diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/README.md b/lib/node_modules/@stdlib/math/base/special/ahaversinf/README.md new file mode 100644 index 000000000000..d5c3091541f0 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/README.md @@ -0,0 +1,220 @@ + + +# ahaversinf + +> Compute the [inverse half-value versed sine][archaversine] of a single-precision floating-point number. + +
+ +The [inverse half-value versed sine][archaversine] is defined as + + + +```math +\mathop{\mathrm{ahaversin}}(\theta) = 2 \cdot \arcsin(\sqrt{\theta}) +``` + + + + + +
+ + + +
+ +## Usage + +```javascript +var ahaversinf = require( '@stdlib/math/base/special/ahaversinf' ); +``` + +#### ahaversinf( x ) + +Computes the [inverse half-value versed sine][archaversine] of a single-precision floating-point number. + +```javascript +var v = ahaversinf( 0.0 ); +// returns 0.0 + +v = ahaversinf( 1.0 ); +// returns ~3.1416 + +v = ahaversinf( 0.5 ); +// returns ~1.5708 +``` + +If `x < 0`, `x > 1`, or `x` is `NaN`, the function returns `NaN`. + +```javascript +var v = ahaversinf( 1.5 ); +// returns NaN + +v = ahaversinf( -3.14 ); +// returns NaN + +v = ahaversinf( NaN ); +// returns NaN +``` + +
+ + + +
+ +## Examples + + + +```javascript +var linspace = require( '@stdlib/array/base/linspace' ); +var ahaversinf = require( '@stdlib/math/base/special/ahaversinf' ); + +var x = linspace( 0.0, 1.0, 100 ); + +var i; +for ( i = 0; i < x.length; i++ ) { + console.log( ahaversinf( x[ i ] ) ); +} +``` + +
+ + + + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/ahaversinf.h" +``` + +#### stdlib_base_ahaversinf( x ) + +Computes the [inverse half-value versed sine][archaversine] of a single-precision floating-point number (in radians). + +```c +float out = stdlib_base_ahaversinf( 0.0f ); +// returns 0.0f +``` + +If `x < 0`, `x > 1`, or `x` is `NaN`, the function returns `NaN`. + +```c +float out = stdlib_base_ahaversinf( -3.14f ); +// returns NaN +``` + +The function accepts the following arguments: + +- **x**: `[in] float` input value. + +```c +float stdlib_base_ahaversinf( const float x ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/ahaversinf.h" +#include + +int main( void ) { + const float x[] = { -2.0f, -1.6f, -1.2f, -0.8f, -0.4f, 0.4f, 0.8f, 1.2f, 1.6f, 2.0f }; + + float v; + int i; + for ( i = 0; i < 10; i++ ) { + v = stdlib_base_ahaversinf( x[ i ] ); + printf( "ahaversin(%f) = %f\n", x[ i ], v ); + } +} +``` + +
+ + + +
+ + + + + +
+ +
+ + + + + +
+ +[archaversine]: https://en.wikipedia.org/wiki/Versine + + + + + +
+ + diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/benchmark.js new file mode 100644 index 000000000000..694166a854ff --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/benchmark.js @@ -0,0 +1,51 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var bench = require( '@stdlib/bench' ); +var randu = require( '@stdlib/random/base/randu' ); +var isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var pkg = require( './../package.json' ).name; +var ahaversinf = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( b ) { + var x; + var y; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + x = randu(); + y = ahaversinf( x ); + if ( isnanf( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnanf( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/benchmark.native.js new file mode 100644 index 000000000000..03f8b1b9baa5 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/benchmark.native.js @@ -0,0 +1,60 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var resolve = require( 'path' ).resolve; +var bench = require( '@stdlib/bench' ); +var randu = require( '@stdlib/random/base/randu' ); +var isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var ahaversinf = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( ahaversinf instanceof Error ) +}; + + +// MAIN // + +bench( pkg+'::native', opts, function benchmark( b ) { + var x; + var y; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + x = randu(); + y = ahaversinf( x ); + if ( isnanf( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnanf( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/c/Makefile b/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/c/Makefile new file mode 100644 index 000000000000..e4542b1e66e9 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/c/Makefile @@ -0,0 +1,107 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2018 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 := @ +endif + +# Determine the OS: +# +# [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 +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate [position independent code][1]: +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of C targets: +c_targets := benchmark.out + + +# TARGETS # + +# Default target. +# +# This target is the default target. + +all: $(c_targets) + +.PHONY: all + + +# Compile C source. +# +# This target compiles C source files. + +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) -o $@ $< -lm + + +# Run a benchmark. +# +# This target runs a benchmark. + +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + + +# Perform clean-up. +# +# This target removes generated files. + +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/c/benchmark.c b/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/c/benchmark.c new file mode 100644 index 000000000000..84925aa9a378 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/c/benchmark.c @@ -0,0 +1,132 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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 +#include +#include +#include +#include + +#define NAME "ahaversinf" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +static void print_version( void ) { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +static void print_summary( int total, int passing ) { + printf( "#\n" ); + printf( "1..%d\n", total ); // TAP plan + printf( "# total %d\n", total ); + printf( "# pass %d\n", passing ); + printf( "#\n" ); + printf( "# ok\n" ); +} + +/** +* Prints benchmarks results. +* +* @param elapsed elapsed time in seconds +*/ +static void print_results( double elapsed ) { + double rate = (double)ITERATIONS / elapsed; + printf( " ---\n" ); + printf( " iterations: %d\n", ITERATIONS ); + printf( " elapsed: %0.9f\n", elapsed ); + printf( " rate: %0.9f\n", rate ); + printf( " ...\n" ); +} + +/** +* Returns a clock time. +* +* @return clock time +*/ +static double tic( void ) { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec/1.0e6; +} + +/** +* Generates a random number on the interval [0,1). +* +* @return random number +*/ +static float rand_float( void ) { + int r = rand(); + return (float)r / ( (float)RAND_MAX + 1.0f ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark( void ) { + double elapsed; + float x; + float y; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + x = rand_float(); + y = 2.0f * asinf( sqrtf( 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::%s\n", NAME ); + elapsed = benchmark(); + print_results( elapsed ); + printf( "ok %d benchmark finished\n", i+1 ); + } + print_summary( REPEATS, REPEATS ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/c/native/Makefile new file mode 100644 index 000000000000..f69e9da2b4d3 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/c/native/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate position independent code ([1][1], [2][2]). +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`): +INCLUDE ?= + +# List of source files: +SOURCE_FILES ?= + +# List of libraries (e.g., `-lopenblas -lpthread`): +LIBRARIES ?= + +# List of library paths (e.g., `-L /foo/bar -L /beep/boop`): +LIBPATH ?= + +# List of C targets: +c_targets := benchmark.out + + +# RULES # + +#/ +# Compiles source files. +# +# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`) +# @param {string} [CFLAGS] - C compiler options +# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`) +# @param {string} [SOURCE_FILES] - list of source files +# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`) +# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`) +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler (e.g., `gcc`) +# @param {string} CFLAGS - C compiler options +# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`) +# @param {string} SOURCE_FILES - list of source files +# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`) +# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`) +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES) + +#/ +# Runs compiled benchmarks. +# +# @example +# make run +#/ +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/c/native/benchmark.c new file mode 100644 index 000000000000..d641b516236a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/benchmark/c/native/benchmark.c @@ -0,0 +1,133 @@ +/** +* @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/ahaversinf.h" +#include +#include +#include +#include +#include + +#define NAME "ahaversinf" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +static void print_version( void ) { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +static void print_summary( int total, int passing ) { + printf( "#\n" ); + printf( "1..%d\n", total ); // TAP plan + printf( "# total %d\n", total ); + printf( "# pass %d\n", passing ); + printf( "#\n" ); + printf( "# ok\n" ); +} + +/** +* Prints benchmarks results. +* +* @param elapsed elapsed time in seconds +*/ +static void print_results( double elapsed ) { + double rate = (double)ITERATIONS / elapsed; + printf( " ---\n" ); + printf( " iterations: %d\n", ITERATIONS ); + printf( " elapsed: %0.9f\n", elapsed ); + printf( " rate: %0.9f\n", rate ); + printf( " ...\n" ); +} + +/** +* Returns a clock time. +* +* @return clock time +*/ +static double tic( void ) { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec/1.0e6; +} + +/** +* Generates a random number on the interval [0,1). +* +* @return random number +*/ +static float rand_float( void ) { + int r = rand(); + return (float)r / ( (float)RAND_MAX + 1.0 ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark( void ) { + double elapsed; + float x; + float y; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + x = rand_float(); + y = stdlib_base_ahaversinf( x ); + if ( y != y ) { + printf( "should not return NaN\n" ); + break; + } + } + elapsed = tic() - t; + if ( y != y ) { + printf( "should not return NaN\n" ); + } + return elapsed; +} + +/** +* Main execution sequence. +*/ +int main( void ) { + double elapsed; + int i; + + // Use the current time to seed the random number generator: + srand( time( NULL ) ); + + print_version(); + for ( i = 0; i < REPEATS; i++ ) { + printf( "# c::native::%s\n", NAME ); + elapsed = benchmark(); + print_results( elapsed ); + printf( "ok %d benchmark finished\n", i+1 ); + } + print_summary( REPEATS, REPEATS ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/binding.gyp b/lib/node_modules/@stdlib/math/base/special/ahaversinf/binding.gyp new file mode 100644 index 000000000000..ec3992233442 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/binding.gyp @@ -0,0 +1,170 @@ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +# A `.gyp` file for building a Node.js native add-on. +# +# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md +# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md +{ + # List of files to include in this file: + 'includes': [ + './include.gypi', + ], + + # Define variables to be used throughout the configuration for all targets: + 'variables': { + # Target name should match the add-on export name: + 'addon_target_name%': 'addon', + + # Set variables based on the host OS: + 'conditions': [ + [ + 'OS=="win"', + { + # Define the object file suffix: + 'obj': 'obj', + }, + { + # Define the object file suffix: + 'obj': 'o', + } + ], # end condition (OS=="win") + ], # end conditions + }, # end variables + + # Define compile targets: + 'targets': [ + + # Target to generate an add-on: + { + # The target name should match the add-on export name: + 'target_name': '<(addon_target_name)', + + # Define dependencies: + 'dependencies': [], + + # Define directories which contain relevant include headers: + 'include_dirs': [ + # Local include directory: + '<@(include_dirs)', + ], + + # List of source files: + 'sources': [ + '<@(src_files)', + ], + + # Settings which should be applied when a target's object files are used as linker input: + 'link_settings': { + # Define libraries: + 'libraries': [ + '<@(libraries)', + ], + + # Define library directories: + 'library_dirs': [ + '<@(library_dirs)', + ], + }, + + # C/C++ compiler flags: + 'cflags': [ + # Enable commonly used warning options: + '-Wall', + + # Aggressive optimization: + '-O3', + ], + + # C specific compiler flags: + 'cflags_c': [ + # Specify the C standard to which a program is expected to conform: + '-std=c99', + ], + + # C++ specific compiler flags: + 'cflags_cpp': [ + # Specify the C++ standard to which a program is expected to conform: + '-std=c++11', + ], + + # Linker flags: + 'ldflags': [], + + # Apply conditions based on the host OS: + 'conditions': [ + [ + 'OS=="mac"', + { + # Linker flags: + 'ldflags': [ + '-undefined dynamic_lookup', + '-Wl,-no-pie', + '-Wl,-search_paths_first', + ], + }, + ], # end condition (OS=="mac") + [ + 'OS!="win"', + { + # C/C++ flags: + 'cflags': [ + # Generate platform-independent code: + '-fPIC', + ], + }, + ], # end condition (OS!="win") + ], # end conditions + }, # end target <(addon_target_name) + + # Target to copy a generated add-on to a standard location: + { + 'target_name': 'copy_addon', + + # Declare that the output of this target is not linked: + 'type': 'none', + + # Define dependencies: + 'dependencies': [ + # Require that the add-on be generated before building this target: + '<(addon_target_name)', + ], + + # Define a list of actions: + 'actions': [ + { + 'action_name': 'copy_addon', + 'message': 'Copying addon...', + + # Explicitly list the inputs in the command-line invocation below: + 'inputs': [], + + # Declare the expected outputs: + 'outputs': [ + '<(addon_output_dir)/<(addon_target_name).node', + ], + + # Define the command-line invocation: + 'action': [ + 'cp', + '<(PRODUCT_DIR)/<(addon_target_name).node', + '<(addon_output_dir)/<(addon_target_name).node', + ], + }, + ], # end actions + }, # end target copy_addon + ], # end targets +} diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/docs/img/equation_archaversine.svg b/lib/node_modules/@stdlib/math/base/special/ahaversinf/docs/img/equation_archaversine.svg new file mode 100644 index 000000000000..74e827ec1bbf --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/docs/img/equation_archaversine.svg @@ -0,0 +1,53 @@ + +a h a v e r s i n left-parenthesis theta right-parenthesis equals 2 dot arc sine left-parenthesis StartRoot theta EndRoot right-parenthesis + + + \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/docs/repl.txt b/lib/node_modules/@stdlib/math/base/special/ahaversinf/docs/repl.txt new file mode 100644 index 000000000000..c3bd287d26bb --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/docs/repl.txt @@ -0,0 +1,29 @@ + +{{alias}}( x ) + Computes the inverse half-value versed sine of a single-precision + floating-point number. + + The inverse half-value versed sine is defined as `2*asin(sqrt(x))`. + + If `x < 0`, `x > 1`, or `x` is `NaN`, the function returns `NaN`. + + Parameters + ---------- + x: number + Input value. + + Returns + ------- + y: number + Inverse half-value versed sine. + + Examples + -------- + > var y = {{alias}}( 0.5 ) + ~1.5708 + > y = {{alias}}( 0.0 ) + 0.0 + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/docs/types/index.d.ts b/lib/node_modules/@stdlib/math/base/special/ahaversinf/docs/types/index.d.ts new file mode 100644 index 000000000000..d8e0ec19e961 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/docs/types/index.d.ts @@ -0,0 +1,48 @@ +/* +* @license Apache-2.0 +* +* 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. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +// TypeScript Version: 4.1 + +/** +* Computes the inverse half-value versed sine of a single-precision floating-point number. +* +* @param x - input value +* @returns inverse half-value versed sine +* +* @example +* var v = ahaversinf( 0.0 ); +* // returns 0.0 +* +* @example +* var v = ahaversinf( 1.0 ); +* // returns ~3.1416 +* +* @example +* var v = ahaversinf( 0.5 ); +* // returns ~1.5708 +* +* @example +* var v = ahaversinf( NaN ); +* // returns NaN +*/ +declare function ahaversinf( x: number ): number; + + +// EXPORTS // + +export = ahaversinf; diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/docs/types/test.ts b/lib/node_modules/@stdlib/math/base/special/ahaversinf/docs/types/test.ts new file mode 100644 index 000000000000..76b870d6c64b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/docs/types/test.ts @@ -0,0 +1,44 @@ +/* +* @license Apache-2.0 +* +* 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. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +import ahaversinf = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + ahaversinf( 8 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided a value other than a number... +{ + ahaversinf( true ); // $ExpectError + ahaversinf( false ); // $ExpectError + ahaversinf( null ); // $ExpectError + ahaversinf( undefined ); // $ExpectError + ahaversinf( '5' ); // $ExpectError + ahaversinf( [] ); // $ExpectError + ahaversinf( {} ); // $ExpectError + ahaversinf( ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided insufficient arguments... +{ + ahaversinf(); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/ahaversinf/examples/c/Makefile new file mode 100644 index 000000000000..6aed70daf167 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/examples/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate position independent code ([1][1], [2][2]). +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`): +INCLUDE ?= + +# List of source files: +SOURCE_FILES ?= + +# List of libraries (e.g., `-lopenblas -lpthread`): +LIBRARIES ?= + +# List of library paths (e.g., `-L /foo/bar -L /beep/boop`): +LIBPATH ?= + +# List of C targets: +c_targets := example.out + + +# RULES # + +#/ +# Compiles source files. +# +# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`) +# @param {string} [CFLAGS] - C compiler options +# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`) +# @param {string} [SOURCE_FILES] - list of source files +# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`) +# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`) +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler (e.g., `gcc`) +# @param {string} CFLAGS - C compiler options +# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`) +# @param {string} SOURCE_FILES - list of source files +# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`) +# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`) +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES) + +#/ +# Runs compiled examples. +# +# @example +# make run +#/ +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/ahaversinf/examples/c/example.c new file mode 100644 index 000000000000..96f27e4e3a62 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/examples/c/example.c @@ -0,0 +1,31 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +#include "stdlib/math/base/special/ahaversinf.h" +#include + +int main( void ) { + const float x[] = { -2.0f, -1.6f, -1.2f, -0.8f, -0.4f, 0.4f, 0.8f, 1.2f, 1.6f, 2.0f }; + float v; + int i; + + for ( i = 0; i < 10; i++ ) { + v = stdlib_base_ahaversinf( x[ i ] ); + printf( "ahaversinf(%f) = %f\n", x[ i ], v ); + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/examples/index.js b/lib/node_modules/@stdlib/math/base/special/ahaversinf/examples/index.js new file mode 100644 index 000000000000..fb170853eff0 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/examples/index.js @@ -0,0 +1,29 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +var linspace = require( '@stdlib/array/base/linspace' ); +var ahaversinf = require( './../lib' ); + +var x = linspace( 0.0, 1.0, 100 ); + +var i; +for ( i = 0; i < x.length; i++ ) { + console.log( 'ahaversinf(%d) = %d', x[ i ], ahaversinf( x[ i ] ) ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/include.gypi b/lib/node_modules/@stdlib/math/base/special/ahaversinf/include.gypi new file mode 100644 index 000000000000..575cb043c0bf --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/include.gypi @@ -0,0 +1,53 @@ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +# A GYP include file for building a Node.js native add-on. +# +# Main documentation: +# +# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md +# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md +{ + # Define variables to be used throughout the configuration for all targets: + 'variables': { + # Source directory: + 'src_dir': './src', + + # Include directories: + 'include_dirs': [ + '=0.10.0", + "npm": ">2.7.0" + }, + "os": [ + "aix", + "darwin", + "freebsd", + "linux", + "macos", + "openbsd", + "sunos", + "win32", + "windows" + ], + "keywords": [ + "stdlib", + "stdmath", + "mathematics", + "math", + "ahaversin", + "ahaversine", + "arcversin", + "arcversine", + "versed sine", + "ahaversinus", + "haversine", + "haversin", + "archav", + "invhav", + "ahav", + "ahvs", + "ahv", + "hav", + "arc", + "versed", + "half-value", + "sine", + "sin", + "asin", + "trig", + "trigonometry", + "radians", + "angle" + ] +} diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/src/Makefile b/lib/node_modules/@stdlib/math/base/special/ahaversinf/src/Makefile new file mode 100644 index 000000000000..bcf18aa46655 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/src/Makefile @@ -0,0 +1,70 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + + +# RULES # + +#/ +# Removes generated files for building an add-on. +# +# @example +# make clean-addon +#/ +clean-addon: + $(QUIET) -rm -f *.o *.node + +.PHONY: clean-addon + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: clean-addon + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/src/addon.c b/lib/node_modules/@stdlib/math/base/special/ahaversinf/src/addon.c new file mode 100644 index 000000000000..bebef90918e4 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/src/addon.c @@ -0,0 +1,23 @@ +/** +* @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/ahaversinf.h" +#include "stdlib/math/base/napi/unary.h" + +// cppcheck-suppress shadowFunction +STDLIB_MATH_BASE_NAPI_MODULE_F_F( stdlib_base_ahaversinf ) diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/src/main.c b/lib/node_modules/@stdlib/math/base/special/ahaversinf/src/main.c new file mode 100644 index 000000000000..dcc1d93f7635 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/src/main.c @@ -0,0 +1,35 @@ +/** +* @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/ahaversinf.h" +#include "stdlib/math/base/special/asinf.h" +#include "stdlib/math/base/special/sqrtf.h" + +/** +* Computes the inverse half value versed sine of a single-precision floating-point number. +* +* @param x input value +* @return output value +* +* @example +* double out = stdlib_base_ahaversin( 0.0f ); +* // returns 0.0f +*/ +float stdlib_base_ahaversinf( const float x ) { + return 2.0f * stdlib_base_asinf( stdlib_base_sqrtf( x ) ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/fixtures/julia/REQUIRE new file mode 100644 index 000000000000..308c3be89c85 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/fixtures/julia/REQUIRE @@ -0,0 +1,2 @@ +julia 1.5 +JSON 0.21 diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/fixtures/julia/data.json b/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/fixtures/julia/data.json new file mode 100644 index 000000000000..bcfe21a72a58 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/fixtures/julia/data.json @@ -0,0 +1 @@ +{"expected":[0.0,0.044702735,0.06322448,0.077440314,0.08942782,0.09999169,0.109544545,0.1183315,0.12651226,0.13419771,0.14146864,0.14838596,0.15499704,0.16133952,0.16744395,0.17333546,0.17903507,0.1845606,0.18992719,0.195148,0.20023441,0.20519643,0.21004286,0.21478154,0.21941946,0.22396286,0.2284174,0.23278816,0.2370798,0.24129653,0.2454422,0.24952039,0.25353432,0.25748703,0.26138124,0.2652196,0.26900443,0.27273804,0.27642244,0.28005964,0.28365135,0.28719938,0.29070526,0.2941706,0.2975967,0.30098495,0.3043366,0.3076529,0.3109349,0.31418377,0.3174004,0.3205859,0.3237411,0.32686692,0.3299642,0.33303368,0.33607617,0.33909243,0.34208307,0.34504882,0.3479903,0.3509081,0.35380283,0.35667506,0.3595253,0.36235413,0.365162,0.36794934,0.37071672,0.3734645,0.37619317,0.37890315,0.38159475,0.38426846,0.38692456,0.3895635,0.39218557,0.39479113,0.39738047,0.39995396,0.40251186,0.4050545,0.40758213,0.41009507,0.41259357,0.4150779,0.41754827,0.42000496,0.42244825,0.42487827,0.42729536,0.42969966,0.43209141,0.43447083,0.43683812,0.43919346,0.44153705,0.44386908,0.4461897,0.44849917,0.4507976,0.45308512,0.45536196,0.45762828,0.45988423,0.46212992,0.46436554,0.46659124,0.4688071,0.47101334,0.4732101,0.47539744,0.4775755,0.4797445,0.48190442,0.4840555,0.48619783,0.48833147,0.49045658,0.4925733,0.49468166,0.49678186,0.49887392,0.50095797,0.5030342,0.5051025,0.50716317,0.5092162,0.5112617,0.5132998,0.51533055,0.5173541,0.5193704,0.52137953,0.5233818,0.52537715,0.5273656,0.5293473,0.53132224,0.5332907,0.5352525,0.5372079,0.53915685,0.5410995,0.54303586,0.5449661,0.5468902,0.5488082,0.5507202,0.5526263,0.5545265,0.55642086,0.55830956,0.5601925,0.56206983,0.56394154,0.56580776,0.5676685,0.5695239,0.5713738,0.57321846,0.57505786,0.576892,0.5787211,0.580545,0.58236396,0.5841778,0.5859867,0.58779067,0.58958983,0.59138405,0.5931736,0.5949584,0.59673846,0.5985139,0.6002847,0.60205096,0.6038127,0.6055699,0.6073227,0.6090711,0.6108151,0.6125547,0.6142901,0.6160212,0.6177481,0.61947083,0.6211894,0.6229038,0.6246142,0.6263205,0.62802273,0.62972105,0.6314154,0.6331059,0.6347924,0.63647515,0.63815403,0.63982916,0.6415005,0.643168,0.6448319,0.6464921,0.6481487,0.6498017,0.6514511,0.65309685,0.65473914,0.656378,0.6580133,0.6596451,0.6612735,0.6628985,0.6645202,0.66613847,0.66775346,0.66936505,0.6709735,0.6725786,0.6741805,0.6757792,0.6773747,0.6789672,0.68055636,0.68214244,0.6837255,0.6853054,0.6868823,0.68845624,0.69002706,0.69159496,0.69315994,0.6947219,0.69628096,0.6978371,0.6993904,0.7009408,0.70248836,0.70403314,0.7055751,0.7071142,0.7086506,0.7101843,0.7117152,0.71324337,0.7147688,0.7162917,0.7178118,0.71932936,0.7208443,0.72235656,0.7238663,0.7253734,0.726878,0.72837996,0.7298795,0.73137647,0.732871,0.7343631,0.7358526,0.73733974,0.7388244,0.7403067,0.7417866,0.743264,0.7447391,0.7462119,0.7476823,0.7491504,0.75061613,0.75207967,0.7535408,0.75499976,0.7564564,0.7579108,0.759363,0.7608129,0.7622607,0.76370627,0.76514965,0.76659083,0.76802987,0.7694668,0.7709016,0.77233434,0.7737649,0.77519333,0.7766198,0.7780441,0.77946633,0.7808866,0.7823048,0.783721,0.7851352,0.78654736,0.78795755,0.78936577,0.790772,0.79217637,0.7935786,0.7949791,0.79637754,0.7977742,0.7991689,0.80056167,0.8019526,0.8033416,0.8047288,0.80611414,0.8074977,0.8088793,0.81025916,0.8116372,0.81301343,0.814388,0.8157606,0.8171315,0.81850064,0.819868,0.8212337,0.8225976,0.82395977,0.82532024,0.826679,0.8280361,0.8293915,0.83074516,0.83209723,0.8334476,0.83479625,0.8361434,0.83748883,0.83883256,0.8401748,0.8415153,0.8428543,0.8441917,0.84552747,0.84686166,0.84819424,0.8495254,0.8508549,0.85218287,0.85350925,0.8548341,0.8561575,0.85747933,0.8587997,0.8601185,0.86143583,0.8627517,0.86406606,0.865379,0.8666904,0.8680004,0.8693088,0.8706159,0.87192154,0.8732258,0.8745285,0.8758299,0.87712985,0.8784284,0.8797256,0.8810213,0.8823157,0.8836087,0.88490033,0.88619053,0.8874795,0.88876706,0.8900532,0.8913381,0.89262164,0.8939039,0.8951848,0.89646435,0.8977426,0.8990196,0.90029526,0.90156966,0.9028428,0.9041146,0.90538514,0.9066545,0.9079225,0.9091893,0.9104548,0.9117191,0.91298217,0.91424394,0.9155046,0.9167639,0.9180221,0.91927904,0.92053473,0.92178935,0.9230427,0.9242949,0.9255458,0.92679566,0.92804426,0.9292917,0.930538,0.9317832,0.93302715,0.93427,0.93551177,0.9367523,0.9379918,0.93923014,0.94046724,0.9417034,0.9429384,0.9441722,0.94540495,0.9466367,0.9478673,0.94909674,0.9503252,0.9515525,0.95277876,0.95400393,0.95522803,0.9564511,0.9576732,0.9588941,0.96011406,0.9613329,0.96255076,0.9637676,0.9649834,0.9661981,0.9674118,0.96862453,0.9698363,0.971047,0.9722567,0.9734654,0.9746732,0.97587985,0.97708565,0.9782904,0.97949415,0.980697,0.98189884,0.98309976,0.98429966,0.9854986,0.98669666,0.9878937,0.9890899,0.99028504,0.9914793,0.9926726,0.993865,0.9950564,0.996247,0.99743664,0.99862534,0.99981314,1.001,1.0021861,1.0033711,1.0045553,1.0057386,1.006921,1.0081027,1.0092833,1.010463,1.011642,1.01282,1.0139972,1.0151736,1.016349,1.0175235,1.0186974,1.0198703,1.0210423,1.0222136,1.0233839,1.0245534,1.0257221,1.02689,1.0280571,1.0292233,1.0303887,1.0315534,1.0327172,1.0338802,1.0350423,1.0362037,1.0373644,1.0385242,1.0396831,1.0408413,1.0419987,1.0431554,1.0443113,1.0454664,1.0466207,1.0477742,1.0489271,1.050079,1.0512303,1.0523808,1.0535307,1.0546795,1.0558277,1.0569752,1.058122,1.0592681,1.0604132,1.0615579,1.0627016,1.0638448,1.0649871,1.0661288,1.0672697,1.0684098,1.0695493,1.070688,1.0718263,1.0729635,1.0741003,1.0752362,1.0763714,1.0775061,1.07864,1.0797731,1.0809056,1.0820373,1.0831685,1.084299,1.0854288,1.0865579,1.0876863,1.0888141,1.0899413,1.0910677,1.0921935,1.0933187,1.0944432,1.095567,1.0966902,1.0978125,1.0989344,1.1000557,1.1011764,1.1022964,1.1034157,1.1045343,1.1056523,1.1067699,1.1078866,1.1090028,1.1101184,1.1112334,1.1123476,1.1134615,1.1145746,1.1156871,1.116799,1.1179103,1.119021,1.120131,1.1212406,1.1223495,1.1234578,1.1245655,1.1256728,1.1267793,1.1278852,1.1289907,1.1300955,1.1311997,1.1323034,1.1334065,1.134509,1.1356109,1.1367124,1.1378133,1.1389135,1.1400133,1.1411124,1.142211,1.1433092,1.1444067,1.1455036,1.1466,1.1476959,1.1487912,1.1498861,1.1509804,1.1520741,1.1531672,1.15426,1.1553521,1.1564437,1.1575347,1.1586254,1.1597154,1.1608049,1.1618941,1.1629825,1.1640705,1.165158,1.166245,1.1673315,1.1684173,1.1695029,1.1705878,1.1716723,1.1727563,1.1738397,1.1749227,1.1760052,1.1770872,1.1781688,1.1792498,1.1803303,1.1814104,1.18249,1.1835692,1.1846478,1.1857259,1.1868036,1.1878809,1.1889577,1.1900339,1.1911098,1.1921852,1.1932601,1.1943345,1.1954085,1.1964821,1.1975552,1.1986277,1.1997,1.2007717,1.201843,1.2029139,1.2039843,1.2050543,1.2061238,1.2071929,1.2082616,1.2093298,1.2103976,1.211465,1.2125319,1.2135985,1.2146646,1.2157302,1.2167954,1.2178603,1.2189246,1.2199886,1.2210523,1.2221154,1.2231783,1.2242405,1.2253026,1.2263641,1.2274251,1.228486,1.2295463,1.2306062,1.2316657,1.2327249,1.2337836,1.2348421,1.2358998,1.2369576,1.2380146,1.2390715,1.2401279,1.241184,1.2422396,1.2432948,1.2443497,1.2454042,1.2464584,1.2475121,1.2485657,1.2496185,1.2506713,1.2517234,1.2527754,1.253827,1.254878,1.255929,1.2569795,1.2580296,1.2590793,1.2601289,1.2611779,1.2622266,1.2632748,1.2643229,1.2653706,1.2664177,1.2674648,1.2685113,1.2695577,1.2706035,1.2716492,1.2726945,1.2737395,1.274784,1.2758284,1.2768722,1.2779158,1.2789592,1.280002,1.2810446,1.2820868,1.2831289,1.2841705,1.2852119,1.2862529,1.2872937,1.288334,1.289374,1.2904139,1.2914532,1.2924923,1.2935312,1.2945697,1.2956079,1.2966459,1.2976834,1.2987207,1.2997577,1.3007944,1.3018308,1.3028669,1.3039029,1.3049383,1.3059735,1.3070084,1.3080431,1.3090775,1.3101115,1.3111453,1.3121789,1.3132122,1.314245,1.3152777,1.31631,1.3173423,1.318374,1.3194056,1.320437,1.3214678,1.3224987,1.3235291,1.3245592,1.3255892,1.326619,1.3276483,1.3286775,1.3297064,1.330735,1.3317633,1.3327914,1.3338193,1.3348469,1.3358742,1.3369013,1.3379282,1.3389548,1.3399812,1.3410072,1.342033,1.3430587,1.3440839,1.3451091,1.346134,1.3471586,1.3481829,1.3492072,1.350231,1.3512548,1.3522782,1.3533014,1.3543245,1.3553473,1.3563697,1.357392,1.3584142,1.359436,1.3604577,1.3614789,1.3625002,1.3635211,1.3645419,1.3655624,1.3665828,1.3676028,1.3686225,1.3696424,1.3706617,1.371681,1.3727,1.3737189,1.3747375,1.3757559,1.3767741,1.3777921,1.3788098,1.3798275,1.380845,1.381862,1.3828791,1.383896,1.3849125,1.3859289,1.3869451,1.3879611,1.3889772,1.3899927,1.3910081,1.3920234,1.3930385,1.3940535,1.3950682,1.3960826,1.397097,1.3981112,1.3991251,1.400139,1.4011527,1.402166,1.4031793,1.4041924,1.4052055,1.4062183,1.4072309,1.4082433,1.4092555,1.4102676,1.4112796,1.4122913,1.4133029,1.4143144,1.4153255,1.4163367,1.4173477,1.4183586,1.4193691,1.4203796,1.42139,1.4224002,1.4234102,1.4244201,1.4254298,1.4264394,1.4274487,1.4284581,1.4294672,1.4304762,1.4314849,1.4324937,1.4335022,1.4345108,1.435519,1.4365271,1.4375352,1.438543,1.4395506,1.4405583,1.4415658,1.4425732,1.4435804,1.4445875,1.4455943,1.4466013,1.4476079,1.4486145,1.449621,1.4506272,1.4516335,1.4526396,1.4536453,1.4546512,1.4556571,1.4566625,1.4576682,1.4586735,1.4596786,1.4606838,1.4616889,1.4626938,1.4636986,1.4647033,1.4657079,1.4667125,1.4677168,1.4687212,1.4697254,1.4707292,1.4717332,1.4727372,1.4737409,1.4747446,1.4757483,1.4767516,1.4777551,1.4787583,1.4797616,1.4807646,1.4817678,1.4827706,1.4837735,1.4847763,1.4857788,1.4867815,1.4877839,1.4887865,1.4897887,1.490791,1.4917932,1.4927951,1.4937972,1.4947991,1.4958011,1.4968028,1.4978045,1.4988061,1.4998076,1.5008091,1.5018106,1.5028118,1.503813,1.5048145,1.5058155,1.5068167,1.5078177,1.5088186,1.5098195,1.5108204,1.5118212,1.5128219,1.5138224,1.514823,1.5158237,1.516824,1.5178245,1.5188249,1.5198252,1.5208255,1.5218257,1.522826,1.523826,1.5248262,1.5258262,1.5268261,1.527826,1.5288259,1.5298259,1.5308256,1.5318254,1.5328252,1.5338248,1.5348245,1.5358242,1.5368239,1.5378233,1.5388229,1.5398223,1.5408218,1.5418214,1.5428206,1.54382,1.5448194,1.5458188,1.546818,1.5478173,1.5488166,1.5498157,1.550815,1.5518142,1.5528134,1.5538125,1.5548117,1.5558108,1.5568099,1.5578089,1.558808,1.5598071,1.5608062,1.5618051,1.5628042,1.5638032,1.5648022,1.5658014,1.5668004,1.5677993,1.5687983,1.5697973,1.5707963,1.5717952,1.5727942,1.5737933,1.5747923,1.5757914,1.5767903,1.5777894,1.5787885,1.5797874,1.5807865,1.5817856,1.5827847,1.5837837,1.5847827,1.5857818,1.586781,1.5877801,1.5887793,1.5897784,1.5907778,1.5917768,1.5927761,1.5937753,1.5947746,1.595774,1.5967733,1.5977726,1.598772,1.5997714,1.6007708,1.6017704,1.6027697,1.6037694,1.6047689,1.6057684,1.6067681,1.6077677,1.6087675,1.6097672,1.610767,1.6117668,1.6127667,1.6137667,1.6147666,1.6157665,1.6167665,1.6177666,1.6187668,1.619767,1.620767,1.6217675,1.6227677,1.6237681,1.6247686,1.6257691,1.6267697,1.6277702,1.6287708,1.6297716,1.6307725,1.6317732,1.632774,1.633775,1.6347761,1.6357771,1.6367782,1.6377795,1.6387806,1.6397822,1.6407835,1.641785,1.6427866,1.6437882,1.6447898,1.6457916,1.6467935,1.6477956,1.6487975,1.6497996,1.6508017,1.651804,1.6528064,1.6538087,1.6548111,1.6558137,1.6568166,1.6578193,1.6588221,1.659825,1.6608279,1.661831,1.6628343,1.6638377,1.664841,1.6658444,1.6668481,1.6678517,1.6688555,1.6698594,1.6708635,1.6718674,1.6728717,1.6738758,1.6748803,1.6758847,1.6768893,1.677894,1.6788988,1.6799039,1.6809089,1.681914,1.6829191,1.6839247,1.68493,1.6859357,1.6869413,1.6879473,1.6889533,1.6899593,1.6909654,1.6919719,1.6929783,1.6939847,1.6949915,1.6959982,1.6970053,1.6980124,1.6990196,1.7000268,1.7010344,1.702042,1.7030497,1.7040575,1.7050656,1.7060738,1.707082,1.7080903,1.7090989,1.7101077,1.7111164,1.7121254,1.7131346,1.7141439,1.7151533,1.7161628,1.7171725,1.7181826,1.7191925,1.7202028,1.721213,1.7222235,1.7232343,1.7242451,1.7252558,1.7262669,1.7272784,1.7282897,1.7293013,1.7303131,1.7313249,1.7323372,1.7333494,1.7343619,1.7353745,1.7363873,1.7374002,1.7384133,1.7394265,1.7404399,1.7414538,1.7424675,1.7434814,1.7444956,1.7455101,1.7465246,1.7475393,1.7485541,1.7495693,1.7505846,1.7515999,1.7526156,1.7536314,1.7546475,1.7556638,1.7566801,1.7576966,1.7587135,1.7597305,1.7607477,1.7617651,1.7627828,1.7638006,1.7648184,1.7658367,1.7668551,1.7678738,1.7688926,1.7699115,1.7709309,1.7719504,1.7729701,1.7739899,1.7750099,1.7760302,1.7770509,1.7780716,1.7790926,1.7801137,1.7811352,1.7821567,1.7831787,1.7842007,1.785223,1.7862456,1.7872683,1.7882912,1.7893144,1.7903379,1.7913616,1.7923855,1.7934096,1.7944341,1.7954588,1.7964835,1.7975087,1.798534,1.7995596,1.8005854,1.8016115,1.8026378,1.8036644,1.8046913,1.8057183,1.8067456,1.8077735,1.8088013,1.8098292,1.8108578,1.8118863,1.8129152,1.8139443,1.8149737,1.8160034,1.8170334,1.8180636,1.8190941,1.8201247,1.8211558,1.8221871,1.8232187,1.8242505,1.8252826,1.8263149,1.8273478,1.8283807,1.8294137,1.8304474,1.8314812,1.8325151,1.8335496,1.8345841,1.8356192,1.8366543,1.8376898,1.8387256,1.8397619,1.8407983,1.841835,1.8428718,1.8439091,1.8449469,1.8459848,1.8470229,1.8480614,1.8491004,1.8501394,1.8511788,1.8522185,1.8532587,1.8542991,1.8553396,1.8563807,1.857422,1.8584638,1.8595058,1.860548,1.8615905,1.8626337,1.8636769,1.8647203,1.8657643,1.8668088,1.8678532,1.8688982,1.8699435,1.870989,1.8720351,1.8730812,1.8741279,1.8751749,1.8762223,1.8772697,1.8783177,1.8793662,1.8804147,1.881464,1.8825134,1.8835629,1.8846132,1.8856636,1.8867145,1.8877656,1.8888172,1.8898691,1.8909214,1.891974,1.8930271,1.8940804,1.8951343,1.8961884,1.8972428,1.8982978,1.8993533,1.9004087,1.9014647,1.9025211,1.9035778,1.9046351,1.9056927,1.9067507,1.907809,1.9088678,1.9099269,1.9109864,1.9120463,1.9131068,1.9141675,1.9152285,1.9162902,1.917352,1.9184146,1.9194771,1.9205403,1.9216039,1.9226679,1.9237325,1.9247972,1.9258624,1.9269279,1.9279944,1.9290607,1.9301276,1.931195,1.9322628,1.933331,1.9343998,1.9354688,1.9365385,1.9376085,1.9386786,1.9397495,1.9408208,1.9418927,1.9429648,1.9440376,1.9451106,1.9461843,1.9472581,1.9483325,1.9494073,1.9504828,1.9515588,1.9526349,1.9537117,1.9547889,1.9558668,1.9569448,1.9580235,1.9591025,1.9601824,1.9612625,1.962343,1.9634238,1.9645053,1.9655875,1.96667,1.9677529,1.9688364,1.9699205,1.9710047,1.9720898,1.9731752,1.9742613,1.9753476,1.9764347,1.9775223,1.9786102,1.9796985,1.9807878,1.9818773,1.9829671,1.9840579,1.9851489,1.9862406,1.9873326,1.9884253,1.9895185,1.9906121,1.9917065,1.9928013,1.9938968,1.9949926,1.9960889,1.997186,1.9982836,1.9993815,2.0004802,2.0015793,2.0026789,2.0037794,2.0048802,2.0059814,2.0070834,2.008186,2.009289,2.010393,2.011497,2.012602,2.0137074,2.0148132,2.01592,2.0170271,2.0181348,2.0192432,2.020352,2.0214615,2.0225718,2.0236824,2.0247936,2.0259056,2.027018,2.0281312,2.029245,2.0303593,2.0314744,2.0325897,2.033706,2.0348227,2.0359402,2.0370584,2.038177,2.0392964,2.0404162,2.0415368,2.042658,2.0437799,2.0449026,2.0460258,2.0471497,2.048274,2.0493991,2.050525,2.0516515,2.0527785,2.0539062,2.0550346,2.0561638,2.0572937,2.058424,2.0595553,2.0606868,2.0618198,2.062953,2.0640867,2.065221,2.0663562,2.0674925,2.068629,2.0697663,2.0709043,2.0720434,2.0731828,2.074323,2.0754638,2.0766053,2.077748,2.0788908,2.0800347,2.0811791,2.0823247,2.0834706,2.0846174,2.085765,2.086913,2.088062,2.0892117,2.0903623,2.0915136,2.0926657,2.0938184,2.094972,2.0961263,2.0972815,2.0984373,2.0995939,2.1007514,2.1019094,2.1030686,2.1042283,2.1053889,2.1065502,2.1077125,2.1088755,2.1100392,2.1112037,2.1123693,2.1135356,2.1147027,2.1158705,2.1170392,2.118209,2.1193793,2.1205504,2.1217222,2.1228955,2.124069,2.1252437,2.126419,2.1275954,2.1287727,2.1299505,2.1311295,2.1323094,2.13349,2.1346717,2.135854,2.1370373,2.1382217,2.1394067,2.1405928,2.1417797,2.1429672,2.144156,2.1453457,2.1465364,2.1477277,2.14892,2.1501133,2.1513076,2.1525028,2.153699,2.1548963,2.156094,2.1572928,2.158493,2.159694,2.1608956,2.1620984,2.1633022,2.1645072,2.1657126,2.1669195,2.1681273,2.1693358,2.1705456,2.1717563,2.172968,2.1741807,2.1753948,2.1766093,2.1778252,2.1790419,2.1802597,2.1814787,2.1826985,2.1839194,2.1851416,2.1863647,2.1875887,2.188814,2.19004,2.1912677,2.192496,2.1937256,2.1949558,2.1961877,2.1974206,2.1986544,2.1998892,2.2011254,2.2023628,2.203601,2.2048402,2.206081,2.2073226,2.2085655,2.2098095,2.2110546,2.212301,2.2135484,2.214797,2.2160468,2.2172978,2.21855,2.2198033,2.221058,2.2223136,2.2235706,2.2248287,2.226088,2.2273486,2.2286105,2.2298737,2.2311378,2.2324035,2.2336702,2.2349384,2.2362075,2.237478,2.2387497,2.240023,2.2412975,2.242573,2.24385,2.2451282,2.2464077,2.247689,2.248971,2.2502546,2.2515392,2.2528255,2.254113,2.255402,2.2566922,2.2579842,2.259277,2.2605715,2.261867,2.2631643,2.264463,2.2657628,2.267064,2.2683668,2.2696712,2.2709768,2.2722838,2.2735922,2.2749023,2.276214,2.2775266,2.278841,2.2801569,2.281474,2.2827928,2.2841132,2.285435,2.2867587,2.2880833,2.2894096,2.2907376,2.2920673,2.2933984,2.2947311,2.296065,2.297401,2.2987385,2.3000774,2.3014178,2.3027601,2.3041039,2.3054495,2.3067963,2.308145,2.3094957,2.3108475,2.3122013,2.3135564,2.3149135,2.3162725,2.3176327,2.318995,2.320359,2.321725,2.323092,2.3244612,2.325832,2.3272047,2.3285792,2.3299556,2.3313336,2.3327134,2.3340952,2.3354785,2.336864,2.338251,2.3396401,2.341031,2.342424,2.3438187,2.345215,2.3466134,2.3480139,2.3494163,2.3508205,2.3522267,2.3536353,2.3550453,2.3564572,2.3578715,2.3592877,2.360706,2.362126,2.3635483,2.3649728,2.3663993,2.367828,2.3692584,2.3706913,2.3721259,2.3735628,2.3750017,2.376443,2.3778865,2.3793318,2.3807795,2.3822296,2.3836818,2.3851364,2.3865929,2.388052,2.389513,2.3909767,2.3924422,2.3939104,2.3953807,2.3968537,2.3983285,2.3998063,2.4012861,2.4027684,2.4042528,2.4057403,2.4072294,2.4087214,2.4102163,2.4117131,2.4132128,2.4147146,2.4162195,2.4177265,2.419236,2.4207485,2.4222634,2.423781,2.425301,2.4268239,2.4283493,2.4298775,2.4314082,2.4329422,2.4344783,2.4360178,2.4375596,2.4391043,2.440652,2.442202,2.4437556,2.4453115,2.4468708,2.448433,2.4499977,2.4515655,2.4531364,2.4547105,2.4562871,2.4578671,2.4594502,2.4610364,2.4626255,2.464218,2.4658134,2.4674122,2.469014,2.4706192,2.4722276,2.4738393,2.475454,2.4770725,2.4786942,2.4803193,2.4819474,2.4835792,2.485215,2.4868534,2.4884958,2.4901416,2.491791,2.493444,2.4951003,2.4967608,2.4984245,2.5000923,2.5017638,2.5034387,2.5051174,2.5068002,2.5084867,2.5101774,2.5118716,2.5135698,2.5152721,2.5169785,2.5186887,2.5204031,2.522122,2.5238447,2.5255713,2.5273023,2.529038,2.5307777,2.5325217,2.5342698,2.5360224,2.53778,2.5395417,2.5413082,2.5430787,2.5448544,2.5466344,2.548419,2.5502086,2.5520031,2.553802,2.555606,2.5574148,2.559229,2.5610478,2.5628717,2.5647006,2.5665348,2.5683742,2.5702188,2.5720687,2.5739243,2.575785,2.5776513,2.5795228,2.5814,2.5832832,2.5851717,2.5870662,2.5889664,2.5908725,2.5927846,2.5947025,2.5966265,2.5985568,2.6004932,2.602436,2.6043847,2.60634,2.6083016,2.6102705,2.6122456,2.614227,2.6162157,2.6182108,2.6202133,2.6222227,2.6242385,2.626262,2.628293,2.6303308,2.6323762,2.6344292,2.6364903,2.6385584,2.6406348,2.6427186,2.644811,2.646911,2.6490192,2.6511362,2.6532614,2.6553953,2.6575372,2.6596882,2.661848,2.664017,2.6661952,2.6683824,2.6705794,2.6727855,2.6750016,2.6772273,2.679463,2.6817086,2.6839645,2.6862304,2.6885076,2.690795,2.6930933,2.695403,2.6977236,2.7000558,2.702399,2.7047546,2.707122,2.7095013,2.7118928,2.7142975,2.7167146,2.719144,2.7215877,2.7240446,2.726515,2.7289991,2.7314975,2.7340102,2.7365384,2.7390811,2.7416384,2.7442122,2.7468016,2.7494068,2.7520292,2.754668,2.757324,2.7599983,2.7626898,2.7653992,2.7681282,2.7708762,2.7736437,2.7764308,2.7792385,2.782067,2.7849178,2.7877898,2.7906847,2.7936025,2.796544,2.7995095,2.8025002,2.8055162,2.8085592,2.8116283,2.8147254,2.817851,2.8210063,2.8241925,2.8274093,2.8306575,2.8339398,2.8372562,2.8406076,2.8439963,2.847422,2.850887,2.8543935,2.8579414,2.8615332,2.8651702,2.8688548,2.8725886,2.8763728,2.8802114,2.884105,2.8880582,2.8920724,2.8961504,2.9002957,2.9045131,2.9088047,2.9131753,2.9176297,2.922173,2.9268112,2.93155,2.9363966,2.9413579,2.9464445,2.9516659,2.9570317,2.962558,2.968257,2.9741495,2.9802535,2.9865956,2.9932063,3.000125,3.0073957,3.0150795,3.02326,3.0320494,3.0416002,3.0521643,3.0641525,3.0783694,3.096888,3.1415927],"x":[0.0,0.0004995004995004995,0.000999000999000999,0.0014985014985014985,0.001998001998001998,0.0024975024975024975,0.002997002997002997,0.0034965034965034965,0.003996003996003996,0.004495504495504496,0.004995004995004995,0.005494505494505495,0.005994005994005994,0.006493506493506494,0.006993006993006993,0.007492507492507493,0.007992007992007992,0.008491508491508492,0.008991008991008992,0.00949050949050949,0.00999000999000999,0.01048951048951049,0.01098901098901099,0.011488511488511488,0.011988011988011988,0.012487512487512488,0.012987012987012988,0.013486513486513486,0.013986013986013986,0.014485514485514486,0.014985014985014986,0.015484515484515484,0.015984015984015984,0.016483516483516484,0.016983016983016984,0.017482517482517484,0.017982017982017984,0.01848151848151848,0.01898101898101898,0.01948051948051948,0.01998001998001998,0.02047952047952048,0.02097902097902098,0.02147852147852148,0.02197802197802198,0.022477522477522476,0.022977022977022976,0.023476523476523476,0.023976023976023976,0.024475524475524476,0.024975024975024976,0.025474525474525476,0.025974025974025976,0.026473526473526472,0.026973026973026972,0.027472527472527472,0.027972027972027972,0.028471528471528472,0.028971028971028972,0.029470529470529472,0.029970029970029972,0.030469530469530468,0.030969030969030968,0.03146853146853147,0.03196803196803197,0.032467532467532464,0.03296703296703297,0.033466533466533464,0.03396603396603397,0.034465534465534464,0.03496503496503497,0.035464535464535464,0.03596403596403597,0.036463536463536464,0.03696303696303696,0.037462537462537464,0.03796203796203796,0.038461538461538464,0.03896103896103896,0.039460539460539464,0.03996003996003996,0.040459540459540456,0.04095904095904096,0.041458541458541456,0.04195804195804196,0.042457542457542456,0.04295704295704296,0.043456543456543456,0.04395604395604396,0.044455544455544456,0.04495504495504495,0.045454545454545456,0.04595404595404595,0.046453546453546456,0.04695304695304695,0.047452547452547456,0.04795204795204795,0.04845154845154845,0.04895104895104895,0.04945054945054945,0.04995004995004995,0.05044955044955045,0.05094905094905095,0.05144855144855145,0.05194805194805195,0.05244755244755245,0.052947052947052944,0.05344655344655345,0.053946053946053944,0.05444555444555445,0.054945054945054944,0.05544455544455545,0.055944055944055944,0.05644355644355644,0.056943056943056944,0.05744255744255744,0.057942057942057944,0.05844155844155844,0.058941058941058944,0.05944055944055944,0.059940059940059943,0.06043956043956044,0.060939060939060936,0.06143856143856144,0.061938061938061936,0.06243756243756244,0.06293706293706294,0.06343656343656344,0.06393606393606394,0.06443556443556443,0.06493506493506493,0.06543456543456544,0.06593406593406594,0.06643356643356643,0.06693306693306693,0.06743256743256744,0.06793206793206794,0.06843156843156843,0.06893106893106893,0.06943056943056942,0.06993006993006994,0.07042957042957043,0.07092907092907093,0.07142857142857142,0.07192807192807193,0.07242757242757243,0.07292707292707293,0.07342657342657342,0.07392607392607392,0.07442557442557443,0.07492507492507493,0.07542457542457542,0.07592407592407592,0.07642357642357642,0.07692307692307693,0.07742257742257742,0.07792207792207792,0.07842157842157842,0.07892107892107893,0.07942057942057942,0.07992007992007992,0.08041958041958042,0.08091908091908091,0.08141858141858142,0.08191808191808192,0.08241758241758242,0.08291708291708291,0.08341658341658342,0.08391608391608392,0.08441558441558442,0.08491508491508491,0.08541458541458541,0.08591408591408592,0.08641358641358642,0.08691308691308691,0.08741258741258741,0.08791208791208792,0.08841158841158842,0.08891108891108891,0.08941058941058941,0.0899100899100899,0.09040959040959042,0.09090909090909091,0.09140859140859141,0.0919080919080919,0.0924075924075924,0.09290709290709291,0.09340659340659341,0.0939060939060939,0.0944055944055944,0.09490509490509491,0.09540459540459541,0.0959040959040959,0.0964035964035964,0.0969030969030969,0.09740259740259741,0.0979020979020979,0.0984015984015984,0.0989010989010989,0.09940059940059941,0.0999000999000999,0.1003996003996004,0.1008991008991009,0.10139860139860139,0.1018981018981019,0.1023976023976024,0.1028971028971029,0.10339660339660339,0.1038961038961039,0.1043956043956044,0.1048951048951049,0.10539460539460539,0.10589410589410589,0.1063936063936064,0.1068931068931069,0.10739260739260739,0.10789210789210789,0.10839160839160839,0.1088911088911089,0.10939060939060939,0.10989010989010989,0.11038961038961038,0.1108891108891109,0.11138861138861139,0.11188811188811189,0.11238761238761238,0.11288711288711288,0.11338661338661339,0.11388611388611389,0.11438561438561438,0.11488511488511488,0.11538461538461539,0.11588411588411589,0.11638361638361638,0.11688311688311688,0.11738261738261738,0.11788211788211789,0.11838161838161838,0.11888111888111888,0.11938061938061938,0.11988011988011989,0.12037962037962038,0.12087912087912088,0.12137862137862138,0.12187812187812187,0.12237762237762238,0.12287712287712288,0.12337662337662338,0.12387612387612387,0.12437562437562437,0.12487512487512488,0.12537462537462538,0.1258741258741259,0.12637362637362637,0.12687312687312688,0.12737262737262736,0.12787212787212787,0.12837162837162838,0.12887112887112886,0.12937062937062938,0.12987012987012986,0.13036963036963037,0.13086913086913088,0.13136863136863136,0.13186813186813187,0.13236763236763235,0.13286713286713286,0.13336663336663337,0.13386613386613386,0.13436563436563437,0.13486513486513488,0.13536463536463536,0.13586413586413587,0.13636363636363635,0.13686313686313686,0.13736263736263737,0.13786213786213786,0.13836163836163837,0.13886113886113885,0.13936063936063936,0.13986013986013987,0.14035964035964035,0.14085914085914086,0.14135864135864135,0.14185814185814186,0.14235764235764237,0.14285714285714285,0.14335664335664336,0.14385614385614387,0.14435564435564435,0.14485514485514486,0.14535464535464535,0.14585414585414586,0.14635364635364637,0.14685314685314685,0.14735264735264736,0.14785214785214784,0.14835164835164835,0.14885114885114886,0.14935064935064934,0.14985014985014986,0.15034965034965034,0.15084915084915085,0.15134865134865136,0.15184815184815184,0.15234765234765235,0.15284715284715283,0.15334665334665334,0.15384615384615385,0.15434565434565434,0.15484515484515485,0.15534465534465536,0.15584415584415584,0.15634365634365635,0.15684315684315683,0.15734265734265734,0.15784215784215785,0.15834165834165834,0.15884115884115885,0.15934065934065933,0.15984015984015984,0.16033966033966035,0.16083916083916083,0.16133866133866134,0.16183816183816183,0.16233766233766234,0.16283716283716285,0.16333666333666333,0.16383616383616384,0.16433566433566432,0.16483516483516483,0.16533466533466534,0.16583416583416583,0.16633366633366634,0.16683316683316685,0.16733266733266733,0.16783216783216784,0.16833166833166832,0.16883116883116883,0.16933066933066934,0.16983016983016982,0.17032967032967034,0.17082917082917082,0.17132867132867133,0.17182817182817184,0.17232767232767232,0.17282717282717283,0.17332667332667331,0.17382617382617382,0.17432567432567433,0.17482517482517482,0.17532467532467533,0.17582417582417584,0.17632367632367632,0.17682317682317683,0.1773226773226773,0.17782217782217782,0.17832167832167833,0.17882117882117882,0.17932067932067933,0.1798201798201798,0.18031968031968032,0.18081918081918083,0.1813186813186813,0.18181818181818182,0.1823176823176823,0.18281718281718282,0.18331668331668333,0.1838161838161838,0.18431568431568432,0.1848151848151848,0.1853146853146853,0.18581418581418582,0.1863136863136863,0.18681318681318682,0.18731268731268733,0.1878121878121878,0.18831168831168832,0.1888111888111888,0.1893106893106893,0.18981018981018982,0.1903096903096903,0.19080919080919082,0.1913086913086913,0.1918081918081918,0.19230769230769232,0.1928071928071928,0.1933066933066933,0.1938061938061938,0.1943056943056943,0.19480519480519481,0.1953046953046953,0.1958041958041958,0.1963036963036963,0.1968031968031968,0.1973026973026973,0.1978021978021978,0.1983016983016983,0.19880119880119881,0.1993006993006993,0.1998001998001998,0.2002997002997003,0.2007992007992008,0.2012987012987013,0.2017982017982018,0.2022977022977023,0.20279720279720279,0.2032967032967033,0.2037962037962038,0.2042957042957043,0.2047952047952048,0.20529470529470528,0.2057942057942058,0.2062937062937063,0.20679320679320679,0.2072927072927073,0.2077922077922078,0.2082917082917083,0.2087912087912088,0.20929070929070928,0.2097902097902098,0.2102897102897103,0.21078921078921078,0.2112887112887113,0.21178821178821178,0.2122877122877123,0.2127872127872128,0.21328671328671328,0.2137862137862138,0.21428571428571427,0.21478521478521478,0.2152847152847153,0.21578421578421578,0.2162837162837163,0.21678321678321677,0.21728271728271728,0.2177822177822178,0.21828171828171827,0.21878121878121878,0.2192807192807193,0.21978021978021978,0.2202797202797203,0.22077922077922077,0.22127872127872128,0.2217782217782218,0.22227772227772227,0.22277722277722278,0.22327672327672327,0.22377622377622378,0.2242757242757243,0.22477522477522477,0.22527472527472528,0.22577422577422576,0.22627372627372627,0.22677322677322678,0.22727272727272727,0.22777222777222778,0.22827172827172826,0.22877122877122877,0.22927072927072928,0.22977022977022976,0.23026973026973027,0.23076923076923078,0.23126873126873126,0.23176823176823177,0.23226773226773226,0.23276723276723277,0.23326673326673328,0.23376623376623376,0.23426573426573427,0.23476523476523475,0.23526473526473526,0.23576423576423577,0.23626373626373626,0.23676323676323677,0.23726273726273725,0.23776223776223776,0.23826173826173827,0.23876123876123875,0.23926073926073926,0.23976023976023977,0.24025974025974026,0.24075924075924077,0.24125874125874125,0.24175824175824176,0.24225774225774227,0.24275724275724275,0.24325674325674326,0.24375624375624375,0.24425574425574426,0.24475524475524477,0.24525474525474525,0.24575424575424576,0.24625374625374624,0.24675324675324675,0.24725274725274726,0.24775224775224775,0.24825174825174826,0.24875124875124874,0.24925074925074925,0.24975024975024976,0.25024975024975027,0.25074925074925075,0.25124875124875123,0.2517482517482518,0.25224775224775225,0.25274725274725274,0.2532467532467532,0.25374625374625376,0.25424575424575424,0.2547452547452547,0.25524475524475526,0.25574425574425574,0.2562437562437562,0.25674325674325676,0.25724275724275725,0.25774225774225773,0.25824175824175827,0.25874125874125875,0.25924075924075923,0.2597402597402597,0.26023976023976025,0.26073926073926074,0.2612387612387612,0.26173826173826176,0.26223776223776224,0.2627372627372627,0.26323676323676326,0.26373626373626374,0.2642357642357642,0.2647352647352647,0.26523476523476525,0.26573426573426573,0.2662337662337662,0.26673326673326675,0.26723276723276723,0.2677322677322677,0.26823176823176825,0.26873126873126874,0.2692307692307692,0.26973026973026976,0.27022977022977024,0.2707292707292707,0.2712287712287712,0.27172827172827174,0.2722277722277722,0.2727272727272727,0.27322677322677325,0.27372627372627373,0.2742257742257742,0.27472527472527475,0.27522477522477523,0.2757242757242757,0.2762237762237762,0.27672327672327673,0.2772227772227772,0.2777222777222777,0.27822177822177824,0.2787212787212787,0.2792207792207792,0.27972027972027974,0.2802197802197802,0.2807192807192807,0.28121878121878124,0.2817182817182817,0.2822177822177822,0.2827172827172827,0.28321678321678323,0.2837162837162837,0.2842157842157842,0.28471528471528473,0.2852147852147852,0.2857142857142857,0.28621378621378624,0.2867132867132867,0.2872127872127872,0.28771228771228774,0.2882117882117882,0.2887112887112887,0.2892107892107892,0.2897102897102897,0.2902097902097902,0.2907092907092907,0.29120879120879123,0.2917082917082917,0.2922077922077922,0.29270729270729273,0.2932067932067932,0.2937062937062937,0.2942057942057942,0.2947052947052947,0.2952047952047952,0.2957042957042957,0.2962037962037962,0.2967032967032967,0.2972027972027972,0.2977022977022977,0.2982017982017982,0.2987012987012987,0.29920079920079923,0.2997002997002997,0.3001998001998002,0.3006993006993007,0.3011988011988012,0.3016983016983017,0.3021978021978022,0.3026973026973027,0.3031968031968032,0.3036963036963037,0.3041958041958042,0.3046953046953047,0.3051948051948052,0.30569430569430567,0.3061938061938062,0.3066933066933067,0.30719280719280717,0.3076923076923077,0.3081918081918082,0.3086913086913087,0.3091908091908092,0.3096903096903097,0.3101898101898102,0.3106893106893107,0.3111888111888112,0.3116883116883117,0.31218781218781216,0.3126873126873127,0.3131868131868132,0.31368631368631367,0.3141858141858142,0.3146853146853147,0.31518481518481517,0.3156843156843157,0.3161838161838162,0.3166833166833167,0.31718281718281716,0.3176823176823177,0.3181818181818182,0.31868131868131866,0.3191808191808192,0.3196803196803197,0.32017982017982016,0.3206793206793207,0.3211788211788212,0.32167832167832167,0.3221778221778222,0.3226773226773227,0.32317682317682317,0.32367632367632365,0.3241758241758242,0.3246753246753247,0.32517482517482516,0.3256743256743257,0.3261738261738262,0.32667332667332666,0.3271728271728272,0.3276723276723277,0.32817182817182816,0.32867132867132864,0.3291708291708292,0.32967032967032966,0.33016983016983015,0.3306693306693307,0.33116883116883117,0.33166833166833165,0.3321678321678322,0.33266733266733267,0.33316683316683315,0.3336663336663337,0.3341658341658342,0.33466533466533466,0.33516483516483514,0.3356643356643357,0.33616383616383616,0.33666333666333664,0.3371628371628372,0.33766233766233766,0.33816183816183815,0.3386613386613387,0.33916083916083917,0.33966033966033965,0.34015984015984013,0.34065934065934067,0.34115884115884115,0.34165834165834164,0.3421578421578422,0.34265734265734266,0.34315684315684314,0.3436563436563437,0.34415584415584416,0.34465534465534464,0.3451548451548452,0.34565434565434566,0.34615384615384615,0.34665334665334663,0.34715284715284717,0.34765234765234765,0.34815184815184813,0.34865134865134867,0.34915084915084915,0.34965034965034963,0.3501498501498502,0.35064935064935066,0.35114885114885114,0.3516483516483517,0.35214785214785216,0.35264735264735264,0.3531468531468531,0.35364635364635366,0.35414585414585414,0.3546453546453546,0.35514485514485516,0.35564435564435565,0.35614385614385613,0.35664335664335667,0.35714285714285715,0.35764235764235763,0.3581418581418581,0.35864135864135865,0.35914085914085914,0.3596403596403596,0.36013986013986016,0.36063936063936064,0.3611388611388611,0.36163836163836166,0.36213786213786214,0.3626373626373626,0.36313686313686316,0.36363636363636365,0.36413586413586413,0.3646353646353646,0.36513486513486515,0.36563436563436563,0.3661338661338661,0.36663336663336665,0.36713286713286714,0.3676323676323676,0.36813186813186816,0.36863136863136864,0.3691308691308691,0.3696303696303696,0.37012987012987014,0.3706293706293706,0.3711288711288711,0.37162837162837165,0.37212787212787213,0.3726273726273726,0.37312687312687315,0.37362637362637363,0.3741258741258741,0.37462537462537465,0.37512487512487513,0.3756243756243756,0.3761238761238761,0.37662337662337664,0.3771228771228771,0.3776223776223776,0.37812187812187814,0.3786213786213786,0.3791208791208791,0.37962037962037964,0.3801198801198801,0.3806193806193806,0.3811188811188811,0.38161838161838163,0.3821178821178821,0.3826173826173826,0.38311688311688313,0.3836163836163836,0.3841158841158841,0.38461538461538464,0.3851148851148851,0.3856143856143856,0.38611388611388614,0.3866133866133866,0.3871128871128871,0.3876123876123876,0.3881118881118881,0.3886113886113886,0.3891108891108891,0.38961038961038963,0.3901098901098901,0.3906093906093906,0.39110889110889113,0.3916083916083916,0.3921078921078921,0.3926073926073926,0.3931068931068931,0.3936063936063936,0.3941058941058941,0.3946053946053946,0.3951048951048951,0.3956043956043956,0.3961038961038961,0.3966033966033966,0.3971028971028971,0.39760239760239763,0.3981018981018981,0.3986013986013986,0.3991008991008991,0.3996003996003996,0.4000999000999001,0.4005994005994006,0.4010989010989011,0.4015984015984016,0.4020979020979021,0.4025974025974026,0.4030969030969031,0.4035964035964036,0.40409590409590407,0.4045954045954046,0.4050949050949051,0.40559440559440557,0.4060939060939061,0.4065934065934066,0.4070929070929071,0.4075924075924076,0.4080919080919081,0.4085914085914086,0.4090909090909091,0.4095904095904096,0.4100899100899101,0.41058941058941056,0.4110889110889111,0.4115884115884116,0.41208791208791207,0.4125874125874126,0.4130869130869131,0.41358641358641357,0.4140859140859141,0.4145854145854146,0.4150849150849151,0.4155844155844156,0.4160839160839161,0.4165834165834166,0.41708291708291706,0.4175824175824176,0.4180819180819181,0.41858141858141856,0.4190809190809191,0.4195804195804196,0.42007992007992007,0.4205794205794206,0.4210789210789211,0.42157842157842157,0.42207792207792205,0.4225774225774226,0.4230769230769231,0.42357642357642356,0.4240759240759241,0.4245754245754246,0.42507492507492506,0.4255744255744256,0.4260739260739261,0.42657342657342656,0.4270729270729271,0.4275724275724276,0.42807192807192807,0.42857142857142855,0.4290709290709291,0.42957042957042957,0.43006993006993005,0.4305694305694306,0.43106893106893107,0.43156843156843155,0.4320679320679321,0.4325674325674326,0.43306693306693306,0.43356643356643354,0.4340659340659341,0.43456543456543456,0.43506493506493504,0.4355644355644356,0.43606393606393606,0.43656343656343655,0.4370629370629371,0.43756243756243757,0.43806193806193805,0.4385614385614386,0.43906093906093907,0.43956043956043955,0.44005994005994004,0.4405594405594406,0.44105894105894106,0.44155844155844154,0.4420579420579421,0.44255744255744256,0.44305694305694304,0.4435564435564436,0.44405594405594406,0.44455544455544455,0.44505494505494503,0.44555444555444557,0.44605394605394605,0.44655344655344653,0.44705294705294707,0.44755244755244755,0.44805194805194803,0.4485514485514486,0.44905094905094906,0.44955044955044954,0.4500499500499501,0.45054945054945056,0.45104895104895104,0.4515484515484515,0.45204795204795206,0.45254745254745254,0.453046953046953,0.45354645354645357,0.45404595404595405,0.45454545454545453,0.45504495504495507,0.45554445554445555,0.45604395604395603,0.4565434565434565,0.45704295704295705,0.45754245754245754,0.458041958041958,0.45854145854145856,0.45904095904095904,0.4595404595404595,0.46003996003996006,0.46053946053946054,0.461038961038961,0.46153846153846156,0.46203796203796205,0.46253746253746253,0.463036963036963,0.46353646353646355,0.46403596403596403,0.4645354645354645,0.46503496503496505,0.46553446553446554,0.466033966033966,0.46653346653346656,0.46703296703296704,0.4675324675324675,0.468031968031968,0.46853146853146854,0.469030969030969,0.4695304695304695,0.47002997002997005,0.47052947052947053,0.471028971028971,0.47152847152847155,0.47202797202797203,0.4725274725274725,0.47302697302697305,0.47352647352647353,0.474025974025974,0.4745254745254745,0.47502497502497504,0.4755244755244755,0.476023976023976,0.47652347652347654,0.477022977022977,0.4775224775224775,0.47802197802197804,0.4785214785214785,0.479020979020979,0.47952047952047955,0.48001998001998003,0.4805194805194805,0.481018981018981,0.48151848151848153,0.482017982017982,0.4825174825174825,0.48301698301698304,0.4835164835164835,0.484015984015984,0.48451548451548454,0.485014985014985,0.4855144855144855,0.486013986013986,0.4865134865134865,0.487012987012987,0.4875124875124875,0.48801198801198803,0.4885114885114885,0.489010989010989,0.48951048951048953,0.49000999000999,0.4905094905094905,0.49100899100899104,0.4915084915084915,0.492007992007992,0.4925074925074925,0.493006993006993,0.4935064935064935,0.494005994005994,0.4945054945054945,0.495004995004995,0.4955044955044955,0.49600399600399603,0.4965034965034965,0.497002997002997,0.4975024975024975,0.498001998001998,0.4985014985014985,0.499000999000999,0.4995004995004995,0.5,0.5004995004995005,0.500999000999001,0.5014985014985015,0.501998001998002,0.5024975024975025,0.502997002997003,0.5034965034965035,0.503996003996004,0.5044955044955045,0.504995004995005,0.5054945054945055,0.505994005994006,0.5064935064935064,0.506993006993007,0.5074925074925075,0.5079920079920079,0.5084915084915085,0.508991008991009,0.5094905094905094,0.50999000999001,0.5104895104895105,0.510989010989011,0.5114885114885115,0.511988011988012,0.5124875124875125,0.512987012987013,0.5134865134865135,0.513986013986014,0.5144855144855145,0.514985014985015,0.5154845154845155,0.515984015984016,0.5164835164835165,0.516983016983017,0.5174825174825175,0.5179820179820179,0.5184815184815185,0.518981018981019,0.5194805194805194,0.51998001998002,0.5204795204795205,0.5209790209790209,0.5214785214785215,0.521978021978022,0.5224775224775224,0.522977022977023,0.5234765234765235,0.5239760239760239,0.5244755244755245,0.524975024975025,0.5254745254745254,0.525974025974026,0.5264735264735265,0.526973026973027,0.5274725274725275,0.527972027972028,0.5284715284715285,0.528971028971029,0.5294705294705294,0.52997002997003,0.5304695304695305,0.5309690309690309,0.5314685314685315,0.531968031968032,0.5324675324675324,0.532967032967033,0.5334665334665335,0.5339660339660339,0.5344655344655345,0.534965034965035,0.5354645354645354,0.535964035964036,0.5364635364635365,0.5369630369630369,0.5374625374625375,0.537962037962038,0.5384615384615384,0.538961038961039,0.5394605394605395,0.5399600399600399,0.5404595404595405,0.5409590409590409,0.5414585414585414,0.541958041958042,0.5424575424575424,0.542957042957043,0.5434565434565435,0.5439560439560439,0.5444555444555444,0.544955044955045,0.5454545454545454,0.545954045954046,0.5464535464535465,0.5469530469530469,0.5474525474525475,0.547952047952048,0.5484515484515484,0.548951048951049,0.5494505494505495,0.5499500499500499,0.5504495504495505,0.550949050949051,0.5514485514485514,0.551948051948052,0.5524475524475524,0.5529470529470529,0.5534465534465535,0.5539460539460539,0.5544455544455544,0.554945054945055,0.5554445554445554,0.5559440559440559,0.5564435564435565,0.5569430569430569,0.5574425574425574,0.557942057942058,0.5584415584415584,0.5589410589410589,0.5594405594405595,0.5599400599400599,0.5604395604395604,0.560939060939061,0.5614385614385614,0.561938061938062,0.5624375624375625,0.5629370629370629,0.5634365634365635,0.563936063936064,0.5644355644355644,0.564935064935065,0.5654345654345654,0.5659340659340659,0.5664335664335665,0.5669330669330669,0.5674325674325674,0.567932067932068,0.5684315684315684,0.5689310689310689,0.5694305694305695,0.5699300699300699,0.5704295704295704,0.570929070929071,0.5714285714285714,0.5719280719280719,0.5724275724275725,0.5729270729270729,0.5734265734265734,0.573926073926074,0.5744255744255744,0.5749250749250749,0.5754245754245755,0.5759240759240759,0.5764235764235764,0.5769230769230769,0.5774225774225774,0.577922077922078,0.5784215784215784,0.5789210789210789,0.5794205794205795,0.5799200799200799,0.5804195804195804,0.580919080919081,0.5814185814185814,0.5819180819180819,0.5824175824175825,0.5829170829170829,0.5834165834165834,0.583916083916084,0.5844155844155844,0.5849150849150849,0.5854145854145855,0.5859140859140859,0.5864135864135864,0.586913086913087,0.5874125874125874,0.5879120879120879,0.5884115884115884,0.5889110889110889,0.5894105894105894,0.5899100899100899,0.5904095904095904,0.5909090909090909,0.5914085914085914,0.5919080919080919,0.5924075924075924,0.5929070929070929,0.5934065934065934,0.593906093906094,0.5944055944055944,0.5949050949050949,0.5954045954045954,0.5959040959040959,0.5964035964035964,0.596903096903097,0.5974025974025974,0.5979020979020979,0.5984015984015985,0.5989010989010989,0.5994005994005994,0.5999000999000998,0.6003996003996004,0.6008991008991009,0.6013986013986014,0.6018981018981019,0.6023976023976024,0.6028971028971029,0.6033966033966034,0.6038961038961039,0.6043956043956044,0.6048951048951049,0.6053946053946054,0.6058941058941059,0.6063936063936064,0.6068931068931069,0.6073926073926074,0.6078921078921079,0.6083916083916084,0.6088911088911089,0.6093906093906094,0.6098901098901099,0.6103896103896104,0.6108891108891109,0.6113886113886113,0.6118881118881119,0.6123876123876124,0.6128871128871128,0.6133866133866134,0.6138861138861139,0.6143856143856143,0.6148851148851149,0.6153846153846154,0.6158841158841158,0.6163836163836164,0.6168831168831169,0.6173826173826173,0.6178821178821179,0.6183816183816184,0.6188811188811189,0.6193806193806194,0.6198801198801199,0.6203796203796204,0.6208791208791209,0.6213786213786214,0.6218781218781219,0.6223776223776224,0.6228771228771228,0.6233766233766234,0.6238761238761239,0.6243756243756243,0.6248751248751249,0.6253746253746254,0.6258741258741258,0.6263736263736264,0.6268731268731269,0.6273726273726273,0.6278721278721279,0.6283716283716284,0.6288711288711288,0.6293706293706294,0.6298701298701299,0.6303696303696303,0.6308691308691309,0.6313686313686314,0.6318681318681318,0.6323676323676324,0.6328671328671329,0.6333666333666333,0.6338661338661339,0.6343656343656343,0.6348651348651349,0.6353646353646354,0.6358641358641358,0.6363636363636364,0.6368631368631369,0.6373626373626373,0.6378621378621379,0.6383616383616384,0.6388611388611388,0.6393606393606394,0.6398601398601399,0.6403596403596403,0.6408591408591409,0.6413586413586414,0.6418581418581418,0.6423576423576424,0.6428571428571429,0.6433566433566433,0.6438561438561439,0.6443556443556444,0.6448551448551448,0.6453546453546454,0.6458541458541458,0.6463536463536463,0.6468531468531469,0.6473526473526473,0.6478521478521478,0.6483516483516484,0.6488511488511488,0.6493506493506493,0.6498501498501499,0.6503496503496503,0.6508491508491508,0.6513486513486514,0.6518481518481518,0.6523476523476524,0.6528471528471529,0.6533466533466533,0.6538461538461539,0.6543456543456544,0.6548451548451548,0.6553446553446554,0.6558441558441559,0.6563436563436563,0.6568431568431569,0.6573426573426573,0.6578421578421578,0.6583416583416584,0.6588411588411588,0.6593406593406593,0.6598401598401599,0.6603396603396603,0.6608391608391608,0.6613386613386614,0.6618381618381618,0.6623376623376623,0.6628371628371629,0.6633366633366633,0.6638361638361638,0.6643356643356644,0.6648351648351648,0.6653346653346653,0.6658341658341659,0.6663336663336663,0.6668331668331668,0.6673326673326674,0.6678321678321678,0.6683316683316683,0.6688311688311688,0.6693306693306693,0.6698301698301699,0.6703296703296703,0.6708291708291708,0.6713286713286714,0.6718281718281718,0.6723276723276723,0.6728271728271729,0.6733266733266733,0.6738261738261738,0.6743256743256744,0.6748251748251748,0.6753246753246753,0.6758241758241759,0.6763236763236763,0.6768231768231768,0.6773226773226774,0.6778221778221778,0.6783216783216783,0.6788211788211789,0.6793206793206793,0.6798201798201798,0.6803196803196803,0.6808191808191808,0.6813186813186813,0.6818181818181818,0.6823176823176823,0.6828171828171828,0.6833166833166833,0.6838161838161838,0.6843156843156843,0.6848151848151848,0.6853146853146853,0.6858141858141859,0.6863136863136863,0.6868131868131868,0.6873126873126874,0.6878121878121878,0.6883116883116883,0.6888111888111889,0.6893106893106893,0.6898101898101898,0.6903096903096904,0.6908091908091908,0.6913086913086913,0.6918081918081919,0.6923076923076923,0.6928071928071928,0.6933066933066933,0.6938061938061938,0.6943056943056943,0.6948051948051948,0.6953046953046953,0.6958041958041958,0.6963036963036963,0.6968031968031968,0.6973026973026973,0.6978021978021978,0.6983016983016983,0.6988011988011988,0.6993006993006993,0.6998001998001998,0.7002997002997003,0.7007992007992008,0.7012987012987013,0.7017982017982018,0.7022977022977023,0.7027972027972028,0.7032967032967034,0.7037962037962038,0.7042957042957043,0.7047952047952047,0.7052947052947053,0.7057942057942058,0.7062937062937062,0.7067932067932068,0.7072927072927073,0.7077922077922078,0.7082917082917083,0.7087912087912088,0.7092907092907093,0.7097902097902098,0.7102897102897103,0.7107892107892108,0.7112887112887113,0.7117882117882118,0.7122877122877123,0.7127872127872128,0.7132867132867133,0.7137862137862138,0.7142857142857143,0.7147852147852148,0.7152847152847153,0.7157842157842158,0.7162837162837162,0.7167832167832168,0.7172827172827173,0.7177822177822177,0.7182817182817183,0.7187812187812188,0.7192807192807192,0.7197802197802198,0.7202797202797203,0.7207792207792207,0.7212787212787213,0.7217782217782218,0.7222777222777222,0.7227772227772228,0.7232767232767233,0.7237762237762237,0.7242757242757243,0.7247752247752248,0.7252747252747253,0.7257742257742258,0.7262737262737263,0.7267732267732268,0.7272727272727273,0.7277722277722277,0.7282717282717283,0.7287712287712288,0.7292707292707292,0.7297702297702298,0.7302697302697303,0.7307692307692307,0.7312687312687313,0.7317682317682318,0.7322677322677322,0.7327672327672328,0.7332667332667333,0.7337662337662337,0.7342657342657343,0.7347652347652348,0.7352647352647352,0.7357642357642358,0.7362637362637363,0.7367632367632367,0.7372627372627373,0.7377622377622378,0.7382617382617382,0.7387612387612388,0.7392607392607392,0.7397602397602397,0.7402597402597403,0.7407592407592407,0.7412587412587412,0.7417582417582418,0.7422577422577422,0.7427572427572428,0.7432567432567433,0.7437562437562437,0.7442557442557443,0.7447552447552448,0.7452547452547452,0.7457542457542458,0.7462537462537463,0.7467532467532467,0.7472527472527473,0.7477522477522478,0.7482517482517482,0.7487512487512488,0.7492507492507493,0.7497502497502497,0.7502497502497503,0.7507492507492507,0.7512487512487512,0.7517482517482518,0.7522477522477522,0.7527472527472527,0.7532467532467533,0.7537462537462537,0.7542457542457542,0.7547452547452548,0.7552447552447552,0.7557442557442557,0.7562437562437563,0.7567432567432567,0.7572427572427572,0.7577422577422578,0.7582417582417582,0.7587412587412588,0.7592407592407593,0.7597402597402597,0.7602397602397603,0.7607392607392608,0.7612387612387612,0.7617382617382618,0.7622377622377622,0.7627372627372627,0.7632367632367633,0.7637362637362637,0.7642357642357642,0.7647352647352648,0.7652347652347652,0.7657342657342657,0.7662337662337663,0.7667332667332667,0.7672327672327672,0.7677322677322678,0.7682317682317682,0.7687312687312687,0.7692307692307693,0.7697302697302697,0.7702297702297702,0.7707292707292708,0.7712287712287712,0.7717282717282717,0.7722277722277723,0.7727272727272727,0.7732267732267732,0.7737262737262737,0.7742257742257742,0.7747252747252747,0.7752247752247752,0.7757242757242757,0.7762237762237763,0.7767232767232767,0.7772227772227772,0.7777222777222778,0.7782217782217782,0.7787212787212787,0.7792207792207793,0.7797202797202797,0.7802197802197802,0.7807192807192808,0.7812187812187812,0.7817182817182817,0.7822177822177823,0.7827172827172827,0.7832167832167832,0.7837162837162838,0.7842157842157842,0.7847152847152847,0.7852147852147852,0.7857142857142857,0.7862137862137862,0.7867132867132867,0.7872127872127872,0.7877122877122877,0.7882117882117882,0.7887112887112887,0.7892107892107892,0.7897102897102897,0.7902097902097902,0.7907092907092907,0.7912087912087912,0.7917082917082917,0.7922077922077922,0.7927072927072927,0.7932067932067932,0.7937062937062938,0.7942057942057942,0.7947052947052947,0.7952047952047953,0.7957042957042957,0.7962037962037962,0.7967032967032966,0.7972027972027972,0.7977022977022977,0.7982017982017982,0.7987012987012987,0.7992007992007992,0.7997002997002997,0.8001998001998002,0.8006993006993007,0.8011988011988012,0.8016983016983017,0.8021978021978022,0.8026973026973027,0.8031968031968032,0.8036963036963037,0.8041958041958042,0.8046953046953047,0.8051948051948052,0.8056943056943057,0.8061938061938062,0.8066933066933067,0.8071928071928072,0.8076923076923077,0.8081918081918081,0.8086913086913087,0.8091908091908092,0.8096903096903096,0.8101898101898102,0.8106893106893107,0.8111888111888111,0.8116883116883117,0.8121878121878122,0.8126873126873126,0.8131868131868132,0.8136863136863137,0.8141858141858141,0.8146853146853147,0.8151848151848152,0.8156843156843157,0.8161838161838162,0.8166833166833167,0.8171828171828172,0.8176823176823177,0.8181818181818182,0.8186813186813187,0.8191808191808192,0.8196803196803197,0.8201798201798202,0.8206793206793207,0.8211788211788211,0.8216783216783217,0.8221778221778222,0.8226773226773226,0.8231768231768232,0.8236763236763237,0.8241758241758241,0.8246753246753247,0.8251748251748252,0.8256743256743256,0.8261738261738262,0.8266733266733267,0.8271728271728271,0.8276723276723277,0.8281718281718282,0.8286713286713286,0.8291708291708292,0.8296703296703297,0.8301698301698301,0.8306693306693307,0.8311688311688312,0.8316683316683317,0.8321678321678322,0.8326673326673326,0.8331668331668332,0.8336663336663337,0.8341658341658341,0.8346653346653347,0.8351648351648352,0.8356643356643356,0.8361638361638362,0.8366633366633367,0.8371628371628371,0.8376623376623377,0.8381618381618382,0.8386613386613386,0.8391608391608392,0.8396603396603397,0.8401598401598401,0.8406593406593407,0.8411588411588412,0.8416583416583416,0.8421578421578422,0.8426573426573427,0.8431568431568431,0.8436563436563437,0.8441558441558441,0.8446553446553446,0.8451548451548452,0.8456543456543456,0.8461538461538461,0.8466533466533467,0.8471528471528471,0.8476523476523476,0.8481518481518482,0.8486513486513486,0.8491508491508492,0.8496503496503497,0.8501498501498501,0.8506493506493507,0.8511488511488512,0.8516483516483516,0.8521478521478522,0.8526473526473527,0.8531468531468531,0.8536463536463537,0.8541458541458542,0.8546453546453546,0.8551448551448552,0.8556443556443556,0.8561438561438561,0.8566433566433567,0.8571428571428571,0.8576423576423576,0.8581418581418582,0.8586413586413586,0.8591408591408591,0.8596403596403597,0.8601398601398601,0.8606393606393606,0.8611388611388612,0.8616383616383616,0.8621378621378621,0.8626373626373627,0.8631368631368631,0.8636363636363636,0.8641358641358642,0.8646353646353646,0.8651348651348651,0.8656343656343657,0.8661338661338661,0.8666333666333667,0.8671328671328671,0.8676323676323676,0.8681318681318682,0.8686313686313686,0.8691308691308691,0.8696303696303697,0.8701298701298701,0.8706293706293706,0.8711288711288712,0.8716283716283716,0.8721278721278721,0.8726273726273727,0.8731268731268731,0.8736263736263736,0.8741258741258742,0.8746253746253746,0.8751248751248751,0.8756243756243757,0.8761238761238761,0.8766233766233766,0.8771228771228772,0.8776223776223776,0.8781218781218781,0.8786213786213786,0.8791208791208791,0.8796203796203796,0.8801198801198801,0.8806193806193806,0.8811188811188811,0.8816183816183816,0.8821178821178821,0.8826173826173827,0.8831168831168831,0.8836163836163836,0.8841158841158842,0.8846153846153846,0.8851148851148851,0.8856143856143857,0.8861138861138861,0.8866133866133866,0.8871128871128872,0.8876123876123876,0.8881118881118881,0.8886113886113887,0.8891108891108891,0.8896103896103896,0.8901098901098901,0.8906093906093906,0.8911088911088911,0.8916083916083916,0.8921078921078921,0.8926073926073926,0.8931068931068931,0.8936063936063936,0.8941058941058941,0.8946053946053946,0.8951048951048951,0.8956043956043956,0.8961038961038961,0.8966033966033966,0.8971028971028971,0.8976023976023976,0.8981018981018981,0.8986013986013986,0.8991008991008991,0.8996003996003996,0.9000999000999002,0.9005994005994006,0.9010989010989011,0.9015984015984015,0.9020979020979021,0.9025974025974026,0.903096903096903,0.9035964035964036,0.9040959040959041,0.9045954045954046,0.9050949050949051,0.9055944055944056,0.906093906093906,0.9065934065934066,0.9070929070929071,0.9075924075924076,0.9080919080919081,0.9085914085914086,0.9090909090909091,0.9095904095904096,0.9100899100899101,0.9105894105894106,0.9110889110889111,0.9115884115884116,0.9120879120879121,0.9125874125874126,0.913086913086913,0.9135864135864136,0.9140859140859141,0.9145854145854145,0.9150849150849151,0.9155844155844156,0.916083916083916,0.9165834165834166,0.9170829170829171,0.9175824175824175,0.9180819180819181,0.9185814185814186,0.919080919080919,0.9195804195804196,0.9200799200799201,0.9205794205794205,0.9210789210789211,0.9215784215784216,0.922077922077922,0.9225774225774226,0.9230769230769231,0.9235764235764236,0.9240759240759241,0.9245754245754245,0.9250749250749251,0.9255744255744256,0.926073926073926,0.9265734265734266,0.9270729270729271,0.9275724275724275,0.9280719280719281,0.9285714285714286,0.929070929070929,0.9295704295704296,0.9300699300699301,0.9305694305694305,0.9310689310689311,0.9315684315684316,0.932067932067932,0.9325674325674326,0.9330669330669331,0.9335664335664335,0.9340659340659341,0.9345654345654346,0.935064935064935,0.9355644355644356,0.936063936063936,0.9365634365634365,0.9370629370629371,0.9375624375624375,0.938061938061938,0.9385614385614386,0.939060939060939,0.9395604395604396,0.9400599400599401,0.9405594405594405,0.9410589410589411,0.9415584415584416,0.942057942057942,0.9425574425574426,0.9430569430569431,0.9435564435564435,0.9440559440559441,0.9445554445554446,0.945054945054945,0.9455544455544456,0.9460539460539461,0.9465534465534465,0.9470529470529471,0.9475524475524476,0.948051948051948,0.9485514485514486,0.949050949050949,0.9495504495504495,0.9500499500499501,0.9505494505494505,0.951048951048951,0.9515484515484516,0.952047952047952,0.9525474525474525,0.9530469530469531,0.9535464535464535,0.954045954045954,0.9545454545454546,0.955044955044955,0.9555444555444556,0.9560439560439561,0.9565434565434565,0.957042957042957,0.9575424575424576,0.958041958041958,0.9585414585414586,0.9590409590409591,0.9595404595404595,0.9600399600399601,0.9605394605394605,0.961038961038961,0.9615384615384616,0.962037962037962,0.9625374625374625,0.9630369630369631,0.9635364635364635,0.964035964035964,0.9645354645354646,0.965034965034965,0.9655344655344655,0.9660339660339661,0.9665334665334665,0.967032967032967,0.9675324675324676,0.968031968031968,0.9685314685314685,0.9690309690309691,0.9695304695304695,0.97002997002997,0.9705294705294706,0.971028971028971,0.9715284715284715,0.972027972027972,0.9725274725274725,0.973026973026973,0.9735264735264735,0.974025974025974,0.9745254745254746,0.975024975024975,0.9755244755244755,0.9760239760239761,0.9765234765234765,0.977022977022977,0.9775224775224776,0.978021978021978,0.9785214785214785,0.9790209790209791,0.9795204795204795,0.98001998001998,0.9805194805194806,0.981018981018981,0.9815184815184815,0.9820179820179821,0.9825174825174825,0.983016983016983,0.9835164835164835,0.984015984015984,0.9845154845154845,0.985014985014985,0.9855144855144855,0.986013986013986,0.9865134865134865,0.987012987012987,0.9875124875124875,0.988011988011988,0.9885114885114885,0.989010989010989,0.9895104895104895,0.99000999000999,0.9905094905094906,0.991008991008991,0.9915084915084915,0.9920079920079921,0.9925074925074925,0.993006993006993,0.9935064935064936,0.994005994005994,0.9945054945054945,0.995004995004995,0.9955044955044955,0.996003996003996,0.9965034965034965,0.997002997002997,0.9975024975024975,0.998001998001998,0.9985014985014985,0.999000999000999,0.9995004995004995,1.0]} diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/fixtures/julia/runner.jl new file mode 100644 index 000000000000..06c99d04d86c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/fixtures/julia/runner.jl @@ -0,0 +1,70 @@ +#!/usr/bin/env julia +# +# @license Apache-2.0 +# +# Copyright (c) 2018 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +import JSON + +""" + gen( domain, name ) + +Generate fixture data and write to file. + +# Arguments + +* `domain`: domain +* `name::AbstractString`: output filename + +# Examples + +``` julia +julia> x = range( 0.0, stop = 1.0, length = 2001 ); +julia> gen( x, \"data.json\" ); +``` +""" +function gen( domain, name ) + x = collect( domain ); + y = Float32.( 2.0 ) .* asin.( sqrt.( Float32.( x ) ) ); + + # Store data to be written to file as a collection: + data = Dict([ + ("x", x), + ("expected", y) + ]); + + # Based on the script directory, create an output filepath: + filepath = joinpath( dir, name ); + + # Write the data to the output filepath as JSON: + outfile = open( filepath, "w" ); + write( outfile, JSON.json(data) ); + write( outfile, "\n" ); + close( outfile ); +end + +# Get the filename: +file = @__FILE__; + +# Extract the directory in which this file resides: +dir = dirname( file ); + +# Generate fixture data for decimal values: +x = range( 0.0, stop = 1.0, length = 2003 ); +gen( x, "data.json" ); + +# Generate fixture data for small positive values: +x = range( 1e-200, stop = 1e-208, length = 2003 ); +gen( x, "small_positive.json" ); diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/fixtures/julia/small_positive.json b/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/fixtures/julia/small_positive.json new file mode 100644 index 000000000000..abba201105fd --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/fixtures/julia/small_positive.json @@ -0,0 +1 @@ +{"expected":[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],"x":[1.0e-200,9.995004995054944e-201,9.99000999010989e-201,9.985014985164835e-201,9.98001998021978e-201,9.975024975274725e-201,9.970029970329671e-201,9.965034965384615e-201,9.96003996043956e-201,9.955044955494505e-201,9.950049950549451e-201,9.945054945604396e-201,9.94005994065934e-201,9.935064935714285e-201,9.930069930769231e-201,9.925074925824176e-201,9.92007992087912e-201,9.915084915934065e-201,9.910089910989011e-201,9.905094906043956e-201,9.9000999010989e-201,9.895104896153845e-201,9.890109891208791e-201,9.885114886263736e-201,9.880119881318681e-201,9.875124876373625e-201,9.870129871428572e-201,9.865134866483516e-201,9.860139861538461e-201,9.855144856593407e-201,9.850149851648352e-201,9.845154846703296e-201,9.840159841758241e-201,9.835164836813187e-201,9.830169831868132e-201,9.825174826923077e-201,9.820179821978021e-201,9.815184817032967e-201,9.810189812087912e-201,9.805194807142857e-201,9.800199802197801e-201,9.795204797252748e-201,9.790209792307692e-201,9.785214787362637e-201,9.780219782417582e-201,9.775224777472528e-201,9.770229772527472e-201,9.765234767582417e-201,9.760239762637362e-201,9.755244757692308e-201,9.750249752747253e-201,9.745254747802197e-201,9.740259742857142e-201,9.735264737912088e-201,9.730269732967033e-201,9.725274728021977e-201,9.720279723076924e-201,9.715284718131868e-201,9.710289713186813e-201,9.705294708241758e-201,9.700299703296704e-201,9.695304698351648e-201,9.690309693406593e-201,9.685314688461538e-201,9.680319683516484e-201,9.675324678571429e-201,9.670329673626373e-201,9.665334668681318e-201,9.660339663736264e-201,9.655344658791209e-201,9.650349653846153e-201,9.645354648901098e-201,9.640359643956044e-201,9.635364639010989e-201,9.630369634065934e-201,9.625374629120878e-201,9.620379624175824e-201,9.615384619230769e-201,9.610389614285714e-201,9.605394609340658e-201,9.600399604395605e-201,9.595404599450549e-201,9.590409594505494e-201,9.58541458956044e-201,9.580419584615385e-201,9.57542457967033e-201,9.570429574725274e-201,9.56543456978022e-201,9.560439564835165e-201,9.55544455989011e-201,9.550449554945054e-201,9.54545455e-201,9.540459545054945e-201,9.53546454010989e-201,9.530469535164834e-201,9.52547453021978e-201,9.520479525274725e-201,9.51548452032967e-201,9.510489515384615e-201,9.505494510439561e-201,9.500499505494505e-201,9.49550450054945e-201,9.490509495604395e-201,9.485514490659341e-201,9.480519485714286e-201,9.47552448076923e-201,9.470529475824175e-201,9.465534470879121e-201,9.460539465934066e-201,9.45554446098901e-201,9.450549456043957e-201,9.445554451098901e-201,9.440559446153846e-201,9.43556444120879e-201,9.430569436263737e-201,9.425574431318681e-201,9.420579426373626e-201,9.415584421428571e-201,9.410589416483517e-201,9.405594411538462e-201,9.400599406593406e-201,9.395604401648351e-201,9.390609396703297e-201,9.385614391758242e-201,9.380619386813186e-201,9.375624381868131e-201,9.370629376923077e-201,9.365634371978022e-201,9.360639367032967e-201,9.355644362087911e-201,9.350649357142857e-201,9.345654352197802e-201,9.340659347252747e-201,9.335664342307691e-201,9.330669337362638e-201,9.325674332417582e-201,9.320679327472527e-201,9.315684322527473e-201,9.310689317582418e-201,9.305694312637362e-201,9.300699307692307e-201,9.295704302747253e-201,9.290709297802198e-201,9.285714292857143e-201,9.280719287912087e-201,9.275724282967033e-201,9.270729278021978e-201,9.265734273076923e-201,9.260739268131867e-201,9.255744263186814e-201,9.250749258241758e-201,9.245754253296703e-201,9.240759248351648e-201,9.235764243406594e-201,9.230769238461538e-201,9.225774233516483e-201,9.220779228571428e-201,9.215784223626374e-201,9.210789218681319e-201,9.205794213736263e-201,9.20079920879121e-201,9.195804203846154e-201,9.190809198901099e-201,9.185814193956043e-201,9.18081918901099e-201,9.175824184065934e-201,9.170829179120879e-201,9.165834174175824e-201,9.16083916923077e-201,9.155844164285714e-201,9.150849159340659e-201,9.145854154395604e-201,9.14085914945055e-201,9.135864144505495e-201,9.130869139560439e-201,9.125874134615384e-201,9.12087912967033e-201,9.115884124725275e-201,9.11088911978022e-201,9.105894114835164e-201,9.10089910989011e-201,9.095904104945055e-201,9.0909091e-201,9.085914095054944e-201,9.08091909010989e-201,9.075924085164835e-201,9.07092908021978e-201,9.065934075274726e-201,9.06093907032967e-201,9.055944065384615e-201,9.05094906043956e-201,9.045954055494506e-201,9.04095905054945e-201,9.035964045604395e-201,9.03096904065934e-201,9.025974035714286e-201,9.020979030769231e-201,9.015984025824176e-201,9.01098902087912e-201,9.005994015934066e-201,9.000999010989011e-201,8.996004006043956e-201,8.9910090010989e-201,8.986013996153846e-201,8.981018991208791e-201,8.976023986263736e-201,8.97102898131868e-201,8.966033976373627e-201,8.961038971428571e-201,8.956043966483516e-201,8.95104896153846e-201,8.946053956593407e-201,8.941058951648352e-201,8.936063946703296e-201,8.931068941758242e-201,8.926073936813187e-201,8.921078931868132e-201,8.916083926923076e-201,8.911088921978022e-201,8.906093917032967e-201,8.901098912087912e-201,8.896103907142857e-201,8.891108902197803e-201,8.886113897252747e-201,8.881118892307692e-201,8.876123887362637e-201,8.871128882417583e-201,8.866133877472527e-201,8.861138872527472e-201,8.856143867582417e-201,8.851148862637363e-201,8.846153857692308e-201,8.841158852747252e-201,8.836163847802197e-201,8.831168842857143e-201,8.826173837912088e-201,8.821178832967032e-201,8.816183828021977e-201,8.811188823076923e-201,8.806193818131868e-201,8.801198813186813e-201,8.796203808241759e-201,8.791208803296703e-201,8.786213798351648e-201,8.781218793406593e-201,8.776223788461539e-201,8.771228783516484e-201,8.766233778571428e-201,8.761238773626373e-201,8.756243768681319e-201,8.751248763736264e-201,8.746253758791208e-201,8.741258753846153e-201,8.7362637489011e-201,8.731268743956044e-201,8.726273739010989e-201,8.721278734065933e-201,8.71628372912088e-201,8.711288724175824e-201,8.706293719230769e-201,8.701298714285713e-201,8.69630370934066e-201,8.691308704395604e-201,8.686313699450549e-201,8.681318694505494e-201,8.67632368956044e-201,8.671328684615384e-201,8.666333679670329e-201,8.661338674725275e-201,8.65634366978022e-201,8.651348664835165e-201,8.64635365989011e-201,8.641358654945055e-201,8.63636365e-201,8.631368645054945e-201,8.62637364010989e-201,8.621378635164836e-201,8.61638363021978e-201,8.611388625274725e-201,8.60639362032967e-201,8.601398615384616e-201,8.59640361043956e-201,8.591408605494505e-201,8.58641360054945e-201,8.581418595604396e-201,8.57642359065934e-201,8.571428585714285e-201,8.56643358076923e-201,8.561438575824176e-201,8.556443570879121e-201,8.551448565934065e-201,8.54645356098901e-201,8.541458556043956e-201,8.536463551098901e-201,8.531468546153846e-201,8.526473541208792e-201,8.521478536263736e-201,8.516483531318681e-201,8.511488526373626e-201,8.506493521428572e-201,8.501498516483517e-201,8.496503511538461e-201,8.491508506593406e-201,8.486513501648352e-201,8.481518496703297e-201,8.476523491758241e-201,8.471528486813186e-201,8.466533481868132e-201,8.461538476923077e-201,8.456543471978022e-201,8.451548467032966e-201,8.446553462087912e-201,8.441558457142857e-201,8.436563452197802e-201,8.431568447252746e-201,8.426573442307693e-201,8.421578437362637e-201,8.416583432417582e-201,8.411588427472527e-201,8.406593422527473e-201,8.401598417582417e-201,8.396603412637362e-201,8.391608407692308e-201,8.386613402747253e-201,8.381618397802198e-201,8.376623392857142e-201,8.371628387912088e-201,8.366633382967033e-201,8.361638378021978e-201,8.356643373076922e-201,8.351648368131869e-201,8.346653363186813e-201,8.341658358241758e-201,8.336663353296703e-201,8.331668348351649e-201,8.326673343406593e-201,8.321678338461538e-201,8.316683333516483e-201,8.311688328571429e-201,8.306693323626374e-201,8.301698318681318e-201,8.296703313736263e-201,8.291708308791209e-201,8.286713303846154e-201,8.281718298901098e-201,8.276723293956043e-201,8.271728289010989e-201,8.266733284065934e-201,8.261738279120879e-201,8.256743274175825e-201,8.25174826923077e-201,8.246753264285714e-201,8.241758259340659e-201,8.236763254395605e-201,8.23176824945055e-201,8.226773244505494e-201,8.221778239560439e-201,8.216783234615385e-201,8.21178822967033e-201,8.206793224725274e-201,8.201798219780219e-201,8.196803214835165e-201,8.19180820989011e-201,8.186813204945055e-201,8.181818199999999e-201,8.176823195054945e-201,8.17182819010989e-201,8.166833185164835e-201,8.16183818021978e-201,8.156843175274726e-201,8.15184817032967e-201,8.146853165384615e-201,8.14185816043956e-201,8.136863155494506e-201,8.13186815054945e-201,8.126873145604395e-201,8.121878140659341e-201,8.116883135714286e-201,8.11188813076923e-201,8.106893125824175e-201,8.101898120879121e-201,8.096903115934066e-201,8.09190811098901e-201,8.086913106043955e-201,8.081918101098902e-201,8.076923096153846e-201,8.071928091208791e-201,8.066933086263736e-201,8.061938081318682e-201,8.056943076373626e-201,8.051948071428571e-201,8.046953066483516e-201,8.041958061538462e-201,8.036963056593407e-201,8.031968051648351e-201,8.026973046703296e-201,8.021978041758242e-201,8.016983036813187e-201,8.011988031868131e-201,8.006993026923076e-201,8.001998021978022e-201,7.997003017032967e-201,7.992008012087912e-201,7.987013007142858e-201,7.982018002197802e-201,7.977022997252747e-201,7.972027992307692e-201,7.967032987362638e-201,7.962037982417583e-201,7.957042977472527e-201,7.952047972527472e-201,7.947052967582418e-201,7.942057962637363e-201,7.937062957692307e-201,7.932067952747252e-201,7.927072947802198e-201,7.922077942857143e-201,7.917082937912088e-201,7.912087932967032e-201,7.907092928021978e-201,7.902097923076923e-201,7.897102918131868e-201,7.892107913186812e-201,7.887112908241759e-201,7.882117903296703e-201,7.877122898351648e-201,7.872127893406593e-201,7.867132888461539e-201,7.862137883516483e-201,7.857142878571428e-201,7.852147873626374e-201,7.847152868681319e-201,7.842157863736264e-201,7.837162858791208e-201,7.832167853846154e-201,7.827172848901099e-201,7.822177843956044e-201,7.817182839010988e-201,7.812187834065934e-201,7.807192829120879e-201,7.802197824175824e-201,7.797202819230769e-201,7.792207814285715e-201,7.78721280934066e-201,7.782217804395604e-201,7.777222799450549e-201,7.772227794505495e-201,7.76723278956044e-201,7.762237784615384e-201,7.757242779670329e-201,7.752247774725275e-201,7.74725276978022e-201,7.742257764835164e-201,7.73726275989011e-201,7.732267754945055e-201,7.72727275e-201,7.722277745054945e-201,7.71728274010989e-201,7.712287735164835e-201,7.70729273021978e-201,7.702297725274725e-201,7.697302720329671e-201,7.692307715384615e-201,7.68731271043956e-201,7.682317705494505e-201,7.677322700549451e-201,7.672327695604396e-201,7.66733269065934e-201,7.662337685714285e-201,7.657342680769231e-201,7.652347675824176e-201,7.64735267087912e-201,7.642357665934065e-201,7.637362660989011e-201,7.632367656043956e-201,7.6273726510989e-201,7.622377646153845e-201,7.617382641208791e-201,7.612387636263736e-201,7.607392631318681e-201,7.602397626373627e-201,7.597402621428572e-201,7.592407616483516e-201,7.587412611538461e-201,7.582417606593407e-201,7.577422601648352e-201,7.572427596703296e-201,7.567432591758241e-201,7.562437586813187e-201,7.557442581868132e-201,7.552447576923077e-201,7.547452571978021e-201,7.542457567032967e-201,7.537462562087912e-201,7.532467557142857e-201,7.527472552197801e-201,7.522477547252748e-201,7.517482542307692e-201,7.512487537362637e-201,7.507492532417582e-201,7.502497527472528e-201,7.497502522527472e-201,7.492507517582417e-201,7.487512512637362e-201,7.482517507692308e-201,7.477522502747253e-201,7.472527497802197e-201,7.467532492857143e-201,7.462537487912088e-201,7.457542482967033e-201,7.452547478021977e-201,7.447552473076924e-201,7.442557468131868e-201,7.437562463186813e-201,7.432567458241758e-201,7.427572453296704e-201,7.422577448351648e-201,7.417582443406593e-201,7.412587438461538e-201,7.407592433516484e-201,7.402597428571429e-201,7.397602423626373e-201,7.392607418681318e-201,7.387612413736264e-201,7.382617408791209e-201,7.377622403846153e-201,7.372627398901098e-201,7.367632393956044e-201,7.362637389010989e-201,7.357642384065934e-201,7.352647379120878e-201,7.347652374175824e-201,7.342657369230769e-201,7.337662364285714e-201,7.33266735934066e-201,7.327672354395605e-201,7.32267734945055e-201,7.317682344505494e-201,7.31268733956044e-201,7.307692334615385e-201,7.30269732967033e-201,7.297702324725274e-201,7.29270731978022e-201,7.287712314835165e-201,7.28271730989011e-201,7.277722304945054e-201,7.2727273e-201,7.267732295054945e-201,7.26273729010989e-201,7.257742285164834e-201,7.25274728021978e-201,7.247752275274725e-201,7.24275727032967e-201,7.237762265384615e-201,7.232767260439561e-201,7.227772255494505e-201,7.22277725054945e-201,7.217782245604395e-201,7.212787240659341e-201,7.207792235714286e-201,7.20279723076923e-201,7.197802225824176e-201,7.192807220879121e-201,7.187812215934066e-201,7.18281721098901e-201,7.177822206043957e-201,7.172827201098901e-201,7.167832196153846e-201,7.16283719120879e-201,7.157842186263737e-201,7.152847181318681e-201,7.147852176373626e-201,7.142857171428571e-201,7.137862166483517e-201,7.132867161538462e-201,7.127872156593406e-201,7.122877151648351e-201,7.117882146703297e-201,7.112887141758242e-201,7.107892136813186e-201,7.102897131868131e-201,7.097902126923077e-201,7.092907121978022e-201,7.087912117032967e-201,7.082917112087911e-201,7.077922107142857e-201,7.072927102197802e-201,7.067932097252747e-201,7.062937092307693e-201,7.057942087362638e-201,7.052947082417582e-201,7.047952077472527e-201,7.042957072527473e-201,7.037962067582418e-201,7.032967062637362e-201,7.027972057692307e-201,7.022977052747253e-201,7.017982047802198e-201,7.012987042857143e-201,7.007992037912087e-201,7.002997032967033e-201,6.998002028021978e-201,6.993007023076923e-201,6.988012018131867e-201,6.983017013186814e-201,6.978022008241758e-201,6.973027003296703e-201,6.968031998351648e-201,6.963036993406594e-201,6.958041988461538e-201,6.953046983516483e-201,6.948051978571428e-201,6.943056973626374e-201,6.938061968681319e-201,6.933066963736263e-201,6.92807195879121e-201,6.923076953846154e-201,6.918081948901099e-201,6.913086943956043e-201,6.90809193901099e-201,6.903096934065934e-201,6.898101929120879e-201,6.893106924175824e-201,6.88811191923077e-201,6.883116914285714e-201,6.878121909340659e-201,6.873126904395604e-201,6.86813189945055e-201,6.863136894505495e-201,6.858141889560439e-201,6.853146884615384e-201,6.84815187967033e-201,6.843156874725275e-201,6.83816186978022e-201,6.833166864835164e-201,6.82817185989011e-201,6.823176854945055e-201,6.81818185e-201,6.813186845054944e-201,6.80819184010989e-201,6.803196835164835e-201,6.79820183021978e-201,6.793206825274726e-201,6.78821182032967e-201,6.783216815384615e-201,6.77822181043956e-201,6.773226805494506e-201,6.76823180054945e-201,6.763236795604395e-201,6.75824179065934e-201,6.753246785714286e-201,6.748251780769231e-201,6.743256775824176e-201,6.73826177087912e-201,6.733266765934066e-201,6.728271760989011e-201,6.723276756043956e-201,6.7182817510989e-201,6.713286746153847e-201,6.708291741208791e-201,6.703296736263736e-201,6.69830173131868e-201,6.693306726373627e-201,6.688311721428571e-201,6.683316716483516e-201,6.67832171153846e-201,6.673326706593407e-201,6.668331701648352e-201,6.663336696703296e-201,6.658341691758242e-201,6.653346686813187e-201,6.648351681868132e-201,6.643356676923076e-201,6.638361671978022e-201,6.633366667032967e-201,6.628371662087912e-201,6.623376657142857e-201,6.618381652197803e-201,6.613386647252747e-201,6.608391642307692e-201,6.603396637362637e-201,6.598401632417583e-201,6.593406627472527e-201,6.588411622527472e-201,6.583416617582417e-201,6.578421612637363e-201,6.573426607692308e-201,6.568431602747252e-201,6.563436597802197e-201,6.558441592857143e-201,6.553446587912088e-201,6.548451582967033e-201,6.543456578021977e-201,6.538461573076923e-201,6.533466568131868e-201,6.5284715631868134e-201,6.523476558241758e-201,6.5184815532967035e-201,6.513486548351648e-201,6.5084915434065936e-201,6.503496538461538e-201,6.498501533516484e-201,6.493506528571428e-201,6.488511523626374e-201,6.4835165186813184e-201,6.478521513736264e-201,6.4735265087912085e-201,6.468531503846154e-201,6.4635364989010986e-201,6.458541493956044e-201,6.453546489010989e-201,6.448551484065934e-201,6.443556479120879e-201,6.438561474175824e-201,6.433566469230769e-201,6.428571464285714e-201,6.423576459340659e-201,6.418581454395604e-201,6.413586449450549e-201,6.4085914445054944e-201,6.40359643956044e-201,6.3986014346153845e-201,6.39360642967033e-201,6.3886114247252746e-201,6.38361641978022e-201,6.378621414835165e-201,6.37362640989011e-201,6.368631404945055e-201,6.3636364e-201,6.358641395054945e-201,6.35364639010989e-201,6.348651385164835e-201,6.34365638021978e-201,6.338661375274725e-201,6.3336663703296704e-201,6.328671365384615e-201,6.3236763604395605e-201,6.318681355494505e-201,6.3136863505494505e-201,6.308691345604395e-201,6.3036963406593406e-201,6.298701335714285e-201,6.293706330769231e-201,6.2887113258241754e-201,6.283716320879121e-201,6.2787213159340655e-201,6.273726310989011e-201,6.268731306043956e-201,6.263736301098901e-201,6.258741296153846e-201,6.253746291208791e-201,6.2487512862637364e-201,6.243756281318681e-201,6.2387612763736265e-201,6.233766271428571e-201,6.2287712664835166e-201,6.223776261538461e-201,6.218781256593407e-201,6.2137862516483514e-201,6.208791246703297e-201,6.2037962417582415e-201,6.198801236813187e-201,6.1938062318681315e-201,6.188811226923077e-201,6.1838162219780216e-201,6.178821217032967e-201,6.173826212087912e-201,6.168831207142857e-201,6.163836202197802e-201,6.158841197252747e-201,6.153846192307692e-201,6.148851187362637e-201,6.143856182417582e-201,6.138861177472527e-201,6.133866172527473e-201,6.1288711675824174e-201,6.123876162637363e-201,6.1188811576923075e-201,6.113886152747253e-201,6.1088911478021976e-201,6.103896142857143e-201,6.098901137912088e-201,6.093906132967033e-201,6.088911128021978e-201,6.083916123076923e-201,6.078921118131868e-201,6.073926113186813e-201,6.068931108241758e-201,6.063936103296703e-201,6.058941098351648e-201,6.0539460934065934e-201,6.048951088461538e-201,6.0439560835164835e-201,6.038961078571428e-201,6.0339660736263736e-201,6.028971068681318e-201,6.023976063736264e-201,6.018981058791208e-201,6.013986053846154e-201,6.0089910489010984e-201,6.003996043956044e-201,5.999001039010989e-201,5.994006034065934e-201,5.989011029120879e-201,5.984016024175824e-201,5.9790210192307694e-201,5.974026014285714e-201,5.9690310093406595e-201,5.964036004395604e-201,5.9590409994505496e-201,5.954045994505494e-201,5.94905098956044e-201,5.944055984615384e-201,5.93906097967033e-201,5.9340659747252744e-201,5.92907096978022e-201,5.9240759648351645e-201,5.91908095989011e-201,5.9140859549450546e-201,5.90909095e-201,5.904095945054945e-201,5.89910094010989e-201,5.894105935164835e-201,5.88911093021978e-201,5.884115925274725e-201,5.87912092032967e-201,5.874125915384616e-201,5.86913091043956e-201,5.864135905494506e-201,5.8591409005494504e-201,5.854145895604396e-201,5.8491508906593405e-201,5.844155885714286e-201,5.8391608807692306e-201,5.834165875824176e-201,5.829170870879121e-201,5.824175865934066e-201,5.819180860989011e-201,5.814185856043956e-201,5.809190851098901e-201,5.804195846153846e-201,5.799200841208791e-201,5.794205836263736e-201,5.789210831318681e-201,5.7842158263736264e-201,5.779220821428571e-201,5.7742258164835165e-201,5.769230811538461e-201,5.7642358065934066e-201,5.759240801648351e-201,5.7542457967032966e-201,5.749250791758241e-201,5.744255786813187e-201,5.739260781868132e-201,5.734265776923077e-201,5.729270771978022e-201,5.724275767032967e-201,5.719280762087912e-201,5.714285757142857e-201,5.7092907521978024e-201,5.704295747252747e-201,5.6993007423076925e-201,5.694305737362637e-201,5.6893107324175825e-201,5.684315727472527e-201,5.6793207225274726e-201,5.674325717582417e-201,5.669330712637363e-201,5.6643357076923074e-201,5.659340702747253e-201,5.6543456978021975e-201,5.649350692857143e-201,5.6443556879120875e-201,5.639360682967033e-201,5.6343656780219776e-201,5.629370673076923e-201,5.624375668131868e-201,5.619380663186813e-201,5.614385658241758e-201,5.609390653296703e-201,5.6043956483516486e-201,5.599400643406593e-201,5.594405638461539e-201,5.5894106335164834e-201,5.584415628571429e-201,5.5794206236263734e-201,5.574425618681319e-201,5.5694306137362635e-201,5.564435608791209e-201,5.5594406038461536e-201,5.554445598901099e-201,5.549450593956044e-201,5.544455589010989e-201,5.539460584065934e-201,5.534465579120879e-201,5.529470574175824e-201,5.524475569230769e-201,5.519480564285714e-201,5.514485559340659e-201,5.509490554395604e-201,5.5044955494505494e-201,5.499500544505494e-201,5.4945055395604395e-201,5.489510534615384e-201,5.4845155296703296e-201,5.479520524725274e-201,5.47452551978022e-201,5.469530514835165e-201,5.46453550989011e-201,5.459540504945055e-201,5.4545455e-201,5.449550495054945e-201,5.44455549010989e-201,5.439560485164835e-201,5.43456548021978e-201,5.4295704752747254e-201,5.42457547032967e-201,5.4195804653846155e-201,5.41458546043956e-201,5.4095904554945056e-201,5.40459545054945e-201,5.399600445604396e-201,5.39460544065934e-201,5.389610435714286e-201,5.3846154307692304e-201,5.379620425824176e-201,5.3746254208791205e-201,5.369630415934066e-201,5.3646354109890106e-201,5.359640406043956e-201,5.354645401098901e-201,5.349650396153846e-201,5.344655391208791e-201,5.339660386263736e-201,5.3346653813186816e-201,5.329670376373626e-201,5.324675371428572e-201,5.319680366483516e-201,5.314685361538462e-201,5.3096903565934064e-201,5.304695351648352e-201,5.2997003467032965e-201,5.294705341758242e-201,5.2897103368131866e-201,5.284715331868132e-201,5.279720326923077e-201,5.274725321978022e-201,5.269730317032967e-201,5.264735312087912e-201,5.259740307142857e-201,5.254745302197802e-201,5.249750297252747e-201,5.244755292307692e-201,5.239760287362637e-201,5.2347652824175824e-201,5.229770277472527e-201,5.2247752725274725e-201,5.219780267582417e-201,5.2147852626373626e-201,5.209790257692308e-201,5.204795252747253e-201,5.199800247802198e-201,5.194805242857143e-201,5.189810237912088e-201,5.184815232967033e-201,5.179820228021978e-201,5.174825223076923e-201,5.169830218131868e-201,5.164835213186813e-201,5.1598402082417584e-201,5.154845203296703e-201,5.1498501983516485e-201,5.144855193406593e-201,5.1398601884615385e-201,5.134865183516483e-201,5.1298701785714286e-201,5.124875173626373e-201,5.119880168681319e-201,5.1148851637362634e-201,5.109890158791209e-201,5.1048951538461535e-201,5.099900148901099e-201,5.0949051439560436e-201,5.089910139010989e-201,5.0849151340659336e-201,5.079920129120879e-201,5.0749251241758244e-201,5.069930119230769e-201,5.0649351142857145e-201,5.059940109340659e-201,5.0549451043956046e-201,5.049950099450549e-201,5.044955094505495e-201,5.0399600895604394e-201,5.034965084615385e-201,5.0299700796703295e-201,5.024975074725275e-201,5.0199800697802195e-201,5.014985064835165e-201,5.0099900598901096e-201,5.004995054945055e-201,5.00000005e-201,4.995005045054945e-201,4.99001004010989e-201,4.985015035164835e-201,4.98002003021978e-201,4.975025025274725e-201,4.97003002032967e-201,4.965035015384615e-201,4.96004001043956e-201,4.9550450054945054e-201,4.95005000054945e-201,4.9450549956043955e-201,4.940059990659341e-201,4.9350649857142856e-201,4.930069980769231e-201,4.925074975824176e-201,4.920079970879121e-201,4.915084965934066e-201,4.910089960989011e-201,4.905094956043956e-201,4.900099951098901e-201,4.895104946153846e-201,4.890109941208791e-201,4.885114936263736e-201,4.8801199313186814e-201,4.875124926373626e-201,4.8701299214285715e-201,4.865134916483516e-201,4.8601399115384616e-201,4.855144906593406e-201,4.850149901648352e-201,4.845154896703296e-201,4.840159891758242e-201,4.8351648868131864e-201,4.830169881868132e-201,4.8251748769230765e-201,4.820179871978022e-201,4.8151848670329666e-201,4.810189862087912e-201,4.8051948571428574e-201,4.800199852197802e-201,4.7952048472527475e-201,4.790209842307692e-201,4.7852148373626376e-201,4.780219832417582e-201,4.775224827472528e-201,4.770229822527472e-201,4.765234817582418e-201,4.7602398126373624e-201,4.755244807692308e-201,4.7502498027472525e-201,4.745254797802198e-201,4.7402597928571426e-201,4.735264787912088e-201,4.730269782967033e-201,4.725274778021978e-201,4.720279773076923e-201,4.715284768131868e-201,4.710289763186813e-201,4.705294758241758e-201,4.700299753296703e-201,4.695304748351648e-201,4.690309743406593e-201,4.6853147384615384e-201,4.680319733516483e-201,4.6753247285714285e-201,4.670329723626374e-201,4.6653347186813186e-201,4.660339713736264e-201,4.655344708791209e-201,4.650349703846154e-201,4.645354698901099e-201,4.640359693956044e-201,4.635364689010989e-201,4.630369684065934e-201,4.625374679120879e-201,4.620379674175824e-201,4.615384669230769e-201,4.6103896642857144e-201,4.605394659340659e-201,4.6003996543956045e-201,4.595404649450549e-201,4.5904096445054945e-201,4.585414639560439e-201,4.5804196346153846e-201,4.575424629670329e-201,4.570429624725275e-201,4.5654346197802194e-201,4.560439614835165e-201,4.5554446098901095e-201,4.550449604945055e-201,4.5454545999999996e-201,4.540459595054945e-201,4.5354645901098904e-201,4.530469585164835e-201,4.5254745802197804e-201,4.520479575274725e-201,4.5154845703296705e-201,4.510489565384615e-201,4.5054945604395606e-201,4.500499555494505e-201,4.495504550549451e-201,4.4905095456043954e-201,4.485514540659341e-201,4.4805195357142855e-201,4.475524530769231e-201,4.4705295258241755e-201,4.465534520879121e-201,4.4605395159340656e-201,4.455544510989011e-201,4.450549506043956e-201,4.445554501098901e-201,4.440559496153846e-201,4.435564491208791e-201,4.430569486263736e-201,4.425574481318681e-201,4.420579476373626e-201,4.415584471428571e-201,4.410589466483517e-201,4.4055944615384614e-201,4.400599456593407e-201,4.3956044516483515e-201,4.390609446703297e-201,4.3856144417582416e-201,4.380619436813187e-201,4.375624431868132e-201,4.370629426923077e-201,4.365634421978022e-201,4.360639417032967e-201,4.355644412087912e-201,4.350649407142857e-201,4.345654402197802e-201,4.340659397252747e-201,4.335664392307692e-201,4.3306693873626374e-201,4.325674382417582e-201,4.3206793774725275e-201,4.315684372527472e-201,4.3106893675824176e-201,4.305694362637362e-201,4.300699357692308e-201,4.295704352747252e-201,4.290709347802198e-201,4.2857143428571424e-201,4.280719337912088e-201,4.275724332967033e-201,4.270729328021978e-201,4.265734323076923e-201,4.260739318131868e-201,4.2557443131868134e-201,4.250749308241758e-201,4.2457543032967035e-201,4.240759298351648e-201,4.2357642934065936e-201,4.230769288461538e-201,4.225774283516484e-201,4.220779278571428e-201,4.215784273626374e-201,4.2107892686813184e-201,4.205794263736264e-201,4.2007992587912085e-201,4.195804253846154e-201,4.1908092489010986e-201,4.185814243956044e-201,4.180819239010989e-201,4.175824234065934e-201,4.170829229120879e-201,4.165834224175824e-201,4.160839219230769e-201,4.155844214285714e-201,4.150849209340659e-201,4.145854204395604e-201,4.14085919945055e-201,4.1358641945054944e-201,4.13086918956044e-201,4.1258741846153845e-201,4.12087917967033e-201,4.1158841747252746e-201,4.11088916978022e-201,4.105894164835165e-201,4.10089915989011e-201,4.095904154945055e-201,4.09090915e-201,4.085914145054945e-201,4.08091914010989e-201,4.075924135164835e-201,4.07092913021978e-201,4.065934125274725e-201,4.0609391203296704e-201,4.055944115384615e-201,4.0509491104395605e-201,4.045954105494505e-201,4.0409591005494506e-201,4.035964095604395e-201,4.030969090659341e-201,4.025974085714285e-201,4.020979080769231e-201,4.0159840758241754e-201,4.010989070879121e-201,4.005994065934066e-201,4.000999060989011e-201,3.996004056043956e-201,3.991009051098901e-201,3.9860140461538464e-201,3.981019041208791e-201,3.9760240362637365e-201,3.971029031318681e-201,3.9660340263736265e-201,3.961039021428571e-201,3.9560440164835166e-201,3.951049011538461e-201,3.946054006593407e-201,3.9410590016483514e-201,3.936063996703297e-201,3.9310689917582415e-201,3.926073986813187e-201,3.9210789818681315e-201,3.916083976923077e-201,3.9110889719780216e-201,3.906093967032967e-201,3.901098962087912e-201,3.896103957142857e-201,3.891108952197802e-201,3.886113947252747e-201,3.881118942307692e-201,3.876123937362637e-201,3.871128932417583e-201,3.8661339274725274e-201,3.861138922527473e-201,3.8561439175824175e-201,3.851148912637363e-201,3.8461539076923075e-201,3.841158902747253e-201,3.8361638978021976e-201,3.831168892857143e-201,3.826173887912088e-201,3.821178882967033e-201,3.816183878021978e-201,3.811188873076923e-201,3.806193868131868e-201,3.801198863186813e-201,3.796203858241758e-201,3.791208853296703e-201,3.786213848351648e-201,3.7812188434065934e-201,3.776223838461538e-201,3.7712288335164835e-201,3.766233828571428e-201,3.7612388236263736e-201,3.756243818681318e-201,3.751248813736264e-201,3.746253808791209e-201,3.741258803846154e-201,3.736263798901099e-201,3.731268793956044e-201,3.726273789010989e-201,3.721278784065934e-201,3.716283779120879e-201,3.711288774175824e-201,3.7062937692307694e-201,3.701298764285714e-201,3.6963037593406595e-201,3.691308754395604e-201,3.6863137494505496e-201,3.681318744505494e-201,3.67632373956044e-201,3.671328734615384e-201,3.66633372967033e-201,3.6613387247252744e-201,3.65634371978022e-201,3.6513487148351645e-201,3.64635370989011e-201,3.6413587049450546e-201,3.6363637e-201,3.631368695054945e-201,3.62637369010989e-201,3.621378685164835e-201,3.61638368021978e-201,3.6113886752747256e-201,3.60639367032967e-201,3.601398665384616e-201,3.59640366043956e-201,3.591408655494506e-201,3.5864136505494504e-201,3.581418645604396e-201,3.5764236406593405e-201,3.571428635714286e-201,3.5664336307692306e-201,3.561438625824176e-201,3.556443620879121e-201,3.551448615934066e-201,3.546453610989011e-201,3.541458606043956e-201,3.536463601098901e-201,3.531468596153846e-201,3.526473591208791e-201,3.521478586263736e-201,3.516483581318681e-201,3.5114885763736264e-201,3.506493571428571e-201,3.5014985664835165e-201,3.496503561538461e-201,3.4915085565934066e-201,3.486513551648351e-201,3.481518546703297e-201,3.476523541758242e-201,3.471528536813187e-201,3.466533531868132e-201,3.461538526923077e-201,3.456543521978022e-201,3.451548517032967e-201,3.446553512087912e-201,3.441558507142857e-201,3.4365635021978024e-201,3.431568497252747e-201,3.4265734923076925e-201,3.421578487362637e-201,3.4165834824175825e-201,3.411588477472527e-201,3.4065934725274726e-201,3.401598467582417e-201,3.396603462637363e-201,3.3916084576923074e-201,3.386613452747253e-201,3.3816184478021975e-201,3.376623442857143e-201,3.3716284379120876e-201,3.366633432967033e-201,3.361638428021978e-201,3.356643423076923e-201,3.351648418131868e-201,3.346653413186813e-201,3.3416584082417585e-201,3.336663403296703e-201,3.3316683983516486e-201,3.326673393406593e-201,3.321678388461539e-201,3.3166833835164834e-201,3.311688378571429e-201,3.3066933736263735e-201,3.301698368681319e-201,3.2967033637362635e-201,3.291708358791209e-201,3.2867133538461536e-201,3.281718348901099e-201,3.276723343956044e-201,3.271728339010989e-201,3.266733334065934e-201,3.2617383291208792e-201,3.2567433241758242e-201,3.2517483192307693e-201,3.2467533142857143e-201,3.2417583093406594e-201,3.2367633043956044e-201,3.2317682994505494e-201,3.2267732945054945e-201,3.2217782895604395e-201,3.2167832846153846e-201,3.2117882796703296e-201,3.2067932747252746e-201,3.2017982697802197e-201,3.1968032648351647e-201,3.1918082598901098e-201,3.1868132549450548e-201,3.18181825e-201,3.176823245054945e-201,3.17182824010989e-201,3.166833235164835e-201,3.16183823021978e-201,3.156843225274725e-201,3.15184822032967e-201,3.1468532153846155e-201,3.1418582104395605e-201,3.1368632054945056e-201,3.1318682005494506e-201,3.1268731956043957e-201,3.1218781906593407e-201,3.1168831857142858e-201,3.1118881807692308e-201,3.106893175824176e-201,3.101898170879121e-201,3.096903165934066e-201,3.091908160989011e-201,3.086913156043956e-201,3.081918151098901e-201,3.076923146153846e-201,3.071928141208791e-201,3.066933136263736e-201,3.0619381313186812e-201,3.0569431263736263e-201,3.0519481214285713e-201,3.0469531164835163e-201,3.0419581115384614e-201,3.0369631065934064e-201,3.0319681016483515e-201,3.0269730967032965e-201,3.0219780917582415e-201,3.0169830868131866e-201,3.011988081868132e-201,3.006993076923077e-201,3.001998071978022e-201,2.997003067032967e-201,2.992008062087912e-201,2.9870130571428572e-201,2.9820180521978022e-201,2.9770230472527473e-201,2.9720280423076923e-201,2.9670330373626374e-201,2.9620380324175824e-201,2.9570430274725274e-201,2.9520480225274725e-201,2.9470530175824175e-201,2.9420580126373626e-201,2.9370630076923076e-201,2.9320680027472527e-201,2.9270729978021977e-201,2.9220779928571427e-201,2.9170829879120878e-201,2.9120879829670328e-201,2.907092978021978e-201,2.902097973076923e-201,2.897102968131868e-201,2.892107963186813e-201,2.887112958241758e-201,2.882117953296703e-201,2.8771229483516485e-201,2.8721279434065935e-201,2.8671329384615386e-201,2.8621379335164836e-201,2.8571429285714286e-201,2.8521479236263737e-201,2.8471529186813187e-201,2.8421579137362638e-201,2.8371629087912088e-201,2.832167903846154e-201,2.827172898901099e-201,2.822177893956044e-201,2.817182889010989e-201,2.812187884065934e-201,2.807192879120879e-201,2.802197874175824e-201,2.797202869230769e-201,2.792207864285714e-201,2.7872128593406592e-201,2.7822178543956043e-201,2.7772228494505493e-201,2.7722278445054943e-201,2.7672328395604394e-201,2.7622378346153844e-201,2.7572428296703295e-201,2.7522478247252745e-201,2.74725281978022e-201,2.742257814835165e-201,2.73726280989011e-201,2.732267804945055e-201,2.7272728e-201,2.722277795054945e-201,2.71728279010989e-201,2.7122877851648352e-201,2.7072927802197802e-201,2.7022977752747253e-201,2.6973027703296703e-201,2.6923077653846154e-201,2.6873127604395604e-201,2.6823177554945054e-201,2.6773227505494505e-201,2.6723277456043955e-201,2.6673327406593406e-201,2.6623377357142856e-201,2.6573427307692307e-201,2.6523477258241757e-201,2.6473527208791207e-201,2.6423577159340658e-201,2.637362710989011e-201,2.632367706043956e-201,2.627372701098901e-201,2.622377696153846e-201,2.617382691208791e-201,2.6123876862637364e-201,2.6073926813186814e-201,2.6023976763736265e-201,2.5974026714285715e-201,2.5924076664835166e-201,2.5874126615384616e-201,2.5824176565934066e-201,2.5774226516483517e-201,2.5724276467032967e-201,2.5674326417582418e-201,2.5624376368131868e-201,2.557442631868132e-201,2.552447626923077e-201,2.547452621978022e-201,2.542457617032967e-201,2.537462612087912e-201,2.532467607142857e-201,2.527472602197802e-201,2.522477597252747e-201,2.517482592307692e-201,2.5124875873626372e-201,2.5074925824175823e-201,2.5024975774725273e-201,2.4975025725274723e-201,2.4925075675824174e-201,2.4875125626373624e-201,2.4825175576923075e-201,2.477522552747253e-201,2.472527547802198e-201,2.467532542857143e-201,2.462537537912088e-201,2.457542532967033e-201,2.452547528021978e-201,2.447552523076923e-201,2.442557518131868e-201,2.4375625131868132e-201,2.4325675082417582e-201,2.4275725032967033e-201,2.4225774983516483e-201,2.4175824934065934e-201,2.4125874884615384e-201,2.4075924835164835e-201,2.4025974785714285e-201,2.3976024736263735e-201,2.3926074686813186e-201,2.3876124637362636e-201,2.3826174587912087e-201,2.3776224538461537e-201,2.3726274489010987e-201,2.3676324439560438e-201,2.362637439010989e-201,2.357642434065934e-201,2.352647429120879e-201,2.3476524241758243e-201,2.3426574192307694e-201,2.3376624142857144e-201,2.3326674093406594e-201,2.3276724043956045e-201,2.3226773994505495e-201,2.3176823945054946e-201,2.3126873895604396e-201,2.3076923846153846e-201,2.3026973796703297e-201,2.2977023747252747e-201,2.2927073697802198e-201,2.2877123648351648e-201,2.28271735989011e-201,2.277722354945055e-201,2.27272735e-201,2.267732345054945e-201,2.26273734010989e-201,2.257742335164835e-201,2.25274733021978e-201,2.247752325274725e-201,2.24275732032967e-201,2.2377623153846152e-201,2.2327673104395603e-201,2.2277723054945053e-201,2.2227773005494503e-201,2.2177822956043954e-201,2.2127872906593408e-201,2.207792285714286e-201,2.202797280769231e-201,2.197802275824176e-201,2.192807270879121e-201,2.187812265934066e-201,2.182817260989011e-201,2.177822256043956e-201,2.172827251098901e-201,2.167832246153846e-201,2.1628372412087912e-201,2.1578422362637362e-201,2.1528472313186813e-201,2.1478522263736263e-201,2.1428572214285714e-201,2.1378622164835164e-201,2.1328672115384615e-201,2.1278722065934065e-201,2.1228772016483515e-201,2.1178821967032966e-201,2.1128871917582416e-201,2.1078921868131867e-201,2.1028971818681317e-201,2.0979021769230767e-201,2.0929071719780218e-201,2.087912167032967e-201,2.0829171620879122e-201,2.0779221571428573e-201,2.0729271521978023e-201,2.0679321472527474e-201,2.0629371423076924e-201,2.0579421373626374e-201,2.0529471324175825e-201,2.0479521274725275e-201,2.0429571225274726e-201,2.0379621175824176e-201,2.0329671126373626e-201,2.0279721076923077e-201,2.0229771027472527e-201,2.0179820978021978e-201,2.0129870928571428e-201,2.007992087912088e-201,2.002997082967033e-201,1.998002078021978e-201,1.993007073076923e-201,1.988012068131868e-201,1.983017063186813e-201,1.978022058241758e-201,1.973027053296703e-201,1.9680320483516482e-201,1.9630370434065932e-201,1.9580420384615383e-201,1.9530470335164833e-201,1.9480520285714287e-201,1.9430570236263738e-201,1.9380620186813188e-201,1.933067013736264e-201,1.928072008791209e-201,1.923077003846154e-201,1.918081998901099e-201,1.913086993956044e-201,1.908091989010989e-201,1.903096984065934e-201,1.898101979120879e-201,1.893106974175824e-201,1.8881119692307692e-201,1.8831169642857143e-201,1.8781219593406593e-201,1.8731269543956043e-201,1.8681319494505494e-201,1.8631369445054944e-201,1.8581419395604395e-201,1.8531469346153845e-201,1.8481519296703295e-201,1.8431569247252746e-201,1.8381619197802196e-201,1.8331669148351647e-201,1.8281719098901097e-201,1.8231769049450547e-201,1.8181818999999998e-201,1.8131868950549452e-201,1.8081918901098902e-201,1.8031968851648353e-201,1.7982018802197803e-201,1.7932068752747254e-201,1.7882118703296704e-201,1.7832168653846154e-201,1.7782218604395605e-201,1.7732268554945055e-201,1.7682318505494506e-201,1.7632368456043956e-201,1.7582418406593406e-201,1.7532468357142857e-201,1.7482518307692307e-201,1.7432568258241758e-201,1.7382618208791208e-201,1.733266815934066e-201,1.728271810989011e-201,1.723276806043956e-201,1.718281801098901e-201,1.713286796153846e-201,1.708291791208791e-201,1.703296786263736e-201,1.698301781318681e-201,1.6933067763736262e-201,1.6883117714285712e-201,1.6833167664835166e-201,1.6783217615384617e-201,1.6733267565934067e-201,1.6683317516483518e-201,1.6633367467032968e-201,1.658341741758242e-201,1.653346736813187e-201,1.648351731868132e-201,1.643356726923077e-201,1.638361721978022e-201,1.633366717032967e-201,1.628371712087912e-201,1.6233767071428571e-201,1.6183817021978022e-201,1.6133866972527472e-201,1.6083916923076923e-201,1.6033966873626373e-201,1.5984016824175823e-201,1.5934066774725274e-201,1.5884116725274724e-201,1.5834166675824176e-201,1.5784216626373627e-201,1.5734266576923077e-201,1.5684316527472528e-201,1.5634366478021978e-201,1.5584416428571429e-201,1.5534466379120879e-201,1.548451632967033e-201,1.543456628021978e-201,1.538461623076923e-201,1.533466618131868e-201,1.5284716131868131e-201,1.5234766082417581e-201,1.5184816032967032e-201,1.5134865983516484e-201,1.5084915934065934e-201,1.5034965884615385e-201,1.4985015835164835e-201,1.4935065785714286e-201,1.4885115736263736e-201,1.4835165686813187e-201,1.4785215637362637e-201,1.4735265587912087e-201,1.4685315538461538e-201,1.4635365489010988e-201,1.4585415439560439e-201,1.4535465390109889e-201,1.4485515340659341e-201,1.4435565291208792e-201,1.4385615241758242e-201,1.4335665192307692e-201,1.4285715142857143e-201,1.4235765093406593e-201,1.4185815043956044e-201,1.4135864994505494e-201,1.4085914945054945e-201,1.4035964895604395e-201,1.3986014846153845e-201,1.3936064796703296e-201,1.3886114747252746e-201,1.3836164697802198e-201,1.3786214648351649e-201,1.37362645989011e-201,1.368631454945055e-201,1.36363645e-201,1.358641445054945e-201,1.3536464401098901e-201,1.3486514351648351e-201,1.3436564302197802e-201,1.3386614252747252e-201,1.3336664203296703e-201,1.3286714153846153e-201,1.3236764104395603e-201,1.3186814054945054e-201,1.3136864005494506e-201,1.3086913956043956e-201,1.3036963906593407e-201,1.2987013857142857e-201,1.2937063807692308e-201,1.2887113758241758e-201,1.2837163708791209e-201,1.2787213659340659e-201,1.273726360989011e-201,1.268731356043956e-201,1.263736351098901e-201,1.258741346153846e-201,1.2537463412087911e-201,1.2487513362637363e-201,1.2437563313186814e-201,1.2387613263736264e-201,1.2337663214285714e-201,1.2287713164835165e-201,1.2237763115384615e-201,1.2187813065934066e-201,1.2137863016483516e-201,1.2087912967032967e-201,1.2037962917582417e-201,1.1988012868131867e-201,1.1938062818681318e-201,1.1888112769230768e-201,1.183816271978022e-201,1.178821267032967e-201,1.1738262620879121e-201,1.1688312571428572e-201,1.1638362521978022e-201,1.1588412472527473e-201,1.1538462423076923e-201,1.1488512373626373e-201,1.1438562324175824e-201,1.1388612274725274e-201,1.1338662225274725e-201,1.1288712175824175e-201,1.1238762126373625e-201,1.1188812076923076e-201,1.1138862027472528e-201,1.1088911978021978e-201,1.1038961928571429e-201,1.098901187912088e-201,1.093906182967033e-201,1.088911178021978e-201,1.083916173076923e-201,1.0789211681318681e-201,1.0739261631868131e-201,1.0689311582417582e-201,1.0639361532967032e-201,1.0589411483516483e-201,1.0539461434065933e-201,1.0489511384615385e-201,1.0439561335164836e-201,1.0389611285714286e-201,1.0339661236263736e-201,1.0289711186813187e-201,1.0239761137362637e-201,1.0189811087912088e-201,1.0139861038461538e-201,1.0089910989010989e-201,1.0039960939560439e-201,9.99001089010989e-202,9.94006084065934e-202,9.89011079120879e-202,9.840160741758242e-202,9.790210692307693e-202,9.740260642857143e-202,9.690310593406594e-202,9.640360543956044e-202,9.590410494505495e-202,9.540460445054945e-202,9.490510395604395e-202,9.440560346153846e-202,9.390610296703296e-202,9.340660247252747e-202,9.290710197802197e-202,9.240760148351647e-202,9.190810098901098e-202,9.14086004945055e-202,9.09091e-202,9.04095995054945e-202,8.991009901098901e-202,8.941059851648352e-202,8.891109802197802e-202,8.841159752747253e-202,8.791209703296703e-202,8.741259653846153e-202,8.691309604395604e-202,8.641359554945054e-202,8.591409505494505e-202,8.541459456043955e-202,8.491509406593407e-202,8.441559357142858e-202,8.391609307692308e-202,8.341659258241759e-202,8.291709208791209e-202,8.24175915934066e-202,8.19180910989011e-202,8.14185906043956e-202,8.091909010989011e-202,8.041958961538461e-202,7.992008912087912e-202,7.942058862637363e-202,7.892108813186813e-202,7.842158763736264e-202,7.792208714285714e-202,7.742258664835164e-202,7.692308615384615e-202,7.642358565934066e-202,7.5924085164835165e-202,7.542458467032967e-202,7.492508417582417e-202,7.442558368131868e-202,7.392608318681318e-202,7.3426582692307695e-202,7.29270821978022e-202,7.24275817032967e-202,7.192808120879121e-202,7.142858071428571e-202,7.092908021978022e-202,7.042957972527472e-202,6.993007923076923e-202,6.943057873626374e-202,6.893107824175824e-202,6.843157774725275e-202,6.793207725274725e-202,6.743257675824175e-202,6.693307626373626e-202,6.643357576923077e-202,6.5934075274725275e-202,6.543457478021978e-202,6.493507428571428e-202,6.443557379120879e-202,6.393607329670329e-202,6.3436572802197805e-202,6.293707230769231e-202,6.243757181318681e-202,6.193807131868132e-202,6.143857082417582e-202,6.093907032967033e-202,6.043956983516483e-202,5.994006934065934e-202,5.944056884615385e-202,5.894106835164835e-202,5.844156785714286e-202,5.794206736263736e-202,5.744256686813186e-202,5.694306637362638e-202,5.644356587912088e-202,5.5944065384615385e-202,5.544456489010989e-202,5.494506439560439e-202,5.44455639010989e-202,5.39460634065934e-202,5.3446562912087915e-202,5.294706241758242e-202,5.244756192307692e-202,5.194806142857143e-202,5.144856093406593e-202,5.094906043956044e-202,5.044955994505494e-202,4.995005945054945e-202,4.945055895604396e-202,4.895105846153846e-202,4.845155796703297e-202,4.795205747252747e-202,4.745255697802197e-202,4.695305648351649e-202,4.645355598901099e-202,4.5954055494505495e-202,4.5454555e-202,4.49550545054945e-202,4.445555401098901e-202,4.395605351648351e-202,4.3456553021978025e-202,4.295705252747253e-202,4.245755203296703e-202,4.195805153846154e-202,4.145855104395604e-202,4.095905054945055e-202,4.0459550054945055e-202,3.996004956043956e-202,3.9460549065934067e-202,3.896104857142857e-202,3.8461548076923076e-202,3.796204758241758e-202,3.746254708791209e-202,3.6963046593406593e-202,3.6463546098901097e-202,3.5964045604395605e-202,3.546454510989011e-202,3.4965044615384614e-202,3.4465544120879122e-202,3.3966043626373627e-202,3.346654313186813e-202,3.2967042637362635e-202,3.2467542142857144e-202,3.1968041648351648e-202,3.146854115384615e-202,3.096904065934066e-202,3.0469540164835165e-202,2.997003967032967e-202,2.9470539175824177e-202,2.897103868131868e-202,2.8471538186813186e-202,2.797203769230769e-202,2.74725371978022e-202,2.6973036703296703e-202,2.6473536208791207e-202,2.5974035714285716e-202,2.547453521978022e-202,2.4975034725274724e-202,2.4475534230769232e-202,2.3976033736263737e-202,2.347653324175824e-202,2.2977032747252745e-202,2.2477532252747254e-202,2.1978031758241758e-202,2.147853126373626e-202,2.097903076923077e-202,2.0479530274725275e-202,1.9980029780219779e-202,1.9480529285714285e-202,1.8981028791208792e-202,1.8481528296703296e-202,1.7982027802197802e-202,1.7482527307692306e-202,1.6983026813186813e-202,1.648352631868132e-202,1.5984025824175823e-202,1.548452532967033e-202,1.4985024835164834e-202,1.448552434065934e-202,1.3986023846153847e-202,1.348652335164835e-202,1.2987022857142857e-202,1.2487522362637361e-202,1.1988021868131868e-202,1.1488521373626374e-202,1.0989020879120878e-202,1.0489520384615385e-202,9.99001989010989e-203,9.490519395604395e-203,8.9910189010989e-203,8.491518406593407e-203,7.992017912087912e-203,7.492517417582418e-203,6.993016923076923e-203,6.493516428571428e-203,5.994015934065934e-203,5.49451543956044e-203,4.995014945054945e-203,4.4955144505494503e-203,3.996013956043956e-203,3.4965134615384614e-203,2.997012967032967e-203,2.4975124725274725e-203,1.998011978021978e-203,1.4985114835164834e-203,9.990109890109889e-204,4.995104945054945e-204,1.0e-208]} diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/test.js b/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/test.js new file mode 100644 index 000000000000..2f6f1afd94ff --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/test.js @@ -0,0 +1,117 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var tape = require( 'tape' ); +var isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var randu = require( '@stdlib/random/base/randu' ); +var absf = require( '@stdlib/math/base/special/absf' ); +var EPS = require( '@stdlib/constants/float32/eps' ); +var ahaversinf = require( './../lib' ); + + +// FIXTURES // + +var data = require( './fixtures/julia/data.json' ); +var smallPositive = require( './fixtures/julia/small_positive.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof ahaversinf, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function computes the inverse half-value versed sine', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = data.x; + expected = data.expected; + + for ( i = 0; i < x.length; i++ ) { + y = ahaversinf( x[i] ); + if ( y === expected[ i ] ) { + t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] ); + } else { + delta = absf( y - expected[i] ); + tol = 3 * EPS * absf( expected[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes the inverse half-value versed sine (small positive numbers)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = smallPositive.x; + expected = smallPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = ahaversinf( x[i] ); + if ( y === expected[ i ] ) { + t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] ); + } else { + delta = absf( y - expected[i] ); + tol = 3 * EPS * absf( expected[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' ); + } + } + t.end(); +}); + +tape( 'the function returns `NaN` if provided `NaN`', function test( t ) { + var v = ahaversinf( NaN ); + t.strictEqual( isnanf( v ), true, 'returns NaN' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided a value less than `0`', function test( t ) { + var v; + var i; + for ( i = 0; i < 1e4; i++ ) { + v = -( randu() * 1.0e6 ) - EPS; + t.strictEqual( isnanf( ahaversinf( v ) ), true, 'returns NaN when provided '+v ); + } + t.end(); +}); + +tape( 'the function returns `NaN` if provided a value greater than `1`', function test( t ) { + var v; + var i; + for ( i = 0; i < 1e4; i++ ) { + v = ( randu() * 1.0e6 ) + 1.0 + EPS; + t.strictEqual( isnanf( ahaversinf( v ) ), true, 'returns NaN when provided '+v ); + } + t.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/test.native.js new file mode 100644 index 000000000000..69eabc1c1f31 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ahaversinf/test/test.native.js @@ -0,0 +1,126 @@ +/** +* @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 isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var randu = require( '@stdlib/random/base/randu' ); +var absf = require( '@stdlib/math/base/special/absf' ); +var EPS = require( '@stdlib/constants/float32/eps' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// FIXTURES // + +var data = require( './fixtures/julia/data.json' ); +var smallPositive = require( './fixtures/julia/small_positive.json' ); + + +// VARIABLES // + +var ahaversinf = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( ahaversinf instanceof Error ) +}; + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof ahaversinf, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function computes the inverse half-value versed sine', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = data.x; + expected = data.expected; + + for ( i = 0; i < x.length; i++ ) { + y = ahaversinf( x[i] ); + if ( y === expected[ i ] ) { + t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] ); + } else { + delta = absf( y - expected[i] ); + tol = 3.0 * EPS * absf( expected[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes the inverse half-value versed sine (small positive numbers)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = smallPositive.x; + expected = smallPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = ahaversinf( x[i] ); + if ( y === expected[ i ] ) { + t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] ); + } else { + delta = absf( y - expected[i] ); + tol = 3.0 * EPS * absf( expected[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' ); + } + } + t.end(); +}); + +tape( 'the function returns `NaN` if provided `NaN`', opts, function test( t ) { + var v = ahaversinf( NaN ); + t.strictEqual( isnanf( v ), true, 'returns NaN' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided a value less than `0`', opts, function test( t ) { + var v; + var i; + for ( i = 0; i < 1e4; i++ ) { + v = -( randu() * 1.0e6 ) - EPS; + t.strictEqual( isnanf( ahaversinf( v ) ), true, 'returns NaN when provided '+v ); + } + t.end(); +}); + +tape( 'the function returns `NaN` if provided a value greater than `1`', opts, function test( t ) { + var v; + var i; + for ( i = 0; i < 1e4; i++ ) { + v = ( randu() * 1.0e6 ) + 1.0 + EPS; + t.strictEqual( isnanf( ahaversinf( v ) ), true, 'returns NaN when provided '+v ); + } + t.end(); +});