
+/**
+* Computes the log loss gradient with respect to a model parameter.
+*
+* ## Notes
+*
+* - If `y` is not +1 or -1, the function returns `NaN`.
+*
+* @param x - input value
+* @param y - true target value
+* @param p - predicted value
+* @returns log loss gradient
+*
+* @example
+* var v = logGradient( 2.3, 1.0, 0.782 );
+* // returns ~-0.722
+*
+* @example
+* var v = logGradient( 1.4, 1.0, 0.202 );
+* // returns ~-0.63
+*
+* @example
+* var v = logGradient( 1.0, 1.0, -0.999 );
+* // returns ~-0.731
+*
+* @example
+* var v = logGradient( 5.0, -1.0, 0.234 );
+* // returns ~2.791
+*
+* @example
+* var v = logGradient( -3.2, -1.0, 0.2 );
+* // returns ~-1.759
+*
+* @example
+* var v = logGradient( -4.5, 1.0, -0.9 );
+* // returns ~3.199
+*/
+declare function logGradient( x: number, y: number, p: number ): number;
+
+
+// EXPORTS //
+
+export = logGradient;
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/docs/types/test.ts b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/docs/types/test.ts
new file mode 100644
index 000000000000..6a4db144bf6c
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/docs/types/test.ts
@@ -0,0 +1,71 @@
+/*
+* @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 logGradient = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+ logGradient( 2.3, 1.0, 0.782 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided a first argument which is not a number...
+{
+ logGradient( true, 1.0, 0.8975 ); // $ExpectError
+ logGradient( false, 1.0, 0.8975 ); // $ExpectError
+ logGradient( null, 1.0, 0.8975 ); // $ExpectError
+ logGradient( undefined, 1.0, 0.8975 ); // $ExpectError
+ logGradient( '5', 1.0, 0.8975 ); // $ExpectError
+ logGradient( [], 1.0, 0.8975 ); // $ExpectError
+ logGradient( {}, 1.0, 0.8975 ); // $ExpectError
+ logGradient( ( x: number ): number => x, 1.0, 0.8975 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a second argument which is not a number...
+{
+ logGradient( 1.0, true, 0.8975 ); // $ExpectError
+ logGradient( 1.0, false, 0.8975 ); // $ExpectError
+ logGradient( 1.0, null, 0.8975 ); // $ExpectError
+ logGradient( 1.0, undefined, 0.8975 ); // $ExpectError
+ logGradient( 1.0, '5', 0.8975 ); // $ExpectError
+ logGradient( 1.0, [], 0.8975 ); // $ExpectError
+ logGradient( 1.0, {}, 0.8975 ); // $ExpectError
+ logGradient( 1.0, ( x: number ): number => x, 0.8975 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a third argument which is not a number...
+{
+ logGradient( 2.3, 1.0, true ); // $ExpectError
+ logGradient( 2.3, 1.0, false ); // $ExpectError
+ logGradient( 2.3, 1.0, null ); // $ExpectError
+ logGradient( 2.3, 1.0, undefined ); // $ExpectError
+ logGradient( 2.3, 1.0, '5' ); // $ExpectError
+ logGradient( 2.3, 1.0, [] ); // $ExpectError
+ logGradient( 2.3, 1.0, {} ); // $ExpectError
+ logGradient( 2.3, 1.0, ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an unsupported number of arguments...
+{
+ logGradient(); // $ExpectError
+ logGradient( 1.0 ); // $ExpectError
+ logGradient( 1.0, 2.3 ); // $ExpectError
+ logGradient( 1.0, 0.900, 0.787, 2.0 ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/examples/c/Makefile b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/examples/c/Makefile
new file mode 100644
index 000000000000..c8f8e9a1517b
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/examples/c/Makefile
@@ -0,0 +1,146 @@
+#/
+# @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.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+ QUIET := @
+else
+ QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+ OS := WINNT
+endif
+endif
+endif
+endif
+
+# Define the program used for compiling C source files:
+ifdef C_COMPILER
+ CC := $(C_COMPILER)
+else
+ CC := gcc
+endif
+
+# Define the command-line options when compiling C files:
+CFLAGS ?= \
+ -std=c99 \
+ -O3 \
+ -Wall \
+ -pedantic
+
+# Determine whether to generate position independent code ([1][1], [2][2]).
+#
+# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
+# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
+ifeq ($(OS), WINNT)
+ fPIC ?=
+else
+ fPIC ?= -fPIC
+endif
+
+# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`):
+INCLUDE ?=
+
+# List of source files:
+SOURCE_FILES ?=
+
+# List of libraries (e.g., `-lopenblas -lpthread`):
+LIBRARIES ?=
+
+# List of library paths (e.g., `-L /foo/bar -L /beep/boop`):
+LIBPATH ?=
+
+# List of C targets:
+c_targets := example.out
+
+
+# RULES #
+
+#/
+# Compiles source files.
+#
+# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`)
+# @param {string} [CFLAGS] - C compiler options
+# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`)
+# @param {string} [SOURCE_FILES] - list of source files
+# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`)
+# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`)
+#
+# @example
+# make
+#
+# @example
+# make all
+#/
+all: $(c_targets)
+
+.PHONY: all
+
+#/
+# Compiles C source files.
+#
+# @private
+# @param {string} CC - C compiler (e.g., `gcc`)
+# @param {string} CFLAGS - C compiler options
+# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`)
+# @param {string} SOURCE_FILES - list of source files
+# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`)
+# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`)
+#/
+$(c_targets): %.out: %.c
+ $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES)
+
+#/
+# Runs compiled examples.
+#
+# @example
+# make run
+#/
+run: $(c_targets)
+ $(QUIET) ./$<
+
+.PHONY: run
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean:
+ $(QUIET) -rm -f *.o *.out
+
+.PHONY: clean
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/examples/c/example.c b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/examples/c/example.c
new file mode 100644
index 000000000000..6593cfe7f5c4
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/examples/c/example.c
@@ -0,0 +1,33 @@
+/**
+* @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.
+*/
+
+#include "stdlib/ml/base/loss/float64/log_gradient.h"
+#include
+
+int main( void ) {
+ const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0 };
+ const double y[] = { -1.0, -1.0, -1.0, -1.0, -1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };
+ const double p[] = { -5.0, -3.89, -2.78, -1.67, -0.56, 0.56, 1.67, 2.78, 3.89, 5.0 };
+
+ double v;
+ int i;
+ for ( i = 0; i < 10; i++ ) {
+ v = stdlib_base_float64_log_gradient( x[ i ], y[ i ], p[ i ] );
+ printf( "logGradient(%lf, %lf, %lf) = %lf\n", x[ i ], y[ i ], p[ i ], v );
+ }
+}
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/examples/index.js b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/examples/index.js
new file mode 100644
index 000000000000..f2c2c0b8294f
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/examples/index.js
@@ -0,0 +1,35 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+var uniform = require( '@stdlib/random/array/uniform' );
+var sample = require( '@stdlib/random/sample' );
+var logEachMap = require( '@stdlib/console/log-each-map' );
+var logGradient = require( './../lib' );
+
+var opts = {
+ 'dtype': 'float64'
+};
+var x = uniform( 100, -10.0, 10.0, opts );
+var y = sample( [ -1.0, 1.0 ], {
+ 'size': 100
+});
+var p = uniform( 100, -5.0, 5.0, opts );
+
+logEachMap( 'logGradient(%0.4f, %0.4f, %0.4f) = %0.4f', x, y, p, logGradient );
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/include.gypi b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/include.gypi
new file mode 100644
index 000000000000..bee8d41a2caf
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/include.gypi
@@ -0,0 +1,53 @@
+# @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.
+
+# A GYP include file for building a Node.js native add-on.
+#
+# Main documentation:
+#
+# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md
+# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md
+{
+ # Define variables to be used throughout the configuration for all targets:
+ 'variables': {
+ # Source directory:
+ 'src_dir': './src',
+
+ # Include directories:
+ 'include_dirs': [
+ '=0.10.0",
+ "npm": ">2.7.0"
+ },
+ "os": [
+ "aix",
+ "darwin",
+ "freebsd",
+ "linux",
+ "macos",
+ "openbsd",
+ "sunos",
+ "win32",
+ "windows"
+ ],
+ "keywords": [
+ "stdlib",
+ "machine learning",
+ "ml",
+ "loss",
+ "float64",
+ "log",
+ "log loss",
+ "log loss gradient",
+ "gradient",
+ "double-precision",
+ "double",
+ "dbl"
+ ],
+ "__stdlib__": {}
+}
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/src/Makefile b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/src/Makefile
new file mode 100644
index 000000000000..2caf905cedbe
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/src/Makefile
@@ -0,0 +1,70 @@
+#/
+# @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.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+ QUIET := @
+else
+ QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+ OS := WINNT
+endif
+endif
+endif
+endif
+
+
+# RULES #
+
+#/
+# Removes generated files for building an add-on.
+#
+# @example
+# make clean-addon
+#/
+clean-addon:
+ $(QUIET) -rm -f *.o *.node
+
+.PHONY: clean-addon
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean: clean-addon
+
+.PHONY: clean
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/src/addon.c b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/src/addon.c
new file mode 100644
index 000000000000..1be9ae2fb6bd
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/src/addon.c
@@ -0,0 +1,22 @@
+/**
+* @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.
+*/
+
+#include "stdlib/ml/base/loss/float64/log_gradient.h"
+#include "stdlib/math/base/napi/ternary.h"
+
+STDLIB_MATH_BASE_NAPI_MODULE_DDD_D( stdlib_base_float64_log_gradient )
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/src/main.c b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/src/main.c
new file mode 100644
index 000000000000..b4b9897034c3
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/src/main.c
@@ -0,0 +1,44 @@
+/**
+* @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.
+*/
+
+#include "stdlib/ml/base/loss/float64/log_gradient.h"
+#include "stdlib/math/base/assert/is_nan.h"
+#include "stdlib/math/base/special/exp.h"
+#include "stdlib/constants/float64/nan.h"
+
+/**
+* Computes the log loss gradient with respect to a model parameter.
+*
+* @param x input value
+* @param y true target value
+* @param p predicted value
+* @return log loss gradient
+*
+* @example
+* double out = stdlib_base_float64_log_gradient( 1.4, 1.0, 0.202 );
+* // returns ~-0.63
+*/
+double stdlib_base_float64_log_gradient( const double x, const double y, const double p ) {
+ if (
+ stdlib_base_is_nan( x ) || stdlib_base_is_nan( y ) || stdlib_base_is_nan( p ) ||
+ ( y != -1.0 && y != 1.0 )
+ ) {
+ return STDLIB_CONSTANT_FLOAT64_NAN;
+ }
+ return -( x * y ) / ( 1.0 + stdlib_base_exp( y * p ) );
+}
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/REQUIRE
new file mode 100644
index 000000000000..7c8193c06e65
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/REQUIRE
@@ -0,0 +1,2 @@
+julia 1.4.2
+JSON 0.21.0
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/runner.jl
new file mode 100755
index 000000000000..ac24aafda01f
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/runner.jl
@@ -0,0 +1,91 @@
+#!/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, y, p, name )
+
+Generate fixture data and write to file.
+
+# Arguments
+
+* `x`: input domain
+* `y`: response domain
+* `p`: prediction domain
+* `name::AbstractString`: output filename
+
+# Examples
+
+``` julia
+julia> x = range( -1000.0, 1000.0, 2001 );
+julia> y = rand( [-1.0, 1.0], 2001 )
+julia> p = range( -1000.0, 1000.0, 2001 );
+julia> gen( x, y, p, "data.json" );
+```
+"""
+function gen( x, y, p, name )
+ v = -( x .* y ) ./ ( 1.0 .+ exp.( y .* p ) );
+
+ # Store data to be written to file as a collection:
+ data = Dict([
+ ("x", x),
+ ("y", y),
+ ("p", p),
+ ("expected", v)
+ ]);
+
+ # 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);
+
+# Positive tiny values:
+y = rand( [ -1.0, 1.0 ], 503 )
+x = range( 0.0, stop=1e-20, length=503 );
+p = range( 0.0, stop=1e-20, length=503 );
+gen( x, y, p, "tiny_positive.json" );
+
+# Small positive values:
+y = rand( [ -1.0, 1.0 ], 503 )
+x = range( 0.0, stop=2.0, length=503 );
+p = range( 0.0, stop=2.0, length=503 );
+gen( x, y, p, "small_positive.json" );
+
+# Negative tiny values:
+y = rand( [ -1.0, 1.0 ], 503 )
+x = range( -1e-20, stop=0.0, length=503 );
+p = range( -1e-20, stop=0.0, length=503 );
+gen( x, y, p, "tiny_negative.json" );
+
+# Small negative values:
+y = rand( [ -1.0, 1.0 ], 503 )
+x = range( -2.0, stop=0.0, length=503 );
+p = range( -2.0, stop=0.0, length=503 );
+gen( x, y, p, "small_negative.json" );
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/small_negative.json b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/small_negative.json
new file mode 100644
index 000000000000..fb60ab0ce32a
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/small_negative.json
@@ -0,0 +1 @@
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diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/small_positive.json b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/small_positive.json
new file mode 100644
index 000000000000..c7a5c65cfc2d
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/small_positive.json
@@ -0,0 +1 @@
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diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/tiny_negative.json b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/tiny_negative.json
new file mode 100644
index 000000000000..74d2180d1adf
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/tiny_negative.json
@@ -0,0 +1 @@
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diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/tiny_positive.json b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/tiny_positive.json
new file mode 100644
index 000000000000..2304ee5a0ff6
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/fixtures/julia/tiny_positive.json
@@ -0,0 +1 @@
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diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/test.js b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/test.js
new file mode 100644
index 000000000000..133dacf9d80b
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/test.js
@@ -0,0 +1,144 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var tape = require( 'tape' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var isAlmostSameValue = require( '@stdlib/number/float64/base/assert/is-almost-same-value' );
+var logGradient = require( './../lib' );
+
+
+// FIXTURES //
+
+var tinyPositive = require( './fixtures/julia/tiny_positive.json' );
+var smallPositive = require( './fixtures/julia/small_positive.json' );
+var tinyNegative = require( './fixtures/julia/tiny_negative.json' );
+var smallNegative = require( './fixtures/julia/small_negative.json' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof logGradient, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function computes the log loss gradient for tiny positive values', function test( t ) {
+ var expected;
+ var x;
+ var y;
+ var p;
+ var v;
+ var i;
+
+ x = tinyPositive.x;
+ y = tinyPositive.y;
+ p = tinyPositive.p;
+ expected = tinyPositive.expected;
+ for ( i = 0; i < y.length; i++ ) {
+ v = logGradient( x[ i ], y[ i ], p[ i ] );
+ t.strictEqual( isAlmostSameValue( v, expected[ i ], 0 ), true, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape( 'the function computes the log loss gradient for small positive values', function test( t ) {
+ var expected;
+ var x;
+ var y;
+ var p;
+ var v;
+ var i;
+
+ x = smallPositive.x;
+ y = smallPositive.y;
+ p = smallPositive.p;
+ expected = smallPositive.expected;
+ for ( i = 0; i < y.length; i++ ) {
+ v = logGradient( x[ i ], y[ i ], p[ i ] );
+ t.strictEqual( isAlmostSameValue( v, expected[ i ], 1 ), true, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape( 'the function computes the log loss gradient for tiny negative values', function test( t ) {
+ var expected;
+ var x;
+ var y;
+ var p;
+ var v;
+ var i;
+
+ x = tinyNegative.x;
+ y = tinyNegative.y;
+ p = tinyNegative.p;
+ expected = tinyNegative.expected;
+ for ( i = 0; i < y.length; i++ ) {
+ v = logGradient( x[ i ], y[ i ], p[ i ] );
+ t.strictEqual( isAlmostSameValue( v, expected[ i ], 0 ), true, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape( 'the function computes the log loss gradient for small negative values', function test( t ) {
+ var expected;
+ var x;
+ var y;
+ var p;
+ var v;
+ var i;
+
+ x = smallNegative.x;
+ y = smallNegative.y;
+ p = smallNegative.p;
+ expected = smallNegative.expected;
+ for ( i = 0; i < y.length; i++ ) {
+ v = logGradient( x[ i ], y[ i ], p[ i ] );
+ t.strictEqual( isAlmostSameValue( v, expected[ i ], 2 ), true, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape( 'the function returns `NaN` if provided `NaN`', function test( t ) {
+ var v;
+
+ v = logGradient( NaN, 1.0, 0.782 );
+ t.strictEqual( isnan( v ), true, 'returns expected value' );
+
+ v = logGradient( 2.0, NaN, 0.782 );
+ t.strictEqual( isnan( v ), true, 'returns expected value' );
+
+ v = logGradient( 2.0, 1.0, NaN );
+ t.strictEqual( isnan( v ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function returns `NaN` if y is not +1 or -1', function test( t ) {
+ var v;
+
+ v = logGradient( -0.9, 3.0, 1.0 );
+ t.strictEqual( isnan( v ), true, 'returns expected value' );
+
+ v = logGradient( 0.453, 0.76, 2.0 );
+ t.strictEqual( isnan( v ), true, 'returns expected value' );
+ t.end();
+});
diff --git a/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/test.native.js b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/test.native.js
new file mode 100644
index 000000000000..724e9eea9e9a
--- /dev/null
+++ b/lib/node_modules/@stdlib/ml/base/loss/float64/log-gradient/test/test.native.js
@@ -0,0 +1,153 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var resolve = require( 'path' ).resolve;
+var tape = require( 'tape' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var isAlmostSameValue = require( '@stdlib/number/float64/base/assert/is-almost-same-value' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+
+
+// FIXTURES //
+
+var tinyPositive = require( './fixtures/julia/tiny_positive.json' );
+var smallPositive = require( './fixtures/julia/small_positive.json' );
+var tinyNegative = require( './fixtures/julia/tiny_negative.json' );
+var smallNegative = require( './fixtures/julia/small_negative.json' );
+
+
+// VARIABLES //
+
+var logGradient = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+ 'skip': ( logGradient instanceof Error )
+};
+
+
+// TESTS //
+
+tape( 'main export is a function', opts, function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof logGradient, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function computes the log loss gradient for tiny positive values', opts, function test( t ) {
+ var expected;
+ var x;
+ var y;
+ var p;
+ var v;
+ var i;
+
+ x = tinyPositive.x;
+ y = tinyPositive.y;
+ p = tinyPositive.p;
+ expected = tinyPositive.expected;
+ for ( i = 0; i < y.length; i++ ) {
+ v = logGradient( x[ i ], y[ i ], p[ i ] );
+ t.strictEqual( isAlmostSameValue( v, expected[ i ], 0 ), true, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape( 'the function computes the log loss gradient for small positive values', opts, function test( t ) {
+ var expected;
+ var x;
+ var y;
+ var p;
+ var v;
+ var i;
+
+ x = smallPositive.x;
+ y = smallPositive.y;
+ p = smallPositive.p;
+ expected = smallPositive.expected;
+ for ( i = 0; i < y.length; i++ ) {
+ v = logGradient( x[ i ], y[ i ], p[ i ] );
+ t.strictEqual( isAlmostSameValue( v, expected[ i ], 1 ), true, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape( 'the function computes the log loss gradient for tiny negative values', opts, function test( t ) {
+ var expected;
+ var x;
+ var y;
+ var p;
+ var v;
+ var i;
+
+ x = tinyNegative.x;
+ y = tinyNegative.y;
+ p = tinyNegative.p;
+ expected = tinyNegative.expected;
+ for ( i = 0; i < y.length; i++ ) {
+ v = logGradient( x[ i ], y[ i ], p[ i ] );
+ t.strictEqual( isAlmostSameValue( v, expected[ i ], 0 ), true, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape( 'the function computes the log loss gradient for small negative values', opts, function test( t ) {
+ var expected;
+ var x;
+ var y;
+ var p;
+ var v;
+ var i;
+
+ x = smallNegative.x;
+ y = smallNegative.y;
+ p = smallNegative.p;
+ expected = smallNegative.expected;
+ for ( i = 0; i < y.length; i++ ) {
+ v = logGradient( x[ i ], y[ i ], p[ i ] );
+ t.strictEqual( isAlmostSameValue( v, expected[ i ], 2 ), true, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape( 'the function returns `NaN` if provided `NaN`', opts, function test( t ) {
+ var v;
+
+ v = logGradient( NaN, 1.0, 0.782 );
+ t.strictEqual( isnan( v ), true, 'returns expected value' );
+
+ v = logGradient( 2.0, NaN, 0.782 );
+ t.strictEqual( isnan( v ), true, 'returns expected value' );
+
+ v = logGradient( 2.0, 1.0, NaN );
+ t.strictEqual( isnan( v ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function returns `NaN` if y is not +1 or -1', opts, function test( t ) {
+ var v;
+
+ v = logGradient( -0.9, 3.0, 1.0 );
+ t.strictEqual( isnan( v ), true, 'returns expected value' );
+
+ v = logGradient( 0.453, 0.76, 2.0 );
+ t.strictEqual( isnan( v ), true, 'returns expected value' );
+ t.end();
+});