diff --git a/lib/node_modules/@stdlib/math/base/special/spence/README.md b/lib/node_modules/@stdlib/math/base/special/spence/README.md index 995f6941c47..0754ac094af 100644 --- a/lib/node_modules/@stdlib/math/base/special/spence/README.md +++ b/lib/node_modules/@stdlib/math/base/special/spence/README.md @@ -20,7 +20,7 @@ limitations under the License. # spence -> [Spence’s function][spence], also known as the dilogarithm. +> [Spence's function][spence], also known as the dilogarithm.
@@ -68,7 +68,7 @@ var spence = require( '@stdlib/math/base/special/spence' ); #### spence( x ) -Evaluates [Spence’s function][spence], which is alternatively known as the dilogarithm. +Evaluates [Spence's function][spence], which is alternatively known as the dilogarithm. ```javascript var v = spence( 3.0 ); @@ -115,6 +115,94 @@ for ( i = 0; i < 100; i++ ) { + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/spence.h" +``` + +#### stdlib_base_spence( x ) + +Evaluates [Spence's function][spence], which is alternatively known as the dilogarithm. + +```c +double out = stdlib_base_spence( 3.0 ); +// returns ~-1.437 + +out = stdlib_base_spence( 0.0 ); +// returns ~1.645 +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. + +```c +double stdlib_base_spence( const double x ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/spence.h" +#include + +int main( void ) { + const double x[] = { 3.0, 9.0, 0.0, -10.0 }; + + double y; + int i; + for ( i = 0; i < 4; i++ ) { + y = stdlib_base_spence( x[ i ] ); + printf( "spence(%lf) = %lf\n", x[ i ], y ); + } +} +``` + +
+ + + +
+ + +
diff --git a/lib/node_modules/@stdlib/math/base/special/spence/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/spence/benchmark/benchmark.native.js new file mode 100644 index 00000000000..7a788d89471 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/spence/benchmark/benchmark.native.js @@ -0,0 +1,60 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 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 randu = require( '@stdlib/random/base/randu' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var spence = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( spence instanceof Error ) +}; + + +// MAIN // + +bench( pkg+'::native', opts, function benchmark( b ) { + var x; + var y; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + x = randu() * 1000.0; + y = spence( x ); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/spence/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/spence/benchmark/c/native/Makefile new file mode 100644 index 00000000000..f69e9da2b4d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/spence/benchmark/c/native/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2024 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/math/base/special/spence/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/spence/benchmark/c/native/benchmark.c new file mode 100644 index 00000000000..92fd21d0a49 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/spence/benchmark/c/native/benchmark.c @@ -0,0 +1,136 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 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. +*/ + +/** +* Benchmark `spence`. +*/ +#include "stdlib/math/base/special/spence.h" +#include +#include +#include +#include +#include + +#define NAME "spence" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +void print_version() { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +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 +*/ +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 +*/ +double tic() { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec/1.0e6; +} + +/** +* Generates a random number on the interval [0,1]. +* +* @return random number +*/ +double rand_double() { + int r = rand(); + return (double)r / ( (double)RAND_MAX + 1.0 ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +double benchmark() { + double elapsed; + double x; + double y; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + x = ( 1000.0 * rand_double() ) - 0.0; + y = stdlib_base_spence( x ); + if ( y != y ) { + printf( "should not return NaN\n" ); + break; + } + } + elapsed = tic() - t; + if ( y != y ) { + printf( "should not return NaN\n" ); + } + 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/math/base/special/spence/binding.gyp b/lib/node_modules/@stdlib/math/base/special/spence/binding.gyp new file mode 100644 index 00000000000..ec399223344 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/spence/binding.gyp @@ -0,0 +1,170 @@ +# @license Apache-2.0 +# +# Copyright (c) 2024 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/math/base/special/spence/docs/repl.txt b/lib/node_modules/@stdlib/math/base/special/spence/docs/repl.txt index 58467ffe089..691604beb15 100644 --- a/lib/node_modules/@stdlib/math/base/special/spence/docs/repl.txt +++ b/lib/node_modules/@stdlib/math/base/special/spence/docs/repl.txt @@ -1,6 +1,6 @@ {{alias}}( x ) - Evaluates Spence’s function, which is also known as the dilogarithm. + Evaluates Spence's function, which is also known as the dilogarithm. Parameters ---------- diff --git a/lib/node_modules/@stdlib/math/base/special/spence/docs/types/index.d.ts b/lib/node_modules/@stdlib/math/base/special/spence/docs/types/index.d.ts index ddd7eaf32a9..b882e1ba12d 100644 --- a/lib/node_modules/@stdlib/math/base/special/spence/docs/types/index.d.ts +++ b/lib/node_modules/@stdlib/math/base/special/spence/docs/types/index.d.ts @@ -19,7 +19,7 @@ // TypeScript Version: 4.1 /** -* Evaluates Spence’s function, which is also known as the dilogarithm. +* Evaluates Spence's function, which is also known as the dilogarithm. * * @param x - input value * @returns function value diff --git a/lib/node_modules/@stdlib/math/base/special/spence/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/spence/examples/c/Makefile new file mode 100644 index 00000000000..6aed70daf16 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/spence/examples/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2024 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/math/base/special/spence/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/spence/examples/c/example.c new file mode 100644 index 00000000000..206ae637e04 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/spence/examples/c/example.c @@ -0,0 +1,31 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 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/math/base/special/spence.h" +#include + +int main( void ) { + const double x[] = { 3.0, 9.0, 0.0, -10.0 }; + + double y; + int i; + for ( i = 0; i < 4; i++ ) { + y = stdlib_base_spence( x[ i ] ); + printf( "spence(%lf) = %lf\n", x[ i ], y ); + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/spence/include.gypi b/lib/node_modules/@stdlib/math/base/special/spence/include.gypi new file mode 100644 index 00000000000..575cb043c0b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/spence/include.gypi @@ -0,0 +1,53 @@ +# @license Apache-2.0 +# +# Copyright (c) 2024 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': [ + ' 2.0 ) { @@ -101,17 +106,15 @@ function spence( x ) { if ( x > 1.5 ) { w = (1.0 / x) - 1.0; flg |= 2; - } - else if ( x < 0.5 ) { + } else if ( x < 0.5 ) { w = -x; flg |= 1; - } - else { + } else { w = x - 1.0; } y = -w * polyvalA( w ) / polyvalB( w ); if ( flg & 1 ) { - y = ( PI_SQUARED/6.0 ) - ( ln( x ) * ln( 1.0-x ) ) - y; + y = PI2O6 - ( ln( x ) * ln( 1.0-x ) ) - y; } if ( flg & 2 ) { z = ln( x ); diff --git a/lib/node_modules/@stdlib/math/base/special/spence/lib/native.js b/lib/node_modules/@stdlib/math/base/special/spence/lib/native.js new file mode 100644 index 00000000000..de7bd0f80d9 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/spence/lib/native.js @@ -0,0 +1,58 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 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 addon = require( './../src/addon.node' ); + + +// MAIN // + +/** +* Evaluates Spence's function, which is also known as the dilogarithm. +* +* @private +* @param {NonNegativeNumber} x - input value +* @returns {number} function value +* +* @example +* var v = spence( 3.0 ); +* // returns ~-1.437 +* +* @example +* var v = spence( 0.0 ); +* // returns ~1.645 +* +* @example +* var v = spence( -9.0 ); +* // returns NaN +* +* @example +* var v = spence( NaN ); +* // returns NaN +*/ +function spence( x ) { + return addon( x ); +} + + +// EXPORTS // + +module.exports = spence; diff --git a/lib/node_modules/@stdlib/math/base/special/spence/lib/polyval_a.js b/lib/node_modules/@stdlib/math/base/special/spence/lib/polyval_a.js index 0505b0c7356..ad1b3e3dfca 100644 --- a/lib/node_modules/@stdlib/math/base/special/spence/lib/polyval_a.js +++ b/lib/node_modules/@stdlib/math/base/special/spence/lib/polyval_a.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2022 The Stdlib Authors. +* Copyright (c) 2024 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. diff --git a/lib/node_modules/@stdlib/math/base/special/spence/lib/polyval_b.js b/lib/node_modules/@stdlib/math/base/special/spence/lib/polyval_b.js index 68e5a10ebf9..ace83508e59 100644 --- a/lib/node_modules/@stdlib/math/base/special/spence/lib/polyval_b.js +++ b/lib/node_modules/@stdlib/math/base/special/spence/lib/polyval_b.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2022 The Stdlib Authors. +* Copyright (c) 2024 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. diff --git a/lib/node_modules/@stdlib/math/base/special/spence/manifest.json b/lib/node_modules/@stdlib/math/base/special/spence/manifest.json new file mode 100644 index 00000000000..502ee883353 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/spence/manifest.json @@ -0,0 +1,78 @@ +{ + "options": { + "task": "build" + }, + "fields": [ + { + "field": "src", + "resolve": true, + "relative": true + }, + { + "field": "include", + "resolve": true, + "relative": true + }, + { + "field": "libraries", + "resolve": false, + "relative": false + }, + { + "field": "libpath", + "resolve": true, + "relative": false + } + ], + "confs": [ + { + "task": "build", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/napi/unary", + "@stdlib/math/base/assert/is-nan", + "@stdlib/math/base/special/ln", + "@stdlib/constants/float64/pi-squared" + ] + }, + { + "task": "benchmark", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/assert/is-nan", + "@stdlib/math/base/special/ln", + "@stdlib/constants/float64/pi-squared" + ] + }, + { + "task": "examples", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/assert/is-nan", + "@stdlib/math/base/special/ln", + "@stdlib/constants/float64/pi-squared" + ] + } + ] +} diff --git a/lib/node_modules/@stdlib/math/base/special/spence/package.json b/lib/node_modules/@stdlib/math/base/special/spence/package.json index d3702e25c27..fc8392a45ea 100644 --- a/lib/node_modules/@stdlib/math/base/special/spence/package.json +++ b/lib/node_modules/@stdlib/math/base/special/spence/package.json @@ -1,7 +1,7 @@ { "name": "@stdlib/math/base/special/spence", "version": "0.0.0", - "description": "Spence’s function, also known as the dilogarithm.", + "description": "Spence's function, also known as the dilogarithm.", "license": "Apache-2.0", "author": { "name": "The Stdlib Authors", diff --git a/lib/node_modules/@stdlib/math/base/special/spence/scripts/evalpoly.js b/lib/node_modules/@stdlib/math/base/special/spence/scripts/evalpoly.js index 07d1ec18620..f430ce98317 100644 --- a/lib/node_modules/@stdlib/math/base/special/spence/scripts/evalpoly.js +++ b/lib/node_modules/@stdlib/math/base/special/spence/scripts/evalpoly.js @@ -24,10 +24,15 @@ // MODULES // var resolve = require( 'path' ).resolve; +var readFileSync = require( '@stdlib/fs/read-file' ).sync; var writeFileSync = require( '@stdlib/fs/write-file' ).sync; var currentYear = require( '@stdlib/time/current-year' ); +var substringBefore = require( '@stdlib/string/substring-before' ); +var substringAfter = require( '@stdlib/string/substring-after' ); +var format = require( '@stdlib/string/format' ); var licenseHeader = require( '@stdlib/_tools/licenses/header' ); var compile = require( '@stdlib/math/base/tools/evalpoly-compile' ); +var compileC = require( '@stdlib/math/base/tools/evalpoly-compile-c' ); // VARIABLES // @@ -62,6 +67,33 @@ var header = licenseHeader( 'Apache-2.0', 'js', { header += '\n/* This is a generated file. Do not edit directly. */\n'; +// FUNCTIONS // + +/** +* Inserts a compiled function into file content. +* +* @private +* @param {string} text - source content +* @param {string} id - function identifier +* @param {string} str - function string +* @returns {string} updated content +*/ +function insert( text, id, str ) { + var before; + var after; + var begin; + var end; + + begin = '// BEGIN: '+id; + end = '// END: '+id; + + before = substringBefore( text, begin ); + after = substringAfter( text, end ); + + return format( '%s// BEGIN: %s\n\n%s\n%s%s', before, id, str, end, after ); +} + + // MAIN // /** @@ -71,7 +103,9 @@ header += '\n/* This is a generated file. Do not edit directly. */\n'; */ function main() { var fpath; + var copts; var opts; + var file; var str; opts = { @@ -85,6 +119,24 @@ function main() { fpath = resolve( __dirname, '..', 'lib', 'polyval_b.js' ); str = header + compile( B ); writeFileSync( fpath, str, opts ); + + copts = { + 'dtype': 'double', + 'name': '' + }; + + fpath = resolve( __dirname, '..', 'src', 'main.c' ); + file = readFileSync( fpath, opts ); + + copts.name = 'polyval_a'; + str = compileC( A, copts ); + file = insert( file, copts.name, str ); + + copts.name = 'polyval_b'; + str = compileC( B, copts ); + file = insert( file, copts.name, str ); + + writeFileSync( fpath, file, opts ); } main(); diff --git a/lib/node_modules/@stdlib/math/base/special/spence/src/Makefile b/lib/node_modules/@stdlib/math/base/special/spence/src/Makefile new file mode 100644 index 00000000000..bcf18aa4665 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/spence/src/Makefile @@ -0,0 +1,70 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2024 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/math/base/special/spence/src/addon.c b/lib/node_modules/@stdlib/math/base/special/spence/src/addon.c new file mode 100644 index 00000000000..543f885c70f --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/spence/src/addon.c @@ -0,0 +1,22 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 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/math/base/special/spence.h" +#include "stdlib/math/base/napi/unary.h" + +STDLIB_MATH_BASE_NAPI_MODULE_D_D( stdlib_base_spence ) diff --git a/lib/node_modules/@stdlib/math/base/special/spence/src/main.c b/lib/node_modules/@stdlib/math/base/special/spence/src/main.c new file mode 100644 index 00000000000..7b30a150ff2 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/spence/src/main.c @@ -0,0 +1,149 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 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. +* +* +* ## Notice +* +* The original C code, long comment, copyright, license, and constants are from [Cephes]{@link http://www.netlib.org/cephes}. The implementation follows the original, but has been modified for JavaScript. +* +* ```text +* Copyright 1985, 1987, 1989, 2000 by Stephen L. Moshier +* +* Some software in this archive may be from the book _Methods and Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster International, 1989) or from the Cephes Mathematical Library, a commercial product. In either event, it is copyrighted by the author. What you see here may be used freely but it comes with no support or guarantee. +* +* Stephen L. Moshier +* moshier@na-net.ornl.gov +* ``` +*/ + +#include "stdlib/math/base/special/spence.h" +#include "stdlib/math/base/assert/is_nan.h" +#include "stdlib/math/base/special/ln.h" +#include "stdlib/constants/float64/pi_squared.h" +#include + +// π^2 / 6 +static const double PI2O6 = STDLIB_CONSTANT_FLOAT64_PI_SQUARED / 6.0; + +/* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */ + +// BEGIN: polyval_a + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_a( const double x ) { + return 1.0 + (x * (3.297713409852251 + (x * (4.256971560081218 + (x * (2.7114985119655346 + (x * (0.8796913117545303 + (x * (0.13384763957830903 + (x * (0.007315890452380947 + (x * 0.000046512858607399003))))))))))))); +} + +// END: polyval_a + +// BEGIN: polyval_b + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_b( const double x ) { + return 1.0 + (x * (3.547713409852251 + (x * (5.03278880143317 + (x * (3.6380053334513707 + (x * (1.4117259775183106 + (x * (0.2829748606025681 + (x * (0.02540437639325444 + (x * 0.0006909904889125533))))))))))))); +} + +// END: polyval_b + +/* End auto-generated functions. */ + +/** +* Evaluates Spence's function, which is also known as the dilogarithm. +* +* ## Method +* +* - A rational approximation gives the integral in the interval (0.5, 1.5). +* - Transformation formulas for \\( \tfrac{1}{x} \\) and \\( 1 - x \\) are employed outside the basic expansion range. +* +* ## Notes +* +* - Relative error: +* +* | arithmetic | domain | # trials | peak | rms | +* |:----------:|:-----------:|:--------:|:-------:|:-------:| +* | IEEE | 0,4 | 30000 | 3.9e-15 | 5.4e-16 | +* +* @param x input value +* @return function value +* +* @example +* double y = stdlib_base_spence( 3.0 ); +* // returns ~-1.437 +*/ +double stdlib_base_spence( const double x ) { + int32_t flg; + double xc; + double w; + double y; + double z; + + if ( stdlib_base_is_nan( x ) || x < 0.0 ) { + return 0.0 / 0.0; // NaN + } + if ( x == 1.0 ) { + return 0.0; + } + if ( x == 0.0 ) { + return PI2O6; + } + flg = 0; + xc = x; + if ( xc > 2.0 ) { + xc = 1.0 / xc; + flg |= 2; + } + if ( xc > 1.5 ) { + w = ( 1.0 / xc ) - 1.0; + flg |= 2; + } else if ( xc < 0.5 ) { + w = -xc; + flg |= 1; + } else { + w = xc - 1.0; + } + y = -w * polyval_a( w ) / polyval_b( w ); + if ( flg & 1 ) { + y = PI2O6 - ( stdlib_base_ln( xc ) * stdlib_base_ln( 1.0 - xc ) ) - y; + } + if ( flg & 2 ) { + z = stdlib_base_ln( xc ); + y = -( 0.5 * z * z ) - y; + } + return y; +} diff --git a/lib/node_modules/@stdlib/math/base/special/spence/test/test.js b/lib/node_modules/@stdlib/math/base/special/spence/test/test.js index 1d2d4f53d65..28a293a636f 100644 --- a/lib/node_modules/@stdlib/math/base/special/spence/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/spence/test/test.js @@ -58,7 +58,7 @@ tape( 'the function accurately computes the dilogarithm for small positive numbe v = spence( x[ i ] ); delta = abs( v - expected[ i ] ); tol = 2.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Tolerance: ' + tol + '.' ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. actual: ' + v + '. expected: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); } t.end(); }); @@ -78,7 +78,7 @@ tape( 'the function accurately computes the dilogarithm for medium positive numb v = spence( x[ i ] ); delta = abs( v - expected[ i ] ); tol = 2.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Tolerance: ' + tol + '.' ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. actual: ' + v + '. expected: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); } t.end(); }); @@ -98,20 +98,20 @@ tape( 'the function accurately computes the dilogarithm for large positive numbe v = spence( x[ i ] ); delta = abs( v - expected[ i ] ); tol = EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Tolerance: ' + tol + '.' ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. actual: ' + v + '. expected: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); } t.end(); }); tape( 'the function returns `0.0` if provided `1.0` for `x`', function test( t ) { var val = spence( 1.0 ); - t.equal( val, 0.0, 'equals 0.0' ); + t.equal( val, 0.0, 'returns expected value' ); t.end(); }); tape( 'the function returns `PI^2/6` if provided `0.0` for `x`', function test( t ) { var val = spence( 0.0 ); - t.equal( val, PI_SQUARED / 6.0, 'PI^2/6' ); + t.equal( val, PI_SQUARED / 6.0, 'returns expected value' ); t.end(); }); @@ -121,13 +121,13 @@ tape( 'the function returns `NaN` for negative numbers', function test( t ) { for ( x = -100; x < 0; x++ ) { val = spence( x ); - t.equal( isnan( val ), true, 'equals NaN' ); + t.equal( isnan( val ), true, 'returns expected value' ); } t.end(); }); tape( 'the function returns `NaN` if provided `NaN`', function test( t ) { var val = spence( NaN ); - t.equal( isnan( val ), true, 'equals NaN' ); + t.equal( isnan( val ), true, 'returns expected value' ); t.end(); }); diff --git a/lib/node_modules/@stdlib/math/base/special/spence/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/spence/test/test.native.js new file mode 100644 index 00000000000..7c31908f4f5 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/spence/test/test.native.js @@ -0,0 +1,144 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 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 abs = require( '@stdlib/math/base/special/abs' ); +var PI_SQUARED = require( '@stdlib/constants/float64/pi-squared' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// FIXTURES // + +var small = require( './fixtures/python/small.json' ); +var medium = require( './fixtures/python/medium.json' ); +var large = require( './fixtures/python/large.json' ); + + +// VARIABLES // + +var spence = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( spence instanceof Error ) +}; + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof spence, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function accurately computes the dilogarithm for small positive numbers', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = small.x; + expected = small.expected; + + for ( i = 0; i < x.length; i++ ) { + v = spence( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 2.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes the dilogarithm for medium positive numbers', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = medium.x; + expected = medium.expected; + + for ( i = 0; i < x.length; i++ ) { + v = spence( x[ i ] ); + delta = abs( v - expected[ 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/2298#discussion_r1624765205 + tol = 8.3 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. actual: ' + v + '. expected: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes the dilogarithm for large positive numbers', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = large.x; + expected = large.expected; + + for ( i = 0; i < x.length; i++ ) { + v = spence( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 2.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. actual: ' + v + '. expected: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + t.end(); +}); + +tape( 'the function returns `0.0` if provided `1.0` for `x`', opts, function test( t ) { + var val = spence( 1.0 ); + t.equal( val, 0.0, 'returns expected value' ); + t.end(); +}); + +tape( 'the function returns `PI^2/6` if provided `0.0` for `x`', opts, function test( t ) { + var val = spence( 0.0 ); + t.equal( val, PI_SQUARED / 6.0, 'returns expected value' ); + t.end(); +}); + +tape( 'the function returns `NaN` for negative numbers', opts, function test( t ) { + var val; + var x; + + for ( x = -100; x < 0; x++ ) { + val = spence( x ); + t.equal( isnan( val ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function returns `NaN` if provided `NaN`', opts, function test( t ) { + var val = spence( NaN ); + t.equal( isnan( val ), true, 'returns expected value' ); + t.end(); +});