diff --git a/CHANGELOG.md b/CHANGELOG.md index 881f8ee5e..98d478dd1 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -3774,6 +3774,28 @@ This release closes the following issue: +
+ +#### [@stdlib/math/base/special/rempio2](https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/rempio2) + +
+ +
+ +##### Features + +- [`0b633eb`](https://github.com/stdlib-js/stdlib/commit/0b633eb2afe0641b963621048a3ce93795c8d92b) - add C implementation for `math/base/special/rempio2` + +
+ + + +
+ +
+ + +
#### [@stdlib/math/base/special/round](https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/round) @@ -4352,6 +4374,7 @@ A total of 24 people contributed to this release. Thank you to the following con
+- [`0b633eb`](https://github.com/stdlib-js/stdlib/commit/0b633eb2afe0641b963621048a3ce93795c8d92b) - **feat:** add C implementation for `math/base/special/rempio2` _(by Gunj Joshi, Philipp Burckhardt, Athan Reines)_ - [`1b5abe6`](https://github.com/stdlib-js/stdlib/commit/1b5abe6cb97ca371aeeae5ef5e39e9ef20898e52) - **chore:** update package meta data [(#2344)](https://github.com/stdlib-js/stdlib/pull/2344) _(by stdlib-bot, Athan Reines)_ - [`e612af5`](https://github.com/stdlib-js/stdlib/commit/e612af58d0e5374e3ed17f0278d2538aec9b37e1) - **docs:** update namespace table of contents [(#2314)](https://github.com/stdlib-js/stdlib/pull/2314) _(by stdlib-bot, Athan Reines)_ - [`95cd4ef`](https://github.com/stdlib-js/stdlib/commit/95cd4ef83e181ffbf50aeef1a6e44e14338d1261) - **docs:** update namespace TypeScript declarations [(#2312)](https://github.com/stdlib-js/stdlib/pull/2312) _(by stdlib-bot, Athan Reines)_ diff --git a/base/special/rempio2/README.md b/base/special/rempio2/README.md index 32551ba1d..978033ba6 100644 --- a/base/special/rempio2/README.md +++ b/base/special/rempio2/README.md @@ -32,7 +32,7 @@ var rempio2 = require( '@stdlib/math/base/special/rempio2' ); #### rempio2( x, y ) -Computes `x - nπ/2 = r`. The function returns `n` and stores the remainder `r` as two numbers in `y`, such that `y[0]+y[1] = r`. +Computes `x - nπ/2 = r`. ```javascript var y = [ 0.0, 0.0 ]; @@ -46,7 +46,7 @@ var y2 = y[ 1 ]; // returns ~3.618e-17 ``` -When `x` is `NaN` or infinite, the function returns zero and sets the elements of `y` to `NaN`. +When `x` is `NaN` or infinite, the function returns `0` and sets the elements of `y` to `NaN`. ```javascript var y = [ 0.0, 0.0 ]; @@ -80,6 +80,7 @@ y2 = y[ 1 ]; ## Notes +- The function returns `n` and stores the remainder `r` as two numbers in `y`, such that `y[0]+y[1] = r`. - For input values larger than `2^20*π/2` in magnitude, the function **only** returns the last three binary digits of `n` and not the full result.
@@ -111,6 +112,105 @@ for ( i = 0; i < x.length; i++ ) { + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/rempio2.h" +``` + +#### stdlib_base_rempio2( x, &rem1, &rem2 ) + +Computes `x - nπ/2 = r`. + +```c +#include + +double rem1; +double rem2; + +int32_t n = stdlib_base_rempio2( 4.0, &rem1, &rem2 ); +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. +- **rem1**: `[out] double*` destination for first remainder number. +- **rem2**: `[out] double*` destination for second remainder number. + +```c +int32_t stdlib_base_rempio2( const double x, double *rem1, double *rem2 ); +``` + +
+ + + + + +
+ +### Notes + +- The function returns `n` and stores the remainder `r` as two numbers in `rem1` and `rem2`, respectively, such that `rem1+rem2 = r`. + +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/rempio2.h" +#include +#include +#include + +int main( void ) { + const double x[] = { 0.0, 1.0, 4.0, 128.0 }; + + double rem1; + double rem2; + int32_t n; + int i; + for ( i = 0; i < 4; i++ ) { + n = stdlib_base_rempio2( x[ i ], &rem1, &rem2 ); + printf( "%lf - %"PRId32"π/2 = %lf + %lf\n", x[ i ], n, rem1, rem2 ); + } +} +``` + +
+ + + +
+ + +
diff --git a/base/special/rempio2/benchmark/benchmark.native.js b/base/special/rempio2/benchmark/benchmark.native.js new file mode 100644 index 000000000..aa3062c94 --- /dev/null +++ b/base/special/rempio2/benchmark/benchmark.native.js @@ -0,0 +1,63 @@ +/** +* @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 rempio2 = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( rempio2 instanceof Error ) +}; + + +// MAIN // + +bench( pkg+'::native', opts, function benchmark( b ) { + var x; + var y; + var n; + var i; + + y = [ 0.0, 0.0 ]; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + x = ( randu() * 200.0 ) - 100.0; + n = rempio2( x, y ); + if ( isnan( n ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( n ) || isnan( y[0] ) || isnan( y[1] ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/base/special/rempio2/benchmark/c/native/Makefile b/base/special/rempio2/benchmark/c/native/Makefile new file mode 100644 index 000000000..f69e9da2b --- /dev/null +++ b/base/special/rempio2/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/rempio2/benchmark/c/native/benchmark.c b/base/special/rempio2/benchmark/c/native/benchmark.c new file mode 100644 index 000000000..78439da42 --- /dev/null +++ b/base/special/rempio2/benchmark/c/native/benchmark.c @@ -0,0 +1,138 @@ +/** +* @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 `rempio2`. +*/ +#include "stdlib/math/base/special/rempio2.h" +#include +#include +#include +#include +#include + +#define NAME "rempio2" +#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 rem1; + double rem2; + double x; + double y; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + x = ( rand_double() * 200.0 ) - 100.0; + y = stdlib_base_rempio2( x, &rem1, &rem2 ); + 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/rempio2/binding.gyp b/base/special/rempio2/binding.gyp new file mode 100644 index 000000000..ec3992233 --- /dev/null +++ b/base/special/rempio2/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/rempio2/examples/c/Makefile b/base/special/rempio2/examples/c/Makefile new file mode 100644 index 000000000..6aed70daf --- /dev/null +++ b/base/special/rempio2/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/rempio2/examples/c/example.c b/base/special/rempio2/examples/c/example.c new file mode 100644 index 000000000..4b314d364 --- /dev/null +++ b/base/special/rempio2/examples/c/example.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/rempio2.h" +#include +#include +#include + +int main( void ) { + const double x[] = { 0.0, 1.0, 4.0, 128.0 }; + + double rem1; + double rem2; + int32_t n; + int i; + for ( i = 0; i < 4; i++ ) { + n = stdlib_base_rempio2( x[ i ], &rem1, &rem2 ); + printf( "%lf - %"PRId32"π/2 = %lf + %lf\n", x[ i ], n, rem1, rem2 ); + } +} diff --git a/base/special/rempio2/include.gypi b/base/special/rempio2/include.gypi new file mode 100644 index 000000000..575cb043c --- /dev/null +++ b/base/special/rempio2/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': [ + ' + +/* +* If C++, prevent name mangling so that the compiler emits a binary file having undecorated names, thus mirroring the behavior of a C compiler. +*/ +#ifdef __cplusplus +extern "C" { +#endif + +/** +* Computes `x - nπ/2 = r`. +*/ +int32_t stdlib_base_rempio2( const double x, double *rem1, double *rem2 ); + +#ifdef __cplusplus +} +#endif + +#endif // !STDLIB_MATH_BASE_SPECIAL_REMPIO2_H diff --git a/base/special/rempio2/lib/kernel_rempio2.js b/base/special/rempio2/lib/kernel_rempio2.js index 65849e6d3..d402f1957 100644 --- a/base/special/rempio2/lib/kernel_rempio2.js +++ b/base/special/rempio2/lib/kernel_rempio2.js @@ -206,9 +206,7 @@ function compute( x, y, jz, q, q0, jk, jv, jx, f ) { jz += k; return compute( x, y, jz, q, q0, jk, jv, jx, f ); } - } - // Chop off zero terms... - if ( z === 0.0 ) { + // Chop off zero terms... jz -= 1; q0 -= 24; while ( IQ[ jz ] === 0 ) { @@ -272,7 +270,105 @@ function compute( x, y, jz, q, q0, jk, jv, jx, f ) { * * ## Method * -* - The method is to compute the integer (`mod 8`) and fraction parts of `2x/π` without doing the full multiplication. In general, we skip the part of the product that is known to be a huge integer (more accurately, equals `0 mod 8` ). Thus, the number of operations is independent of the exponent of the input. +* - The method is to compute the integer (mod 8) and fraction parts of (2/π) * x without doing the full multiplication. In general, we skip the part of the product that are known to be a huge integer (more accurately, = 0 mod 8 ). Thus the number of operations are independent of the exponent of the input. +* +* - (2/π) is represented by an array of 24-bit integers in `ipio2[]`. +* +* - Input parameters: +* +* - `x[]` The input value (must be positive) is broken into `nx` pieces of 24-bit integers in double precision format. `x[i]` will be the i-th 24 bit of x. The scaled exponent of `x[0]` is given in input parameter `e0` (i.e., `x[0]*2^e0` match x's up to 24 bits). +* +* Example of breaking a double positive `z` into `x[0]+x[1]+x[2]`: +* +* ```tex +* e0 = \mathrm{ilogb}(z) - 23 +* z = \mathrm{scalbn}(z, -e0) +* ``` +* +* for `i = 0,1,2` +* +* ```tex +* x[i] = \lfloor z \rfloor +* z = (z - x[i]) \times 2^{24} +* ``` +* +* - `y[]` output result in an array of double precision numbers. +* +* The dimension of `y[]` is: +* 24-bit precision 1 +* 53-bit precision 2 +* 64-bit precision 2 +* 113-bit precision 3 +* +* The actual value is the sum of them. Thus, for 113-bit precision, one may have to do something like: +* +* ```tex +* \mathrm{long\ double} \: t, w, r_{\text{head}}, r_{\text{tail}}; \\ +* t &= (\mathrm{long\ double}) y[2] + (\mathrm{long\ double}) y[1]; \\ +* w &= (\mathrm{long\ double}) y[0]; \\ +* r_{\text{head}} &= t + w; \\ +* r_{\text{tail}} &= w - (r_{\text{head}} - t); +* ``` +* +* - `e0` The exponent of `x[0]`. Must be <= 16360 or you need to expand the `ipio2` table. +* +* - `nx` dimension of `x[]` +* +* - `prec` an integer indicating the precision: +* 0 24 bits (single) +* 1 53 bits (double) +* 2 64 bits (extended) +* 3 113 bits (quad) +* +* - External function: +* +* - double `scalbn()`, `floor()`; +* +* - Here is the description of some local variables: +* +* - `jk` `jk+1` is the initial number of terms of `ipio2[]` needed in the computation. The minimum and recommended value for `jk` is 3,4,4,6 for single, double, extended, and quad. `jk+1` must be 2 larger than you might expect so that our recomputation test works. (Up to 24 bits in the integer part (the 24 bits of it that we compute) and 23 bits in the fraction part may be lost to cancellation before we recompute.) +* +* - `jz` local integer variable indicating the number of terms of `ipio2[]` used. +* +* - `jx` `nx - 1` +* +* - `jv` index for pointing to the suitable `ipio2[]` for the computation. In general, we want +* +* ```tex +* \frac{{2^{e0} \cdot x[0] \cdot \mathrm{ipio2}[jv-1] \cdot 2^{-24jv}}}{{8}} +* ``` +* +* to be an integer. Thus +* +* ```tex +* e0 - 3 - 24 \cdot jv \geq 0 \quad \text{or} \quad \frac{{e0 - 3}}{{24}} \geq jv +* ``` +* +* Hence +* +* ```tex +* jv = \max(0, \frac{{e0 - 3}}{{24}}) +* ``` +* +* - `jp` `jp+1` is the number of terms in `PIo2[]` needed, `jp = jk`. +* +* - `q[]` double array with integral value, representing the 24-bits chunk of the product of `x` and `2/π`. +* +* - `q0` the corresponding exponent of `q[0]`. Note that the exponent for `q[i]` would be `q0-24*i`. +* +* - `PIo2[]` double precision array, obtained by cutting `π/2` into 24 bits chunks. +* +* - `f[]` `ipso2[]` in floating point +* +* - `iq[]` integer array by breaking up `q[]` in 24-bits chunk. +* +* - `fq[]` final product of `x*(2/π)` in `fq[0],..,fq[jk]` +* +* - `ih` integer. If >0 it indicates `q[]` is >= 0.5, hence it also indicates the _sign_ of the result. +* +* - Constants: +* +* - The hexadecimal values are the intended ones for the following constants. The decimal values may be used, provided that the compiler will convert from decimal to binary accurately enough to produce the hexadecimal values shown. * * @private * @param {PositiveNumber} x - input value diff --git a/base/special/rempio2/lib/native.js b/base/special/rempio2/lib/native.js new file mode 100644 index 000000000..ab9ea199e --- /dev/null +++ b/base/special/rempio2/lib/native.js @@ -0,0 +1,56 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var addon = require( './../src/addon.node' ); + + +// MAIN // + +/** +* Computes `x - nπ/2 = r`. +* +* @private +* @param {number} x - input value +* @param {Float64Array} y - remainder elements +* @returns {integer} factor of `π/2` +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* +* var y = new Float64Array( [ 0.0, 0.0 ] ); +* var n = rempio2( 128.0, y ); +* // returns 81 +* +* var y1 = y[ 0 ]; +* // returns ~0.765 +* +* var y2 = y[ 1 ]; +* // returns ~3.618e-17 +*/ +function rempio2( x, y ) { + return addon( x, y ); +} + + +// EXPORTS // + +module.exports = rempio2; diff --git a/base/special/rempio2/manifest.json b/base/special/rempio2/manifest.json new file mode 100644 index 000000000..11524178f --- /dev/null +++ b/base/special/rempio2/manifest.json @@ -0,0 +1,100 @@ +{ + "options": { + "task": "build" + }, + "fields": [ + { + "field": "src", + "resolve": true, + "relative": true + }, + { + "field": "include", + "resolve": true, + "relative": true + }, + { + "field": "libraries", + "resolve": false, + "relative": false + }, + { + "field": "libpath", + "resolve": true, + "relative": false + } + ], + "confs": [ + { + "task": "build", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/napi/argv", + "@stdlib/napi/argv-double", + "@stdlib/napi/argv-float64array", + "@stdlib/napi/create-double", + "@stdlib/napi/export", + "@stdlib/math/base/special/round", + "@stdlib/math/base/special/floor", + "@stdlib/math/base/special/ldexp", + "@stdlib/number/float64/base/get-high-word", + "@stdlib/number/float64/base/get-low-word", + "@stdlib/number/float64/base/from-words", + "@stdlib/constants/float64/high-word-abs-mask", + "@stdlib/constants/float64/high-word-exponent-mask", + "@stdlib/constants/float64/high-word-sign-mask" + ] + }, + { + "task": "benchmark", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/special/round", + "@stdlib/math/base/special/floor", + "@stdlib/math/base/special/ldexp", + "@stdlib/number/float64/base/get-high-word", + "@stdlib/number/float64/base/get-low-word", + "@stdlib/number/float64/base/from-words", + "@stdlib/constants/float64/high-word-abs-mask", + "@stdlib/constants/float64/high-word-exponent-mask", + "@stdlib/constants/float64/high-word-sign-mask" + ] + }, + { + "task": "examples", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/special/round", + "@stdlib/math/base/special/floor", + "@stdlib/math/base/special/ldexp", + "@stdlib/number/float64/base/get-high-word", + "@stdlib/number/float64/base/get-low-word", + "@stdlib/number/float64/base/from-words", + "@stdlib/constants/float64/high-word-abs-mask", + "@stdlib/constants/float64/high-word-exponent-mask", + "@stdlib/constants/float64/high-word-sign-mask" + ] + } + ] +} diff --git a/base/special/rempio2/src/Makefile b/base/special/rempio2/src/Makefile new file mode 100644 index 000000000..bcf18aa46 --- /dev/null +++ b/base/special/rempio2/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/base/special/rempio2/src/addon.c b/base/special/rempio2/src/addon.c new file mode 100644 index 000000000..daf621386 --- /dev/null +++ b/base/special/rempio2/src/addon.c @@ -0,0 +1,43 @@ +/** +* @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/rempio2.h" +#include "stdlib/napi/argv.h" +#include "stdlib/napi/argv_double.h" +#include "stdlib/napi/argv_float64array.h" +#include "stdlib/napi/create_double.h" +#include "stdlib/napi/export.h" +#include + +/** +* Receives JavaScript callback invocation data. +* +* @private +* @param env environment under which the function is invoked +* @param info callback data +* @return Node-API value +*/ +static napi_value addon( napi_env env, napi_callback_info info ) { + STDLIB_NAPI_ARGV( env, info, argv, argc, 2 ); + STDLIB_NAPI_ARGV_DOUBLE( env, x, argv, 0 ); + STDLIB_NAPI_ARGV_FLOAT64ARRAY( env, y, ylen, argv, 1 ); + STDLIB_NAPI_CREATE_DOUBLE( env, stdlib_base_rempio2( x, &y[0], &y[1] ), n ); + return n; +} + +STDLIB_NAPI_MODULE_EXPORT_FCN( addon ) diff --git a/base/special/rempio2/src/main.c b/base/special/rempio2/src/main.c new file mode 100644 index 000000000..dc7289455 --- /dev/null +++ b/base/special/rempio2/src/main.c @@ -0,0 +1,628 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +* +* +* ## Notice +* +* The following copyright, license, and long comment were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/12.2.0/lib/msun/src/e_rem_pio2.c}. The implementation follows the original, but has been modified according to project conventions. +* +* ```text +* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. +* +* Developed at SunPro, a Sun Microsystems, Inc. business. +* Permission to use, copy, modify, and distribute this +* software is freely granted, provided that this notice +* is preserved. +* ``` +*/ + +#include "stdlib/math/base/special/rempio2.h" +#include "stdlib/math/base/special/round.h" +#include "stdlib/math/base/special/floor.h" +#include "stdlib/math/base/special/ldexp.h" +#include "stdlib/number/float64/base/get_high_word.h" +#include "stdlib/number/float64/base/get_low_word.h" +#include "stdlib/number/float64/base/from_words.h" +#include "stdlib/constants/float64/high_word_abs_mask.h" +#include "stdlib/constants/float64/high_word_exponent_mask.h" +#include "stdlib/constants/float64/high_word_sign_mask.h" +#include + +static const double ZERO = 0.00000000000000000000e+00; // 0x00000000, 0x00000000 +static const double TWO24 = 1.67772160000000000000e+07; // 0x41700000, 0x00000000 +static const double TWON24 = 5.96046447753906250000e-08; // 0x3E700000, 0x00000000 +static const double INVPIO2 = 6.36619772367581382433e-01; // 0x3FE45F30, 0x6DC9C883 +static const double PIO2_1 = 1.57079632673412561417e+00; // 0x3FF921FB, 0x54400000 +static const double PIO2_1T = 6.07710050650619224932e-11; // 0x3DD0B461, 0x1A626331 +static const double PIO2_2 = 6.07710050630396597660e-11; // 0x3DD0B461, 0x1A600000 +static const double PIO2_2T = 2.02226624879595063154e-21; // 0x3BA3198A, 0x2E037073 +static const double PIO2_3 = 2.02226624871116645580e-21; // 0x3BA3198A, 0x2E000000 +static const double PIO2_3T = 8.47842766036889956997e-32; // 0x397B839A, 0x252049C1 + +// High word significand for π and π/2: 0x921fb = 598523 => 00000000000010010010000111111011 +static const int32_t PI_HIGH_WORD_SIGNIFICAND = 0x921fb; + +// High word for π/4: 0x3fe921fb = 1072243195 => 00111111111010010010000111111011 +static const int32_t PIO4_HIGH_WORD = 0x3fe921fb; + +// High word for 3π/4: 0x4002d97c = 1073928572 => 01000000000000101101100101111100 +static const int32_t THREE_PIO4_HIGH_WORD = 0x4002d97c; + +// High word for 5π/4: 0x400f6a7a = 1074752122 => 01000000000011110110101001111010 +static const int32_t FIVE_PIO4_HIGH_WORD = 0x400f6a7a; + +// High word for 6π/4: 0x4012d97c = 1074977148 => 01000000000100101101100101111100 +static const int32_t THREE_PIO2_HIGH_WORD = 0x4012d97c; + +// High word for 7π/4: 0x4015fdbc = 1075183036 => 01000000000101011111110110111100 +static const int32_t SEVEN_PIO4_HIGH_WORD = 0x4015fdbc; + +// High word for 8π/4: 0x401921fb = 1075388923 => 01000000000110010010000111111011 +static const int32_t TWO_PI_HIGH_WORD = 0x401921fb; + +// High word for 9π/4: 0x401c463b = 1075594811 => 01000000000111000100011000111011 +static const int32_t NINE_PIO4_HIGH_WORD = 0x401c463b; + +// 2^20*π/2 = 1647099.3291652855 => 0100000100111001001000011111101101010100010001000010110100011000 => high word => 0x413921fb = 1094263291 => 01000001001110010010000111111011 +static const int32_t MEDIUM = 0x413921fb; + +// Exponent mask (2047 => 0x7ff): +static const int32_t EXPONENT_MASK = 0x7ff; + + +/* +* Table of constants for `2/π` (`396` hex digits, `476` decimal). +* +* Integer array which contains the (`24*i`)-th to (`24*i+23`)-th bit of `2/π` after binary point. The corresponding floating value is +* +* ```tex +* \operatorname{ipio2}[i] \cdot 2^{-24(i+1)} +* ``` +* +* This table must have at least `(e0-3)/24 + jk` terms. For quad precision (`e0 <= 16360`, `jk = 6`), this is `686`. +*/ +static const int32_t IPIO2[] = { + 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, + 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, + 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, + 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, + 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, + 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, + 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, + 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, + 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, + 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, + 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B +}; + +// Double precision array, obtained by cutting `π/2` into `24` bits chunks... +static const double PIO2[] = { + 1.57079625129699707031e+00, // 0x3FF921FB, 0x40000000 + 7.54978941586159635335e-08, // 0x3E74442D, 0x00000000 + 5.39030252995776476554e-15, // 0x3CF84698, 0x80000000 + 3.28200341580791294123e-22, // 0x3B78CC51, 0x60000000 + 1.27065575308067607349e-29, // 0x39F01B83, 0x80000000 + 1.22933308981111328932e-36, // 0x387A2520, 0x40000000 + 2.73370053816464559624e-44, // 0x36E38222, 0x80000000 + 2.16741683877804819444e-51 // 0x3569F31D, 0x00000000 +}; + +/** +* Returns the last three binary digits of `N` with `y = x - Nπ/2` so that `|y| < π/2`. +* +* ## Method +* +* - The method is to compute the integer (mod 8) and fraction parts of (2/π) * x without doing the full multiplication. In general, we skip the part of the product that are known to be a huge integer (more accurately, = 0 mod 8 ). Thus the number of operations are independent of the exponent of the input. +* +* - (2/π) is represented by an array of 24-bit integers in `ipio2[]`. +* +* - Input parameters: +* +* - `x[]` The input value (must be positive) is broken into `nx` pieces of 24-bit integers in double precision format. `x[i]` will be the i-th 24 bit of x. The scaled exponent of `x[0]` is given in input parameter `e0` (i.e., `x[0]*2^e0` match x's up to 24 bits). +* +* Example of breaking a double positive `z` into `x[0]+x[1]+x[2]`: +* +* ```tex +* e0 = \mathrm{ilogb}(z) - 23 +* z = \mathrm{scalbn}(z, -e0) +* ``` +* +* for `i = 0,1,2` +* +* ```tex +* x[i] = \lfloor z \rfloor +* z = (z - x[i]) \times 2^{24} +* ``` +* +* - `y[]` output result in an array of double precision numbers. +* +* The dimension of `y[]` is: +* 24-bit precision 1 +* 53-bit precision 2 +* 64-bit precision 2 +* 113-bit precision 3 +* +* The actual value is the sum of them. Thus, for 113-bit precision, one may have to do something like: +* +* ```tex +* \mathrm{long\ double} \: t, w, r_{\text{head}}, r_{\text{tail}}; \\ +* t &= (\mathrm{long\ double}) y[2] + (\mathrm{long\ double}) y[1]; \\ +* w &= (\mathrm{long\ double}) y[0]; \\ +* r_{\text{head}} &= t + w; \\ +* r_{\text{tail}} &= w - (r_{\text{head}} - t); +* ``` +* +* - `e0` The exponent of `x[0]`. Must be <= 16360 or you need to expand the `ipio2` table. +* +* - `nx` dimension of `x[]` +* +* - `prec` an integer indicating the precision: +* 0 24 bits (single) +* 1 53 bits (double) +* 2 64 bits (extended) +* 3 113 bits (quad) +* +* - External function: +* +* - double `scalbn()`, `floor()`; +* +* - Here is the description of some local variables: +* +* - `jk` `jk+1` is the initial number of terms of `ipio2[]` needed in the computation. The minimum and recommended value for `jk` is 3,4,4,6 for single, double, extended, and quad. `jk+1` must be 2 larger than you might expect so that our recomputation test works. (Up to 24 bits in the integer part (the 24 bits of it that we compute) and 23 bits in the fraction part may be lost to cancellation before we recompute.) +* +* - `jz` local integer variable indicating the number of terms of `ipio2[]` used. +* +* - `jx` `nx - 1` +* +* - `jv` index for pointing to the suitable `ipio2[]` for the computation. In general, we want +* +* ```tex +* \frac{{2^{e0} \cdot x[0] \cdot \mathrm{ipio2}[jv-1] \cdot 2^{-24jv}}}{{8}} +* ``` +* +* to be an integer. Thus +* +* ```tex +* e0 - 3 - 24 \cdot jv \geq 0 \quad \text{or} \quad \frac{{e0 - 3}}{{24}} \geq jv +* ``` +* +* Hence +* +* ```tex +* jv = \max(0, \frac{{e0 - 3}}{{24}}) +* ``` +* +* - `jp` `jp+1` is the number of terms in `PIo2[]` needed, `jp = jk`. +* +* - `q[]` double array with integral value, representing the 24-bits chunk of the product of `x` and `2/π`. +* +* - `q0` the corresponding exponent of `q[0]`. Note that the exponent for `q[i]` would be `q0-24*i`. +* +* - `PIo2[]` double precision array, obtained by cutting `π/2` into 24 bits chunks. +* +* - `f[]` `ipso2[]` in floating point +* +* - `iq[]` integer array by breaking up `q[]` in 24-bits chunk. +* +* - `fq[]` final product of `x*(2/π)` in `fq[0],..,fq[jk]` +* +* - `ih` integer. If >0 it indicates `q[]` is >= 0.5, hence it also indicates the _sign_ of the result. +* +* - Constants: +* +* - The hexadecimal values are the intended ones for the following constants. The decimal values may be used, provided that the compiler will convert from decimal to binary accurately enough to produce the hexadecimal values shown. +* +* @private +* @param x input value +* @param rem1 remainder element 1 +* @param rem2 remainder element 2 +* @param e0 the exponent of `x[0]` (must be <= 16360) +* @param nx dimension of `x[]` +* @return last 3 binary digits +*/ +int32_t rempio2Kernel( const double* x, double *y, int32_t e0, int32_t nx ) { + double F[ 20 ] = { 0.0 }; + double Q[ 20 ] = { 0.0 }; + int32_t IQ[ 20 ]; + double FQ[ 20 ]; + int32_t carry; + int32_t jz; + int32_t jx; + int32_t jv; + int32_t jp; + int32_t jk; + int32_t q0; + int32_t ih; + int32_t n; + int32_t i; + int32_t j; + int32_t k; + int32_t m; + double fw; + double z; + + // Initialize `jk` for double-precision floating-point numbers: + jk = 4; + jp = jk; + + // Determine `jx`, `jv`, `q0` (note that `q0 < 3`): + jx = nx - 1; + jv = ( e0 - 3 ) / 24; + if ( jv < 0 ) { + jv = 0; + } + q0 = e0 - ( 24 * ( jv + 1 ) ); + + // Set up `F[0]` to `F[jx+jk]` where `F[jx+jk] = IPIO2[jv+jk]`: + j = jv - jx; + m = jx + jk; + for ( i = 0; i <= m; i++ ) { + if ( j < 0 ) { + F[ i ] = ZERO; + } else { + F[ i ] = ( double )IPIO2[ j ]; + } + j++; + } + + // Compute `Q[0],Q[1],...,Q[jk]`: + for ( i = 0; i <= jk; i++ ) { + fw = 0.0; + for ( j = 0; j <= jx; j++ ) { + fw += x[ j ] * F[ jx + ( i - j ) ]; + } + Q[ i ] = fw; + } + + jz = jk; +recompute: + // Distill `q[]` into `IQ[]` in reverse order... + z = Q[ jz ]; + j = jz; + for ( i = 0; j > 0; i++ ) { + fw = ( double )( ( int32_t )( TWON24 * z ) ); + IQ[ i ] = (int32_t)( z - ( TWO24 * fw ) ); + z = Q[ j - 1 ] + fw; + j--; + } + // Compute `n`... + z = stdlib_base_ldexp( z, q0 ); + z -= 8.0 * stdlib_base_floor( z * 0.125 ); // Trim off integer >= 8 + n = ( int32_t )z; + z -= ( double )n; + ih = 0; + if ( q0 > 0 ) { + // Need `IQ[jz-1]` to determine `n`... + i = ( IQ[ jz - 1 ] >> ( 24 - q0 ) ); + n += i; + IQ[ jz - 1 ] -= ( i << ( 24 - q0 ) ); + ih = ( IQ[ jz - 1 ] >> ( 23 - q0 ) ); + } else if ( q0 == 0 ) { + ih = ( IQ[ jz - 1 ] >> 23 ); + } else if ( z >= 0.5 ) { + ih = 2; + } + + // Case: q > 0.5 + if ( ih > 0 ) { + n += 1; + carry = 0; + // Compute `1-q`: + for ( i = 0; i < jz; i++ ) { + j = IQ[ i ]; + if ( carry == 0 ) { + if ( j != 0 ) { + carry = 1; + IQ[ i ] = 0x1000000 - j; + } + } else { + IQ[ i ] = 0xffffff - j; + } + } + if ( q0 > 0 ) { + // Rare case: chance is 1 in 12... + switch ( q0 ) { + case 1: + IQ[ jz - 1 ] &= 0x7fffff; + break; + case 2: + IQ[ jz - 1 ] &= 0x3fffff; + break; + } + } + if ( ih == 2 ) { + z = 1.0 - z; + if ( carry != 0 ) { + z -= stdlib_base_ldexp( 1.0, q0 ); + } + } + } + + // Check if re-computation is needed... + if ( z == ZERO ) { + j = 0; + for ( i = jz - 1; i >= jk; i-- ) { + j |= IQ[ i ]; + } + if ( j == 0 ) { + // Need re-computation... + for ( k = 1; IQ[ jk - k ] == 0; k++ ) { + // `k` is the number of terms needed... + } + + for ( i = jz + 1; i <= jz + k; i++ ) { + // Add `q[jz+1]` to `q[jz+k]`... + F[ jx + i ] = ( double )IPIO2[ jv + i ]; + fw = 0.0; + for ( j = 0; j <= jx; j++ ) { + fw += x[ j ] * F[ jx + ( i - j ) ]; + } + Q[ i ] = fw; + } + jz += k; + goto recompute; + } + // Chop off zero terms... + jz -= 1; + q0 -= 24; + while ( IQ[ jz ] == 0 ) { + jz--; + q0 -= 24; + } + } else { + // Break `z` into 24-bit if necessary... + z = stdlib_base_ldexp( z, -q0 ); + if ( z >= TWO24 ) { + fw = ( double )( ( int32_t )( TWON24 * z ) ); + IQ[ jz ] = ( int32_t )( z - ( TWO24 * fw ) ); + jz += 1; + q0 += 24; + IQ[ jz ] = ( int32_t )fw; + } else { + IQ[ jz ] = ( int32_t )z; + } + } + + // Convert integer "bit" chunk to floating-point value... + fw = stdlib_base_ldexp( 1.0, q0 ); + for ( i = jz; i >= 0; i-- ) { + Q[ i ] = fw * ( double )IQ[ i ]; + fw *= TWON24; + } + + // Compute `PIO2[0,...,jp]*q[jz,...,0]`... + for ( i = jz; i >= 0; i-- ) { + fw = 0.0; + for ( k = 0; k <= jp && k <= jz - i; k++ ) { + fw += PIO2[ k ] * Q[ i + k ]; + } + FQ[ jz - i ] = fw; + } + // Compress `FQ[]` into `y[]`... + fw = 0.0; + for ( i = jz; i >= 0; i-- ) { + fw += FQ[ i ]; + } + if ( ih == 0 ) { + y[ 0 ] = fw; + } else { + y[ 0 ] = -fw; + } + fw = FQ[ 0 ] - fw; + for ( i = 1; i <= jz; i++ ) { + fw += FQ[i]; + } + if ( ih == 0 ) { + y[ 1 ] = fw; + } else { + y[ 1 ] = -fw; + } + return n & 7; +} + + +/** +* Computes `x - nπ/2 = r`. +* +* ## Notes +* +* - Returns `n` and stores the remainder `r` as two numbers `rem1` and `rem2`, such that `rem1+rem2 = r`. +* +* @param x input value +* @param rem1 remainder element 1 +* @param rem2 remainder element 2 +* @return factor of `π/2` +* +* @example +* #include +* +* double rem1; +* double rem2; +* int32_t n = stdlib_base_rempio2( 128.0, &rem1, &rem2 ); +*/ +int32_t stdlib_base_rempio2( const double x, double *rem1, double *rem2 ) { + double TX[ 3 ]; + double TY[ 2 ]; + uint32_t uhigh; + uint32_t ulow; + uint32_t uhx; + int32_t high; + int32_t low; + int32_t ix; + int32_t hx; + int32_t e0; + int32_t nx; + int32_t i; + int32_t j; + int32_t n; + double z; + double w; + double t; + double r; + + // high word of x + stdlib_base_float64_get_high_word( x, &uhx ); + hx = ( int32_t )uhx; + ix = hx & STDLIB_CONSTANT_FLOAT64_HIGH_WORD_ABS_MASK; + + // Case: |x| ~<= π/4 (no need for reduction) + if ( ix <= PIO4_HIGH_WORD ) { + *rem1 = x; + *rem2 = 0; + return 0; + } + // Case: |x| ~<= 5π/4 + if ( ix <= FIVE_PIO4_HIGH_WORD ) { + // Case: |x| ~= π/2 or π + if ( ( ix & STDLIB_CONSTANT_FLOAT64_HIGH_WORD_SIGN_MASK ) == PI_HIGH_WORD_SIGNIFICAND ) { + // Cancellation => use medium case + goto medium; + } + // Case: |x| ~<= 3π/4 + if ( ix <= THREE_PIO4_HIGH_WORD ) { + if ( hx > 0 ) { + // one round good to 85 bits + z = x - PIO2_1; + *rem1 = z - PIO2_1T; + *rem2 = ( z - *rem1 ) - PIO2_1T; + return 1; + } else { + z = x + PIO2_1; + *rem1 = z + PIO2_1T; + *rem2 = ( z - *rem1 ) + PIO2_1T; + return -1; + } + } else { + if ( hx > 0 ) { + z = x - ( 2.0 * PIO2_1 ); + *rem1 = z - ( 2 * PIO2_1T ); + *rem2 = ( z - *rem1 ) - ( 2 * PIO2_1T ); + return 2; + } else { + z = x + ( 2.0 * PIO2_1 ); + *rem1 = z + ( 2.0 * PIO2_1T ); + *rem2 = ( z - *rem1 ) + ( 2.0 * PIO2_1T ); + return -2; + } + } + } + // Case: |x| ~<= 9π/4 + if ( ix <= NINE_PIO4_HIGH_WORD ) { + // Case: |x| ~<= 7π/4 + if ( ix <= SEVEN_PIO4_HIGH_WORD ) { + // Case: |x| ~= 3π/2 + if ( ix == THREE_PIO2_HIGH_WORD ) { + goto medium; + } + if ( hx > 0 ) { + z = x - ( 3 * PIO2_1 ); + *rem1 = z - ( 3 * PIO2_1T ); + *rem2 = ( z - *rem1 ) - ( 3 * PIO2_1T ); + return 3; + } else { + z = x + ( 3 * PIO2_1 ); + *rem1 = z + ( 3 * PIO2_1T ); + *rem2 = ( z - *rem1 ) + ( 3.0 * PIO2_1T ); + return -3; + } + } else { + // Case: |x| ~= 4π/2 + if ( ix == TWO_PI_HIGH_WORD ) { + goto medium; + } + if ( hx > 0 ) { + z = x - ( 4 * PIO2_1 ); + *rem1 = z - ( 4 * PIO2_1T ); + *rem2 = ( z - *rem1 ) - ( 4 * PIO2_1T ); + return 4; + } else { + z = x + ( 4 * PIO2_1 ); + *rem1 = z + ( 4 * PIO2_1T ); + *rem2 = ( z - *rem1 ) + ( 4 * PIO2_1T ); + return -4; + } + } + } + // Case: |x| ~< 2^20*π/2 (medium size) + if ( ix < MEDIUM ) { +medium: + n = stdlib_base_round( x * INVPIO2 ); + r = x - ( n * PIO2_1 ); + w = n * PIO2_1T; + + // First rounding (good to 85 bits)... + j = ix >> 20; + *rem1 = r - w; + stdlib_base_float64_get_high_word( *rem1, &uhigh ); + high = ( int32_t )uhigh; + i = j - ( ( high >> 20 ) & EXPONENT_MASK ); + + // Check if a second iteration is needed (good to 118 bits)... + if ( i > 16 ) { + t = r; + w = n * PIO2_2; + r = t - w; + w = ( n * PIO2_2T ) - ( ( t - r ) - w ); + *rem1 = r - w; + stdlib_base_float64_get_high_word( *rem1, &uhigh ); + high = ( int32_t )uhigh; + i = j - ( ( high >> 20 ) & EXPONENT_MASK ); + + // Check if a third iteration is needed (151 bits accumulated)... + if ( i > 49 ) { + // will cover all possible cases + t = r; + w = n * PIO2_3; + r = t - w; + w = ( n * PIO2_3T ) - ( ( t - r ) - w ); + *rem1 = r - w; + } + } + *rem2 = ( r - *rem1 ) - w; + return n; + } + // Case: x is NaN or infinity + if( ix >= STDLIB_CONSTANT_FLOAT64_HIGH_WORD_EXPONENT_MASK ) { + *rem1 = 0.0 / 0.0; // NaN + *rem2 = 0.0 / 0.0; // NaN + return 0; + } + // Set z = scalbn(|x|, ilogb(x)-23)... + stdlib_base_float64_get_low_word( x, &ulow ); + low = ( int32_t )ulow; + e0 = ( ix >> 20 ) - 1046; // `e0 = ilogb(z) - 23` => unbiased exponent minus 23 + stdlib_base_float64_from_words( ix - ( int32_t ) ( e0 << 20 ), low, &z ); + for ( i = 0; i < 2; i++ ) { + TX[ i ] = ( double )( ( int32_t )z ); + z = ( z - TX[ i ] ) * TWO24; + } + TX[ 2 ] = z; + nx = 3; + while ( TX[ nx - 1 ] == ZERO ) { + // Skip zero term... + nx--; + } + n = rempio2Kernel( TX, TY, e0, nx); + if ( hx < 0 ) { + *rem1 = -TY[ 0 ]; + *rem2 = -TY[ 1 ]; + return -n; + } + *rem1 = TY[ 0 ]; + *rem2 = TY[ 1 ]; + return n; +} diff --git a/base/special/rempio2/test/test.js b/base/special/rempio2/test/test.js index a32611791..5a4132d2a 100644 --- a/base/special/rempio2/test/test.js +++ b/base/special/rempio2/test/test.js @@ -48,24 +48,24 @@ tape( 'main export is a function', function test( t ) { tape( 'the function returns `0` and sets the elements of `y` to `NaN` if provided `NaN`', function test( t ) { var y = [ 0.0, 0.0 ]; var n = rempio2( NaN, y ); - t.strictEqual( n, 0.0, 'returns 0' ); - t.strictEqual( isnan( y[0] ), true, 'sets y[0] to NaN' ); - t.strictEqual( isnan( y[1] ), true, 'sets y[1] to NaN' ); + t.strictEqual( n, 0.0, 'returns expected value' ); + t.strictEqual( isnan( y[0] ), true, 'returns expected value' ); + t.strictEqual( isnan( y[1] ), true, 'returns expected value' ); t.end(); }); tape( 'the function returns `0` and sets the elements of `y` to `NaN` if provided positive or negative infinity', function test( t ) { var y = [ 0.0, 0.0 ]; var n = rempio2( PINF, y ); - t.strictEqual( n, 0.0, 'returns 0' ); - t.strictEqual( isnan( y[0] ), true, 'sets y[0] to NaN' ); - t.strictEqual( isnan( y[1] ), true, 'sets y[1] to NaN' ); + t.strictEqual( n, 0.0, 'returns expected value' ); + t.strictEqual( isnan( y[0] ), true, 'returns expected value' ); + t.strictEqual( isnan( y[1] ), true, 'returns expected value' ); y = [ 0.0, 0.0 ]; n = rempio2( NINF, y ); - t.strictEqual( n, 0.0, 'returns 0' ); - t.strictEqual( isnan( y[0] ), true, 'sets y[0] to NaN' ); - t.strictEqual( isnan( y[1] ), true, 'sets y[1] to NaN' ); + t.strictEqual( n, 0.0, 'returns expected value' ); + t.strictEqual( isnan( y[0] ), true, 'returns expected value' ); + t.strictEqual( isnan( y[1] ), true, 'returns expected value' ); t.end(); }); @@ -83,14 +83,14 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating x = randu()*100.0; n = rempio2( x, y ); - t.strictEqual( isInteger( n ), true, 'returns integer' ); - t.strictEqual( isNumber( y[0] ), true, 'assigns a number value to y[0]' ); - t.strictEqual( isNumber( y[1] ), true, 'assigns a number value to y[1]' ); + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); z = ( PIO2*n ) + ( y[0]+y[1] ); delta = abs( z - x ); tol = EPS * abs( x ); - t.strictEqual( delta <= tol, true, 'can recover input value' ); + t.strictEqual( delta <= tol, true, 'returns expected value' ); } t.end(); }); @@ -109,14 +109,14 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating x = randu()*1.0e-100; n = rempio2( x, y ); - t.strictEqual( isInteger( n ), true, 'returns integer' ); - t.strictEqual( isNumber( y[0] ), true, 'assigns a number value to y[0]' ); - t.strictEqual( isNumber( y[1] ), true, 'assigns a number value to y[1]' ); + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); z = ( PIO2*n ) + ( y[0]+y[1] ); delta = abs( z - x ); tol = EPS * abs( x ); - t.strictEqual( delta <= tol, true, 'can recover input value' ); + t.strictEqual( delta <= tol, true, 'returns expected value' ); } t.end(); }); @@ -135,14 +135,14 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating x = -100.0 * randu(); n = rempio2( x, y ); - t.strictEqual( isInteger( n ), true, 'returns integer' ); - t.strictEqual( isNumber( y[0] ), true, 'assigns a number value to y[0]' ); - t.strictEqual( isNumber( y[1] ), true, 'assigns a number value to y[1]' ); + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); z = ( PIO2*n ) + ( y[0]+y[1] ); delta = abs( z - x ); tol = EPS * abs( x ); - t.strictEqual( delta <= tol, true, 'can recover input value' ); + t.strictEqual( delta <= tol, true, 'returns expected value' ); } t.end(); }); @@ -161,14 +161,14 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating x = -1.0e-100 * randu(); n = rempio2( x, y ); - t.strictEqual( isInteger( n ), true, 'returns integer' ); - t.strictEqual( isNumber( y[0] ), true, 'assigns a number value to y[0]' ); - t.strictEqual( isNumber( y[1] ), true, 'assigns a number value to y[1]' ); + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); z = ( PIO2*n ) + ( y[0]+y[1] ); delta = abs( z - x ); tol = EPS * abs( x ); - t.strictEqual( delta <= tol, true, 'can recover input value' ); + t.strictEqual( delta <= tol, true, 'returns expected value' ); } t.end(); }); @@ -187,14 +187,14 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating for ( i = 0; i < x.length; i++ ) { n = rempio2( x[i], y ); - t.strictEqual( isInteger( n ), true, 'returns integer' ); - t.strictEqual( isNumber( y[0] ), true, 'assigns a number value to y[0]' ); - t.strictEqual( isNumber( y[1] ), true, 'assigns a number value to y[1]' ); + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); z = ( PIO2*n ) + ( y[0]+y[1] ); delta = abs( z - x[i] ); tol = EPS * abs( x[i] ); - t.strictEqual( delta <= tol, true, 'can recover input value' ); + t.strictEqual( delta <= tol, true, 'returns expected value' ); } t.end(); }); @@ -209,10 +209,10 @@ tape( 'for large positive input values, the function returns the last three bina y = [ 0.0, 0.0 ]; for ( i = 0; i < x.length; i++ ) { n = rempio2( x[i], y ); - t.strictEqual( isInteger( n ), true, 'returns integer' ); - t.strictEqual( isNumber( y[0] ), true, 'assigns a number value to y[0]' ); - t.strictEqual( isNumber( y[1] ), true, 'assigns a number value to y[1]' ); - t.strictEqual( n < 8, true, 'returns a value smaller than 8' ); + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); + t.strictEqual( n < 8, true, 'returns expected value' ); } t.end(); }); @@ -227,10 +227,10 @@ tape( 'for large negative input values, the function returns the last three bina y = [ 0.0, 0.0 ]; for ( i = 0; i < x.length; i++ ) { n = rempio2( x[i], y ); - t.strictEqual( isInteger( n ), true, 'returns integer' ); - t.strictEqual( isNumber( y[0] ), true, 'assigns a number value to y[0]' ); - t.strictEqual( isNumber( y[1] ), true, 'assigns a number value to y[1]' ); - t.strictEqual( n < 8, true, 'returns a value smaller than 8' ); + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); + t.strictEqual( n < 8, true, 'returns expected value' ); } t.end(); }); @@ -245,10 +245,10 @@ tape( 'for huge positive input values, the function returns the last three binar y = [ 0.0, 0.0 ]; for ( i = 0; i < x.length; i++ ) { n = rempio2( x[i], y ); - t.strictEqual( isInteger( n ), true, 'returns integer' ); - t.strictEqual( isNumber( y[0] ), true, 'assigns a number value to y[0]' ); - t.strictEqual( isNumber( y[1] ), true, 'assigns a number value to y[1]' ); - t.strictEqual( n < 8, true, 'returns a value smaller than 8' ); + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); + t.strictEqual( n < 8, true, 'returns expected value' ); } t.end(); }); @@ -263,10 +263,10 @@ tape( 'for huge negative input values, the function returns the last three binar y = [ 0.0, 0.0 ]; for ( i = 0; i < x.length; i++ ) { n = rempio2( x[i], y ); - t.strictEqual( isInteger( n ), true, 'returns integer' ); - t.strictEqual( isNumber( y[0] ), true, 'assigns a number value to y[0]' ); - t.strictEqual( isNumber( y[1] ), true, 'assigns a number value to y[1]' ); - t.strictEqual( n < 8, true, 'returns a value smaller than 8' ); + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); + t.strictEqual( n < 8, true, 'returns expected value' ); } t.end(); }); diff --git a/base/special/rempio2/test/test.native.js b/base/special/rempio2/test/test.native.js new file mode 100644 index 000000000..0cdb998a0 --- /dev/null +++ b/base/special/rempio2/test/test.native.js @@ -0,0 +1,282 @@ +/** +* @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 isInteger = require( '@stdlib/assert/is-integer' ); +var isNumber = require( '@stdlib/assert/is-number' ); +var isnan = require( './../../../../base/assert/is-nan' ); +var incrspace = require( '@stdlib/array/base/incrspace' ); +var linspace = require( '@stdlib/array/base/linspace' ); +var randu = require( '@stdlib/random/base/randu' ); +var abs = require( './../../../../base/special/abs' ); +var pow = require( './../../../../base/special/pow' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var PIO2 = require( '@stdlib/constants/float64/half-pi' ); +var PIO4 = require( '@stdlib/constants/float64/fourth-pi' ); +var Float64Array = require( '@stdlib/array/float64' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// VARIABLES // + +var rempio2 = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( rempio2 instanceof Error ) +}; + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof rempio2, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function returns `0` and sets the elements of `y` to `NaN` if provided `NaN`', opts, function test( t ) { + var y = new Float64Array( [ 0.0, 0.0 ] ); + var n = rempio2( NaN, y ); + t.strictEqual( n, 0.0, 'returns expected value' ); + t.strictEqual( isnan( y[0] ), true, 'returns expected value' ); + t.strictEqual( isnan( y[1] ), true, 'returns expected value' ); + t.end(); +}); + +tape( 'the function returns `0` and sets the elements of `y` to `NaN` if provided positive or negative infinity', opts, function test( t ) { + var y = new Float64Array( [ 0.0, 0.0 ] ); + var n = rempio2( PINF, y ); + t.strictEqual( n, 0.0, 'returns expected value' ); + t.strictEqual( isnan( y[0] ), true, 'returns expected value' ); + t.strictEqual( isnan( y[1] ), true, 'returns expected value' ); + + y = new Float64Array( [ 0.0, 0.0 ] ); + n = rempio2( NINF, y ); + t.strictEqual( n, 0.0, 'returns expected value' ); + t.strictEqual( isnan( y[0] ), true, 'returns expected value' ); + t.strictEqual( isnan( y[1] ), true, 'returns expected value' ); + t.end(); +}); + +tape( 'the function returns `n` and stores `r` as two double-precision floating points numbers in `y` such that `x - nπ/2 = r` (positive)', opts, function test( t ) { + var delta; + var tol; + var x; + var y; + var z; + var n; + var i; + + y = new Float64Array( [ 0.0, 0.0 ] ); + for ( i = 0; i < 200; i++ ) { + x = randu()*100.0; + n = rempio2( x, y ); + + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); + + z = ( PIO2*n ) + ( y[0]+y[1] ); + delta = abs( z - x ); + tol = EPS * abs( x ); + t.strictEqual( delta <= tol, true, 'can recover input value' ); + } + t.end(); +}); + +tape( 'the function returns `n` and stores `r` as two double-precision floating points numbers in `y` such that `x - nπ/2 = r` (tiny positive)', opts, function test( t ) { + var delta; + var tol; + var x; + var y; + var z; + var n; + var i; + + y = new Float64Array( [ 0.0, 0.0 ] ); + for ( i = 0; i < 200; i++ ) { + x = randu()*1.0e-100; + n = rempio2( x, y ); + + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); + + z = ( PIO2*n ) + ( y[0]+y[1] ); + delta = abs( z - x ); + tol = EPS * abs( x ); + t.strictEqual( delta <= tol, true, 'can recover input value' ); + } + t.end(); +}); + +tape( 'the function returns `n` and stores `r` as two double-precision floating points numbers in `y` such that `x - nπ/2 = r` (negative)', opts, function test( t ) { + var delta; + var tol; + var x; + var y; + var z; + var n; + var i; + + y = new Float64Array( [ 0.0, 0.0 ] ); + for ( i = 0; i < 200; i++ ) { + x = -100.0 * randu(); + n = rempio2( x, y ); + + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); + + z = ( PIO2*n ) + ( y[0]+y[1] ); + delta = abs( z - x ); + tol = EPS * abs( x ); + t.strictEqual( delta <= tol, true, 'can recover input value' ); + } + t.end(); +}); + +tape( 'the function returns `n` and stores `r` as two double-precision floating points numbers in `y` such that `x - nπ/2 = r` (tiny negative)', opts, function test( t ) { + var delta; + var tol; + var x; + var y; + var z; + var n; + var i; + + y = new Float64Array( [ 0.0, 0.0 ] ); + for ( i = 0; i < 200; i++ ) { + x = -1.0e-100 * randu(); + n = rempio2( x, y ); + + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); + + z = ( PIO2*n ) + ( y[0]+y[1] ); + delta = abs( z - x ); + tol = EPS * abs( x ); + t.strictEqual( delta <= tol, true, 'can recover input value' ); + } + t.end(); +}); + +tape( 'the function returns `n` and stores `r` as two double-precision floating points numbers in `y` such that `x - nπ/2 = r` (multiples of π/4)', opts, function test( t ) { + var delta; + var tol; + var x; + var y; + var z; + var n; + var i; + + x = incrspace( -10.0*PIO4, 10.0*PIO4, PIO4 ); + y = new Float64Array( [ 0.0, 0.0 ] ); + for ( i = 0; i < x.length; i++ ) { + n = rempio2( x[i], y ); + + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); + + z = ( PIO2*n ) + ( y[0]+y[1] ); + delta = abs( z - x[i] ); + tol = EPS * abs( x[i] ); + t.strictEqual( delta <= tol, true, 'can recover input value' ); + } + t.end(); +}); + +tape( 'for large positive input values, the function returns the last three binary digits of `n` and stores `r` as two double-precision floating points numbers in `y`', opts, function test( t ) { + var x; + var y; + var n; + var i; + + x = linspace( pow( 2.0, 20 )*PIO2, pow( 2.0, 60 )*PIO2, 4000 ); + y = new Float64Array( [ 0.0, 0.0 ] ); + for ( i = 0; i < x.length; i++ ) { + n = rempio2( x[i], y ); + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); + t.strictEqual( n < 8, true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'for large negative input values, the function returns the last three binary digits of `n` and stores `r` as two double-precision floating points numbers in `y`', opts, function test( t ) { + var x; + var y; + var n; + var i; + + x = linspace( -pow( 2.0, 20 )*PIO2, -pow( 2.0, 60 )*PIO2, 4000 ); + y = new Float64Array( [ 0.0, 0.0 ] ); + for ( i = 0; i < x.length; i++ ) { + n = rempio2( x[i], y ); + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); + t.strictEqual( n < 8, true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'for huge positive input values, the function returns the last three binary digits of `n` and stores `r` as two double-precision floating points numbers in `y`', opts, function test( t ) { + var x; + var y; + var n; + var i; + + x = linspace( pow( 2.0, 60 )*PIO2, pow( 2.0, 1020 )*PIO2, 6000 ); + y = new Float64Array( [ 0.0, 0.0 ] ); + for ( i = 0; i < x.length; i++ ) { + n = rempio2( x[i], y ); + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); + t.strictEqual( n < 8, true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'for huge negative input values, the function returns the last three binary digits of `n` and stores `r` as two double-precision floating points numbers in `y`', opts, function test( t ) { + var x; + var y; + var n; + var i; + + x = linspace( -pow( 2.0, 60 )*PIO2, -pow( 2.0, 1020 )*PIO2, 6000 ); + y = new Float64Array( [ 0.0, 0.0 ] ); + for ( i = 0; i < x.length; i++ ) { + n = rempio2( x[i], y ); + t.strictEqual( isInteger( n ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[0] ), true, 'returns expected value' ); + t.strictEqual( isNumber( y[1] ), true, 'returns expected value' ); + t.strictEqual( n < 8, true, 'returns expected value' ); + } + t.end(); +});