From fe2d39b8a7282015fdd6993433c74af7966d25de Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sat, 2 Mar 2024 21:10:08 +0530 Subject: [PATCH 01/49] feat: add C implementation for @stdlib/math/base/special/ellipe This commit introduces a C implementation for the elliptic integral of the second kind (@stdlib/math/base/special/ellipe). --- .../math/base/special/ellipe/README.md | 2 +- .../ellipe/benchmark/benchmark.native.js | 58 +++ .../ellipe/benchmark/c/native/Makefile | 146 +++++++ .../ellipe/benchmark/c/native/benchmark.c | 136 ++++++ .../math/base/special/ellipe/binding.gyp | 170 ++++++++ .../base/special/ellipe/examples/c/Makefile | 146 +++++++ .../base/special/ellipe/examples/c/example.c | 33 ++ .../math/base/special/ellipe/include.gypi | 53 +++ .../include/stdlib/math/base/special/ellipe.h | 39 ++ .../math/base/special/ellipe/lib/index.js | 4 +- .../math/base/special/ellipe/lib/main.js | 4 +- .../math/base/special/ellipe/lib/native.js | 61 +++ .../math/base/special/ellipe/lib/poly_p1.js | 6 +- .../math/base/special/ellipe/lib/poly_p10.js | 6 +- .../math/base/special/ellipe/lib/poly_p11.js | 6 +- .../math/base/special/ellipe/lib/poly_p12.js | 6 +- .../math/base/special/ellipe/lib/poly_p2.js | 6 +- .../math/base/special/ellipe/lib/poly_p3.js | 6 +- .../math/base/special/ellipe/lib/poly_p4.js | 6 +- .../math/base/special/ellipe/lib/poly_p5.js | 6 +- .../math/base/special/ellipe/lib/poly_p6.js | 6 +- .../math/base/special/ellipe/lib/poly_p7.js | 6 +- .../math/base/special/ellipe/lib/poly_p8.js | 6 +- .../math/base/special/ellipe/lib/poly_p9.js | 6 +- .../math/base/special/ellipe/manifest.json | 81 ++++ .../base/special/ellipe/scripts/evalpoly.js | 412 +++++++++++------- .../math/base/special/ellipe/src/Makefile | 70 +++ .../math/base/special/ellipe/src/addon.c | 23 + .../math/base/special/ellipe/src/main.c | 398 +++++++++++++++++ .../test/fixtures/cpp/large_negative.json | 1 + .../test/fixtures/cpp/medium_negative.json | 1 + .../base/special/ellipe/test/test.native.js | 178 ++++++++ 32 files changed, 1898 insertions(+), 190 deletions(-) create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/benchmark.native.js create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/Makefile create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/benchmark.c create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/binding.gyp create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/Makefile create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/include.gypi create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/include/stdlib/math/base/special/ellipe.h create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/lib/native.js create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/manifest.json create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/src/Makefile create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/src/addon.c create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/large_negative.json create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/medium_negative.json create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/test/test.native.js diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md index 8f8856b436d6..09615cfb0f1b 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md @@ -2,7 +2,7 @@ @license Apache-2.0 -Copyright (c) 2019 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/ellipe/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/benchmark.native.js new file mode 100644 index 000000000000..b079507c24aa --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/benchmark.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 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 ellipe = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( ellipe instanceof Error ) +}; + + +// MAIN // + +bench( pkg+'::native', opts, function benchmark( b ) { + var y; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = ellipe( randu() ); + 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/ellipe/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/Makefile new file mode 100644 index 000000000000..0ebf4545e1a9 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/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 \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/benchmark.c new file mode 100644 index 000000000000..99d74c9ed01a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/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 `ellipe`. +*/ +#include "stdlib/math/base/special/ellipe.h" +#include +#include +#include +#include +#include + +#define NAME "ellipe" +#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 = rand_double(); + y = stdlib_base_ellipe( 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 ); +} \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/binding.gyp b/lib/node_modules/@stdlib/math/base/special/ellipe/binding.gyp new file mode 100644 index 000000000000..507cb00291e7 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/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 +} \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/Makefile new file mode 100644 index 000000000000..d53ef397c77d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/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 \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c new file mode 100644 index 000000000000..31759c49f3bb --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c @@ -0,0 +1,33 @@ +/** +* @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/ellipe.h" +#include +#include + +int main() { + double m; + double v; + int i; + + for ( i = 0; i < 100; i++ ) { + m = -1.0 + ( ( (double)rand() / (double)RAND_MAX ) * 2.0 ); + v = stdlib_base_ellipe( m ); + printf( "ellipe(%lf) = %lf\n", m, v ); + } +} \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/include.gypi b/lib/node_modules/@stdlib/math/base/special/ellipe/include.gypi new file mode 100644 index 000000000000..222b0ed152c2 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/include.gypi @@ -0,0 +1,53 @@ +# @license Apache-2.0 +# +# Copyright (c) 2022 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': [ + ' + +static const double HALF_PI = 1.5707963267948966; + +/* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */ + +// BEGIN: poly_p1 + +/** +* 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 poly_p1( const double x ) { + return 1.5910034537907922 + (x * (0.41600074399178694 + (x * (0.24579151426410342 + (x * (0.17948148291490615 + (x * (0.14455605708755515 + (x * (0.12320099331242772 + (x * (0.10893881157429353 + (x * (0.09885340987159291 + (x * (0.09143962920174975 + (x * (0.0858425915954139 + (x * 0.08154111871830322))))))))))))))))))); +} + +// END: poly_p1 + +// BEGIN: poly_p2 + +/** +* 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 poly_p2( const double x ) { + return 1.63525673226458 + (x * (0.4711906261487323 + (x * (0.3097284108314996 + (x * (0.2522083117731357 + (x * (0.22672562321968465 + (x * (0.21577444672958598 + (x * (0.21310877187734892 + (x * (0.21602912460518828 + (x * (0.2232558316330579 + (x * (0.23418050129420992 + (x * (0.24855768297226408 + (x * 0.26636380989261754))))))))))))))))))))); +} + +// END: poly_p2 + +// BEGIN: poly_p3 + +/** +* 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 poly_p3( const double x ) { + return 1.685750354812596 + (x * (0.5417318486132803 + (x * (0.40152443839069024 + (x * (0.3696424734208891 + (x * (0.37606071535458363 + (x * (0.4052358870851259 + (x * (0.45329438175399905 + (x * (0.5205189476511842 + (x * (0.609426039204995 + (x * (0.7242635222829089 + (x * (0.8710138477098124 + (x * 1.057652872753547))))))))))))))))))))); +} + +// END: poly_p3 + +// BEGIN: poly_p4 + +/** +* 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 poly_p4( const double x ) { + return 1.7443505972256133 + (x * (0.6348642753719353 + (x * (0.5398425641644455 + (x * (0.5718927051937874 + (x * (0.6702951362654062 + (x * (0.8325865900109772 + (x * (1.0738574482479333 + (x * (1.4220914606754977 + (x * (1.9203871834023047 + (x * (2.6325525483316543 + (x * (3.6521097473190394 + (x * (5.115867135558866 + (x * 7.224080007363877))))))))))))))))))))))); +} + +// END: poly_p4 + +// BEGIN: poly_p5 + +/** +* 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 poly_p5( const double x ) { + return 1.8138839368169826 + (x * (0.7631632457005573 + (x * (0.7619286053215958 + (x * (0.9510746536684279 + (x * (1.315180671703161 + (x * (1.9285606934774109 + (x * (2.9375093425313787 + (x * (4.594894405442878 + (x * (7.33007122188172 + (x * (11.871512597425301 + (x * (19.45851374822938 + (x * (32.20638657246427 + (x * (53.73749198700555 + (x * 90.27388602941))))))))))))))))))))))))); +} + +// END: poly_p5 + +// BEGIN: poly_p6 + +/** +* 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 poly_p6( const double x ) { + return 1.8989249102715535 + (x * (0.9505217946182445 + (x * (1.1510775899590158 + (x * (1.7502391069863006 + (x * (2.952676812636875 + (x * (5.285800396121451 + (x * (9.83248571665998 + (x * (18.787148683275596 + (x * (36.61468615273698 + (x * (72.45292395127771 + (x * (145.1079577347069 + (x * (293.4786396308497 + (x * (598.385181505501 + (x * (1228.4200130758634 + (x * 2536.5297553827645))))))))))))))))))))))))))); +} + +// END: poly_p6 + +// BEGIN: poly_p7 + +/** +* 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 poly_p7( const double x ) { + return 2.0075983984243764 + (x * (1.2484572312123474 + (x * (1.9262346570764797 + (x * (3.7512896400875877 + (x * (8.119944554932045 + (x * (18.665721308735552 + (x * (44.603924842914374 + (x * (109.50920543094983 + (x * (274.2779548232414 + (x * (697.5598008606327 + (x * (1795.7160145002472 + (x * (4668.38171679039 + (x * (12235.762468136643 + (x * (32290.17809718321 + (x * (85713.07608195965 + (x * (228672.1890493117 + (x * 612757.2711915852))))))))))))))))))))))))))))))); +} + +// END: poly_p7 + +// BEGIN: poly_p8 + +/** +* 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 poly_p8( const double x ) { + return 2.1565156474996434 + (x * (1.7918056418494632 + (x * (3.8267512874657132 + (x * (10.386724683637972 + (x * (31.403314054680703 + (x * (100.92370394986955 + (x * (337.3268282632273 + (x * (1158.7079305678278 + (x * (4060.9907421936323 + (x * (14454.001840343448 + (x * (52076.661075994045 + (x * (189493.65914621568 + (x * (695184.5762413896 + (x * (2567994.048255285 + (x * (9541921.966748387 + (x * (35634927.44218076 + (x * (133669298.46120408 + (x * (503352186.68662846 + (x * (1901975729.53866 + (x * 7208915015.330104))))))))))))))))))))))))))))))))))))); +} + +// END: poly_p8 + +// BEGIN: poly_p9 + +/** +* 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 poly_p9( const double x ) { + return 2.3181226217125106 + (x * (2.6169201502912327 + (x * (7.897935075731356 + (x * (30.502397154466724 + (x * (131.48693655235286 + (x * (602.9847637356492 + (x * (2877.024617809973 + (x * (14110.519919151804 + (x * (70621.4408815654 + (x * (358977.266582531 + (x * (1847238.2637239718 + (x * (9600515.416049214 + (x * (50307677.08502367 + (x * (265444188.6527128 + (x * (1408862325.0287027 + (x * 7515687935.373775))))))))))))))))))))))))))))); +} + +// END: poly_p9 + +// BEGIN: poly_p10 + +/** +* 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 poly_p10( const double x ) { + return 2.473596173751344 + (x * (3.727624244118099 + (x * (15.607393035549306 + (x * (84.12850842805888 + (x * (506.98181970406137 + (x * (3252.2770581451236 + (x * (21713.242419574344 + (x * (149037.04518909327 + (x * (1043999.3310899908 + (x * (7427974.817042039 + (x * (53503839.67558661 + (x * (389249886.99487084 + (x * (2855288351.1008105 + (x * (21090077038.76684 + (x * (156699833947.7902 + (x * (1170222242422.44 + (x * (8777948323668.9375 + (x * (66101242752484.95 + (x * (499488053713388.8 + (x * 37859743397240296.0))))))))))))))))))))))))))))))))))))); +} + +// END: poly_p10 + +// BEGIN: poly_p11 + +/** +* 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 poly_p11( const double x ) { + return 0.0 + (x * (0.0625 + (x * (0.03125 + (x * (0.0205078125 + (x * (0.01513671875 + (x * (0.011934280395507812 + (x * (0.009816169738769531 + (x * (0.008315593004226685 + (x * (0.007199153304100037 + (x * (0.00633745662344154 + (x * (0.00565311038371874 + (x * (0.005097046040418718 + (x * (0.004636680381850056 + (x * (0.004249547423822886 + (x * 0.003919665602267974))))))))))))))))))))))))))); +} + +// END: poly_p11 + +// BEGIN: poly_p12 + +/** +* 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 poly_p12( const double x ) { + return 1.5910034537907922 + (x * (0.41600074399178694 + (x * (0.24579151426410342 + (x * (0.17948148291490615 + (x * (0.14455605708755515 + (x * (0.12320099331242772 + (x * (0.10893881157429353 + (x * (0.09885340987159291 + (x * (0.09143962920174975 + (x * (0.0858425915954139 + (x * 0.08154111871830322))))))))))))))))))); +} + +// END: poly_p12 + +/* End auto-generated functions. */ + +/** +* Computes the complete elliptic integral of the second kind. +* +* ## Method +* +* - The function computes the complete elliptic integral of the second kind in terms of parameter \\( m \\), instead of the elliptic modulus \\( k \\). +* +* ```tex +* K(m) = \int_0^{\pi/2} {\sqrt{1 - m sin^2\theta}} d\theta +* ``` +* +* - The function uses a piecewise approximation polynomial as given in Fukushima (2009). +* +* - For \\( m < 0 \\), the implementation follows Fukushima (2015). Namely, we use Equation 17.4.17 from the _Handbook of Mathematical Functions_ (Abramowitz and Stegun) to compute the function for \\( m < 0 \\) in terms of the piecewise polynomial representation of \\( m > 0 )). +* +* ```tex +* F(\phi|-m) = (1+m)^(-1/2) K(m/(1+m)) - (1+m)^(-1/2) F(\pi/2-\phi|m/(1+m)) +* ``` +* +* Since \\( K(m) \\) is equivalent to \\( F(\phi|m) \\), the above reduces to +* +* ```tex +* F(\phi|-m) = (1+m)^(-1/2) K(m/(1+m)) +* ``` +* +* ## References +* +* - Fukushima, Toshio. 2009. "Fast computation of complete elliptic integrals and Jacobian elliptic functions." _Celestial Mechanics and Dynamical Astronomy_ 105 (4): 305. doi:[10.1007/s10569-009-9228-z](https://doi.org/10.1007/s10569-009-9228-z). +* - Fukushima, Toshio. 2015. "Precise and fast computation of complete elliptic integrals by piecewise minimax rational function approximation." _Journal of Computational and Applied Mathematics_ 282 (July): 71–76. doi:[10.1016/j.cam.2014.12.038](https://doi.org/10.1016/j.cam.2014.12.038). +* +* @param x input value +* @return output value +* +* @example +* double out = stdlib_base_ellipe( 0.5 ); +* // returns ~1.3506 +*/ +double stdlib_base_ellipe( const double m ) { + int8_t FLG; + double edm; + double kdm; + double td; + double km; + double t; + double x; + + FLG = 0; + x = m; + if ( m < 0.0 ) { + x = m / ( m - 1.0 ); + FLG += 1; + } + if ( x == 0.0 ) { + return STDLIB_CONSTANT_FLOAT64_HALF_PI; + } + if ( x == 1.0 ) { + return 1.0; + } + if ( x > 1.0 ) { + return 0.0 / 0.0; //NaN + } + if ( x < 0.1 ) { + t = poly_p1( x - 0.05 ); + } else if ( x < 0.2 ) { + t = poly_p2( x - 0.15 ); + } else if ( x < 0.3 ) { + t = poly_p3( x - 0.25 ); + } else if ( x < 0.4 ) { + t = poly_p4( x - 0.35 ); + } else if ( x < 0.5 ) { + t = poly_p5( x - 0.45 ); + } else if ( x < 0.6 ) { + t = poly_p6( x - 0.55 ); + } else if ( x < 0.7 ) { + t = poly_p7( x - 0.65 ); + } else if ( x < 0.8 ) { + t = poly_p8( x - 0.75 ); + } else if ( x < 0.85 ) { + t = poly_p9( x - 0.825 ); + } else if ( x < 0.9 ) { + t = poly_p10( x - 0.875 ); + } else { + td = 0.95 - x; + kdm = poly_p11( td ); + edm = poly_p12( td ); + km = ellipe( x ); + + // To avoid precision loss near 1, we use Eq. 33 from Fukushima (2009): + t = ( HALF_PI + ( km * (kdm - edm) ) ) / kdm; + } + if ( FLG == 1 ) { + // Complete the transformation mentioned above for m < 0: + return t * stdlib_base_sqrt( 1.0 - m ); + } + return t; +} diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/large_negative.json b/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/large_negative.json new file mode 100644 index 000000000000..ac2e366976b0 --- /dev/null +++ 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\ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/ellipe/test/test.native.js new file mode 100644 index 000000000000..b1c10af1532d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/test/test.native.js @@ -0,0 +1,178 @@ +/** +* @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 PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var HALF_PI = require( '@stdlib/constants/float64/half-pi' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// FIXTURES // + +var mediumPositive = require( './fixtures/cpp/medium_positive.json' ); +var closeToUnity = require( './fixtures/cpp/close_to_unity.json' ); +var mediumNegative = require( './fixtures/cpp/medium_negative.json' ); +var largeNegative = require( './fixtures/cpp/large_negative.json' ); + + +// VARIABLES // + +var ellipe = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( ellipe instanceof Error ) +}; + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof ellipe, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function evaluates the complete elliptic integral of the first kind (medium positive values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + expected = mediumPositive.expected; + x = mediumPositive.x; + for ( i = 0; i < x.length; i++ ) { + y = ellipe( x[i] ); + if ( y === expected[i] ) { + t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[i] ); + tol = 25.0 * EPS * abs( expected[i] ); + t.equal( delta <= tol, true, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the complete elliptic integral of the first kind (values close to positive unity)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + expected = closeToUnity.expected; + x = closeToUnity.x; + for ( i = 0; i < x.length; i++ ) { + y = ellipe( x[i] ); + if ( y === expected[i] ) { + t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[i] ); + tol = 8000.0 * EPS * abs( expected[i] ); + t.equal( delta <= tol, true, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the complete elliptic integral of the first kind (medium negative values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + expected = mediumNegative.expected; + x = mediumNegative.x; + for ( i = 0; i < x.length; i++ ) { + y = ellipe( x[i] ); + if ( y === expected[i] ) { + t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[i] ); + tol = 1.5 * EPS * abs( expected[i] ); + t.equal( delta <= tol, true, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the complete elliptic integral of the first kind (large negative values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + expected = largeNegative.expected; + x = largeNegative.x; + for ( i = 0; i < x.length; i++ ) { + y = ellipe( x[i] ); + if ( y === expected[i] ) { + t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[i] ); + tol = 1e9 * EPS * abs( expected[i] ); + t.equal( delta <= tol, true, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function returns `NaN` if provided values larger than `1.0`', opts, function test( t ) { + var v = ellipe( 1.01 ); + t.equal( isnan( v ), true, 'returns expected value' ); + t.end(); +}); + +tape( 'the function returns `+infinity` if provided `1.0`', opts, function test( t ) { + var v = ellipe( 1.0 ); + t.equal( v, PINF, 'return expected value' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided `+infinity`', opts, function test( t ) { + var v = ellipe( PINF ); + t.equal( isnan( v ), true, 'returns expected value' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided `-infinity`', opts, function test( t ) { + var v = ellipe( NINF ); + t.equal( isnan( v ), true, 'returns expected value' ); + t.end(); +}); + +tape( 'the function returns `π/2` if provided `0`', opts, function test( t ) { + var v = ellipe( 0 ); + t.equal( v, HALF_PI, 'returns expected value' ); + t.end(); +}); From c417c1eca3f15992ec79b68fb4a89850daa953ae Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sat, 2 Mar 2024 21:14:48 +0530 Subject: [PATCH 02/49] feat: add C implementation for @stdlib/math/base/special/ellipe This commit introduces a C implementation for the elliptic integral of the second kind (@stdlib/math/base/special/ellipe). --- .../@stdlib/math/base/special/ellipe/lib/poly_p1.js | 4 ++-- .../@stdlib/math/base/special/ellipe/lib/poly_p10.js | 4 ++-- .../@stdlib/math/base/special/ellipe/lib/poly_p11.js | 4 ++-- .../@stdlib/math/base/special/ellipe/lib/poly_p12.js | 4 ++-- .../@stdlib/math/base/special/ellipe/lib/poly_p2.js | 4 ++-- .../@stdlib/math/base/special/ellipe/lib/poly_p3.js | 4 ++-- .../@stdlib/math/base/special/ellipe/lib/poly_p4.js | 4 ++-- .../@stdlib/math/base/special/ellipe/lib/poly_p5.js | 4 ++-- .../@stdlib/math/base/special/ellipe/lib/poly_p6.js | 4 ++-- .../@stdlib/math/base/special/ellipe/lib/poly_p7.js | 4 ++-- .../@stdlib/math/base/special/ellipe/lib/poly_p8.js | 4 ++-- .../@stdlib/math/base/special/ellipe/lib/poly_p9.js | 4 ++-- 12 files changed, 24 insertions(+), 24 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p1.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p1.js index 2acf79fe79a2..bb0b3ef53515 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p1.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p1.js @@ -36,9 +36,9 @@ */ function evalpoly( x ) { if ( x === 0.0 ) { - return 1.5910034537907922; + return 1.5509733517804722; } - return 1.5910034537907922 + (x * (0.41600074399178694 + (x * (0.24579151426410342 + (x * (0.17948148291490615 + (x * (0.14455605708755515 + (x * (0.12320099331242772 + (x * (0.10893881157429353 + (x * (0.09885340987159291 + (x * (0.09143962920174975 + (x * (0.0858425915954139 + (x * 0.08154111871830322))))))))))))))))))); // eslint-disable-line max-len + return 1.5509733517804722 + (x * (-0.4003010201031985 + (x * (-0.07849861944294194 + (x * (-0.034318853117591995 + (x * (-0.0197180433173655 + (x * (-0.01305950773199331 + (x * (-0.009442372874146548 + (x * (-0.007246728512402157 + (x * (-0.00580742401295609 + (x * -0.004809187786009338))))))))))))))))); // eslint-disable-line max-len } diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p10.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p10.js index 15d33096b516..8135e4fc774d 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p10.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p10.js @@ -36,9 +36,9 @@ */ function evalpoly( x ) { if ( x === 0.0 ) { - return 2.473596173751344; + return 1.1246173251197522; } - return 2.473596173751344 + (x * (3.727624244118099 + (x * (15.607393035549306 + (x * (84.12850842805888 + (x * (506.98181970406137 + (x * (3252.2770581451236 + (x * (21713.242419574344 + (x * (149037.04518909327 + (x * (1043999.3310899908 + (x * (7427974.817042039 + (x * (53503839.67558661 + (x * (389249886.99487084 + (x * (2855288351.1008105 + (x * (21090077038.76684 + (x * (156699833947.7902 + (x * (1170222242422.44 + (x * (8777948323668.9375 + (x * (66101242752484.95 + (x * (499488053713388.8 + (x * 37859743397240296.0))))))))))))))))))))))))))))))))))))); // eslint-disable-line max-len + return 1.1246173251197522 + (x * (-0.7708450563609095 + (x * (-0.8447940536449113 + (x * (-2.4900973094503946 + (x * (-10.239717411543843 + (x * (-49.7490054655148 + (x * (-267.09866751957054 + (x * (-1532.66588382523 + (x * (-9222.313478526092 + (x * (-57502.51612140314 + (x * (-368596.11674161063 + (x * (-2415611.0887010912 + (x * (-16120097.815816568 + (x * (-109209938.52030899 + (x * (-749380758.1942496 + (x * (-5198725846.725541 + (x * -36409256888.1214))))))))))))))))))))))))))))))); // eslint-disable-line max-len } diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p11.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p11.js index 3ea85beb34d2..2acf79fe79a2 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p11.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p11.js @@ -36,9 +36,9 @@ */ function evalpoly( x ) { if ( x === 0.0 ) { - return 0.0; + return 1.5910034537907922; } - return 0.0 + (x * (0.0625 + (x * (0.03125 + (x * (0.0205078125 + (x * (0.01513671875 + (x * (0.011934280395507812 + (x * (0.009816169738769531 + (x * (0.008315593004226685 + (x * (0.007199153304100037 + (x * (0.00633745662344154 + (x * (0.00565311038371874 + (x * (0.005097046040418718 + (x * (0.004636680381850056 + (x * (0.004249547423822886 + (x * 0.003919665602267974))))))))))))))))))))))))))); // eslint-disable-line max-len + return 1.5910034537907922 + (x * (0.41600074399178694 + (x * (0.24579151426410342 + (x * (0.17948148291490615 + (x * (0.14455605708755515 + (x * (0.12320099331242772 + (x * (0.10893881157429353 + (x * (0.09885340987159291 + (x * (0.09143962920174975 + (x * (0.0858425915954139 + (x * 0.08154111871830322))))))))))))))))))); // eslint-disable-line max-len } diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p12.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p12.js index 2acf79fe79a2..bb0b3ef53515 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p12.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p12.js @@ -36,9 +36,9 @@ */ function evalpoly( x ) { if ( x === 0.0 ) { - return 1.5910034537907922; + return 1.5509733517804722; } - return 1.5910034537907922 + (x * (0.41600074399178694 + (x * (0.24579151426410342 + (x * (0.17948148291490615 + (x * (0.14455605708755515 + (x * (0.12320099331242772 + (x * (0.10893881157429353 + (x * (0.09885340987159291 + (x * (0.09143962920174975 + (x * (0.0858425915954139 + (x * 0.08154111871830322))))))))))))))))))); // eslint-disable-line max-len + return 1.5509733517804722 + (x * (-0.4003010201031985 + (x * (-0.07849861944294194 + (x * (-0.034318853117591995 + (x * (-0.0197180433173655 + (x * (-0.01305950773199331 + (x * (-0.009442372874146548 + (x * (-0.007246728512402157 + (x * (-0.00580742401295609 + (x * -0.004809187786009338))))))))))))))))); // eslint-disable-line max-len } diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p2.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p2.js index 9df893eb19b2..fd3aa755cbec 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p2.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p2.js @@ -36,9 +36,9 @@ */ function evalpoly( x ) { if ( x === 0.0 ) { - return 1.63525673226458; + return 1.5101218320928198; } - return 1.63525673226458 + (x * (0.4711906261487323 + (x * (0.3097284108314996 + (x * (0.2522083117731357 + (x * (0.22672562321968465 + (x * (0.21577444672958598 + (x * (0.21310877187734892 + (x * (0.21602912460518828 + (x * (0.2232558316330579 + (x * (0.23418050129420992 + (x * (0.24855768297226408 + (x * 0.26636380989261754))))))))))))))))))))); // eslint-disable-line max-len + return 1.5101218320928198 + (x * (-0.41711633390586755 + (x * (-0.09012382040477457 + (x * (-0.04372994401908431 + (x * (-0.027965493064761784 + (x * (-0.020644781177568104 + (x * (-0.016650786739707237 + (x * (-0.01426196082884252 + (x * (-0.012759847429264804 + (x * (-0.011799303775587354 + (x * -0.011197445703074968))))))))))))))))))); // eslint-disable-line max-len } diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p3.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p3.js index 409727b6d436..2bf797e9a69a 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p3.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p3.js @@ -36,9 +36,9 @@ */ function evalpoly( x ) { if ( x === 0.0 ) { - return 1.685750354812596; + return 1.4674622093394272; } - return 1.685750354812596 + (x * (0.5417318486132803 + (x * (0.40152443839069024 + (x * (0.3696424734208891 + (x * (0.37606071535458363 + (x * (0.4052358870851259 + (x * (0.45329438175399905 + (x * (0.5205189476511842 + (x * (0.609426039204995 + (x * (0.7242635222829089 + (x * (0.8710138477098124 + (x * 1.057652872753547))))))))))))))))))))); // eslint-disable-line max-len + return 1.4674622093394272 + (x * (-0.43657629094633776 + (x * (-0.10515555766694255 + (x * (-0.05737184359324173 + (x * (-0.04139162772734022 + (x * (-0.03452772850528084 + (x * (-0.031495443512532785 + (x * (-0.030527000890325277 + (x * (-0.0309169840192389 + (x * (-0.03237139531475812 + (x * -0.03478996038640416))))))))))))))))))); // eslint-disable-line max-len } diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p4.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p4.js index 26e201ebad20..783b54457c32 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p4.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p4.js @@ -36,9 +36,9 @@ */ function evalpoly( x ) { if ( x === 0.0 ) { - return 1.7443505972256133; + return 1.4226911334908792; } - return 1.7443505972256133 + (x * (0.6348642753719353 + (x * (0.5398425641644455 + (x * (0.5718927051937874 + (x * (0.6702951362654062 + (x * (0.8325865900109772 + (x * (1.0738574482479333 + (x * (1.4220914606754977 + (x * (1.9203871834023047 + (x * (2.6325525483316543 + (x * (3.6521097473190394 + (x * (5.115867135558866 + (x * 7.224080007363877))))))))))))))))))))))); // eslint-disable-line max-len + return 1.4226911334908792 + (x * (-0.4595135196210487 + (x * (-0.12525053982206188 + (x * (-0.07813854509440948 + (x * (-0.06471427847205 + (x * (-0.06208433913173031 + (x * (-0.06519703281557247 + (x * (-0.07279389536257878 + (x * (-0.084959075171781 + (x * (-0.102539850131046 + (x * (-0.12705358515769605 + (x * -0.1607911206912746))))))))))))))))))))); // eslint-disable-line max-len } diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p5.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p5.js index ff42b8d978d5..97bd3a47e641 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p5.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p5.js @@ -36,9 +36,9 @@ */ function evalpoly( x ) { if ( x === 0.0 ) { - return 1.8138839368169826; + return 1.3754019718711163; } - return 1.8138839368169826 + (x * (0.7631632457005573 + (x * (0.7619286053215958 + (x * (0.9510746536684279 + (x * (1.315180671703161 + (x * (1.9285606934774109 + (x * (2.9375093425313787 + (x * (4.594894405442878 + (x * (7.33007122188172 + (x * (11.871512597425301 + (x * (19.45851374822938 + (x * (32.20638657246427 + (x * (53.73749198700555 + (x * 90.27388602941))))))))))))))))))))))))); // eslint-disable-line max-len + return 1.3754019718711163 + (x * (-0.4872021832731848 + (x * (-0.15331170134854022 + (x * (-0.11184944491702783 + (x * (-0.10884095252313576 + (x * (-0.12295422312026907 + (x * (-0.15221716396203505 + (x * (-0.20049532364269734 + (x * (-0.27617433306775174 + (x * (-0.39351311430437586 + (x * (-0.5757544060278792 + (x * (-0.8605232357272398 + (x * -1.3088332057585401))))))))))))))))))))))); // eslint-disable-line max-len } diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p6.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p6.js index 8be641042389..dcf58acf8358 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p6.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p6.js @@ -36,9 +36,9 @@ */ function evalpoly( x ) { if ( x === 0.0 ) { - return 1.8989249102715535; + return 1.3250244979582302; } - return 1.8989249102715535 + (x * (0.9505217946182445 + (x * (1.1510775899590158 + (x * (1.7502391069863006 + (x * (2.952676812636875 + (x * (5.285800396121451 + (x * (9.83248571665998 + (x * (18.787148683275596 + (x * (36.61468615273698 + (x * (72.45292395127771 + (x * (145.1079577347069 + (x * (293.4786396308497 + (x * (598.385181505501 + (x * (1228.4200130758634 + (x * 2536.5297553827645))))))))))))))))))))))))))); // eslint-disable-line max-len + return 1.3250244979582302 + (x * (-0.5217276475575667 + (x * (-0.19490643048212622 + (x * (-0.17162372682201127 + (x * (-0.20275465292641914 + (x * (-0.27879895311853475 + (x * (-0.42069845728100574 + (x * (-0.675948400853106 + (x * (-1.1363431218392293 + (x * (-1.9767211439543984 + (x * (-3.5316967730957227 + (x * (-6.446753640156048 + (x * -11.97703130208884))))))))))))))))))))))); // eslint-disable-line max-len } diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p7.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p7.js index 143e06cec877..b9a42aec8fc6 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p7.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p7.js @@ -36,9 +36,9 @@ */ function evalpoly( x ) { if ( x === 0.0 ) { - return 2.0075983984243764; + return 1.2707074796501499; } - return 2.0075983984243764 + (x * (1.2484572312123474 + (x * (1.9262346570764797 + (x * (3.7512896400875877 + (x * (8.119944554932045 + (x * (18.665721308735552 + (x * (44.603924842914374 + (x * (109.50920543094983 + (x * (274.2779548232414 + (x * (697.5598008606327 + (x * (1795.7160145002472 + (x * (4668.38171679039 + (x * (12235.762468136643 + (x * (32290.17809718321 + (x * (85713.07608195965 + (x * (228672.1890493117 + (x * 612757.2711915852))))))))))))))))))))))))))))))); // eslint-disable-line max-len + return 1.2707074796501499 + (x * (-0.5668391682878666 + (x * (-0.2621607934324926 + (x * (-0.2922441735330774 + (x * (-0.4403978408504232 + (x * (-0.7749476413813975 + (x * (-1.498870837987561 + (x * (-3.089708310445187 + (x * (-6.6675959033810015 + (x * (-14.89436036517319 + (x * (-34.18120574251449 + (x * (-80.15895841905397 + (x * (-191.34894807629848 + (x * (-463.5938853480342 + (x * -1137.38082216936))))))))))))))))))))))))))); // eslint-disable-line max-len } diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p8.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p8.js index 697b3f4220dc..304f3dc4f2f5 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p8.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p8.js @@ -36,9 +36,9 @@ */ function evalpoly( x ) { if ( x === 0.0 ) { - return 2.1565156474996434; + return 1.2110560275684594; } - return 2.1565156474996434 + (x * (1.7918056418494632 + (x * (3.8267512874657132 + (x * (10.386724683637972 + (x * (31.403314054680703 + (x * (100.92370394986955 + (x * (337.3268282632273 + (x * (1158.7079305678278 + (x * (4060.9907421936323 + (x * (14454.001840343448 + (x * (52076.661075994045 + (x * (189493.65914621568 + (x * (695184.5762413896 + (x * (2567994.048255285 + (x * (9541921.966748387 + (x * (35634927.44218076 + (x * (133669298.46120408 + (x * (503352186.68662846 + (x * (1901975729.53866 + (x * 7208915015.330104))))))))))))))))))))))))))))))))))))); // eslint-disable-line max-len + return 1.2110560275684594 + (x * (-0.6303064132874558 + (x * (-0.38716640952066916 + (x * (-0.5922782353119346 + (x * (-1.23755558451305 + (x * (-3.0320566617452474 + (x * (-8.18168822157359 + (x * (-23.55507217389693 + (x * (-71.04099935893065 + (x * (-221.879685319235 + (x * (-712.1364793277636 + (x * (-2336.1253314403966 + (x * (-7801.945954775964 + (x * (-26448.19586059192 + (x * (-90799.48341621365 + (x * (-315126.04064491636 + (x * -1104011.3443115912))))))))))))))))))))))))))))))); // eslint-disable-line max-len } diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p9.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p9.js index 0c01fe74f689..c6ef77d35b52 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p9.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p9.js @@ -36,9 +36,9 @@ */ function evalpoly( x ) { if ( x === 0.0 ) { - return 2.3181226217125106; + return 1.1613071521962828; } - return 2.3181226217125106 + (x * (2.6169201502912327 + (x * (7.897935075731356 + (x * (30.502397154466724 + (x * (131.48693655235286 + (x * (602.9847637356492 + (x * (2877.024617809973 + (x * (14110.519919151804 + (x * (70621.4408815654 + (x * (358977.266582531 + (x * (1847238.2637239718 + (x * (9600515.416049214 + (x * (50307677.08502367 + (x * (265444188.6527128 + (x * (1408862325.0287027 + (x * 7515687935.373775))))))))))))))))))))))))))))); // eslint-disable-line max-len + return 1.1613071521962828 + (x * (-0.7011002845552895 + (x * (-0.5805514744654373 + (x * (-1.2436930610777865 + (x * (-3.679383613496635 + (x * (-12.815909243378957 + (x * (-49.25672530759985 + (x * (-202.18187354340904 + (x * (-869.8602699308701 + (x * (-3877.0058473132895 + (x * (-17761.7071017094 + (x * (-83182.69029154233 + (x * (-396650.4505013548 + (x * -1920033.4136826345))))))))))))))))))))))))); // eslint-disable-line max-len } From b747ddd481d81bb5ae776092c14d298629179372 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:06:49 +0530 Subject: [PATCH 03/49] Update index.js Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/lib/index.js | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/index.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/index.js index 21607db6e54b..efae9da72cd3 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/index.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/index.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2019 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. @@ -30,7 +30,7 @@ * // returns ~1.351 * * v = ellipe( -1.0 ); -* // returns ~1.9101 +* // returns ~1.910 * * v = ellipe( 2.0 ); * // returns NaN From 1265c52f5c24bb1405045cbda2d75ec6c802239f Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:07:25 +0530 Subject: [PATCH 04/49] Update main.js Signed-off-by: GUNJ JOSHI --- lib/node_modules/@stdlib/math/base/special/ellipe/lib/main.js | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/main.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/main.js index 9d0ae556e363..c39d97c19aad 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/main.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2019 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. @@ -98,7 +98,7 @@ var poly12 = require( './poly_p12.js' ); * // returns ~1.351 * * v = ellipe( -1.0 ); -* // returns ~1.9101 +* // returns ~1.910 * * v = ellipe( 2.0 ); * // returns NaN From cb4fe801eaf6ace8518cb340734362f52c176aa0 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:07:52 +0530 Subject: [PATCH 05/49] Update poly_p1.js Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/lib/poly_p1.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p1.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p1.js index bb0b3ef53515..4161a4eaed1d 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p1.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p1.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2022 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. From 0292a30d57c6768c4c23dc0e442c82b7783315c6 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:08:55 +0530 Subject: [PATCH 06/49] Update poly_p10.js Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/lib/poly_p10.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p10.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p10.js index 8135e4fc774d..ffbf78d410e2 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p10.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p10.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2022 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. From 305d5175a46d118f52e3fc1306cc9e94e0ea1cc4 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:09:17 +0530 Subject: [PATCH 07/49] Update poly_p11.js Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/lib/poly_p11.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p11.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p11.js index 2acf79fe79a2..2b5122deff8d 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p11.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p11.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2022 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. From 5e596d51d1b359c881d3bffdc537af0f6b37cfae Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:09:42 +0530 Subject: [PATCH 08/49] Update README.md Signed-off-by: GUNJ JOSHI --- lib/node_modules/@stdlib/math/base/special/ellipe/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md index 09615cfb0f1b..8f8856b436d6 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md @@ -2,7 +2,7 @@ @license Apache-2.0 -Copyright (c) 2024 The Stdlib Authors. +Copyright (c) 2019 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. From 32bec64642ca8910d9f7d49b2cec2dcd882ab889 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:10:16 +0530 Subject: [PATCH 09/49] Update poly_p12.js Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/lib/poly_p12.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p12.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p12.js index bb0b3ef53515..4161a4eaed1d 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p12.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p12.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2022 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. From 7bfad01362a7ab4bd592c55a98e49bf242be7da2 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:12:51 +0530 Subject: [PATCH 10/49] Update poly_p9.js Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/lib/poly_p9.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p9.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p9.js index c6ef77d35b52..2c4d8e4648d0 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p9.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p9.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2022 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. From c9efb70b898ce69242b92b5a3ad2fa1b70477ad5 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:13:13 +0530 Subject: [PATCH 11/49] Update poly_p2.js Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/lib/poly_p2.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p2.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p2.js index fd3aa755cbec..3cc8aae2cd68 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p2.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p2.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2022 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. From b63002f7d78c4eaecff3b9ae5cf7abdfce73044f Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:13:35 +0530 Subject: [PATCH 12/49] Update poly_p3.js Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/lib/poly_p3.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p3.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p3.js index 2bf797e9a69a..f6dfd3fc5053 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p3.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p3.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2022 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. From e6fda42b445c47dcddbca48a4eecc3d217a7b96d Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:13:59 +0530 Subject: [PATCH 13/49] Update poly_p4.js Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/lib/poly_p4.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p4.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p4.js index 783b54457c32..1b0acda71283 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p4.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p4.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2022 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. From 17b6c55f1f668e98e90b9e521ff764a3a507da80 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:14:24 +0530 Subject: [PATCH 14/49] Update poly_p5.js Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/lib/poly_p5.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p5.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p5.js index 97bd3a47e641..3d6673d2b48c 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p5.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p5.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2022 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. From 1722c264d00f017011a444c7b85344c85b58aea2 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:14:58 +0530 Subject: [PATCH 15/49] Update poly_p6.js Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/lib/poly_p6.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p6.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p6.js index dcf58acf8358..9246811a4ffb 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p6.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p6.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2022 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. From 232bf8e461acf7bd83ed0961ec863b15584f973c Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:15:21 +0530 Subject: [PATCH 16/49] Update poly_p7.js Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/lib/poly_p7.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p7.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p7.js index b9a42aec8fc6..8753f668bbd6 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p7.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p7.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2022 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. From 6d9f616935b00cc194b37a33da61bdc5e4c42206 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:15:42 +0530 Subject: [PATCH 17/49] Update poly_p8.js Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/lib/poly_p8.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p8.js b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p8.js index 304f3dc4f2f5..0499483a4a63 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p8.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/lib/poly_p8.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2022 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. From c52374ece3d9f324e480f1b88a9173f994507800 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:25:39 +0530 Subject: [PATCH 18/49] feat: add C implementation for @stdlib/math/base/special/ellipe This commit introduces a C implementation for the elliptic integral of the second kind (@stdlib/math/base/special/ellipe). --- .../base/special/ellipk/scripts/evalpoly.js | 318 ++++++++---------- 1 file changed, 148 insertions(+), 170 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipk/scripts/evalpoly.js b/lib/node_modules/@stdlib/math/base/special/ellipk/scripts/evalpoly.js index 061a63b8ae71..3aab7dda2563 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipk/scripts/evalpoly.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipk/scripts/evalpoly.js @@ -41,215 +41,179 @@ var compileC = require( '@stdlib/math/base/tools/evalpoly-compile-c' ); // Table 2 for expansion about x = 0.05: var P1 = [ - 1.591003453790792180, - 0.416000743991786912, - 0.245791514264103415, - 0.179481482914906162, - 0.144556057087555150, - 0.123200993312427711, - 0.108938811574293531, - 0.098853409871592910, - 0.091439629201749751, - 0.085842591595413900, - 0.081541118718303215 + 1.550973351780472328, + -0.400301020103198524, + -0.078498619442941939, + -0.034318853117591992, + -0.019718043317365499, + -0.013059507731993309, + -0.009442372874146547, + -0.007246728512402157, + -0.005807424012956090, + -0.004809187786009338 ]; // Table 3 for expansion about 0.15: var P2 = [ - 1.635256732264579992, - 0.471190626148732291, - 0.309728410831499587, - 0.252208311773135699, - 0.226725623219684650, - 0.215774446729585976, - 0.213108771877348910, - 0.216029124605188282, - 0.223255831633057896, - 0.234180501294209925, - 0.248557682972264071, - 0.266363809892617521 + 1.510121832092819728, + -0.417116333905867549, + -0.090123820404774569, + -0.043729944019084312, + -0.027965493064761785, + -0.020644781177568105, + -0.016650786739707238, + -0.014261960828842520, + -0.012759847429264803, + -0.011799303775587354, + -0.011197445703074968 ]; // Table 4 for expansion about 0.25: var P3 = [ - 1.685750354812596043, - 0.541731848613280329, - 0.401524438390690257, - 0.369642473420889090, - 0.376060715354583645, - 0.405235887085125919, - 0.453294381753999079, - 0.520518947651184205, - 0.609426039204995055, - 0.724263522282908870, - 0.871013847709812357, - 1.057652872753547036 + 1.467462209339427155, + -0.436576290946337775, + -0.105155557666942554, + -0.057371843593241730, + -0.041391627727340220, + -0.034527728505280841, + -0.031495443512532783, + -0.030527000890325277, + -0.030916984019238900, + -0.032371395314758122, + -0.034789960386404158 ]; // Table 5 for expansion about 0.35: var P4 = [ - 1.744350597225613243, - 0.634864275371935304, - 0.539842564164445538, - 0.571892705193787391, - 0.670295136265406100, - 0.832586590010977199, - 1.073857448247933265, - 1.422091460675497751, - 1.920387183402304829, - 2.632552548331654201, - 3.652109747319039160, - 5.115867135558865806, - 7.224080007363877411 + 1.422691133490879171, + -0.459513519621048674, + -0.125250539822061878, + -0.078138545094409477, + -0.064714278472050002, + -0.062084339131730311, + -0.065197032815572477, + -0.072793895362578779, + -0.084959075171781003, + -0.102539850131045997, + -0.127053585157696036, + -0.160791120691274606 ]; // Table 6 for expansion about 0.45: var P5 = [ - 1.813883936816982644, - 0.763163245700557246, - 0.761928605321595831, - 0.951074653668427927, - 1.315180671703161215, - 1.928560693477410941, - 2.937509342531378755, - 4.594894405442878062, - 7.330071221881720772, - 11.87151259742530180, - 19.45851374822937738, - 32.20638657246426863, - 53.73749198700554656, - 90.27388602940998849 + 1.375401971871116291, + -0.487202183273184837, + -0.153311701348540228, + -0.111849444917027833, + -0.108840952523135768, + -0.122954223120269076, + -0.152217163962035047, + -0.200495323642697339, + -0.276174333067751758, + -0.393513114304375851, + -0.575754406027879147, + -0.860523235727239756, + -1.308833205758540162 ]; // Table 7 for expansion about 0.55: var P6 = [ - 1.898924910271553526, - 0.950521794618244435, - 1.151077589959015808, - 1.750239106986300540, - 2.952676812636875180, - 5.285800396121450889, - 9.832485716659979747, - 18.78714868327559562, - 36.61468615273698145, - 72.45292395127771801, - 145.1079577347069102, - 293.4786396308497026, - 598.3851815055010179, - 1228.420013075863451, - 2536.529755382764488 + 1.325024497958230082, + -0.521727647557566767, + -0.194906430482126213, + -0.171623726822011264, + -0.202754652926419141, + -0.278798953118534762, + -0.420698457281005762, + -0.675948400853106021, + -1.136343121839229244, + -1.976721143954398261, + -3.531696773095722506, + -6.446753640156048150, + -11.97703130208884026 ]; // Table 8 for expansion about 0.65: var P7 = [ - 2.007598398424376302, - 1.248457231212347337, - 1.926234657076479729, - 3.751289640087587680, - 8.119944554932045802, - 18.66572130873555361, - 44.60392484291437063, - 109.5092054309498377, - 274.2779548232413480, - 697.5598008606326163, - 1795.716014500247129, - 4668.381716790389910, - 12235.76246813664335, - 32290.17809718320818, - 85713.07608195964685, - 228672.1890493117096, - 612757.2711915852774 + 1.270707479650149744, + -0.566839168287866583, + -0.262160793432492598, + -0.292244173533077419, + -0.440397840850423189, + -0.774947641381397458, + -1.498870837987561088, + -3.089708310445186667, + -6.667595903381001064, + -14.89436036517319078, + -34.18120574251449024, + -80.15895841905397306, + -191.3489480762984920, + -463.5938853480342030, + -1137.380822169360061 ]; // Table 9 for expansion about 0.75: var P8 = [ - 2.156515647499643235, - 1.791805641849463243, - 3.826751287465713147, - 10.38672468363797208, - 31.40331405468070290, - 100.9237039498695416, - 337.3268282632272897, - 1158.707930567827917, - 4060.990742193632092, - 14454.00184034344795, - 52076.66107599404803, - 189493.6591462156887, - 695184.5762413896145, - 2567994.048255284686, - 9541921.966748386322, - 35634927.44218076174, - 133669298.4612040871, - 503352186.6866284541, - 1901975729.538660119, - 7208915015.330103756 + 1.211056027568459525, + -0.630306413287455807, + -0.387166409520669145, + -0.592278235311934603, + -1.237555584513049844, + -3.032056661745247199, + -8.181688221573590762, + -23.55507217389693250, + -71.04099935893064956, + -221.8796853192349888, + -712.1364793277635425, + -2336.125331440396407, + -7801.945954775964673, + -26448.19586059191933, + -90799.48341621365251, + -315126.0406449163424, + -1104011.344311591159 ]; // Table 10 for expansion about 0.825: var P9 = [ - 2.318122621712510589, - 2.616920150291232841, - 7.897935075731355823, - 30.50239715446672327, - 131.4869365523528456, - 602.9847637356491617, - 2877.024617809972641, - 14110.51991915180325, - 70621.44088156540229, - 358977.2665825309926, - 1847238.263723971684, - 9600515.416049214109, - 50307677.08502366879, - 265444188.6527127967, - 1408862325.028702687, - 7515687935.373774627 + 1.161307152196282836, + -0.701100284555289548, + -0.580551474465437362, + -1.243693061077786614, + -3.679383613496634879, + -12.81590924337895775, + -49.25672530759985272, + -202.1818735434090269, + -869.8602699308701437, + -3877.005847313289571, + -17761.70710170939814, + -83182.69029154232061, + -396650.4505013548170, + -1920033.413682634405 ]; // Table 11 for expansion about 0.875: var P10 = [ - 2.473596173751343912, - 3.727624244118099310, - 15.60739303554930496, - 84.12850842805887747, - 506.9818197040613935, - 3252.277058145123644, - 21713.24241957434256, - 149037.0451890932766, - 1043999.331089990839, - 7427974.817042038995, - 53503839.67558661151, - 389249886.9948708474, - 2855288351.100810619, - 21090077038.76684053, - 156699833947.7902014, - 1170222242422.439893, - 8777948323668.937971, - 66101242752484.95041, - 499488053713388.7989, - 37859743397240299.20 + 1.124617325119752213, + -0.770845056360909542, + -0.844794053644911362, + -2.490097309450394453, + -10.23971741154384360, + -49.74900546551479866, + -267.0986675195705196, + -1532.665883825229947, + -9222.313478526091951, + -57502.51612140314030, + -368596.1167416106063, + -2415611.088701091428, + -16120097.81581656797, + -109209938.5203089915, + -749380758.1942496220, + -5198725846.725541393, + -36409256888.12139973 ]; -// Table 12 for Maclaurin expansion of Jacobi's nome, q, as a function of the elliptic parameter, m: +// Table 2 for the expansion of K(m) around 0.05 var P11 = [ - 0.0, - 1.0 / 16.0, - 1.0 / 32.0, - 21.0 / 1024.0, - 31.0 / 2048.0, - 6257.0 / 524288.0, - 10293.0 / 1048576.0, - 279025.0 / 33554432.0, - 483127.0 / 67108864.0, - 435506703.0 / 68719476736.0, - 776957575.0 / 137438953472.0, - 22417045555.0 / 4398046511104.0, - 40784671953.0 / 8796093022208.0, - 9569130097211.0 / 2251799813685248.0, - 17652604545791.0 / 4503599627370496.0 -]; - -// Talyor expansion of K(m) - E(m) for 0 <= m <= 0.1: -var P12 = [ 1.591003453790792180, 0.416000743991786912, 0.245791514264103415, @@ -263,6 +227,20 @@ var P12 = [ 0.081541118718303215 ]; +// Table 2 for the expansion of E(m) around 0.05 +var P12 = [ + 1.550973351780472328, + -0.400301020103198524, + -0.078498619442941939, + -0.034318853117591992, + -0.019718043317365499, + -0.013059507731993309, + -0.009442372874146547, + -0.007246728512402157, + -0.005807424012956090, + -0.004809187786009338 +]; + // Header to add to output files: var header = licenseHeader( 'Apache-2.0', 'js', { 'year': currentYear(), From 95df2a4b5785d228d6ba2ac6de0d3211d575bd3e Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:28:50 +0530 Subject: [PATCH 19/49] Revert "feat: add C implementation for @stdlib/math/base/special/ellipe" This reverts commit c52374ece3d9f324e480f1b88a9173f994507800. --- .../base/special/ellipk/scripts/evalpoly.js | 318 ++++++++++-------- 1 file changed, 170 insertions(+), 148 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipk/scripts/evalpoly.js b/lib/node_modules/@stdlib/math/base/special/ellipk/scripts/evalpoly.js index 3aab7dda2563..061a63b8ae71 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipk/scripts/evalpoly.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipk/scripts/evalpoly.js @@ -41,179 +41,215 @@ var compileC = require( '@stdlib/math/base/tools/evalpoly-compile-c' ); // Table 2 for expansion about x = 0.05: var P1 = [ - 1.550973351780472328, - -0.400301020103198524, - -0.078498619442941939, - -0.034318853117591992, - -0.019718043317365499, - -0.013059507731993309, - -0.009442372874146547, - -0.007246728512402157, - -0.005807424012956090, - -0.004809187786009338 + 1.591003453790792180, + 0.416000743991786912, + 0.245791514264103415, + 0.179481482914906162, + 0.144556057087555150, + 0.123200993312427711, + 0.108938811574293531, + 0.098853409871592910, + 0.091439629201749751, + 0.085842591595413900, + 0.081541118718303215 ]; // Table 3 for expansion about 0.15: var P2 = [ - 1.510121832092819728, - -0.417116333905867549, - -0.090123820404774569, - -0.043729944019084312, - -0.027965493064761785, - -0.020644781177568105, - -0.016650786739707238, - -0.014261960828842520, - -0.012759847429264803, - -0.011799303775587354, - -0.011197445703074968 + 1.635256732264579992, + 0.471190626148732291, + 0.309728410831499587, + 0.252208311773135699, + 0.226725623219684650, + 0.215774446729585976, + 0.213108771877348910, + 0.216029124605188282, + 0.223255831633057896, + 0.234180501294209925, + 0.248557682972264071, + 0.266363809892617521 ]; // Table 4 for expansion about 0.25: var P3 = [ - 1.467462209339427155, - -0.436576290946337775, - -0.105155557666942554, - -0.057371843593241730, - -0.041391627727340220, - -0.034527728505280841, - -0.031495443512532783, - -0.030527000890325277, - -0.030916984019238900, - -0.032371395314758122, - -0.034789960386404158 + 1.685750354812596043, + 0.541731848613280329, + 0.401524438390690257, + 0.369642473420889090, + 0.376060715354583645, + 0.405235887085125919, + 0.453294381753999079, + 0.520518947651184205, + 0.609426039204995055, + 0.724263522282908870, + 0.871013847709812357, + 1.057652872753547036 ]; // Table 5 for expansion about 0.35: var P4 = [ - 1.422691133490879171, - -0.459513519621048674, - -0.125250539822061878, - -0.078138545094409477, - -0.064714278472050002, - -0.062084339131730311, - -0.065197032815572477, - -0.072793895362578779, - -0.084959075171781003, - -0.102539850131045997, - -0.127053585157696036, - -0.160791120691274606 + 1.744350597225613243, + 0.634864275371935304, + 0.539842564164445538, + 0.571892705193787391, + 0.670295136265406100, + 0.832586590010977199, + 1.073857448247933265, + 1.422091460675497751, + 1.920387183402304829, + 2.632552548331654201, + 3.652109747319039160, + 5.115867135558865806, + 7.224080007363877411 ]; // Table 6 for expansion about 0.45: var P5 = [ - 1.375401971871116291, - -0.487202183273184837, - -0.153311701348540228, - -0.111849444917027833, - -0.108840952523135768, - -0.122954223120269076, - -0.152217163962035047, - -0.200495323642697339, - -0.276174333067751758, - -0.393513114304375851, - -0.575754406027879147, - -0.860523235727239756, - -1.308833205758540162 + 1.813883936816982644, + 0.763163245700557246, + 0.761928605321595831, + 0.951074653668427927, + 1.315180671703161215, + 1.928560693477410941, + 2.937509342531378755, + 4.594894405442878062, + 7.330071221881720772, + 11.87151259742530180, + 19.45851374822937738, + 32.20638657246426863, + 53.73749198700554656, + 90.27388602940998849 ]; // Table 7 for expansion about 0.55: var P6 = [ - 1.325024497958230082, - -0.521727647557566767, - -0.194906430482126213, - -0.171623726822011264, - -0.202754652926419141, - -0.278798953118534762, - -0.420698457281005762, - -0.675948400853106021, - -1.136343121839229244, - -1.976721143954398261, - -3.531696773095722506, - -6.446753640156048150, - -11.97703130208884026 + 1.898924910271553526, + 0.950521794618244435, + 1.151077589959015808, + 1.750239106986300540, + 2.952676812636875180, + 5.285800396121450889, + 9.832485716659979747, + 18.78714868327559562, + 36.61468615273698145, + 72.45292395127771801, + 145.1079577347069102, + 293.4786396308497026, + 598.3851815055010179, + 1228.420013075863451, + 2536.529755382764488 ]; // Table 8 for expansion about 0.65: var P7 = [ - 1.270707479650149744, - -0.566839168287866583, - -0.262160793432492598, - -0.292244173533077419, - -0.440397840850423189, - -0.774947641381397458, - -1.498870837987561088, - -3.089708310445186667, - -6.667595903381001064, - -14.89436036517319078, - -34.18120574251449024, - -80.15895841905397306, - -191.3489480762984920, - -463.5938853480342030, - -1137.380822169360061 + 2.007598398424376302, + 1.248457231212347337, + 1.926234657076479729, + 3.751289640087587680, + 8.119944554932045802, + 18.66572130873555361, + 44.60392484291437063, + 109.5092054309498377, + 274.2779548232413480, + 697.5598008606326163, + 1795.716014500247129, + 4668.381716790389910, + 12235.76246813664335, + 32290.17809718320818, + 85713.07608195964685, + 228672.1890493117096, + 612757.2711915852774 ]; // Table 9 for expansion about 0.75: var P8 = [ - 1.211056027568459525, - -0.630306413287455807, - -0.387166409520669145, - -0.592278235311934603, - -1.237555584513049844, - -3.032056661745247199, - -8.181688221573590762, - -23.55507217389693250, - -71.04099935893064956, - -221.8796853192349888, - -712.1364793277635425, - -2336.125331440396407, - -7801.945954775964673, - -26448.19586059191933, - -90799.48341621365251, - -315126.0406449163424, - -1104011.344311591159 + 2.156515647499643235, + 1.791805641849463243, + 3.826751287465713147, + 10.38672468363797208, + 31.40331405468070290, + 100.9237039498695416, + 337.3268282632272897, + 1158.707930567827917, + 4060.990742193632092, + 14454.00184034344795, + 52076.66107599404803, + 189493.6591462156887, + 695184.5762413896145, + 2567994.048255284686, + 9541921.966748386322, + 35634927.44218076174, + 133669298.4612040871, + 503352186.6866284541, + 1901975729.538660119, + 7208915015.330103756 ]; // Table 10 for expansion about 0.825: var P9 = [ - 1.161307152196282836, - -0.701100284555289548, - -0.580551474465437362, - -1.243693061077786614, - -3.679383613496634879, - -12.81590924337895775, - -49.25672530759985272, - -202.1818735434090269, - -869.8602699308701437, - -3877.005847313289571, - -17761.70710170939814, - -83182.69029154232061, - -396650.4505013548170, - -1920033.413682634405 + 2.318122621712510589, + 2.616920150291232841, + 7.897935075731355823, + 30.50239715446672327, + 131.4869365523528456, + 602.9847637356491617, + 2877.024617809972641, + 14110.51991915180325, + 70621.44088156540229, + 358977.2665825309926, + 1847238.263723971684, + 9600515.416049214109, + 50307677.08502366879, + 265444188.6527127967, + 1408862325.028702687, + 7515687935.373774627 ]; // Table 11 for expansion about 0.875: var P10 = [ - 1.124617325119752213, - -0.770845056360909542, - -0.844794053644911362, - -2.490097309450394453, - -10.23971741154384360, - -49.74900546551479866, - -267.0986675195705196, - -1532.665883825229947, - -9222.313478526091951, - -57502.51612140314030, - -368596.1167416106063, - -2415611.088701091428, - -16120097.81581656797, - -109209938.5203089915, - -749380758.1942496220, - -5198725846.725541393, - -36409256888.12139973 + 2.473596173751343912, + 3.727624244118099310, + 15.60739303554930496, + 84.12850842805887747, + 506.9818197040613935, + 3252.277058145123644, + 21713.24241957434256, + 149037.0451890932766, + 1043999.331089990839, + 7427974.817042038995, + 53503839.67558661151, + 389249886.9948708474, + 2855288351.100810619, + 21090077038.76684053, + 156699833947.7902014, + 1170222242422.439893, + 8777948323668.937971, + 66101242752484.95041, + 499488053713388.7989, + 37859743397240299.20 ]; -// Table 2 for the expansion of K(m) around 0.05 +// Table 12 for Maclaurin expansion of Jacobi's nome, q, as a function of the elliptic parameter, m: var P11 = [ + 0.0, + 1.0 / 16.0, + 1.0 / 32.0, + 21.0 / 1024.0, + 31.0 / 2048.0, + 6257.0 / 524288.0, + 10293.0 / 1048576.0, + 279025.0 / 33554432.0, + 483127.0 / 67108864.0, + 435506703.0 / 68719476736.0, + 776957575.0 / 137438953472.0, + 22417045555.0 / 4398046511104.0, + 40784671953.0 / 8796093022208.0, + 9569130097211.0 / 2251799813685248.0, + 17652604545791.0 / 4503599627370496.0 +]; + +// Talyor expansion of K(m) - E(m) for 0 <= m <= 0.1: +var P12 = [ 1.591003453790792180, 0.416000743991786912, 0.245791514264103415, @@ -227,20 +263,6 @@ var P11 = [ 0.081541118718303215 ]; -// Table 2 for the expansion of E(m) around 0.05 -var P12 = [ - 1.550973351780472328, - -0.400301020103198524, - -0.078498619442941939, - -0.034318853117591992, - -0.019718043317365499, - -0.013059507731993309, - -0.009442372874146547, - -0.007246728512402157, - -0.005807424012956090, - -0.004809187786009338 -]; - // Header to add to output files: var header = licenseHeader( 'Apache-2.0', 'js', { 'year': currentYear(), From 9ea92bc746c0d4ccc46156dc9a55cae2ee4e4a99 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:30:52 +0530 Subject: [PATCH 20/49] Update evalpoly.js Signed-off-by: GUNJ JOSHI --- .../base/special/ellipe/scripts/evalpoly.js | 318 ++++++++---------- 1 file changed, 148 insertions(+), 170 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/scripts/evalpoly.js b/lib/node_modules/@stdlib/math/base/special/ellipe/scripts/evalpoly.js index 95d41b6328c6..f6c84bfaec31 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/scripts/evalpoly.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/scripts/evalpoly.js @@ -41,215 +41,179 @@ var compileC = require( '@stdlib/math/base/tools/evalpoly-compile-c' ); // Table 2 for expansion about x = 0.05: var P1 = [ - 1.591003453790792180, - 0.416000743991786912, - 0.245791514264103415, - 0.179481482914906162, - 0.144556057087555150, - 0.123200993312427711, - 0.108938811574293531, - 0.098853409871592910, - 0.091439629201749751, - 0.085842591595413900, - 0.081541118718303215 + 1.550973351780472328, + -0.400301020103198524, + -0.078498619442941939, + -0.034318853117591992, + -0.019718043317365499, + -0.013059507731993309, + -0.009442372874146547, + -0.007246728512402157, + -0.005807424012956090, + -0.004809187786009338 ]; // Table 3 for expansion about 0.15: var P2 = [ - 1.635256732264579992, - 0.471190626148732291, - 0.309728410831499587, - 0.252208311773135699, - 0.226725623219684650, - 0.215774446729585976, - 0.213108771877348910, - 0.216029124605188282, - 0.223255831633057896, - 0.234180501294209925, - 0.248557682972264071, - 0.266363809892617521 + 1.510121832092819728, + -0.417116333905867549, + -0.090123820404774569, + -0.043729944019084312, + -0.027965493064761785, + -0.020644781177568105, + -0.016650786739707238, + -0.014261960828842520, + -0.012759847429264803, + -0.011799303775587354, + -0.011197445703074968 ]; // Table 4 for expansion about 0.25: var P3 = [ - 1.685750354812596043, - 0.541731848613280329, - 0.401524438390690257, - 0.369642473420889090, - 0.376060715354583645, - 0.405235887085125919, - 0.453294381753999079, - 0.520518947651184205, - 0.609426039204995055, - 0.724263522282908870, - 0.871013847709812357, - 1.057652872753547036 + 1.467462209339427155, + -0.436576290946337775, + -0.105155557666942554, + -0.057371843593241730, + -0.041391627727340220, + -0.034527728505280841, + -0.031495443512532783, + -0.030527000890325277, + -0.030916984019238900, + -0.032371395314758122, + -0.034789960386404158 ]; // Table 5 for expansion about 0.35: var P4 = [ - 1.744350597225613243, - 0.634864275371935304, - 0.539842564164445538, - 0.571892705193787391, - 0.670295136265406100, - 0.832586590010977199, - 1.073857448247933265, - 1.422091460675497751, - 1.920387183402304829, - 2.632552548331654201, - 3.652109747319039160, - 5.115867135558865806, - 7.224080007363877411 + 1.422691133490879171, + -0.459513519621048674, + -0.125250539822061878, + -0.078138545094409477, + -0.064714278472050002, + -0.062084339131730311, + -0.065197032815572477, + -0.072793895362578779, + -0.084959075171781003, + -0.102539850131045997, + -0.127053585157696036, + -0.160791120691274606 ]; // Table 6 for expansion about 0.45: var P5 = [ - 1.813883936816982644, - 0.763163245700557246, - 0.761928605321595831, - 0.951074653668427927, - 1.315180671703161215, - 1.928560693477410941, - 2.937509342531378755, - 4.594894405442878062, - 7.330071221881720772, - 11.87151259742530180, - 19.45851374822937738, - 32.20638657246426863, - 53.73749198700554656, - 90.27388602940998849 + 1.375401971871116291, + -0.487202183273184837, + -0.153311701348540228, + -0.111849444917027833, + -0.108840952523135768, + -0.122954223120269076, + -0.152217163962035047, + -0.200495323642697339, + -0.276174333067751758, + -0.393513114304375851, + -0.575754406027879147, + -0.860523235727239756, + -1.308833205758540162 ]; // Table 7 for expansion about 0.55: var P6 = [ - 1.898924910271553526, - 0.950521794618244435, - 1.151077589959015808, - 1.750239106986300540, - 2.952676812636875180, - 5.285800396121450889, - 9.832485716659979747, - 18.78714868327559562, - 36.61468615273698145, - 72.45292395127771801, - 145.1079577347069102, - 293.4786396308497026, - 598.3851815055010179, - 1228.420013075863451, - 2536.529755382764488 + 1.325024497958230082, + -0.521727647557566767, + -0.194906430482126213, + -0.171623726822011264, + -0.202754652926419141, + -0.278798953118534762, + -0.420698457281005762, + -0.675948400853106021, + -1.136343121839229244, + -1.976721143954398261, + -3.531696773095722506, + -6.446753640156048150, + -11.97703130208884026 ]; // Table 8 for expansion about 0.65: var P7 = [ - 2.007598398424376302, - 1.248457231212347337, - 1.926234657076479729, - 3.751289640087587680, - 8.119944554932045802, - 18.66572130873555361, - 44.60392484291437063, - 109.5092054309498377, - 274.2779548232413480, - 697.5598008606326163, - 1795.716014500247129, - 4668.381716790389910, - 12235.76246813664335, - 32290.17809718320818, - 85713.07608195964685, - 228672.1890493117096, - 612757.2711915852774 + 1.270707479650149744, + -0.566839168287866583, + -0.262160793432492598, + -0.292244173533077419, + -0.440397840850423189, + -0.774947641381397458, + -1.498870837987561088, + -3.089708310445186667, + -6.667595903381001064, + -14.89436036517319078, + -34.18120574251449024, + -80.15895841905397306, + -191.3489480762984920, + -463.5938853480342030, + -1137.380822169360061 ]; // Table 9 for expansion about 0.75: var P8 = [ - 2.156515647499643235, - 1.791805641849463243, - 3.826751287465713147, - 10.38672468363797208, - 31.40331405468070290, - 100.9237039498695416, - 337.3268282632272897, - 1158.707930567827917, - 4060.990742193632092, - 14454.00184034344795, - 52076.66107599404803, - 189493.6591462156887, - 695184.5762413896145, - 2567994.048255284686, - 9541921.966748386322, - 35634927.44218076174, - 133669298.4612040871, - 503352186.6866284541, - 1901975729.538660119, - 7208915015.330103756 + 1.211056027568459525, + -0.630306413287455807, + -0.387166409520669145, + -0.592278235311934603, + -1.237555584513049844, + -3.032056661745247199, + -8.181688221573590762, + -23.55507217389693250, + -71.04099935893064956, + -221.8796853192349888, + -712.1364793277635425, + -2336.125331440396407, + -7801.945954775964673, + -26448.19586059191933, + -90799.48341621365251, + -315126.0406449163424, + -1104011.344311591159 ]; // Table 10 for expansion about 0.825: var P9 = [ - 2.318122621712510589, - 2.616920150291232841, - 7.897935075731355823, - 30.50239715446672327, - 131.4869365523528456, - 602.9847637356491617, - 2877.024617809972641, - 14110.51991915180325, - 70621.44088156540229, - 358977.2665825309926, - 1847238.263723971684, - 9600515.416049214109, - 50307677.08502366879, - 265444188.6527127967, - 1408862325.028702687, - 7515687935.373774627 + 1.161307152196282836, + -0.701100284555289548, + -0.580551474465437362, + -1.243693061077786614, + -3.679383613496634879, + -12.81590924337895775, + -49.25672530759985272, + -202.1818735434090269, + -869.8602699308701437, + -3877.005847313289571, + -17761.70710170939814, + -83182.69029154232061, + -396650.4505013548170, + -1920033.413682634405 ]; // Table 11 for expansion about 0.875: var P10 = [ - 2.473596173751343912, - 3.727624244118099310, - 15.60739303554930496, - 84.12850842805887747, - 506.9818197040613935, - 3252.277058145123644, - 21713.24241957434256, - 149037.0451890932766, - 1043999.331089990839, - 7427974.817042038995, - 53503839.67558661151, - 389249886.9948708474, - 2855288351.100810619, - 21090077038.76684053, - 156699833947.7902014, - 1170222242422.439893, - 8777948323668.937971, - 66101242752484.95041, - 499488053713388.7989, - 37859743397240299.20 + 1.124617325119752213, + -0.770845056360909542, + -0.844794053644911362, + -2.490097309450394453, + -10.23971741154384360, + -49.74900546551479866, + -267.0986675195705196, + -1532.665883825229947, + -9222.313478526091951, + -57502.51612140314030, + -368596.1167416106063, + -2415611.088701091428, + -16120097.81581656797, + -109209938.5203089915, + -749380758.1942496220, + -5198725846.725541393, + -36409256888.12139973 ]; -// Table 12 for Maclaurin expansion of Jacobi's nome, q, as a function of the elliptic parameter, m: +// Table 2 for the expansion of K(m) around 0.05 var P11 = [ - 0.0, - 1.0 / 16.0, - 1.0 / 32.0, - 21.0 / 1024.0, - 31.0 / 2048.0, - 6257.0 / 524288.0, - 10293.0 / 1048576.0, - 279025.0 / 33554432.0, - 483127.0 / 67108864.0, - 435506703.0 / 68719476736.0, - 776957575.0 / 137438953472.0, - 22417045555.0 / 4398046511104.0, - 40784671953.0 / 8796093022208.0, - 9569130097211.0 / 2251799813685248.0, - 17652604545791.0 / 4503599627370496.0 -]; - -// Talyor expansion of K(m) - E(m) for 0 <= m <= 0.1: -var P12 = [ 1.591003453790792180, 0.416000743991786912, 0.245791514264103415, @@ -263,6 +227,20 @@ var P12 = [ 0.081541118718303215 ]; +// Table 2 for the expansion of E(m) around 0.05 +var P12 = [ + 1.550973351780472328, + -0.400301020103198524, + -0.078498619442941939, + -0.034318853117591992, + -0.019718043317365499, + -0.013059507731993309, + -0.009442372874146547, + -0.007246728512402157, + -0.005807424012956090, + -0.004809187786009338 +]; + // Header to add to output files: var header = licenseHeader( 'Apache-2.0', 'js', { 'year': currentYear(), From 7caf7899a3563da92f93706373b344f35b032343 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 11:59:10 +0530 Subject: [PATCH 21/49] feat: add C implementation for @stdlib/math/base/special/ellipe This commit introduces a C implementation for the elliptic integral of the second kind (@stdlib/math/base/special/ellipe). --- .../math/base/special/ellipe/README.md | 106 ++++++++++++++++-- .../math/base/special/ellipe/src/main.c | 27 ----- 2 files changed, 98 insertions(+), 35 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md index 8f8856b436d6..2dcafe87676c 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md @@ -2,7 +2,7 @@ @license Apache-2.0 -Copyright (c) 2019 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. @@ -26,14 +26,14 @@ limitations under the License. The [complete elliptic integral of the second kind][elliptic-integral] is defined as - + ```math -E(m)=\int_0^{\pi/2} \sqrt{1 - m (\sin\theta)^2} d\theta +K(m)=\int_0^\tfrac{\pi}{2} {\sqrt{1-m \sin^2\theta}}{d\theta} ``` - @@ -114,6 +114,96 @@ for ( i = 0; i < 100; i++ ) { + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/ellipe.h" +``` + +#### stdlib_base_ellipe( m ) + +Computes the [complete elliptic integral of the first kind][elliptic-integral]. + +```c +double out = stdlib_base_ellipe( 0.5 ); +// returns ~1.351 + +out = stdlib_base_ellipe( -1.0 ); +// returns ~1.910 +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. + +```c +double stdlib_base_ellipe( const double m ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/ellipe.h" +#include +#include + +int main( void ) { + double m; + double v; + int i; + + for ( i = 0; i < 100; i++ ) { + m = -1.0 + ( ( (double)rand() / (double)RAND_MAX ) * 2.0 ); + v = stdlib_base_ellipe( m ); + printf( "ellipe(%lf) = %lf\n", m, v ); + } +} +``` + +
+ + + +
+ + + * * *
@@ -135,8 +225,8 @@ for ( i = 0; i < 100; i++ ) { ## See Also +- [`@stdlib/math/base/special/ellipe`][@stdlib/math/base/special/ellipe]: compute the complete elliptic integral of the second kind. - [`@stdlib/math/base/special/ellipj`][@stdlib/math/base/special/ellipj]: compute the Jacobi elliptic functions sn, cn, and dn. -- [`@stdlib/math/base/special/ellipk`][@stdlib/math/base/special/ellipk]: compute the complete elliptic integral of the first kind.
@@ -154,9 +244,9 @@ for ( i = 0; i < 100; i++ ) { -[@stdlib/math/base/special/ellipj]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/ellipj +[@stdlib/math/base/special/ellipe]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/ellipe -[@stdlib/math/base/special/ellipk]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/ellipk +[@stdlib/math/base/special/ellipj]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/ellipj diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c b/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c index 9e7dfa3d9094..c5b8010c64e6 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c @@ -303,33 +303,6 @@ static double poly_p12( const double x ) { /** * Computes the complete elliptic integral of the second kind. * -* ## Method -* -* - The function computes the complete elliptic integral of the second kind in terms of parameter \\( m \\), instead of the elliptic modulus \\( k \\). -* -* ```tex -* K(m) = \int_0^{\pi/2} {\sqrt{1 - m sin^2\theta}} d\theta -* ``` -* -* - The function uses a piecewise approximation polynomial as given in Fukushima (2009). -* -* - For \\( m < 0 \\), the implementation follows Fukushima (2015). Namely, we use Equation 17.4.17 from the _Handbook of Mathematical Functions_ (Abramowitz and Stegun) to compute the function for \\( m < 0 \\) in terms of the piecewise polynomial representation of \\( m > 0 )). -* -* ```tex -* F(\phi|-m) = (1+m)^(-1/2) K(m/(1+m)) - (1+m)^(-1/2) F(\pi/2-\phi|m/(1+m)) -* ``` -* -* Since \\( K(m) \\) is equivalent to \\( F(\phi|m) \\), the above reduces to -* -* ```tex -* F(\phi|-m) = (1+m)^(-1/2) K(m/(1+m)) -* ``` -* -* ## References -* -* - Fukushima, Toshio. 2009. "Fast computation of complete elliptic integrals and Jacobian elliptic functions." _Celestial Mechanics and Dynamical Astronomy_ 105 (4): 305. doi:[10.1007/s10569-009-9228-z](https://doi.org/10.1007/s10569-009-9228-z). -* - Fukushima, Toshio. 2015. "Precise and fast computation of complete elliptic integrals by piecewise minimax rational function approximation." _Journal of Computational and Applied Mathematics_ 282 (July): 71–76. doi:[10.1016/j.cam.2014.12.038](https://doi.org/10.1016/j.cam.2014.12.038). -* * @param x input value * @return output value * From aa6b465995664b1bad4f175249b910bf5fb4ebb5 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 12:01:23 +0530 Subject: [PATCH 22/49] Update README.md Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/README.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md index 2dcafe87676c..8343b7a3ea16 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md @@ -26,14 +26,14 @@ limitations under the License. The [complete elliptic integral of the second kind][elliptic-integral] is defined as - + ```math -K(m)=\int_0^\tfrac{\pi}{2} {\sqrt{1-m \sin^2\theta}}{d\theta} +E(m)=\int_0^{\pi/2} \sqrt{1 - m (\sin\theta)^2} d\theta ``` - From 62dbbe9e8b71404ebe6918cb00e1d89506a53c3a Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 12:03:17 +0530 Subject: [PATCH 23/49] Update README.md Signed-off-by: GUNJ JOSHI --- lib/node_modules/@stdlib/math/base/special/ellipe/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md index 8343b7a3ea16..deb00745ebb6 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md @@ -225,8 +225,8 @@ int main( void ) { ## See Also -- [`@stdlib/math/base/special/ellipe`][@stdlib/math/base/special/ellipe]: compute the complete elliptic integral of the second kind. - [`@stdlib/math/base/special/ellipj`][@stdlib/math/base/special/ellipj]: compute the Jacobi elliptic functions sn, cn, and dn. +- [`@stdlib/math/base/special/ellipk`][@stdlib/math/base/special/ellipk]: compute the complete elliptic integral of the first kind. From 86be2c15d967b6f9d79c7efb83c3f1a4d49dab5a Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 12:07:20 +0530 Subject: [PATCH 24/49] Update README.md Signed-off-by: GUNJ JOSHI --- lib/node_modules/@stdlib/math/base/special/ellipe/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md index deb00745ebb6..74eb721bdfe9 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md @@ -244,10 +244,10 @@ int main( void ) { -[@stdlib/math/base/special/ellipe]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/ellipe - [@stdlib/math/base/special/ellipj]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/ellipj +[@stdlib/math/base/special/ellipk]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/ellipk + From 8360e0ce00af81c1fd1baa750989238c6a1ffeb3 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 18:47:05 +0530 Subject: [PATCH 25/49] Update include.gypi Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/include.gypi | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/include.gypi b/lib/node_modules/@stdlib/math/base/special/ellipe/include.gypi index 222b0ed152c2..575cb043c0bf 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/include.gypi +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/include.gypi @@ -1,6 +1,6 @@ # @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. @@ -50,4 +50,4 @@ ' Date: Sun, 3 Mar 2024 19:15:53 +0530 Subject: [PATCH 26/49] Update lib/node_modules/@stdlib/math/base/special/ellipe/README.md Co-authored-by: Pranav <85227306+Pranavchiku@users.noreply.github.com> Signed-off-by: GUNJ JOSHI --- lib/node_modules/@stdlib/math/base/special/ellipe/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md index 74eb721bdfe9..c517d38188cc 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md @@ -142,7 +142,7 @@ for ( i = 0; i < 100; i++ ) { #### stdlib_base_ellipe( m ) -Computes the [complete elliptic integral of the first kind][elliptic-integral]. +Computes the [complete elliptic integral of the second kind][elliptic-integral]. ```c double out = stdlib_base_ellipe( 0.5 ); From 71f3df91fef9fde4a14a982b926dd1d2242421ac Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 19:20:28 +0530 Subject: [PATCH 27/49] Update ellipe.h Signed-off-by: GUNJ JOSHI --- .../special/ellipe/include/stdlib/math/base/special/ellipe.h | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/include/stdlib/math/base/special/ellipe.h b/lib/node_modules/@stdlib/math/base/special/ellipe/include/stdlib/math/base/special/ellipe.h index f37dbb1a5105..cb549d26066d 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/include/stdlib/math/base/special/ellipe.h +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/include/stdlib/math/base/special/ellipe.h @@ -23,8 +23,7 @@ * If C++, prevent name mangling so that the compiler emits a binary file having undecorated names, thus mirroring the behavior of a C compiler. */ #ifdef __cplusplus -extern "C" -{ +extern "C" { #endif /** @@ -36,4 +35,4 @@ extern "C" } #endif -#endif // !STDLIB_MATH_BASE_SPECIAL_ELLIPE_H \ No newline at end of file +#endif // !STDLIB_MATH_BASE_SPECIAL_ELLIPE_H From 5ac173058359aec056df729e2758efdc560fed39 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 19:21:18 +0530 Subject: [PATCH 28/49] Update lib/node_modules/@stdlib/math/base/special/ellipe/include/stdlib/math/base/special/ellipe.h Co-authored-by: Pranav <85227306+Pranavchiku@users.noreply.github.com> Signed-off-by: GUNJ JOSHI --- .../ellipe/include/stdlib/math/base/special/ellipe.h | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/include/stdlib/math/base/special/ellipe.h b/lib/node_modules/@stdlib/math/base/special/ellipe/include/stdlib/math/base/special/ellipe.h index cb549d26066d..845691f743c2 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/include/stdlib/math/base/special/ellipe.h +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/include/stdlib/math/base/special/ellipe.h @@ -26,10 +26,10 @@ extern "C" { #endif - /** - * Computes the complete elliptic integral of the second kind. - */ - double stdlib_base_ellipe( const double m ); +/** +* Computes the complete elliptic integral of the second kind. +*/ +double stdlib_base_ellipe( const double m ); #ifdef __cplusplus } From 0ab415a0206703b3139fdb2db77855bd60b199b7 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 19:22:53 +0530 Subject: [PATCH 29/49] Update lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c Co-authored-by: Pranav <85227306+Pranavchiku@users.noreply.github.com> Signed-off-by: GUNJ JOSHI --- lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c | 2 -- 1 file changed, 2 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c b/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c index c5b8010c64e6..f5091e0f5961 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c @@ -54,8 +54,6 @@ #include "stdlib/constants/float64/half_pi.h" #include -static const double HALF_PI = 1.5707963267948966; - /* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */ // BEGIN: poly_p1 From 470068be0360f43d0e36bbf6a8c3f103448536b4 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 19:23:42 +0530 Subject: [PATCH 30/49] Update lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c Co-authored-by: Pranav <85227306+Pranavchiku@users.noreply.github.com> Signed-off-by: GUNJ JOSHI --- lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c b/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c index f5091e0f5961..a861e89b3312 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c @@ -306,7 +306,7 @@ static double poly_p12( const double x ) { * * @example * double out = stdlib_base_ellipe( 0.5 ); -* // returns ~1.3506 +* // returns ~1.351 */ double stdlib_base_ellipe( const double m ) { int8_t FLG; From 9c964074498f187de35b6e42aa395f945394d660 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 19:24:49 +0530 Subject: [PATCH 31/49] Update lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c Co-authored-by: Pranav <85227306+Pranavchiku@users.noreply.github.com> Signed-off-by: GUNJ JOSHI --- lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c b/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c index a861e89b3312..3a4820897a4b 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c @@ -310,8 +310,8 @@ static double poly_p12( const double x ) { */ double stdlib_base_ellipe( const double m ) { int8_t FLG; - double edm; double kdm; + double edm; double td; double km; double t; From 1ca5b7b026255efa89a53848fa089e68e0cacde8 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 19:25:22 +0530 Subject: [PATCH 32/49] Update lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c Co-authored-by: Pranav <85227306+Pranavchiku@users.noreply.github.com> Signed-off-by: GUNJ JOSHI --- lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c b/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c index 3a4820897a4b..2a4ae796b4cb 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c @@ -359,7 +359,7 @@ double stdlib_base_ellipe( const double m ) { km = ellipe( x ); // To avoid precision loss near 1, we use Eq. 33 from Fukushima (2009): - t = ( HALF_PI + ( km * (kdm - edm) ) ) / kdm; + t = ( STDLIB_CONSTANT_FLOAT64_HALF_PI + ( km * (kdm - edm) ) ) / kdm; } if ( FLG == 1 ) { // Complete the transformation mentioned above for m < 0: From ca64f5b270615a673bedc4d0a2b5d412edcc9e0c Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sun, 3 Mar 2024 19:29:50 +0530 Subject: [PATCH 33/49] Update manifest.json Signed-off-by: GUNJ JOSHI --- .../math/base/special/ellipe/manifest.json | 158 +++++++++--------- 1 file changed, 79 insertions(+), 79 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/manifest.json b/lib/node_modules/@stdlib/math/base/special/ellipe/manifest.json index 61e8535b5190..436f90cc4854 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/manifest.json +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/manifest.json @@ -1,81 +1,81 @@ { - "options": { - "task": "build" + "options": { + "task": "build" + }, + "fields": [ + { + "field": "src", + "resolve": true, + "relative": true }, - "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/constants/float64/half-pi", - "@stdlib/constants/float64/pinf", - "@stdlib/math/base/special/sqrt", - "@stdlib/math/base/special/ln" - ] - }, - { - "task": "benchmark", - "src": [ - "./src/main.c" - ], - "include": [ - "./include" - ], - "libraries": [], - "libpath": [], - "dependencies": [ - "@stdlib/constants/float64/half-pi", - "@stdlib/constants/float64/pinf", - "@stdlib/math/base/special/sqrt", - "@stdlib/math/base/special/ln" - ] - }, - { - "task": "examples", - "src": [ - "./src/main.c" - ], - "include": [ - "./include" - ], - "libraries": [], - "libpath": [], - "dependencies": [ - "@stdlib/constants/float64/half-pi", - "@stdlib/constants/float64/pinf", - "@stdlib/math/base/special/sqrt", - "@stdlib/math/base/special/ln" - ] - } - ] - } \ No newline at end of file + { + "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/constants/float64/half-pi", + "@stdlib/constants/float64/pinf", + "@stdlib/math/base/special/sqrt", + "@stdlib/math/base/special/ln" + ] + }, + { + "task": "benchmark", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/constants/float64/half-pi", + "@stdlib/constants/float64/pinf", + "@stdlib/math/base/special/sqrt", + "@stdlib/math/base/special/ln" + ] + }, + { + "task": "examples", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/constants/float64/half-pi", + "@stdlib/constants/float64/pinf", + "@stdlib/math/base/special/sqrt", + "@stdlib/math/base/special/ln" + ] + } + ] +} From 2591e1ec442e37529dff55c1425f059970ffd3cc Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Mon, 4 Mar 2024 18:23:32 +0530 Subject: [PATCH 34/49] Update lib/node_modules/@stdlib/math/base/special/ellipe/scripts/evalpoly.js Co-authored-by: Pranav <85227306+Pranavchiku@users.noreply.github.com> Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/scripts/evalpoly.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/scripts/evalpoly.js b/lib/node_modules/@stdlib/math/base/special/ellipe/scripts/evalpoly.js index f6c84bfaec31..7229867e0638 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/scripts/evalpoly.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/scripts/evalpoly.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2019 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. From fa8654522c4bfbd9093adbb8b164237d31bb07ee Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Mon, 4 Mar 2024 18:29:51 +0530 Subject: [PATCH 35/49] Update Makefile: added newline Signed-off-by: GUNJ JOSHI --- .../math/base/special/ellipe/benchmark/c/native/Makefile | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/Makefile index 0ebf4545e1a9..f69e9da2b4d3 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/Makefile +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/Makefile @@ -143,4 +143,4 @@ run: $(c_targets) clean: $(QUIET) -rm -f *.o *.out -.PHONY: clean \ No newline at end of file +.PHONY: clean From 9929a53f9e706fe9708e4c4262506498b3cebd89 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Mon, 4 Mar 2024 18:30:34 +0530 Subject: [PATCH 36/49] Update benchmark.c: added newline Signed-off-by: GUNJ JOSHI --- .../math/base/special/ellipe/benchmark/c/native/benchmark.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/benchmark.c index 99d74c9ed01a..0552db4c3c1b 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/benchmark.c +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/benchmark.c @@ -133,4 +133,4 @@ int main( void ) { printf( "ok %d benchmark finished\n", i+1 ); } print_summary( REPEATS, REPEATS ); -} \ No newline at end of file +} From 65084834be3a3ad47bca481cabfad748695e6989 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Mon, 4 Mar 2024 18:31:23 +0530 Subject: [PATCH 37/49] Update binding.gyp: added newline Signed-off-by: GUNJ JOSHI --- lib/node_modules/@stdlib/math/base/special/ellipe/binding.gyp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/binding.gyp b/lib/node_modules/@stdlib/math/base/special/ellipe/binding.gyp index 507cb00291e7..ec3992233442 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/binding.gyp +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/binding.gyp @@ -167,4 +167,4 @@ ], # end actions }, # end target copy_addon ], # end targets -} \ No newline at end of file +} From ced872bba3140b79c7f476aaf97ab80f96097ac8 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Mon, 4 Mar 2024 18:31:45 +0530 Subject: [PATCH 38/49] Update Makefile Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/examples/c/Makefile | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/Makefile index d53ef397c77d..6aed70daf167 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/Makefile +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/Makefile @@ -143,4 +143,4 @@ run: $(c_targets) clean: $(QUIET) -rm -f *.o *.out -.PHONY: clean \ No newline at end of file +.PHONY: clean From dcc1f136373a81b671be0d59c34d58ecaed05b16 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Mon, 4 Mar 2024 18:32:07 +0530 Subject: [PATCH 39/49] Update example.c: added newline Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/examples/c/example.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c index 31759c49f3bb..3caa8997c916 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c @@ -30,4 +30,4 @@ int main() { v = stdlib_base_ellipe( m ); printf( "ellipe(%lf) = %lf\n", m, v ); } -} \ No newline at end of file +} From 11dc7602e3de6b30afbe4b2a95e4067329bb4437 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Mon, 4 Mar 2024 18:33:31 +0530 Subject: [PATCH 40/49] Update large_negative.json: added newline Signed-off-by: GUNJ JOSHI --- .../base/special/ellipe/test/fixtures/cpp/large_negative.json | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/large_negative.json b/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/large_negative.json index ac2e366976b0..f94cb3166c54 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/large_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/large_negative.json @@ -1 +1 @@ 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From c66d19765b9e8ff276d57b52bb346aa9a6800904 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Mon, 4 Mar 2024 18:34:39 +0530 Subject: [PATCH 41/49] Update medium_negative.json: added newline Signed-off-by: GUNJ JOSHI --- .../base/special/ellipe/test/fixtures/cpp/medium_negative.json | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/medium_negative.json b/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/medium_negative.json index 205a3301ea2a..e42e842f3c73 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/medium_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/medium_negative.json @@ -1 +1 @@ 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From c6719873d3e5d8f98d039649cc4c23f1118a2c9f Mon Sep 17 00:00:00 2001 From: Pranav <85227306+Pranavchiku@users.noreply.github.com> Date: Mon, 4 Mar 2024 19:41:54 +0530 Subject: [PATCH 42/49] Update lib/node_modules/@stdlib/math/base/special/ellipe/README.md Signed-off-by: Pranav <85227306+Pranavchiku@users.noreply.github.com> --- lib/node_modules/@stdlib/math/base/special/ellipe/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md index c517d38188cc..b68857550bd2 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md @@ -2,7 +2,7 @@ @license Apache-2.0 -Copyright (c) 2024 The Stdlib Authors. +Copyright (c) 2019 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. From 2421ae59ece79f5bbec2b91d7b613ebd8dc7e207 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Tue, 5 Mar 2024 07:01:16 +0530 Subject: [PATCH 43/49] Update lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c Co-authored-by: Athan Signed-off-by: GUNJ JOSHI --- lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c b/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c index 2a4ae796b4cb..3d92dab58afd 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c @@ -330,7 +330,7 @@ double stdlib_base_ellipe( const double m ) { return 1.0; } if ( x > 1.0 ) { - return 0.0 / 0.0; //NaN + return 0.0 / 0.0; // NaN } if ( x < 0.1 ) { t = poly_p1( x - 0.05 ); From 28049f222235871afd4a6981f0e482bc97eaba2d Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Tue, 5 Mar 2024 10:22:35 +0530 Subject: [PATCH 44/49] Update test.native.js Signed-off-by: GUNJ JOSHI --- .../base/special/ellipe/test/test.native.js | 51 +++++-------------- 1 file changed, 14 insertions(+), 37 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/ellipe/test/test.native.js index b1c10af1532d..373285710255 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/test/test.native.js @@ -35,8 +35,7 @@ var tryRequire = require( '@stdlib/utils/try-require' ); var mediumPositive = require( './fixtures/cpp/medium_positive.json' ); var closeToUnity = require( './fixtures/cpp/close_to_unity.json' ); -var mediumNegative = require( './fixtures/cpp/medium_negative.json' ); -var largeNegative = require( './fixtures/cpp/large_negative.json' ); +var negativeSpotChecks = require( './fixtures/wolframalpha/negative_spot_checks.json' ); // VARIABLES // @@ -55,30 +54,7 @@ tape( 'main export is a function', opts, function test( t ) { t.end(); }); -tape( 'the function evaluates the complete elliptic integral of the first kind (medium positive values)', opts, function test( t ) { - var expected; - var delta; - var tol; - var x; - var y; - var i; - - expected = mediumPositive.expected; - x = mediumPositive.x; - for ( i = 0; i < x.length; i++ ) { - y = ellipe( x[i] ); - if ( y === expected[i] ) { - t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] ); - } else { - delta = abs( y - expected[i] ); - tol = 25.0 * EPS * abs( expected[i] ); - t.equal( delta <= tol, true, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' ); - } - } - t.end(); -}); - -tape( 'the function evaluates the complete elliptic integral of the first kind (values close to positive unity)', opts, function test( t ) { +tape( 'the function evaluates the complete elliptic integral of the second kind (values close to positive unity)', opts, function test( t ) { var expected; var delta; var tol; @@ -94,14 +70,14 @@ tape( 'the function evaluates the complete elliptic integral of the first kind ( t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] ); } else { delta = abs( y - expected[i] ); - tol = 8000.0 * EPS * abs( expected[i] ); + tol = 4.0 * EPS * abs( expected[i] ); t.equal( delta <= tol, true, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' ); } } t.end(); }); -tape( 'the function evaluates the complete elliptic integral of the first kind (medium negative values)', opts, function test( t ) { +tape( 'the function evaluates the complete elliptic integral of the second kind (medium positive values)', opts, function test( t ) { var expected; var delta; var tol; @@ -109,22 +85,22 @@ tape( 'the function evaluates the complete elliptic integral of the first kind ( var y; var i; - expected = mediumNegative.expected; - x = mediumNegative.x; + expected = mediumPositive.expected; + x = mediumPositive.x; for ( i = 0; i < x.length; i++ ) { y = ellipe( x[i] ); if ( y === expected[i] ) { t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] ); } else { delta = abs( y - expected[i] ); - tol = 1.5 * EPS * abs( expected[i] ); + tol = 5.0 * EPS * abs( expected[i] ); t.equal( delta <= tol, true, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' ); } } t.end(); }); -tape( 'the function evaluates the complete elliptic integral of the first kind (large negative values)', opts, function test( t ) { +tape( 'the function evaluates the complete elliptic integral of the second kind (spot checked negative values)', opts, function test( t ) { var expected; var delta; var tol; @@ -132,15 +108,16 @@ tape( 'the function evaluates the complete elliptic integral of the first kind ( var y; var i; - expected = largeNegative.expected; - x = largeNegative.x; + // The spot checked values are derived from Wolfram Alpha and cross-checked against Maxima. For example, to compute E(-0.1): https://www.wolframalpha.com/input/?i=EllipticE(-0.1) + expected = negativeSpotChecks.expected; + x = negativeSpotChecks.x; for ( i = 0; i < x.length; i++ ) { y = ellipe( x[i] ); if ( y === expected[i] ) { t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] ); } else { delta = abs( y - expected[i] ); - tol = 1e9 * EPS * abs( expected[i] ); + tol = 2.2 * EPS * abs( expected[i] ); t.equal( delta <= tol, true, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' ); } } @@ -153,9 +130,9 @@ tape( 'the function returns `NaN` if provided values larger than `1.0`', opts, f t.end(); }); -tape( 'the function returns `+infinity` if provided `1.0`', opts, function test( t ) { +tape( 'the function returns `1.0` if provided `1.0`', opts, function test( t ) { var v = ellipe( 1.0 ); - t.equal( v, PINF, 'return expected value' ); + t.equal( v, 1.0, 'return expected value' ); t.end(); }); From 0a6ad6baceda6eb562cc4248450113e929544ab9 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Tue, 5 Mar 2024 10:30:36 +0530 Subject: [PATCH 45/49] Update example.c: tab indentation. Signed-off-by: GUNJ JOSHI --- .../base/special/ellipe/examples/c/example.c | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c index 3caa8997c916..be92684fca0a 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c @@ -21,13 +21,13 @@ #include int main() { - double m; - double v; - int i; + double m; + double v; + int i; - for ( i = 0; i < 100; i++ ) { - m = -1.0 + ( ( (double)rand() / (double)RAND_MAX ) * 2.0 ); - v = stdlib_base_ellipe( m ); - printf( "ellipe(%lf) = %lf\n", m, v ); - } + for ( i = 0; i < 100; i++ ) { + m = -1.0 + ( ( (double)rand() / (double)RAND_MAX ) * 2.0 ); + v = stdlib_base_ellipe( m ); + printf( "ellipe(%lf) = %lf\n", m, v ); + } } From 407bc904ad87d3b20801ff0a12779787b6daaee2 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Tue, 5 Mar 2024 10:42:24 +0530 Subject: [PATCH 46/49] Update main.c: tab indentation. Signed-off-by: GUNJ JOSHI --- .../math/base/special/ellipe/src/main.c | 114 +++++++++--------- 1 file changed, 57 insertions(+), 57 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c b/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c index 3d92dab58afd..1cb879bc4025 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/src/main.c @@ -309,61 +309,61 @@ static double poly_p12( const double x ) { * // returns ~1.351 */ double stdlib_base_ellipe( const double m ) { - int8_t FLG; - double kdm; - double edm; - double td; - double km; - double t; - double x; - - FLG = 0; - x = m; - if ( m < 0.0 ) { - x = m / ( m - 1.0 ); - FLG += 1; - } - if ( x == 0.0 ) { - return STDLIB_CONSTANT_FLOAT64_HALF_PI; - } - if ( x == 1.0 ) { - return 1.0; - } - if ( x > 1.0 ) { - return 0.0 / 0.0; // NaN - } - if ( x < 0.1 ) { - t = poly_p1( x - 0.05 ); - } else if ( x < 0.2 ) { - t = poly_p2( x - 0.15 ); - } else if ( x < 0.3 ) { - t = poly_p3( x - 0.25 ); - } else if ( x < 0.4 ) { - t = poly_p4( x - 0.35 ); - } else if ( x < 0.5 ) { - t = poly_p5( x - 0.45 ); - } else if ( x < 0.6 ) { - t = poly_p6( x - 0.55 ); - } else if ( x < 0.7 ) { - t = poly_p7( x - 0.65 ); - } else if ( x < 0.8 ) { - t = poly_p8( x - 0.75 ); - } else if ( x < 0.85 ) { - t = poly_p9( x - 0.825 ); - } else if ( x < 0.9 ) { - t = poly_p10( x - 0.875 ); - } else { - td = 0.95 - x; - kdm = poly_p11( td ); - edm = poly_p12( td ); - km = ellipe( x ); - - // To avoid precision loss near 1, we use Eq. 33 from Fukushima (2009): - t = ( STDLIB_CONSTANT_FLOAT64_HALF_PI + ( km * (kdm - edm) ) ) / kdm; - } - if ( FLG == 1 ) { - // Complete the transformation mentioned above for m < 0: - return t * stdlib_base_sqrt( 1.0 - m ); - } - return t; + int8_t FLG; + double kdm; + double edm; + double td; + double km; + double t; + double x; + + FLG = 0; + x = m; + if ( m < 0.0 ) { + x = m / ( m - 1.0 ); + FLG += 1; + } + if ( x == 0.0 ) { + return STDLIB_CONSTANT_FLOAT64_HALF_PI; + } + if ( x == 1.0 ) { + return 1.0; + } + if ( x > 1.0 ) { + return 0.0 / 0.0; // NaN + } + if ( x < 0.1 ) { + t = poly_p1( x - 0.05 ); + } else if ( x < 0.2 ) { + t = poly_p2( x - 0.15 ); + } else if ( x < 0.3 ) { + t = poly_p3( x - 0.25 ); + } else if ( x < 0.4 ) { + t = poly_p4( x - 0.35 ); + } else if ( x < 0.5 ) { + t = poly_p5( x - 0.45 ); + } else if ( x < 0.6 ) { + t = poly_p6( x - 0.55 ); + } else if ( x < 0.7 ) { + t = poly_p7( x - 0.65 ); + } else if ( x < 0.8 ) { + t = poly_p8( x - 0.75 ); + } else if ( x < 0.85 ) { + t = poly_p9( x - 0.825 ); + } else if ( x < 0.9 ) { + t = poly_p10( x - 0.875 ); + } else { + td = 0.95 - x; + kdm = poly_p11( td ); + edm = poly_p12( td ); + km = ellipe( x ); + + // To avoid precision loss near 1, we use Eq. 33 from Fukushima (2009): + t = ( STDLIB_CONSTANT_FLOAT64_HALF_PI + ( km * (kdm - edm) ) ) / kdm; + } + if ( FLG == 1 ) { + // Complete the transformation mentioned above for m < 0: + return t * stdlib_base_sqrt( 1.0 - m ); + } + return t; } From 6775e654a606e43b78521baa26ab77b4826492fc Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Wed, 6 Mar 2024 16:16:58 +0530 Subject: [PATCH 47/49] Update lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c Co-authored-by: Athan Signed-off-by: GUNJ JOSHI --- .../@stdlib/math/base/special/ellipe/examples/c/example.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c index be92684fca0a..8cbeb7c8f97c 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c +++ b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c @@ -20,7 +20,7 @@ #include #include -int main() { +int main( void ) { double m; double v; int i; From 5d657df7ce44215e0b33fc637f59553efc52aec1 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Wed, 6 Mar 2024 16:57:02 +0530 Subject: [PATCH 48/49] Delete `lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/large_negative.json` Signed-off-by: GUNJ JOSHI --- .../base/special/ellipe/test/fixtures/cpp/large_negative.json | 1 - 1 file changed, 1 deletion(-) delete mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/large_negative.json diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/large_negative.json b/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/large_negative.json deleted file mode 100644 index f94cb3166c54..000000000000 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/large_negative.json +++ /dev/null @@ -1 +0,0 @@ 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From 002500fd5023fe8f574bedefc3652e36c47615db Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Wed, 6 Mar 2024 16:57:37 +0530 Subject: [PATCH 49/49] Delete `lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/medium_negative.json` Signed-off-by: GUNJ JOSHI --- .../base/special/ellipe/test/fixtures/cpp/medium_negative.json | 1 - 1 file changed, 1 deletion(-) delete mode 100644 lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/medium_negative.json diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/medium_negative.json b/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/medium_negative.json deleted file mode 100644 index e42e842f3c73..000000000000 --- a/lib/node_modules/@stdlib/math/base/special/ellipe/test/fixtures/cpp/medium_negative.json +++ /dev/null @@ -1 +0,0 @@ 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