diff --git a/base/special/exp2/README.md b/base/special/exp2/README.md index e05c07486..a8a392b5a 100644 --- a/base/special/exp2/README.md +++ b/base/special/exp2/README.md @@ -75,6 +75,96 @@ for ( i = 0; i < 100; i++ ) { + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/exp2.h" +``` + +#### stdlib_base_exp2( x ) + +Evaluates the base `2` [exponential function][exponential-function]. + +```c +double out = stdlib_base_exp2( 3.0 ); +// returns 8.0 + +out = stdlib_base_exp2( -9.0 ); +// returns ~0.002 +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. + +```c +double stdlib_base_exp2( const double x ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/exp2.h" +#include +#include + +int main( void ) { + double x; + double v; + int i; + + for ( i = 0; i < 100; i++ ) { + x = ( ( (double)rand() / (double)RAND_MAX ) * 100.0 ) - 50.0; + v = stdlib_base_exp2( x ); + printf( "2^%lf = %lf\n", x, v ); + } +} +``` + +
+ + + +
+ + +
diff --git a/base/special/exp2/benchmark/benchmark.native.js b/base/special/exp2/benchmark/benchmark.native.js new file mode 100644 index 000000000..7dbe51aed --- /dev/null +++ b/base/special/exp2/benchmark/benchmark.native.js @@ -0,0 +1,60 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var resolve = require( 'path' ).resolve; +var bench = require( '@stdlib/bench' ); +var randu = require( '@stdlib/random/base/randu' ); +var isnan = require( './../../../../base/assert/is-nan' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var exp2 = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( exp2 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() * 2044.0 ) - 1022.0; + y = exp2( x ); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/base/special/exp2/benchmark/c/native/Makefile b/base/special/exp2/benchmark/c/native/Makefile new file mode 100644 index 000000000..f69e9da2b --- /dev/null +++ b/base/special/exp2/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/base/special/exp2/benchmark/c/native/benchmark.c b/base/special/exp2/benchmark/c/native/benchmark.c new file mode 100644 index 000000000..fdb6073ca --- /dev/null +++ b/base/special/exp2/benchmark/c/native/benchmark.c @@ -0,0 +1,136 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +/** +* Benchmark `exp2`. +*/ +#include "stdlib/math/base/special/exp2.h" +#include +#include +#include +#include +#include + +#define NAME "exp2" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +void print_version() { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +void print_summary( int total, int passing ) { + printf( "#\n" ); + printf( "1..%d\n", total ); // TAP plan + printf( "# total %d\n", total ); + printf( "# pass %d\n", passing ); + printf( "#\n" ); + printf( "# ok\n" ); +} + +/** +* Prints benchmarks results. +* +* @param elapsed elapsed time in seconds +*/ +void print_results( double elapsed ) { + double rate = (double)ITERATIONS / elapsed; + printf( " ---\n" ); + printf( " iterations: %d\n", ITERATIONS ); + printf( " elapsed: %0.9f\n", elapsed ); + printf( " rate: %0.9f\n", rate ); + printf( " ...\n" ); +} + +/** +* Returns a clock time. +* +* @return clock time +*/ +double tic() { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec/1.0e6; +} + +/** +* Generates a random number on the interval [0,1]. +* +* @return random number +*/ +double rand_double() { + int r = rand(); + return (double)r / ( (double)RAND_MAX + 1.0 ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +double benchmark() { + double elapsed; + double x; + double y; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + x = ( 2044.0 * rand_double() ) - 1022.0; + y = stdlib_base_exp2( 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/base/special/exp2/binding.gyp b/base/special/exp2/binding.gyp new file mode 100644 index 000000000..ec3992233 --- /dev/null +++ b/base/special/exp2/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/base/special/exp2/examples/c/Makefile b/base/special/exp2/examples/c/Makefile new file mode 100644 index 000000000..6aed70daf --- /dev/null +++ b/base/special/exp2/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/base/special/exp2/examples/c/example.c b/base/special/exp2/examples/c/example.c new file mode 100644 index 000000000..0a7abe91f --- /dev/null +++ b/base/special/exp2/examples/c/example.c @@ -0,0 +1,33 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +#include "stdlib/math/base/special/exp2.h" +#include +#include + +int main( void ) { + double x; + double v; + int i; + + for ( i = 0; i < 100; i++ ) { + x = ( ( (double)rand() / (double)RAND_MAX ) * 100.0 ) - 50.0; + v = stdlib_base_exp2( x ); + printf( "2^%lf = %lf\n", x, v ); + } +} diff --git a/base/special/exp2/include.gypi b/base/special/exp2/include.gypi new file mode 100644 index 000000000..575cb043c --- /dev/null +++ b/base/special/exp2/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': [ + ' STDLIB_CONSTANT_FLOAT64_MAX_BASE2_EXPONENT ) { + return STDLIB_CONSTANT_FLOAT64_PINF; + } + if ( x < STDLIB_CONSTANT_FLOAT64_MIN_BASE2_EXPONENT ) { + return 0.0; + } + + // Separate into integer and fractional parts... + n = stdlib_base_round( x ); + ax = x - n; + xx = ax * ax; + px = ax * polyval_p( xx ); + ax = px / ( polyval_q( xx ) - px ); + ax = 1.0 + stdlib_base_ldexp( ax, 1 ); + + // Scale by power of 2: + return stdlib_base_ldexp( ax, n ); +} diff --git a/base/special/exp2/test/test.native.js b/base/special/exp2/test/test.native.js new file mode 100644 index 000000000..38309bcaa --- /dev/null +++ b/base/special/exp2/test/test.native.js @@ -0,0 +1,192 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var resolve = require( 'path' ).resolve; +var tape = require( 'tape' ); +var isnan = require( './../../../../base/assert/is-nan' ); +var abs = require( './../../../../base/special/abs' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// FIXTURES // + +var mediumNegative = require( './fixtures/julia/medium_negative.json' ); +var mediumPositive = require( './fixtures/julia/medium_positive.json' ); +var smallNegative = require( './fixtures/julia/small_negative.json' ); +var smallPositive = require( './fixtures/julia/small_positive.json' ); +var tiny = require( './fixtures/julia/tiny.json' ); + + +// VARIABLES // + +var exp2 = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( exp2 instanceof Error ) +}; + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof exp2, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function accurately computes `2**x` for negative medium numbers', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = mediumNegative.x; + expected = mediumNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + v = exp2( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes `2**x` for positive medium numbers', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = mediumPositive.x; + expected = mediumPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + v = exp2( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes `2**x` for negative small numbers', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = smallNegative.x; + expected = smallNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + v = exp2( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes `2**x` for positive small numbers', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = smallPositive.x; + expected = smallPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + v = exp2( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes `2**x` for very small `x`', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = tiny.x; + expected = tiny.expected; + + for ( i = 0; i < x.length; i++ ) { + v = exp2( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function returns `+infinity` for very large `x`', opts, function test( t ) { + t.equal( exp2( 1100.0 ), PINF, 'equals +infinity' ); + t.equal( exp2( 1200.0 ), PINF, 'equals +infinity' ); + t.equal( exp2( 1300.0 ), PINF, 'equals +infinity' ); + t.end(); +}); + +tape( 'the function returns `0.0` for negative large `x`', opts, function test( t ) { + t.equal( exp2( -1100.0 ), 0.0, 'equals 0' ); + t.equal( exp2( -1200.0 ), 0.0, 'equals 0' ); + t.equal( exp2( -1300.0 ), 0.0, 'equals 0' ); + t.end(); +}); + +tape( 'the function returns `0.0` if provided `-infinity`', opts, function test( t ) { + t.equal( exp2( NINF ), 0.0, 'equals 0' ); + t.end(); +}); + +tape( 'the function returns `+infinity` if provided `+infinity`', opts, function test( t ) { + t.equal( exp2( PINF ), PINF, 'equals +infinity' ); + t.end(); +}); + +tape( 'the function returns `1` if provided `0`', opts, function test( t ) { + var v = exp2( 0.0 ); + t.equal( v, 1.0, 'equals 1' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided `NaN`', opts, function test( t ) { + var val = exp2( NaN ); + t.equal( isnan( val ), true, 'equals NaN' ); + t.end(); +});