diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/README.md b/lib/node_modules/@stdlib/math/base/special/cinvf/README.md new file mode 100644 index 000000000000..b441ae6c745f --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/README.md @@ -0,0 +1,256 @@ + + +# cinvf + +> Compute the inverse of a single-precision complex floating-point number. + +
+ +The inverse (or reciprocal) of a non-zero complex number `z = a + bi` is defined as + + + +
+ Complex Inverse +
+
+ + + +
+ + + +
+ +## Usage + +```javascript +var cinvf = require( '@stdlib/math/base/special/cinvf' ); +``` + +#### cinvf( z ) + +Computes the inverse of a single-precision complex floating-point number. + +```javascript +var Complex64 = require( '@stdlib/complex/float32/ctor' ); +var real = require( '@stdlib/complex/float32/real' ); +var imag = require( '@stdlib/complex/float32/imag' ); + +var v = cinvf( new Complex64( 2.0, 4.0 ) ); +// returns + +var re = real( v ); +// returns ~0.1 + +var im = imag( v ); +// returns ~-0.2 +``` + +
+ + + +
+ +## Examples + + + +```javascript +var Complex64 = require( '@stdlib/complex/float32/ctor' ); +var uniform = require( '@stdlib/random/array/uniform' ); +var cinvf = require( '@stdlib/math/base/special/cinvf' ); + +var re; +var im; +var z1; +var z2; +var i; + +re = uniform( 100, -50, 50 ); +im = uniform( 100, -50, 50 ); + +for ( i = 0; i < 100; i++ ) { + z1 = new Complex64( re[ i % re.length ], im[ i % im.length ] ); + z2 = cinvf( z1 ); + console.log( '1.0 / (%s) = %s', z1.toString(), z2.toString() ); +} +``` + +
+ + + + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/cinvf.h" +``` + +#### stdlib_base_cinvf( z ) + +Computes the inverse of a single-precision complex floating-point number. + +```c +#include "stdlib/complex/float32/ctor.h" +#include "stdlib/complex/float32/real.h" +#include "stdlib/complex/float32/imag.h" + +stdlib_complex64_t z = stdlib_complex64( 2.0f, 4.0f ); + +stdlib_complex64_t out = stdlib_base_cinvf( z ); + +float re = stdlib_complex64_real( out ); +// returns 0.1f + +float im = stdlib_complex64_imag( out ); +// returns -0.2f +``` + +The function accepts the following arguments: + +- **z**: `[in] stdlib_complex64_t` input value. + +```c +stdlib_complex64_t stdlib_base_cinvf( const stdlib_complex64_t z ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/cinvf.h" +#include "stdlib/complex/float32/ctor.h" +#include "stdlib/complex/float32/reim.h" +#include + +int main() { + const stdlib_complex64_t x[] = { + stdlib_complex64( 3.14f, 1.5f ), + stdlib_complex64( -3.14f, -1.5f ), + stdlib_complex64( 0.0f, 0.0f ), + stdlib_complex64( 0.0f / 0.0f, 0.0f / 0.0f ) + }; + + stdlib_complex64_t v; + stdlib_complex64_t y; + float re1; + float im1; + float re2; + float im2; + int i; + for ( i = 0; i < 4; i++ ) { + v = x[ i ]; + y = stdlib_base_cinvf( v ); + stdlib_complex64_reim( v, &re1, &im1 ); + stdlib_complex64_reim( y, &re2, &im2 ); + printf( "cinvf(%f + %fi) = %f + %fi\n", re1, im1, re2, im2 ); + } +} +``` + +
+ + + +
+ + + +* * * + +
+ +## References + +- Smith, Robert L. 1962. "Algorithm 116: Complex Division." _Commun. ACM_ 5 (8). New York, NY, USA: ACM: 435. doi:[10.1145/368637.368661][@smith:1962a]. +- Stewart, G. W. 1985. "A Note on Complex Division." _ACM Trans. Math. Softw._ 11 (3). New York, NY, USA: ACM: 238–41. doi:[10.1145/214408.214414][@stewart:1985a]. +- Priest, Douglas M. 2004. "Efficient Scaling for Complex Division." _ACM Trans. Math. Softw._ 30 (4). New York, NY, USA: ACM: 389–401. doi:[10.1145/1039813.1039814][@priest:2004a]. +- Baudin, Michael, and Robert L. Smith. 2012. "A Robust Complex Division in Scilab." _arXiv_ abs/1210.4539 \[cs.MS] (October): 1–25. [<https://arxiv.org/abs/1210.4539>][@baudin:2012a]. + +
+ + + + + +
+ +
+ + + + + +
+ +[@smith:1962a]: https://doi.org/10.1145/368637.368661 + +[@stewart:1985a]: https://doi.org/10.1145/214408.214414 + +[@priest:2004a]: https://doi.org/10.1145/1039813.1039814 + +[@baudin:2012a]: https://arxiv.org/abs/1210.4539 + + + + + +
+ + diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/benchmark.js new file mode 100644 index 000000000000..1a41021bd827 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/benchmark.js @@ -0,0 +1,58 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var bench = require( '@stdlib/bench' ); +var uniform = require( '@stdlib/random/base/uniform' ); +var isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var Complex64 = require( '@stdlib/complex/float32/ctor' ); +var real = require( '@stdlib/complex/float32/real' ); +var imag = require( '@stdlib/complex/float32/imag' ); +var pkg = require( './../package.json' ).name; +var cinvf = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( b ) { + var values; + var y; + var i; + + values = [ + new Complex64( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) ), + new Complex64( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) ) + ]; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = cinvf( values[ i % values.length ] ); + if ( isnanf( real( y ) ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnanf( imag( y ) ) ) { + b.fail( 'should not return not NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/benchmark.native.js new file mode 100644 index 000000000000..1b81e3d6b6e2 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/benchmark.native.js @@ -0,0 +1,67 @@ +/** +* @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 uniform = require( '@stdlib/random/base/uniform' ); +var isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var real = require( '@stdlib/complex/float32/real' ); +var imag = require( '@stdlib/complex/float32/imag' ); +var Complex64 = require( '@stdlib/complex/float32/ctor' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var cinvf = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( cinvf instanceof Error ) +}; + + +// MAIN // + +bench( pkg+'::native', opts, function benchmark( b ) { + var values; + var y; + var i; + + values = [ + new Complex64( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) ), + new Complex64( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) ) + ]; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = cinvf( values[ i % values.length ] ); + if ( isnanf( real( y ) ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnanf( imag( y ) ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/c/Makefile b/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/c/Makefile new file mode 100644 index 000000000000..ad9fedcd4fff --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/c/Makefile @@ -0,0 +1,107 @@ +#/ +# @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 := @ +endif + +# Determine the OS: +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate [position independent code][1]: +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of C targets: +c_targets := benchmark.out + + +# TARGETS # + +# Default target. +# +# This target is the default target. + +all: $(c_targets) + +.PHONY: all + + +# Compile C source. +# +# This target compiles C source files. + +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) -o $@ $< -lm + + +# Run a benchmark. +# +# This target runs a benchmark. + +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + + +# Perform clean-up. +# +# This target removes generated files. + +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/c/benchmark.c b/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/c/benchmark.c new file mode 100644 index 000000000000..bfcb222104d0 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/c/benchmark.c @@ -0,0 +1,140 @@ +/** +* @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 +#include +#include +#include +#include + +#define NAME "invf" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +static void print_version( void ) { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +static void print_summary( int total, int passing ) { + printf( "#\n" ); + printf( "1..%d\n", total ); // TAP plan + printf( "# total %d\n", total ); + printf( "# pass %d\n", passing ); + printf( "#\n" ); + printf( "# ok\n" ); +} + +/** +* Prints benchmarks results. +* +* @param elapsed elapsed time in seconds +*/ +static void print_results( double elapsed ) { + double rate = (double)ITERATIONS / elapsed; + printf( " ---\n" ); + printf( " iterations: %d\n", ITERATIONS ); + printf( " elapsed: %0.9f\n", elapsed ); + printf( " rate: %0.9f\n", rate ); + printf( " ...\n" ); +} + +/** +* Returns a clock time. +* +* @return clock time +*/ +static double tic( void ) { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec/1.0e6; +} + +/** +* Generates a random number on the interval [0,1). +* +* @return random number +*/ +static float rand_float( void ) { + int r = rand(); + return (float)r / ( (float)RAND_MAX + 1.0f ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark( void ) { + double elapsed; + float x[ 100 ]; + float y[ 100 ]; + double t; + int i; + + float complex z1; + float complex z2; + + for ( i = 0; i < 100; i++ ) { + x[ i ] = ( 20.0f * rand_float() ) - 10.0f; + y[ i ] = ( 2048.0f * rand_float() ) - 1024.0f; + } + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + z1 = x[ i % 100 ] + y[ i % 100 ]*I; + z2 = 1.0f / z1; + if ( z2 != z2 ) { + printf( "should not return NaN\n" ); + break; + } + } + elapsed = tic() - t; + if ( z2 != z2 ) { + printf( "should not return NaN\n" ); + } + return elapsed; +} + +/** +* Main execution sequence. +*/ +int main( void ) { + double elapsed; + int i; + + // Use the current time to seed the random number generator: + srand( time( NULL ) ); + + print_version(); + for ( i = 0; i < REPEATS; i++ ) { + printf( "# c::%s\n", NAME ); + elapsed = benchmark(); + print_results( elapsed ); + printf( "ok %d benchmark finished\n", i+1 ); + } + print_summary( REPEATS, REPEATS ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/c/native/Makefile new file mode 100644 index 000000000000..f69e9da2b4d3 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/c/native/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate position independent code ([1][1], [2][2]). +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`): +INCLUDE ?= + +# List of source files: +SOURCE_FILES ?= + +# List of libraries (e.g., `-lopenblas -lpthread`): +LIBRARIES ?= + +# List of library paths (e.g., `-L /foo/bar -L /beep/boop`): +LIBPATH ?= + +# List of C targets: +c_targets := benchmark.out + + +# RULES # + +#/ +# Compiles source files. +# +# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`) +# @param {string} [CFLAGS] - C compiler options +# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`) +# @param {string} [SOURCE_FILES] - list of source files +# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`) +# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`) +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler (e.g., `gcc`) +# @param {string} CFLAGS - C compiler options +# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`) +# @param {string} SOURCE_FILES - list of source files +# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`) +# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`) +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES) + +#/ +# Runs compiled benchmarks. +# +# @example +# make run +#/ +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/c/native/benchmark.c new file mode 100644 index 000000000000..4ba88b5e1044 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/benchmark/c/native/benchmark.c @@ -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. +*/ + +#include "stdlib/math/base/special/cinvf.h" +#include "stdlib/complex/float32/ctor.h" +#include "stdlib/complex/float32/reim.h" +#include +#include +#include +#include +#include + +#define NAME "cinvf" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +static void print_version( void ) { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +static void print_summary( int total, int passing ) { + printf( "#\n" ); + printf( "1..%d\n", total ); // TAP plan + printf( "# total %d\n", total ); + printf( "# pass %d\n", passing ); + printf( "#\n" ); + printf( "# ok\n" ); +} + +/** +* Prints benchmarks results. +* +* @param elapsed elapsed time in seconds +*/ +static void print_results( double elapsed ) { + double rate = (double)ITERATIONS / elapsed; + printf( " ---\n" ); + printf( " iterations: %d\n", ITERATIONS ); + printf( " elapsed: %0.9f\n", elapsed ); + printf( " rate: %0.9f\n", rate ); + printf( " ...\n" ); +} + +/** +* Returns a clock time. +* +* @return clock time +*/ +static double tic( void ) { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec/1.0e6; +} + +/** +* Generates a random number on the interval [0,1). +* +* @return random number +*/ +static float rand_float( void ) { + int r = rand(); + return (float)r / ( (float)RAND_MAX + 1.0f ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark( void ) { + double elapsed; + float x[ 100 ]; + float y[ 100 ]; + float re; + float im; + double t; + int i; + + stdlib_complex64_t a; + stdlib_complex64_t b; + + for ( i = 0; i < 100; i++ ) { + x[ i ] = ( 20.0f * rand_float() ) - 10.0f; + y[ i ] = ( 2048.0f * rand_float() ) - 1024.0f; + } + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + a = stdlib_complex64( x[ i % 100 ], y[ i % 100 ] ); + b = stdlib_base_cinvf( a ); + stdlib_complex64_reim( b, &re, &im ); + if ( re != re ) { + printf( "unexpected result\n" ); + break; + } + } + elapsed = tic() - t; + if ( im != im ) { + printf( "unexpected result\n" ); + } + return elapsed; +} + +/** +* Main execution sequence. +*/ +int main( void ) { + double elapsed; + int i; + + // Use the current time to seed the random number generator: + srand( time( NULL ) ); + + print_version(); + for ( i = 0; i < REPEATS; i++ ) { + printf( "# c::native::%s\n", NAME ); + elapsed = benchmark(); + print_results( elapsed ); + printf( "ok %d benchmark finished\n", i+1 ); + } + print_summary( REPEATS, REPEATS ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/binding.gyp b/lib/node_modules/@stdlib/math/base/special/cinvf/binding.gyp new file mode 100644 index 000000000000..ec3992233442 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/binding.gyp @@ -0,0 +1,170 @@ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +# A `.gyp` file for building a Node.js native add-on. +# +# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md +# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md +{ + # List of files to include in this file: + 'includes': [ + './include.gypi', + ], + + # Define variables to be used throughout the configuration for all targets: + 'variables': { + # Target name should match the add-on export name: + 'addon_target_name%': 'addon', + + # Set variables based on the host OS: + 'conditions': [ + [ + 'OS=="win"', + { + # Define the object file suffix: + 'obj': 'obj', + }, + { + # Define the object file suffix: + 'obj': 'o', + } + ], # end condition (OS=="win") + ], # end conditions + }, # end variables + + # Define compile targets: + 'targets': [ + + # Target to generate an add-on: + { + # The target name should match the add-on export name: + 'target_name': '<(addon_target_name)', + + # Define dependencies: + 'dependencies': [], + + # Define directories which contain relevant include headers: + 'include_dirs': [ + # Local include directory: + '<@(include_dirs)', + ], + + # List of source files: + 'sources': [ + '<@(src_files)', + ], + + # Settings which should be applied when a target's object files are used as linker input: + 'link_settings': { + # Define libraries: + 'libraries': [ + '<@(libraries)', + ], + + # Define library directories: + 'library_dirs': [ + '<@(library_dirs)', + ], + }, + + # C/C++ compiler flags: + 'cflags': [ + # Enable commonly used warning options: + '-Wall', + + # Aggressive optimization: + '-O3', + ], + + # C specific compiler flags: + 'cflags_c': [ + # Specify the C standard to which a program is expected to conform: + '-std=c99', + ], + + # C++ specific compiler flags: + 'cflags_cpp': [ + # Specify the C++ standard to which a program is expected to conform: + '-std=c++11', + ], + + # Linker flags: + 'ldflags': [], + + # Apply conditions based on the host OS: + 'conditions': [ + [ + 'OS=="mac"', + { + # Linker flags: + 'ldflags': [ + '-undefined dynamic_lookup', + '-Wl,-no-pie', + '-Wl,-search_paths_first', + ], + }, + ], # end condition (OS=="mac") + [ + 'OS!="win"', + { + # C/C++ flags: + 'cflags': [ + # Generate platform-independent code: + '-fPIC', + ], + }, + ], # end condition (OS!="win") + ], # end conditions + }, # end target <(addon_target_name) + + # Target to copy a generated add-on to a standard location: + { + 'target_name': 'copy_addon', + + # Declare that the output of this target is not linked: + 'type': 'none', + + # Define dependencies: + 'dependencies': [ + # Require that the add-on be generated before building this target: + '<(addon_target_name)', + ], + + # Define a list of actions: + 'actions': [ + { + 'action_name': 'copy_addon', + 'message': 'Copying addon...', + + # Explicitly list the inputs in the command-line invocation below: + 'inputs': [], + + # Declare the expected outputs: + 'outputs': [ + '<(addon_output_dir)/<(addon_target_name).node', + ], + + # Define the command-line invocation: + 'action': [ + 'cp', + '<(PRODUCT_DIR)/<(addon_target_name).node', + '<(addon_output_dir)/<(addon_target_name).node', + ], + }, + ], # end actions + }, # end target copy_addon + ], # end targets +} diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/docs/img/equation_complex_inverse.svg b/lib/node_modules/@stdlib/math/base/special/cinvf/docs/img/equation_complex_inverse.svg new file mode 100644 index 000000000000..8051874e0e6f --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/docs/img/equation_complex_inverse.svg @@ -0,0 +1,74 @@ + +StartFraction 1 Over z EndFraction equals StartFraction z overbar Over z z overbar EndFraction equals StartFraction a Over a squared plus b squared EndFraction minus StartFraction b Over a squared plus b squared EndFraction i period + + + \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/docs/repl.txt b/lib/node_modules/@stdlib/math/base/special/cinvf/docs/repl.txt new file mode 100644 index 000000000000..37c597852bc1 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/docs/repl.txt @@ -0,0 +1,26 @@ + +{{alias}}( z ) + Computes the inverse of a single-precision complex floating-point number. + + Parameters + ---------- + z: Complex64 + Complex number. + + Returns + ------- + out: Complex64 + Result. + + Examples + -------- + > var v = {{alias}}( new {{alias:@stdlib/complex/float32/ctor}}( 2.0, 4.0 ) ) + + > var re = {{alias:@stdlib/complex/float32/real}}( v ) + ~0.1 + > var im = {{alias:@stdlib/complex/float32/imag}}( v ) + ~-0.2 + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/docs/types/index.d.ts b/lib/node_modules/@stdlib/math/base/special/cinvf/docs/types/index.d.ts new file mode 100644 index 000000000000..1b760bb313bc --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/docs/types/index.d.ts @@ -0,0 +1,50 @@ +/* +* @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. +*/ + +// TypeScript Version: 4.1 + +/// + +import { Complex64 } from '@stdlib/types/complex'; + +/** +* Computes the inverse of a single-precision complex floating-point number. +* +* @param z - input value +* @returns result +* +* @example +* var Complex64 = require( '@stdlib/complex/float32/ctor' ); +* var real = require( '@stdlib/complex/float32/real' ); +* var imag = require( '@stdlib/complex/float32/imag' ); +* +* var v = cinvf( new Complex64( 2.0, 4.0 ) ); +* // returns +* +* var re = real( v ); +* // returns ~0.1 +* +* var im = imag( v ); +* // returns ~-0.2 +*/ +declare function cinvf( z: Complex64 ): Complex64; + + +// EXPORTS // + +export = cinvf; diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/docs/types/test.ts b/lib/node_modules/@stdlib/math/base/special/cinvf/docs/types/test.ts new file mode 100644 index 000000000000..60158ef49059 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/docs/types/test.ts @@ -0,0 +1,45 @@ +/* +* @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. +*/ + +import Complex64 = require( '@stdlib/complex/float32/ctor' ); +import cinvf = require( './index' ); + + +// TESTS // + +// The function returns a single-precision complex floating-point number... +{ + cinvf( new Complex64( 1.0, 2.0 ) ); // $ExpectType Complex64 +} + +// The compiler throws an error if the function is provided a value other than a complex number... +{ + cinvf( true ); // $ExpectError + cinvf( false ); // $ExpectError + cinvf( null ); // $ExpectError + cinvf( undefined ); // $ExpectError + cinvf( '5' ); // $ExpectError + cinvf( [] ); // $ExpectError + cinvf( {} ); // $ExpectError + cinvf( ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided an unsupported number of arguments... +{ + cinvf(); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/cinvf/examples/c/Makefile new file mode 100644 index 000000000000..6aed70daf167 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/examples/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate position independent code ([1][1], [2][2]). +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`): +INCLUDE ?= + +# List of source files: +SOURCE_FILES ?= + +# List of libraries (e.g., `-lopenblas -lpthread`): +LIBRARIES ?= + +# List of library paths (e.g., `-L /foo/bar -L /beep/boop`): +LIBPATH ?= + +# List of C targets: +c_targets := example.out + + +# RULES # + +#/ +# Compiles source files. +# +# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`) +# @param {string} [CFLAGS] - C compiler options +# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`) +# @param {string} [SOURCE_FILES] - list of source files +# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`) +# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`) +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler (e.g., `gcc`) +# @param {string} CFLAGS - C compiler options +# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`) +# @param {string} SOURCE_FILES - list of source files +# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`) +# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`) +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES) + +#/ +# Runs compiled examples. +# +# @example +# make run +#/ +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/cinvf/examples/c/example.c new file mode 100644 index 000000000000..5ac9ee173df9 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/examples/c/example.c @@ -0,0 +1,46 @@ +/** +* @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/cinvf.h" +#include "stdlib/complex/float32/ctor.h" +#include "stdlib/complex/float32/reim.h" +#include + +int main() { + const stdlib_complex64_t x[] = { + stdlib_complex64( 3.14f, 1.5f ), + stdlib_complex64( -3.14f, -1.5f ), + stdlib_complex64( 0.0f, 0.0f ), + stdlib_complex64( 0.0f / 0.0f, 0.0f / 0.0f ) + }; + + stdlib_complex64_t v; + stdlib_complex64_t y; + float re1; + float im1; + float re2; + float im2; + int i; + for ( i = 0; i < 4; i++ ) { + v = x[ i ]; + y = stdlib_base_cinvf( v ); + stdlib_complex64_reim( v, &re1, &im1 ); + stdlib_complex64_reim( y, &re2, &im2 ); + printf( "cinvf(%f + %fi) = %f + %fi\n", re1, im1, re2, im2 ); + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/examples/index.js b/lib/node_modules/@stdlib/math/base/special/cinvf/examples/index.js new file mode 100644 index 000000000000..a0d3bac7ce71 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/examples/index.js @@ -0,0 +1,38 @@ +/** +* @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'; + +var Complex64 = require( '@stdlib/complex/float32/ctor' ); +var uniform = require( '@stdlib/random/array/uniform' ); +var cinvf = require( './../lib' ); + +var re; +var im; +var z1; +var z2; +var i; + +re = uniform( 100, -50, 50 ); +im = uniform( 100, -50, 50 ); + +for ( i = 0; i < 100; i++ ) { + z1 = new Complex64( re[ i % re.length ], im[ i % im.length ] ); + z2 = cinvf( z1 ); + console.log( '1.0 / (%s) = %s', z1.toString(), z2.toString() ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/include.gypi b/lib/node_modules/@stdlib/math/base/special/cinvf/include.gypi new file mode 100644 index 000000000000..575cb043c0bf --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/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': [ + ' +* +* var re = real( v ); +* // returns ~0.1 +* +* var im = imag( v ); +* // returns ~-0.2 +*/ + +// MODULES // + +var main = require( './main.js' ); + + +// EXPORTS // + +module.exports = main; diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/lib/main.js b/lib/node_modules/@stdlib/math/base/special/cinvf/lib/main.js new file mode 100644 index 000000000000..5d2aac5142f3 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/lib/main.js @@ -0,0 +1,106 @@ +/** +* @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 absf = require( '@stdlib/math/base/special/absf' ); +var maxf = require( '@stdlib/math/base/special/maxf' ); +var FLOAT32_BIGGEST = require( '@stdlib/constants/float32/max' ); +var FLOAT32_SMALLEST = require( '@stdlib/constants/float32/smallest-normal' ); +var EPS = require( '@stdlib/constants/float32/eps' ); +var Complex64 = require( '@stdlib/complex/float32/ctor' ); +var real = require( '@stdlib/complex/float32/real' ); +var imag = require( '@stdlib/complex/float32/imag' ); + + +// VARIABLES // + +var LARGE_THRESHOLD = FLOAT32_BIGGEST * 0.5; +var SMALL_THRESHOLD = FLOAT32_SMALLEST * ( 2.0 / EPS ); +var RECIP_EPS_SQR = 2.0 / ( EPS * EPS ); + + +// MAIN // + +/** +* Computes the inverse of a single-precision complex floating-point number. +* +* ## References +* +* - Baudin, Michael, and Robert L. Smith. 2012. "A Robust Complex Division in Scilab." _arXiv_ abs/1210.4539 \[cs.MS\] (October): 1–25. . +* +* @param {Complex64} z - complex number +* @returns {Complex64} result +* +* @example +* var Complex64 = require( '@stdlib/complex/float32/ctor' ); +* var real = require( '@stdlib/complex/float32/real' ); +* var imag = require( '@stdlib/complex/float32/imag' ); +* +* var v = cinvf( new Complex64( 2.0, 4.0 ) ); +* // returns +* +* var re = real( v ); +* // returns ~0.1 +* +* var im = imag( v ); +* // returns ~-0.2 +*/ +function cinvf( z ) { + var ab; + var re; + var im; + var s; + var r; + var t; + + re = real( z ); + im = imag( z ); + ab = maxf( absf( re ), absf( im ) ); + s = 1.0; + if ( ab >= LARGE_THRESHOLD ) { + re *= 0.5; + im *= 0.5; + s *= 0.5; + } else if ( ab <= SMALL_THRESHOLD ) { + re *= RECIP_EPS_SQR; + im *= RECIP_EPS_SQR; + s *= RECIP_EPS_SQR; + } + if ( absf( im ) <= absf( re ) ) { + r = im / re; + t = 1.0 / ( re + ( im * r ) ); + re = t; + im = -r * t; + } else { + r = re / im; + t = 1.0 / ( im + ( re * r ) ); + re = r * t; + im = -t; + } + re *= s; + im *= s; + return new Complex64( re, im ); +} + + +// EXPORTS // + +module.exports = cinvf; diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/lib/native.js b/lib/node_modules/@stdlib/math/base/special/cinvf/lib/native.js new file mode 100644 index 000000000000..475ca751643f --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/lib/native.js @@ -0,0 +1,58 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var Complex64 = require( '@stdlib/complex/float32/ctor' ); +var addon = require( './../src/addon.node' ); + + +// MAIN // + +/** +* Computes the inverse of a single-precision complex floating-point number. +* +* @private +* @param {Complex64} z - complex number +* @returns {Complex64} result +* +* @example +* var Complex64 = require( '@stdlib/complex/float32/ctor' ); +* var real = require( '@stdlib/complex/float32/real' ); +* var imag = require( '@stdlib/complex/float32/imag' ); +* +* var v = cinvf( new Complex64( 2.0, 4.0 ) ); +* // returns +* +* var re = real( v ); +* // returns ~0.1 +* +* var im = imag( v ); +* // returns ~-0.2 +*/ +function cinvf( z ) { + var v = addon( z ); + return new Complex64( v.re, v.im ); +} + + +// EXPORTS // + +module.exports = cinvf; diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/manifest.json b/lib/node_modules/@stdlib/math/base/special/cinvf/manifest.json new file mode 100644 index 000000000000..8a98486c54d2 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/manifest.json @@ -0,0 +1,91 @@ +{ + "options": { + "task": "build" + }, + "fields": [ + { + "field": "src", + "resolve": true, + "relative": true + }, + { + "field": "include", + "resolve": true, + "relative": true + }, + { + "field": "libraries", + "resolve": false, + "relative": false + }, + { + "field": "libpath", + "resolve": true, + "relative": false + } + ], + "confs": [ + { + "task": "build", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/napi/unary", + "@stdlib/complex/float32/ctor", + "@stdlib/complex/float32/reim", + "@stdlib/math/base/special/absf", + "@stdlib/math/base/special/maxf", + "@stdlib/constants/float32/max", + "@stdlib/constants/float32/eps", + "@stdlib/constants/float32/smallest-normal" + ] + }, + { + "task": "benchmark", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/complex/float32/ctor", + "@stdlib/complex/float32/reim", + "@stdlib/math/base/special/absf", + "@stdlib/math/base/special/maxf", + "@stdlib/constants/float32/max", + "@stdlib/constants/float32/eps", + "@stdlib/constants/float32/smallest-normal" + ] + }, + { + "task": "examples", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/complex/float32/ctor", + "@stdlib/complex/float32/reim", + "@stdlib/math/base/special/absf", + "@stdlib/math/base/special/maxf", + "@stdlib/constants/float32/max", + "@stdlib/constants/float32/eps", + "@stdlib/constants/float32/smallest-normal" + ] + } + ] +} + diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/package.json b/lib/node_modules/@stdlib/math/base/special/cinvf/package.json new file mode 100644 index 000000000000..cb2ecf96473b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/package.json @@ -0,0 +1,68 @@ +{ + "name": "@stdlib/math/base/special/cinvf", + "version": "0.0.0", + "description": "Compute the inverse of a single-precision complex floating-point number.", + "license": "Apache-2.0", + "author": { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + }, + "contributors": [ + { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + } + ], + "main": "./lib", + "gypfile": true, + "directories": { + "benchmark": "./benchmark", + "doc": "./docs", + "example": "./examples", + "include": "./include", + "lib": "./lib", + "src": "./src", + "test": "./test" + }, + "types": "./docs/types", + "scripts": {}, + "homepage": "https://github.com/stdlib-js/stdlib", + "repository": { + "type": "git", + "url": "git://github.com/stdlib-js/stdlib.git" + }, + "bugs": { + "url": "https://github.com/stdlib-js/stdlib/issues" + }, + "dependencies": {}, + "devDependencies": {}, + "engines": { + "node": ">=0.10.0", + "npm": ">2.7.0" + }, + "os": [ + "aix", + "darwin", + "freebsd", + "linux", + "macos", + "openbsd", + "sunos", + "win32", + "windows" + ], + "keywords": [ + "stdlib", + "stdmath", + "mathematics", + "math", + "cinvf", + "inv", + "inverse", + "reciprocal", + "arithmetic", + "complex", + "cmplx", + "number" + ] +} diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/src/Makefile b/lib/node_modules/@stdlib/math/base/special/cinvf/src/Makefile new file mode 100644 index 000000000000..bcf18aa46655 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/src/Makefile @@ -0,0 +1,70 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + + +# RULES # + +#/ +# Removes generated files for building an add-on. +# +# @example +# make clean-addon +#/ +clean-addon: + $(QUIET) -rm -f *.o *.node + +.PHONY: clean-addon + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: clean-addon + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/src/addon.c b/lib/node_modules/@stdlib/math/base/special/cinvf/src/addon.c new file mode 100644 index 000000000000..136653ecd3d5 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/src/addon.c @@ -0,0 +1,23 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +#include "stdlib/math/base/special/cinvf.h" +#include "stdlib/math/base/napi/unary.h" + +// cppcheck-suppress shadowFunction +STDLIB_MATH_BASE_NAPI_MODULE_C_C( stdlib_base_cinvf ) diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/src/main.c b/lib/node_modules/@stdlib/math/base/special/cinvf/src/main.c new file mode 100644 index 000000000000..bf45ca162e07 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/src/main.c @@ -0,0 +1,99 @@ +/** +* @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/cinvf.h" +#include "stdlib/math/base/special/absf.h" +#include "stdlib/math/base/special/maxf.h" +#include "stdlib/constants/float32/max.h" +#include "stdlib/constants/float32/eps.h" +#include "stdlib/constants/float32/smallest_normal.h" +#include "stdlib/complex/float32/ctor.h" +#include "stdlib/complex/float32/reim.h" + + +// VARIABLES // + +static const float LARGE_THRESHOLD = STDLIB_CONSTANT_FLOAT32_MAX * 0.5f; +static const float SMALL_THRESHOLD = STDLIB_CONSTANT_FLOAT32_SMALLEST_NORMAL * ( 2.0f / STDLIB_CONSTANT_FLOAT32_EPS ); +static const float RECIP_EPS_SQR = 2.0f / ( STDLIB_CONSTANT_FLOAT32_EPS * STDLIB_CONSTANT_FLOAT32_EPS ); + + +// MAIN // + +/** +* Computes the inverse of a single-precision complex floating-point number. +* +* ## References +* +* - Baudin, Michael, and Robert L. Smith. 2012. "A Robust Complex Division in Scilab." _arXiv_ abs/1210.4539 \[cs.MS\] (October): 1–25. . +* +* @param z input value +* @return result +* +* @example +* #include "stdlib/complex/float32/ctor.h" +* #include "stdlib/complex/float32/real.h" +* #include "stdlib/complex/float32/imag.h" +* +* stdlib_complex64_t z = stdlib_complex64( 2.0f, 4.0f ); +* +* stdlib_complex64_t out = stdlib_base_cinvf( z ); +* +* float re = stdlib_complex64_real( out ); +* // returns 0.1f +* +* float im = stdlib_complex64_imag( out ); +* // returns -0.2f +*/ +stdlib_complex64_t stdlib_base_cinvf( const stdlib_complex64_t z ) { + float re; + float im; + float ab; + float s; + float r; + float t; + + stdlib_complex64_reim( z, &re, &im ); + + ab = stdlib_base_maxf( stdlib_base_absf( re ), stdlib_base_absf( im ) ); + s = 1.0f; + if ( ab >= LARGE_THRESHOLD ) { + re *= 0.5f; + im *= 0.5f; + s *= 0.5f; + } + else if ( ab <= SMALL_THRESHOLD ) { + re *= RECIP_EPS_SQR; + im *= RECIP_EPS_SQR; + s *= RECIP_EPS_SQR; + } + if ( stdlib_base_absf( im ) <= stdlib_base_absf( re ) ) { + r = im / re; + t = 1.0f / ( re + ( im * r ) ); + re = t; + im = -r * t; + } else { + r = re / im; + t = 1.0f / ( im + ( re * r ) ); + re = r * t; + im = -t; + } + re *= s; + im *= s; + return stdlib_complex64( re, im ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/REQUIRE new file mode 100644 index 000000000000..308c3be89c85 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/REQUIRE @@ -0,0 +1,2 @@ +julia 1.5 +JSON 0.21 diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/data.json b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/data.json new file mode 100644 index 000000000000..fda32740e650 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/data.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/large_negative_imaginary_components.json b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/large_negative_imaginary_components.json new file mode 100644 index 000000000000..50828a4af630 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/large_negative_imaginary_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/large_negative_real_components.json b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/large_negative_real_components.json new file mode 100644 index 000000000000..7be45250969b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/large_negative_real_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/large_positive_imaginary_components.json b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/large_positive_imaginary_components.json new file mode 100644 index 000000000000..abef656cb03d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/large_positive_imaginary_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/large_positive_real_components.json b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/large_positive_real_components.json new file mode 100644 index 000000000000..ab4364bb3633 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/large_positive_real_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/runner.jl new file mode 100644 index 000000000000..e6ef0fe239b7 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/runner.jl @@ -0,0 +1,116 @@ +#!/usr/bin/env julia +# +# @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. + +import JSON + +""" + gen( re, im, name ) + +Generate fixture data and write to file. + +# Arguments + +* `re`: real components for first complex number +* `im`: imaginary components for first complex number +* `name::AbstractString`: output filename + +# Examples + +``` julia +julia> re = rand( 1000 ); +julia> im = rand( 1000 ); +julia> gen( re, im, \"data.json\" ); +``` +""" +function gen( re, im, name ) + zre = Array{Float32}( undef, length( re ) ); + zim = Array{Float32}( undef, length( re ) ); + for i in eachindex(re) + z = 1.0 / Complex{Float32}( re[ i ], im[ i ] ); + zre[ i ] = real( z ); + zim[ i ] = imag( z ); + end + + # Store data to be written to file as a collection: + data = Dict([ + ("re", re), + ("im", im), + ("qre", zre), + ("qim", zim), + ]); + + # Based on the script directory, create an output filepath: + filepath = joinpath( dir, name ); + + # Write the data to the output filepath as JSON: + outfile = open( filepath, "w" ); + write( outfile, JSON.json(data) ); + write( outfile, "\n" ); + close( outfile ); +end + +# Get the filename: +file = @__FILE__; + +# Extract the directory in which this file resides: +dir = dirname( file ); + +# Large positive real components: +re = rand( Float32, 500 ) .* 1.0e30; +im = ( rand( Float32, 500 ) .* 20.0 ) .- 10.0; +gen( re, im, "large_positive_real_components.json" ); + +# Large negative real components: +re = -rand( Float32, 500 ) .* 1.0e30; +im = ( rand( Float32, 500 ) .* 20.0 ) .- 10.0; +gen( re, im, "large_negative_real_components.json" ); + +# Large positive imaginary components: +re = ( rand( Float32, 500 ) .* 20.0 ) .- 10.0; +im = rand( Float32, 500 ) .* 1.0e30; +gen( re, im, "large_positive_imaginary_components.json" ); + +# Large negative imaginary components: +re = ( rand( Float32, 500 ) .* 20.0 ) .- 10.0; +im = -rand( Float32, 500 ) .* 1.0e30; +gen( re, im, "large_negative_imaginary_components.json" ); + +# Tiny positive real components: +re = rand( Float32, 500 ) .* 1.0e-30; +im = ( rand( Float32, 500 ) .* 20.0 ) .- 10.0; +gen( re, im, "tiny_positive_real_components.json" ); + +# Tiny negative real components: +re = -rand( Float32, 500 ) .* 1.0e-30; +im = ( rand( Float32, 500 ) .* 20.0 ) .- 10.0; +gen( re, im, "tiny_negative_real_components.json" ); + +# Tiny positive imaginary components: +re = ( rand( Float32, 500 ) .* 20.0 ) .- 10.0; +im = rand( Float32, 500 ) .* 1.0e-30; +gen( re, im, "tiny_positive_imaginary_components.json" ); + +# Tiny negative imaginary components: +re = ( rand( Float32, 500 ) .* 20.0 ) .- 10.0; +im = -rand( Float32, 500 ) .* 1.0e-30; +gen( re, im, "tiny_negative_imaginary_components.json" ); + +# Normal: +re = ( rand( Float32, 500 ) .* 100.0 ) .- 50.0; +im = ( rand( Float32, 500 ) .* 100.0 ) .- 50.0; +gen( re, im, "data.json" ); diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/tiny_negative_imaginary_components.json b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/tiny_negative_imaginary_components.json new file mode 100644 index 000000000000..a3783a82a3fb --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/tiny_negative_imaginary_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/tiny_negative_real_components.json b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/tiny_negative_real_components.json new file mode 100644 index 000000000000..00999c528d62 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/tiny_negative_real_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/tiny_positive_imaginary_components.json b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/tiny_positive_imaginary_components.json new file mode 100644 index 000000000000..2c8543b1fd58 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/tiny_positive_imaginary_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/tiny_positive_real_components.json b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/tiny_positive_real_components.json new file mode 100644 index 000000000000..1ca20f713619 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/test/fixtures/julia/tiny_positive_real_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/test/test.js b/lib/node_modules/@stdlib/math/base/special/cinvf/test/test.js new file mode 100644 index 000000000000..f684038b17ce --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/test/test.js @@ -0,0 +1,488 @@ +/** +* @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. +*/ + +/* eslint-disable id-length */ + +'use strict'; + +// MODULES // + +var tape = require( 'tape' ); +var isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var absf = require( '@stdlib/math/base/special/absf' ); +var EPS = require( '@stdlib/constants/float32/eps' ); +var PINF = require( '@stdlib/constants/float32/pinf' ); +var NINF = require( '@stdlib/constants/float32/ninf' ); +var Complex64 = require( '@stdlib/complex/float32/ctor' ); +var real = require( '@stdlib/complex/float32/real' ); +var imag = require( '@stdlib/complex/float32/imag' ); +var cinvf = require( './../lib' ); + + +// FIXTURES // + +var data = require( './fixtures/julia/data.json' ); +var largeNegativeImaginaryComponents = require( './fixtures/julia/large_negative_imaginary_components.json' ); +var largeNegativeRealComponents = require( './fixtures/julia/large_negative_real_components.json' ); +var largePositiveImaginaryComponents = require( './fixtures/julia/large_positive_imaginary_components.json' ); +var largePositiveRealComponents = require( './fixtures/julia/large_positive_real_components.json' ); +var tinyNegativeImaginaryComponents = require( './fixtures/julia/tiny_negative_imaginary_components.json' ); +var tinyNegativeRealComponents = require( './fixtures/julia/tiny_negative_real_components.json' ); +var tinyPositiveImaginaryComponents = require( './fixtures/julia/tiny_positive_imaginary_components.json' ); +var tinyPositiveRealComponents = require( './fixtures/julia/tiny_positive_real_components.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof cinvf, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function computes the inverse of a single-precision complex floating-point number', function test( t ) { + var v; + + v = cinvf( new Complex64( 2.0, 4.0 ) ); + t.strictEqual( real( v ), 0.10000000149011612, 'returns expected value' ); + t.strictEqual( imag( v ), -0.20000000298023224, 'returns expected value' ); + t.end(); +}); + +tape( 'the function computes a complex inverse', function test( t ) { + var delta; + var qre; + var qim; + var tol; + var re; + var im; + var i; + var q; + + re = data.re; + im = data.im; + qre = data.qre; + qim = data.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (large negative imaginary components)', function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = largeNegativeImaginaryComponents.re; + im = largeNegativeImaginaryComponents.im; + qre = largeNegativeImaginaryComponents.qre; + qim = largeNegativeImaginaryComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (large negative real components)', function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = largeNegativeRealComponents.re; + im = largeNegativeRealComponents.im; + qre = largeNegativeRealComponents.qre; + qim = largeNegativeRealComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (large positive imaginary components)', function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = largePositiveImaginaryComponents.re; + im = largePositiveImaginaryComponents.im; + qre = largePositiveImaginaryComponents.qre; + qim = largePositiveImaginaryComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (large positive real components)', function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = largePositiveRealComponents.re; + im = largePositiveRealComponents.im; + qre = largePositiveRealComponents.qre; + qim = largePositiveRealComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (tiny negative imaginary components)', function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = tinyNegativeImaginaryComponents.re; + im = tinyNegativeImaginaryComponents.im; + qre = tinyNegativeImaginaryComponents.qre; + qim = tinyNegativeImaginaryComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (tiny negative real components)', function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = tinyNegativeRealComponents.re; + im = tinyNegativeRealComponents.im; + qre = tinyNegativeRealComponents.qre; + qim = tinyNegativeRealComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (tiny positive imaginary components)', function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = tinyPositiveImaginaryComponents.re; + im = tinyPositiveImaginaryComponents.im; + qre = tinyPositiveImaginaryComponents.qre; + qim = tinyPositiveImaginaryComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (tiny positive real components)', function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = tinyPositiveRealComponents.re; + im = tinyPositiveRealComponents.im; + qre = tinyPositiveRealComponents.qre; + qim = tinyPositiveRealComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function may overflow', function test( t ) { + var v; + + v = cinvf( new Complex64( 1.4e-45, 1.4e-45 ) ); + t.strictEqual( real( v ), PINF, 'returns expected value' ); + t.strictEqual( imag( v ), NINF, 'returns expected value' ); + + v = cinvf( new Complex64( -1.4e-45, 1.4e-45 ) ); + t.strictEqual( real( v ), NINF, 'returns expected value' ); + t.strictEqual( imag( v ), NINF, 'returns expected value' ); + + v = cinvf( new Complex64( -1.4e-45, -1.4e-45 ) ); + t.strictEqual( real( v ), NINF, 'returns expected value' ); + t.strictEqual( imag( v ), PINF, 'returns expected value' ); + + v = cinvf( new Complex64( 1.4e-45, -1.4e-45 ) ); + t.strictEqual( real( v ), PINF, 'returns expected value' ); + t.strictEqual( imag( v ), PINF, 'returns expected value' ); + + v = cinvf( new Complex64( 0.0, 1.4e-45 ) ); + t.strictEqual( real( v ), 0.0, 'returns expected value' ); + t.strictEqual( imag( v ), NINF, 'returns expected value' ); + + v = cinvf( new Complex64( 0.0, -1.4e-45 ) ); + t.strictEqual( real( v ), 0.0, 'returns expected value' ); + t.strictEqual( imag( v ), PINF, 'returns expected value' ); + + v = cinvf( new Complex64( 1.4e-45, 0.0 ) ); + t.strictEqual( real( v ), PINF, 'returns expected value' ); + t.strictEqual( imag( v ), 0.0, 'returns expected value' ); + + v = cinvf( new Complex64( -1.4e-45, 0.0 ) ); + t.strictEqual( real( v ), NINF, 'returns expected value' ); + t.strictEqual( imag( v ), 0.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'if a real or imaginary component is `NaN`, all components are `NaN`', function test( t ) { + var v; + + v = cinvf( new Complex64( NaN, 3.0 ) ); + t.strictEqual( isnanf( real( v ) ), true, 'returns expected value' ); + t.strictEqual( isnanf( imag( v ) ), true, 'returns expected value' ); + + v = cinvf( new Complex64( 5.0, NaN ) ); + t.strictEqual( isnanf( real( v ) ), true, 'returns expected value' ); + t.strictEqual( isnanf( imag( v ) ), true, 'returns expected value' ); + + v = cinvf( new Complex64( NaN, NaN ) ); + t.strictEqual( isnanf( real( v ) ), true, 'returns expected value' ); + t.strictEqual( isnanf( imag( v ) ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns correct value when the magnitude of real or imaginary component exceeds LARGE THRESHOLD', function test( t ) { + var expected; + var values; + var delta; + var tol; + var v; + var i; + + values = [ + new Complex64( 2.0e+38, 200 ), + new Complex64( -2.0e+38, 200 ), + new Complex64( 200, 2.0e+38 ), + new Complex64( 200, -2.0e+38 ) + ]; + + expected = [ + new Complex64( 4.999999675228202e-39, 0 ), + new Complex64( -4.999999675228202e-39, 0 ), + new Complex64( 0, -4.999999675228202e-39 ), + new Complex64( 0, 4.999999675228202e-39 ) + ]; + + for ( i = 0; i < values.length; i++ ) { + v = cinvf( values[ i ] ); + if ( real( v ) === real( expected[ i ] ) ) { + t.strictEqual( real( v ), real( expected[ i ] ), 'returns expected real component' ); + } else { + delta = absf( real( v ) - real( expected[ i ] ) ); + tol = 2.5 * EPS * absf( real( expected[ i ] ) ); + t.ok( delta <= tol, 'within tolerance. x: '+real( values[ i ] )+'+ '+imag( values[ i ] )+'i. real: '+real( v )+'. expected: '+real( expected[ i ] )+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( v ) === imag( expected[ i ] ) ) { + t.strictEqual( imag( v ), imag( expected[ i ] ), 'returns expected real component' ); + } else { + delta = absf( imag( v ) - imag( expected[ i ] ) ); + tol = 2.5 * EPS * absf( imag( expected[ i ] ) ); + t.ok( delta <= tol, 'within tolerance. x: '+real( values[ i ] )+'+ '+imag( values[ i ] )+'i. imag: '+imag( v )+'. expected: '+imag( expected[ i ] )+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + + t.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/cinvf/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/cinvf/test/test.native.js new file mode 100644 index 000000000000..5faba98d1dee --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinvf/test/test.native.js @@ -0,0 +1,497 @@ +/** +* @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. +*/ + +/* eslint-disable id-length */ + +'use strict'; + +// MODULES // + +var resolve = require( 'path' ).resolve; +var tape = require( 'tape' ); +var isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var absf = require( '@stdlib/math/base/special/absf' ); +var EPS = require( '@stdlib/constants/float32/eps' ); +var PINF = require( '@stdlib/constants/float32/pinf' ); +var NINF = require( '@stdlib/constants/float32/ninf' ); +var Complex64 = require( '@stdlib/complex/float32/ctor' ); +var real = require( '@stdlib/complex/float32/real' ); +var imag = require( '@stdlib/complex/float32/imag' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// VARIABLES // + +var cinvf = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( cinvf instanceof Error ) +}; + + +// FIXTURES // + +var data = require( './fixtures/julia/data.json' ); +var largeNegativeImaginaryComponents = require( './fixtures/julia/large_negative_imaginary_components.json' ); +var largeNegativeRealComponents = require( './fixtures/julia/large_negative_real_components.json' ); +var largePositiveImaginaryComponents = require( './fixtures/julia/large_positive_imaginary_components.json' ); +var largePositiveRealComponents = require( './fixtures/julia/large_positive_real_components.json' ); +var tinyNegativeImaginaryComponents = require( './fixtures/julia/tiny_negative_imaginary_components.json' ); +var tinyNegativeRealComponents = require( './fixtures/julia/tiny_negative_real_components.json' ); +var tinyPositiveImaginaryComponents = require( './fixtures/julia/tiny_positive_imaginary_components.json' ); +var tinyPositiveRealComponents = require( './fixtures/julia/tiny_positive_real_components.json' ); + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof cinvf, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function computes the inverse of a single-precision complex floating-point number', opts, function test( t ) { + var v; + + v = cinvf( new Complex64( 2.0, 4.0 ) ); + t.strictEqual( real( v ), 0.10000000149011612, 'returns expected value' ); + t.strictEqual( imag( v ), -0.20000000298023224, 'returns expected value' ); + t.end(); +}); + +tape( 'the function computes a complex inverse', opts, function test( t ) { + var delta; + var qre; + var qim; + var tol; + var re; + var im; + var i; + var q; + + re = data.re; + im = data.im; + qre = data.qre; + qim = data.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (large negative imaginary components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = largeNegativeImaginaryComponents.re; + im = largeNegativeImaginaryComponents.im; + qre = largeNegativeImaginaryComponents.qre; + qim = largeNegativeImaginaryComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (large negative real components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = largeNegativeRealComponents.re; + im = largeNegativeRealComponents.im; + qre = largeNegativeRealComponents.qre; + qim = largeNegativeRealComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (large positive imaginary components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = largePositiveImaginaryComponents.re; + im = largePositiveImaginaryComponents.im; + qre = largePositiveImaginaryComponents.qre; + qim = largePositiveImaginaryComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (large positive real components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = largePositiveRealComponents.re; + im = largePositiveRealComponents.im; + qre = largePositiveRealComponents.qre; + qim = largePositiveRealComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (tiny negative imaginary components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = tinyNegativeImaginaryComponents.re; + im = tinyNegativeImaginaryComponents.im; + qre = tinyNegativeImaginaryComponents.qre; + qim = tinyNegativeImaginaryComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (tiny negative real components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = tinyNegativeRealComponents.re; + im = tinyNegativeRealComponents.im; + qre = tinyNegativeRealComponents.qre; + qim = tinyNegativeRealComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (tiny positive imaginary components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = tinyPositiveImaginaryComponents.re; + im = tinyPositiveImaginaryComponents.im; + qre = tinyPositiveImaginaryComponents.qre; + qim = tinyPositiveImaginaryComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (tiny positive real components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = tinyPositiveRealComponents.re; + im = tinyPositiveRealComponents.im; + qre = tinyPositiveRealComponents.qre; + qim = tinyPositiveRealComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinvf( new Complex64( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( real( q ) - qre[ i ] ); + tol = 2.0 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imag( q ) - qim[ i ] ); + tol = 2.0 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function may overflow', opts, function test( t ) { + var v; + + v = cinvf( new Complex64( 1.4e-45, 1.4e-45 ) ); + t.strictEqual( real( v ), PINF, 'returns expected value' ); + t.strictEqual( imag( v ), NINF, 'returns expected value' ); + + v = cinvf( new Complex64( -1.4e-45, 1.4e-45 ) ); + t.strictEqual( real( v ), NINF, 'returns expected value' ); + t.strictEqual( imag( v ), NINF, 'returns expected value' ); + + v = cinvf( new Complex64( -1.4e-45, -1.4e-45 ) ); + t.strictEqual( real( v ), NINF, 'returns expected value' ); + t.strictEqual( imag( v ), PINF, 'returns expected value' ); + + v = cinvf( new Complex64( 1.4e-45, -1.4e-45 ) ); + t.strictEqual( real( v ), PINF, 'returns expected value' ); + t.strictEqual( imag( v ), PINF, 'returns expected value' ); + + v = cinvf( new Complex64( 0.0, 1.4e-45 ) ); + t.strictEqual( real( v ), 0.0, 'returns expected value' ); + t.strictEqual( imag( v ), NINF, 'returns expected value' ); + + v = cinvf( new Complex64( 0.0, -1.4e-45 ) ); + t.strictEqual( real( v ), 0.0, 'returns expected value' ); + t.strictEqual( imag( v ), PINF, 'returns expected value' ); + + v = cinvf( new Complex64( 1.4e-45, 0.0 ) ); + t.strictEqual( real( v ), PINF, 'returns expected value' ); + t.strictEqual( imag( v ), 0.0, 'returns expected value' ); + + v = cinvf( new Complex64( -1.4e-45, 0.0 ) ); + t.strictEqual( real( v ), NINF, 'returns expected value' ); + t.strictEqual( imag( v ), 0.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'if a real or imaginary component is `NaN`, all components are `NaN`', opts, function test( t ) { + var v; + + v = cinvf( new Complex64( NaN, 3.0 ) ); + t.strictEqual( isnanf( real( v ) ), true, 'returns expected value' ); + t.strictEqual( isnanf( imag( v ) ), true, 'returns expected value' ); + + v = cinvf( new Complex64( 5.0, NaN ) ); + t.strictEqual( isnanf( real( v ) ), true, 'returns expected value' ); + t.strictEqual( isnanf( imag( v ) ), true, 'returns expected value' ); + + v = cinvf( new Complex64( NaN, NaN ) ); + t.strictEqual( isnanf( real( v ) ), true, 'returns expected value' ); + t.strictEqual( isnanf( imag( v ) ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns correct value when the magnitude of real or imaginary component exceeds LARGE THRESHOLD', opts, function test( t ) { + var expected; + var values; + var delta; + var tol; + var v; + var i; + + values = [ + new Complex64( 2.0e+38, 200 ), + new Complex64( -2.0e+38, 200 ), + new Complex64( 200, 2.0e+38 ), + new Complex64( 200, -2.0e+38 ) + ]; + + expected = [ + new Complex64( 4.999999675228202e-39, 0 ), + new Complex64( -4.999999675228202e-39, 0 ), + new Complex64( 0, -4.999999675228202e-39 ), + new Complex64( 0, 4.999999675228202e-39 ) + ]; + + for ( i = 0; i < values.length; i++ ) { + v = cinvf( values[ i ] ); + if ( real( v ) === real( expected[ i ] ) ) { + t.strictEqual( real( v ), real( expected[ i ] ), 'returns expected real component' ); + } else { + delta = absf( real( v ) - real( expected[ i ] ) ); + tol = 2.5 * EPS * absf( real( expected[ i ] ) ); + t.ok( delta <= tol, 'within tolerance. x: '+real( values[ i ] )+'+ '+imag( values[ i ] )+'i. real: '+real( v )+'. expected: '+real( expected[ i ] )+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( v ) === imag( expected[ i ] ) ) { + t.strictEqual( imag( v ), imag( expected[ i ] ), 'returns expected real component' ); + } else { + delta = absf( imag( v ) - imag( expected[ i ] ) ); + tol = 2.5 * EPS * absf( imag( expected[ i ] ) ); + t.ok( delta <= tol, 'within tolerance. x: '+real( values[ i ] )+'+ '+imag( values[ i ] )+'i. imag: '+imag( v )+'. expected: '+imag( expected[ i ] )+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + + t.end(); +});