diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/README.md b/lib/node_modules/@stdlib/complex/float32/base/div/README.md new file mode 100644 index 000000000000..1d83be912a38 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/README.md @@ -0,0 +1,249 @@ + + +# div + +> Divide two single-precision complex floating-point numbers. + +
+ +
+ + + +
+ +## Usage + +```javascript +var div = require( '@stdlib/complex/float32/base/div' ); +``` + +#### div( z1, z2 ) + +Divides two single-precision complex floating-point numbers. + +```javascript +var Complex64 = require( '@stdlib/complex/float32/ctor' ); + +var z1 = new Complex64( -13.0, -1.0 ); +var z2 = new Complex64( -2.0, 1.0 ); + +var v = div( z1, z2 ); +// returns [ 5.0, 3.0 ] +``` + +
+ + + +
+ +## Examples + + + +```javascript +var Complex64Array = require( '@stdlib/array/complex64' ); +var discreteUniform = require( '@stdlib/random/array/discrete-uniform' ); +var logEachMap = require( '@stdlib/console/log-each-map' ); +var div = require( '@stdlib/complex/float32/base/div' ); + +// Generate arrays of random values: +var z1 = new Complex64Array( discreteUniform( 200, -50, 50 ) ); +var z2 = new Complex64Array( discreteUniform( 200, -50, 50 ) ); + +// Perform element-wise division: +logEachMap( '(%s) / (%s) = %s', z1, z2, div ); +``` + +
+ + + + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/complex/float32/base/div.h" +``` + +#### stdlib_base_complex64_div( z1, z2 ) + +Divides two single-precision complex floating-point numbers. + +```c +#include "stdlib/complex/float32/ctor.h" +#include "stdlib/complex/float32/real.h" +#include "stdlib/complex/float32/imag.h" + +stdlib_complex64_t z1 = stdlib_complex64( -13.0, -1.0 ); +stdlib_complex64_t z2 = stdlib_complex64( -2.0, 1.0 ); + +stdlib_complex64_t out = stdlib_base_complex64_div( z1, z2 ); + +float re = stdlib_complex64_real( out ); +// returns 5.0 + +float im = stdlib_complex64_imag( out ); +// returns 3.0 +``` + +The function accepts the following arguments: + +- **z1**: `[in] stdlib_complex64_t` input value. +- **z2**: `[in] stdlib_complex64_t` input value. + +```c +stdlib_complex64_t stdlib_base_complex64_div( const stdlib_complex64_t z1, const stdlib_complex64_t z2 ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/complex/float32/base/div.h" +#include "stdlib/complex/float32/ctor.h" +#include "stdlib/complex/float32/reim.h" +#include + +int main( void ) { + const stdlib_complex64_t x[] = { + stdlib_complex64( 3.14, 1.5 ), + stdlib_complex64( -3.14, 1.5 ), + stdlib_complex64( 0.0, -0.0 ), + stdlib_complex64( 0.0/0.0, 0.0/0.0 ) + }; + + stdlib_complex64_t v; + stdlib_complex64_t y; + float re; + float im; + int i; + for ( i = 0; i < 4; i++ ) { + v = x[ i ]; + stdlib_complex64_reim( v, &re, &im ); + printf( "z = %lf + %lfi\n", re, im ); + + y = stdlib_base_complex64_div( v, v ); + stdlib_complex64_reim( y, &re, &im ); + printf( "div(z, z) = %lf + %lfi\n", re, im ); + } +} +``` + +
+ + + +
+ + + +* * * + +
+ +## 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]. + +
+ + + + + +
+ +* * * + +## See Also + +- [`@stdlib/complex/float32/base/add`][@stdlib/complex/float32/base/add]: add two single-precision complex floating-point numbers. +- [`@stdlib/complex/float32/base/mul`][@stdlib/complex/float32/base/mul]: multiply two single-precision complex floating-point numbers. +- [`@stdlib/complex/float32/base/sub`][@stdlib/complex/float32/base/sub]: subtract two single-precision complex floating-point numbers. + +
+ + + + + +
+ +[@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 + + + +[@stdlib/complex/float32/base/add]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/complex/float32/base/add + +[@stdlib/complex/float32/base/mul]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/complex/float32/base/mul + +[@stdlib/complex/float32/base/sub]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/complex/float32/base/sub + + + +
+ + diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/benchmark.js b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/benchmark.js new file mode 100644 index 000000000000..9b18053d4c19 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/benchmark.js @@ -0,0 +1,111 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 Complex64 = require( '@stdlib/complex/float32/ctor' ); +var isComplex64 = require( '@stdlib/assert/is-complex64' ); +var uniform = require( '@stdlib/random/base/uniform' ); +var realf = require( '@stdlib/complex/float32/real' ); +var imagf = require( '@stdlib/complex/float32/imag' ); +var absf = require( '@stdlib/math/base/special/absf' ); +var pkg = require( './../package.json' ).name; +var div = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( b ) { + var values; + var y; + var i; + var z; + + 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++ ) { + z = values[ i % values.length ]; + y = div( z, z ); + if ( typeof y !== 'object' ) { + b.fail( 'should return an object' ); + } + } + b.toc(); + if ( !isComplex64( y ) ) { + b.fail( 'should return a Complex64' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); + +bench( pkg+'::smiths_algorithm', function benchmark( b ) { + var values; + var y; + var i; + var z; + + 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++ ) { + z = values[ i % values.length ]; + y = div( z, z ); + if ( typeof y !== 'object' ) { + b.fail( 'should return an object' ); + } + } + b.toc(); + if ( !isComplex64( y ) ) { + b.fail( 'should return a Complex64' ); + } + b.pass( 'benchmark finished' ); + b.end(); + + function div( z1, z2 ) { + var re1; + var re2; + var im1; + var im2; + var a; + var b; + + re1 = realf( z1 ); + re2 = realf( z2 ); + im1 = imagf( z1 ); + im2 = imagf( z2 ); + + if ( absf( re2 ) >= absf( im2 ) ) { + a = im2 / re2; + b = re2 + ( im2 * a ); + return new Complex64( ( re1 + (im1 * a) )/b, (im1 - (re1*a) )/b ); + } + a = re2 / im2; + b = ( re2 * a ) + im2; + return new Complex64( ( (re1*a) + im1 )/b, ( (im1*a) - re1 )/b ); + } +}); diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/benchmark.native.js new file mode 100644 index 000000000000..7269f2d21af8 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/benchmark.native.js @@ -0,0 +1,69 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 Complex64 = require( '@stdlib/complex/float32/ctor' ); +var realf = require( '@stdlib/complex/float32/realf' ); +var imagf = require( '@stdlib/complex/float32/imagf' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var div = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( div instanceof Error ) +}; + + +// MAIN // + +bench( pkg+'::native', opts, function benchmark( b ) { + var values; + var out; + var z; + 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++ ) { + z = values[ i%values.length ]; + out = div( z, z ); + if ( typeof out !== 'object' ) { + b.fail( 'should return an object' ); + } + } + b.toc(); + if ( isnanf( realf( out ) ) || isnanf( imagf( out ) ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/c/Makefile b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/c/Makefile new file mode 100644 index 000000000000..d564e8b2d6f9 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/c/Makefile @@ -0,0 +1,127 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2025 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 C targets: +c_targets := benchmark.out + + +# RULES # + +#/ +# Compiles C source files. +# +# @param {string} [C_COMPILER] - C compiler +# @param {string} [CFLAGS] - C compiler flags +# @param {(string|void)} [fPIC] - compiler flag indicating whether to generate position independent code +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler +# @param {string} CFLAGS - C compiler flags +# @param {(string|void)} fPIC - compiler flag indicating whether to generate position independent code +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) -o $@ $< -lm + +#/ +# 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/complex/float32/base/div/benchmark/c/benchmark.c b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/c/benchmark.c new file mode 100644 index 000000000000..89cb503f416d --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/c/benchmark.c @@ -0,0 +1,143 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 "div" +#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 re; + float im; + double t; + int i; + + float complex z1; + float complex z2; + float complex z3; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + re = ( 1000.0f*rand_float() ) - 500.0f; + im = ( 1000.0f*rand_float() ) - 500.0f; + z1 = re + im*I; + + re = ( 1000.0f*rand_float() ) - 500.0f; + im = ( 1000.0f*rand_float() ) - 500.0f; + z2 = re + im*I; + + z3 = z1 / z2; + if ( z3 != z3 ) { + printf( "should not return NaN\n" ); + break; + } + } + elapsed = tic() - t; + if ( z3 != z3 ) { + 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/complex/float32/base/div/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/c/native/Makefile new file mode 100644 index 000000000000..a4bd7b38fd74 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/c/native/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2025 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/complex/float32/base/div/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/c/native/benchmark.c new file mode 100644 index 000000000000..cd188c2e4966 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/c/native/benchmark.c @@ -0,0 +1,147 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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/complex/float32/base/div.h" +#include "stdlib/complex/float32/ctor.h" +#include "stdlib/complex/float32/reim.h" +#include +#include +#include +#include +#include + +#define NAME "div" +#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 re; + float im; + double t; + int i; + + stdlib_complex64_t z1; + stdlib_complex64_t z2; + stdlib_complex64_t z3; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + re = ( 1000.0f*rand_float() ) - 500.0f; + im = ( 1000.0f*rand_float() ) - 500.0f; + z1 = stdlib_complex64( re, im ); + + re = ( 1000.0f*rand_float() ) - 500.0f; + im = ( 1000.0f*rand_float() ) - 500.0f; + z2 = stdlib_complex64( re, im ); + + z3 = stdlib_base_complex64_div( z1, z2 ); + stdlib_complex64_reim( z3, &re, &im ); + if ( re != re ) { + printf( "should not return NaN\n" ); + break; + } + } + elapsed = tic() - t; + if ( im != im ) { + printf( "should not return NaN\n" ); + } + return elapsed; +} + +/** +* Main execution sequence. +*/ +int main( void ) { + double elapsed; + int i; + + // Use the current time to seed the random number generator: + srand( time( NULL ) ); + + print_version(); + for ( i = 0; i < REPEATS; i++ ) { + printf( "# c::native::%s\n", NAME ); + elapsed = benchmark(); + print_results( elapsed ); + printf( "ok %d benchmark finished\n", i+1 ); + } + print_summary( REPEATS, REPEATS ); +} diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/julia/REQUIRE b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/julia/REQUIRE new file mode 100644 index 000000000000..98645e192e41 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/julia/REQUIRE @@ -0,0 +1,2 @@ +julia 1.5 +BenchmarkTools 0.5.0 diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/julia/benchmark.jl b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/julia/benchmark.jl new file mode 100644 index 000000000000..d985f01c1cac --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/benchmark/julia/benchmark.jl @@ -0,0 +1,144 @@ +#!/usr/bin/env julia +# +# @license Apache-2.0 +# +# Copyright (c) 2025 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 BenchmarkTools +using Printf + +# Benchmark variables: +name = "divide"; +repeats = 3; + +""" + print_version() + +Prints the TAP version. + +# Examples + +``` julia +julia> print_version() +``` +""" +function print_version() + @printf( "TAP version 13\n" ); +end + +""" + print_summary( total, passing ) + +Print the benchmark summary. + +# Arguments + +* `total`: total number of tests +* `passing`: number of passing tests + +# Examples + +``` julia +julia> print_summary( 3, 3 ) +``` +""" +function print_summary( total, 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" ); +end + +""" + print_results( iterations, elapsed ) + +Print benchmark results. + +# Arguments + +* `iterations`: number of iterations +* `elapsed`: elapsed time (in seconds) + +# Examples + +``` julia +julia> print_results( 1000000, 0.131009101868 ) +``` +""" +function print_results( iterations, elapsed ) + rate = iterations / elapsed + + @printf( " ---\n" ); + @printf( " iterations: %d\n", iterations ); + @printf( " elapsed: %0.9f\n", elapsed ); + @printf( " rate: %0.9f\n", rate ); + @printf( " ...\n" ); +end + +""" + benchmark() + +Run a benchmark. + +# Notes + +* Benchmark results are returned as a two-element array: [ iterations, elapsed ]. +* The number of iterations is not the true number of iterations. Instead, an 'iteration' is defined as a 'sample', which is a computed estimate for a single evaluation. +* The elapsed time is in seconds. + +# Examples + +``` julia +julia> out = benchmark(); +``` +""" +function benchmark() + t = BenchmarkTools.@benchmark ComplexF32( (rand()*1000.0)-500.0, (rand()*1000.0)-500.0 ) / ComplexF32( (rand()*1000.0)-500.0, (rand()*1000.0)-500.0 ) samples=1e6 + + # Compute the total "elapsed" time and convert from nanoseconds to seconds: + s = sum( t.times ) / 1.0e9; + + # Determine the number of "iterations": + iter = length( t.times ); + + # Return the results: + [ iter, s ]; +end + +""" + main() + +Run benchmarks. + +# Examples + +``` julia +julia> main(); +``` +""" +function main() + print_version(); + for i in 1:repeats + @printf( "# julia::%s\n", name ); + results = benchmark(); + print_results( results[ 1 ], results[ 2 ] ); + @printf( "ok %d benchmark finished\n", i ); + end + print_summary( repeats, repeats ); +end + +main(); diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/binding.gyp b/lib/node_modules/@stdlib/complex/float32/base/div/binding.gyp new file mode 100644 index 000000000000..68a1ca11d160 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/binding.gyp @@ -0,0 +1,170 @@ +# @license Apache-2.0 +# +# Copyright (c) 2025 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/complex/float32/base/div/docs/repl.txt b/lib/node_modules/@stdlib/complex/float32/base/div/docs/repl.txt new file mode 100644 index 000000000000..e0779ce3a027 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/docs/repl.txt @@ -0,0 +1,33 @@ + +{{alias}}( z1, z2 ) + Divides two single-precision complex floating-point numbers. + + Parameters + ---------- + z1: Complex64 + Complex number. + + z2: Complex64 + Complex number. + + Returns + ------- + out: Complex64 + Result. + + Examples + -------- + > var z1 = new {{alias:@stdlib/complex/float32/ctor}}( -13.0, -1.0 ) + + > var z2 = new {{alias:@stdlib/complex/float32/ctor}}( -2.0, 1.0 ) + + > var y = {{alias}}( z1, z2 ) + + > var re = {{alias:@stdlib/complex/float32/real}}( y ) + 5.0 + > var im = {{alias:@stdlib/complex/float32/imag}}( y ) + 3.0 + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/docs/types/index.d.ts b/lib/node_modules/@stdlib/complex/float32/base/div/docs/types/index.d.ts new file mode 100644 index 000000000000..de015bd3c823 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/docs/types/index.d.ts @@ -0,0 +1,46 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2025 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'; + +/** +* Divides two single-precision complex floating-point numbers. +* +* @param z1 - complex number +* @param z2 - complex number +* @returns result +* +* @example +* var Complex64 = require( '@stdlib/complex/float32/ctor' ); +* +* var z1 = new Complex64( -13.0, -1.0 ); +* var z2 = new Complex64( -2.0, 1.0 ); +* +* var out = div( z1, z2 ); +* // returns [ 5.0, 3.0 ] +*/ +declare function div( z1: Complex64, z2: Complex64 ): Complex64; + + +// EXPORTS // + +export = div; diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/docs/types/test.ts b/lib/node_modules/@stdlib/complex/float32/base/div/docs/types/test.ts new file mode 100644 index 000000000000..91c05384653c --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/docs/types/test.ts @@ -0,0 +1,67 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2025 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 div = require( './index' ); + + +// TESTS // + +// The function returns an array of numbers... +{ + const z = new Complex64( 1.0, 1.0 ); + + div( z, z ); // $ExpectType Complex64 +} + +// The compiler throws an error if the function is provided a first argument which is not a complex number... +{ + const z = new Complex64( 1.0, 1.0 ); + + div( true, z ); // $ExpectError + div( false, z ); // $ExpectError + div( null, z ); // $ExpectError + div( undefined, z ); // $ExpectError + div( '5', z ); // $ExpectError + div( [], z ); // $ExpectError + div( {}, z ); // $ExpectError + div( ( x: number ): number => x, z ); // $ExpectError +} + +// The compiler throws an error if the function is provided a second argument which is not a complex number... +{ + const z = new Complex64( 1.0, 1.0 ); + + div( z, true ); // $ExpectError + div( z, false ); // $ExpectError + div( z, null ); // $ExpectError + div( z, undefined ); // $ExpectError + div( z, '5' ); // $ExpectError + div( z, [] ); // $ExpectError + div( z, {} ); // $ExpectError + div( z, ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided an unsupported number of arguments... +{ + const z = new Complex64( 1.0, 1.0 ); + + div(); // $ExpectError + div( z ); // $ExpectError + div( z, z, z ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/examples/c/Makefile b/lib/node_modules/@stdlib/complex/float32/base/div/examples/c/Makefile new file mode 100644 index 000000000000..25ced822f96a --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/examples/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2025 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/complex/float32/base/div/examples/c/example.c b/lib/node_modules/@stdlib/complex/float32/base/div/examples/c/example.c new file mode 100644 index 000000000000..261aee5559b0 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/examples/c/example.c @@ -0,0 +1,46 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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/complex/float32/base/div.h" +#include "stdlib/complex/float32/ctor.h" +#include "stdlib/complex/float32/reim.h" +#include + +int main( void ) { + 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 re; + float im; + int i; + for ( i = 0; i < 4; i++ ) { + v = x[ i ]; + stdlib_complex64_reim( v, &re, &im ); + printf( "z = %f + %fi\n", re, im ); + + y = stdlib_base_complex64_div( v, v ); + stdlib_complex64_reim( y, &re, &im ); + printf( "div(z, z) = %f + %fi\n", re, im ); + } +} diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/examples/index.js b/lib/node_modules/@stdlib/complex/float32/base/div/examples/index.js new file mode 100644 index 000000000000..e732c46a517a --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/examples/index.js @@ -0,0 +1,31 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 Complex64Array = require( '@stdlib/array/complex64' ); +var discreteUniform = require( '@stdlib/random/array/discrete-uniform' ); +var logEachMap = require( '@stdlib/console/log-each-map' ); +var div = require( './../lib' ); + +// Generate arrays of random values: +var z1 = new Complex64Array( discreteUniform( 200, -50, 50 ) ); +var z2 = new Complex64Array( discreteUniform( 200, -50, 50 ) ); + +// Perform element-wise division: +logEachMap( '(%s) / (%s) = %s', z1, z2, div ); diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/include.gypi b/lib/node_modules/@stdlib/complex/float32/base/div/include.gypi new file mode 100644 index 000000000000..ecfaf82a3279 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/include.gypi @@ -0,0 +1,53 @@ +# @license Apache-2.0 +# +# Copyright (c) 2025 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': [ + '[ 5.0, 3.0 ] +*/ + +// MODULES // + +var main = require( './main.js' ); + + +// EXPORTS // + +module.exports = main; diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/lib/internal_compreal.js b/lib/node_modules/@stdlib/complex/float32/base/div/lib/internal_compreal.js new file mode 100644 index 000000000000..6c6bc8b82ae3 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/lib/internal_compreal.js @@ -0,0 +1,61 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 f32 = require( '@stdlib/number/float64/base/to-float32' ); + + +// MAIN // + +/** +* Computes the real part of the quotient. +* +* ## Notes +* +* - See figure 10 of [Baudin (2012)][@baudin:2012]. +* +* [@baudin:2012]: https://arxiv.org/abs/1210.4539 +* +* @private +* @param {number} re1 - real component +* @param {number} im1 - imaginary component +* @param {number} re2 - real component +* @param {number} im2 - imaginary component +* @param {number} r - partial result +* @param {number} t - partial result +* @returns {number} real part of the quotient +*/ +function internalCompreal( re1, im1, re2, im2, r, t ) { + var br; + if ( r === 0.0 ) { + return f32( f32( re1 + f32(im2 * f32(im1/re2)) ) * t ); + } + br = f32( im1 * r ); + if ( br === 0.0 ) { + return f32( f32( re1*t ) + f32( f32(im1*t) * r ) ); + } + return f32( f32( re1+br ) * t ); +} + + +// EXPORTS // + +module.exports = internalCompreal; diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/lib/main.js b/lib/node_modules/@stdlib/complex/float32/base/div/lib/main.js new file mode 100644 index 000000000000..c0faf98ad41d --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/lib/main.js @@ -0,0 +1,118 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 realf = require( '@stdlib/complex/float32/real' ); +var imagf = require( '@stdlib/complex/float32/imag' ); +var Complex64 = require( '@stdlib/complex/float32/ctor' ); +var f32 = require( '@stdlib/number/float64/base/to-float32' ); +var robustInternal = require( './robust_internal.js' ); + + +// VARIABLES // + +var LARGE_THRESHOLD = f32( FLOAT32_BIGGEST * 0.5 ); +var SMALL_THRESHOLD = f32( FLOAT32_SMALLEST * f32( 2.0 / EPS ) ); +var RECIP_EPS_SQR = f32( 2.0 / ( EPS * EPS ) ); + + +// MAIN // + +/** +* Divides two single-precision complex floating-point numbers. +* +* ## References +* +* - Baudin, Michael, and Robert L. Smith. 2012. "A Robust Complex Division in Scilab." _arXiv_ absf/1210.4539 \[cs.MS\] (October): 1–25. . +* +* @param {Complex64} z1 - complex number +* @param {Complex64} z2 - complex number +* @returns {Complex64} result +* +* @example +* var Complex64 = require( '@stdlib/complex/float32/ctor' ); +* +* var z1 = new Complex64( -13.0, -1.0 ); +* var z2 = new Complex64( -2.0, 1.0 ); +* +* var out = div( z1, z2 ); +* // returns [ 5.0, 3.0 ] +*/ +function div( z1, z2 ) { + var re1; + var re2; + var im1; + var im2; + var out; + var ab; + var cd; + var s; + + re1 = realf( z1 ); + re2 = realf( z2 ); + im1 = imagf( z1 ); + im2 = imagf( z2 ); + + ab = maxf( absf(re1), absf(im1) ); + cd = maxf( absf(re2), absf(im2) ); + s = 1.0; + + if ( ab >= LARGE_THRESHOLD ) { + re1 = f32( re1 * 0.5 ); + im1 = f32( im1 * 0.5 ); + s = f32( s * 2.0 ); + } else if ( ab <= SMALL_THRESHOLD ) { + re1 = f32( re1 * RECIP_EPS_SQR ); + im1 = f32( im1 * RECIP_EPS_SQR ); + s = f32( s / RECIP_EPS_SQR ); + } + if ( cd >= LARGE_THRESHOLD ) { + re2 = f32( re2 * 0.5 ); + im2 = f32( im2 * 0.5 ); + s = f32( s * 0.5 ); + } else if ( cd <= SMALL_THRESHOLD ) { + re2 = f32( re2 * RECIP_EPS_SQR ); + im2 = f32( im2 * RECIP_EPS_SQR ); + s = f32( s * RECIP_EPS_SQR ); + } + if ( absf( im2 ) <= absf( re2 ) ) { + out = robustInternal( re1, im1, re2, im2 ); + } else { + out = robustInternal( im1, re1, im2, re2 ); + out[ 1 ] = f32( out[ 1 ] * -1.0 ); + } + out[ 0 ] = f32( out[ 0 ] * s ); + out[ 1 ] = f32( out[ 1 ] * s ); + return new Complex64( out[ 0 ], out[ 1 ] ); +} +var z1 = new Complex64( 1.0e-34, 2.0e-34 ); +var z2 = new Complex64( 1.0, 2.0 ); +var v = div( z1, z2 ); +console.log(v); + +// EXPORTS // + +module.exports = div; diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/lib/native.js b/lib/node_modules/@stdlib/complex/float32/base/div/lib/native.js new file mode 100644 index 000000000000..bea4de5e935b --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/lib/native.js @@ -0,0 +1,54 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 // + +/** +* Divides two single-precision complex floating-point numbers. +* +* @private +* @param {Complex64} z1 - complex number +* @param {Complex64} z2 - complex number +* @returns {Complex64} result +* +* @example +* var Complex64 = require( '@stdlib/complex/float32/ctor' ); +* +* var z1 = new Complex64( -13.0, -1.0 ); +* var z2 = new Complex64( -2.0, 1.0 ); +* +* var out = div( z1, z2 ); +* // returns [ 5.0, 3.0 ] +*/ +function div( z1, z2 ) { + var v = addon( z1, z2 ); + return new Complex64( v.re, v.im ); +} + + +// EXPORTS // + +module.exports = div; diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/lib/robust_internal.js b/lib/node_modules/@stdlib/complex/float32/base/div/lib/robust_internal.js new file mode 100644 index 000000000000..5f8a3e45d448 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/lib/robust_internal.js @@ -0,0 +1,62 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 internalCompreal = require( './internal_compreal.js' ); +var f32 = require( '@stdlib/number/float64/base/to-float32' ); + + +// MAIN // + +/** +* Computes the complex division. +* +* ## Notes +* +* - See figure 10 of [reference][@baudin:2012]. +* +* [@baudin:2012]: https://arxiv.org/abs/1210.4539 +* +* @private +* @param {number} re1 - real component +* @param {number} im1 - imaginary component +* @param {number} re2 - real component +* @param {number} im2 - imaginary component +* @returns {Array} result +*/ +function robustInternal( re1, im1, re2, im2 ) { + var out; + var r; + var t; + + out = [ 0.0, 0.0 ]; + r = f32( im2 / re2 ); + t = f32( 1.0 / f32( re2 + f32(im2*r) ) ); + + out[ 0 ] = internalCompreal( re1, im1, re2, im2, r, t ); + out[ 1 ] = internalCompreal( im1, -re1, re2, im2, r, t ); + return out; +} + + +// EXPORTS // + +module.exports = robustInternal; diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/src/Makefile b/lib/node_modules/@stdlib/complex/float32/base/div/src/Makefile new file mode 100644 index 000000000000..7733b6180cb4 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/src/Makefile @@ -0,0 +1,70 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2025 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/complex/float32/base/div/src/addon.c b/lib/node_modules/@stdlib/complex/float32/base/div/src/addon.c new file mode 100644 index 000000000000..8d8d1fdbe1a7 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/src/addon.c @@ -0,0 +1,22 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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/complex/float32/base/div.h" +#include "stdlib/math/base/napi/binary.h" + +STDLIB_MATH_BASE_NAPI_MODULE_CC_C( stdlib_base_complex64_div ) diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/src/main.c b/lib/node_modules/@stdlib/complex/float32/base/div/src/main.c new file mode 100644 index 000000000000..fc1c7f4260af --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/src/main.c @@ -0,0 +1,173 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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/complex/float32/base/div.h" +#include "stdlib/math/base/special/absf.h" +#include "stdlib/complex/float32/ctor.h" +#include "stdlib/complex/float32/reim.h" +#include "stdlib/constants/float32/max.h" +#include "stdlib/constants/float32/eps.h" +#include "stdlib/constants/float32/smallest_normal.h" + +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 ); + +/** +* Computes the real part of the quotient. +* +* ## Notes +* +* - See figure 10 of [Baudin (2012)][@baudin:2012]. +* +* [@baudin:2012]: https://arxiv.org/absf/1210.4539 +* +* @param re1 real component +* @param im1 imaginary component +* @param re2 real component +* @param im2 imaginary component +* @param r partial result +* @param t partial result +* @return real part of the quotient +*/ +static float internalCompreal( const float re1, const float im1, const float re2, const float im2, const float r, const float t ) { + float br; + if ( r == 0.0f ) { + return ( re1 + (im2 * ( im1 / re2 )) ) * t; + } + br = im1 * r; + if ( br == 0.0f ) { + return ( re1 * t ) + ( ( im1 * t ) * r ); + } + return ( re1 + br ) * t; +} + +/** +* Computes the complex division. +* +* ## Notes +* +* - See figure 10 of [reference][@baudin:2012]. +* +* [@baudin:2012]: https://arxiv.org/absf/1210.4539 +* +* @param re1 real component +* @param im1 imaginary component +* @param re2 real component +* @param im2 imaginary component +* @param re real result +* @param im imaginary result +*/ +static void robustInternal( const float re1, const float im1, const float re2, const float im2, float* re, float* im ) { + float r; + float t; + + r = im2 / re2; + t = 1.0f / ( re2 + ( im2 * r ) ); + + *re = internalCompreal( re1, im1, re2, im2, r, t ); + *im = internalCompreal( im1, -re1, re2, im2, r, t ); +} + +/** +* Divides two single-precision complex floating-point numbers. +* +* @param z1 input value +* @param z2 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 z1 = stdlib_complex64( -13.0f, -1.0f ); +* stdlib_complex64_t z2 = stdlib_complex64( -2.0f, 1.0f ); +* +* stdlib_complex64_t out = stdlib_base_complex64_div( z1, z2 ); +* +* float re = stdlib_complex64_real( out ); +* // returns 5.0f +* +* float im = stdlib_complex64_imag( out ); +* // returns 3.0f +*/ +stdlib_complex64_t stdlib_base_complex64_div( const stdlib_complex64_t z1, const stdlib_complex64_t z2 ) { + float re1; + float re2; + float im1; + float im2; + float t1; + float t2; + float ab; + float cd; + float re; + float im; + float s; + + stdlib_complex64_reim( z1, &re1, &im1 ); + stdlib_complex64_reim( z2, &re2, &im2 ); + + t1 = stdlib_base_absf( re1 ); + t2 = stdlib_base_absf( im1 ); + if ( t1 > t2 ) { + ab = t1; + } else { + ab = t2; + } + t1 = stdlib_base_absf( re2 ); + t2 = stdlib_base_absf( im2 ); + if ( t1 > t2 ) { + cd = t1; + } else { + cd = t2; + } + + s = 1.0f; + + if ( ab >= LARGE_THRESHOLD ) { + re1 *= 0.5f; + im1 *= 0.5f; + s *= 2.0f; + } else if ( ab <= SMALL_THRESHOLD ) { + re1 *= RECIP_EPS_SQR; + im1 *= RECIP_EPS_SQR; + s /= RECIP_EPS_SQR; + } + if ( cd >= LARGE_THRESHOLD ) { + re2 *= 0.5f; + im2 *= 0.5f; + s *= 0.5f; + } else if ( cd <= SMALL_THRESHOLD ) { + re2 *= RECIP_EPS_SQR; + im2 *= RECIP_EPS_SQR; + s *= RECIP_EPS_SQR; + } + re = 0.0f; + im = 0.0f; + if ( stdlib_base_absf( im2 ) <= stdlib_base_absf( re2 ) ) { + robustInternal( re1, im1, re2, im2, &re, &im ); + } else { + robustInternal( im1, re1, im2, re2, &re, &im ); + im *= -1.0f; + } + re *= s; + im *= s; + + return stdlib_complex64( re, im ); +} diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/src/manifest.json b/lib/node_modules/@stdlib/complex/float32/base/div/src/manifest.json new file mode 100644 index 000000000000..a62ea25acee5 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/src/manifest.json @@ -0,0 +1,87 @@ +{ + "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/binary", + "@stdlib/complex/float32/ctor", + "@stdlib/complex/float32/reim", + "@stdlib/math/base/special/absf", + "@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/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/constants/float32/max", + "@stdlib/constants/float32/eps", + "@stdlib/constants/float32/smallest-normal" + ] + } + ] +} diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/src/package.json b/lib/node_modules/@stdlib/complex/float32/base/div/src/package.json new file mode 100644 index 000000000000..50e053ba0e87 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/src/package.json @@ -0,0 +1,67 @@ +{ + "name": "@stdlib/complex/float32/base/div", + "version": "0.0.0", + "description": "Divide two complex numbers.", + "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", + "div", + "divide", + "division", + "arithmetic", + "complex", + "cmplx", + "number" + ] +} diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/REQUIRE new file mode 100644 index 000000000000..308c3be89c85 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/REQUIRE @@ -0,0 +1,2 @@ +julia 1.5 +JSON 0.21 diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/component_scales1.json b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/component_scales1.json new file mode 100644 index 000000000000..e9ef5904fe04 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/component_scales1.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/component_scales2.json b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/component_scales2.json new file mode 100644 index 000000000000..9deed0da173d --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/component_scales2.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/data.json b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/data.json new file mode 100644 index 000000000000..57af2b1905f8 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/data.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/imaginary_component_scales.json b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/imaginary_component_scales.json new file mode 100644 index 000000000000..38cc9824a83c --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/imaginary_component_scales.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/large_negative_imaginary_components.json b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/large_negative_imaginary_components.json new file mode 100644 index 000000000000..38150d4ad5bb --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/large_negative_imaginary_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/large_negative_real_components.json b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/large_negative_real_components.json new file mode 100644 index 000000000000..1cba69e0f1cc --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/large_negative_real_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/large_positive_imaginary_components.json b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/large_positive_imaginary_components.json new file mode 100644 index 000000000000..c9241f3f6a74 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/large_positive_imaginary_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/large_positive_real_components.json b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/large_positive_real_components.json new file mode 100644 index 000000000000..3a2d59184ffc --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/large_positive_real_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/real_component_scales.json b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/real_component_scales.json new file mode 100644 index 000000000000..d02ae9cbbeb0 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/real_component_scales.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/runner.jl new file mode 100755 index 000000000000..a7989e447c47 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/runner.jl @@ -0,0 +1,168 @@ +#!/usr/bin/env julia +# +# @license Apache-2.0 +# +# Copyright (c) 2025 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( re1, im1, re2, im2, name ) + +Generate fixture data and write to file. + +# Arguments + +* `re1`: real components for first complex number +* `im1`: imaginary components for first complex number +* `re2`: real components for second complex number +* `im2`: imaginary components for second complex number +* `name::AbstractString`: output filename + +# Examples + +``` julia +julia> re1 = rand( 1000 ); +julia> im1 = rand( 1000 ); +julia> re2 = rand( 1000 ); +julia> im2 = rand( 1000 ); +julia> gen( re1, im1, re2, im2, \"data.json\" ); +``` +""" +function gen( re1, im1, re2, im2, name ) + zre = Array{Float32}( undef, length(re1) ); + zim = Array{Float32}( undef, length(re1) ); + for i in eachindex(re1) + z = Complex{Float32}( re1[i], im1[i] ) / Complex{Float32}( re2[i], im2[i] ); + zre[ i ] = real( z ); + zim[ i ] = imag( z ); + end + + # Store data to be written to file as a collection: + data = Dict([ + ("re1", re1), + ("im1", im1), + ("re2", re2), + ("im2", im2), + ("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: +re1 = rand( 500 ) .* 1.0e32; +re2 = rand( 500 ) .* 1.0e32; +im1 = ( rand( 500 ) .* 2.0 ) .- 10.0; +im2 = ( rand( 500 ) .* 2.0 ) .- 10.0; +gen( re1, re2, im1, im2, "large_positive_real_components.json" ); + +# Large negative real components: +re1 = -rand( 500 ) .* 1.0e32; +re2 = -rand( 500 ) .* 1.0e32; +im1 = ( rand( 500 ) .* 2.0 ) .- 10.0; +im2 = ( rand( 500 ) .* 2.0 ) .- 10.0; +gen( re1, im1, re2, im2, "large_negative_real_components.json" ); + +# Large positive imaginary components: +re1 = ( rand( 500 ) .* 2.0 ) .- 10.0; +re2 = ( rand( 500 ) .* 2.0 ) .- 10.0; +im1 = rand( 500 ) .* 1.0e32; +im2 = rand( 500 ) .* 1.0e32; +gen( re1, im1, re2, im2, "large_positive_imaginary_components.json" ); + +# Large negative imaginary components: +re1 = ( rand( 500 ) .* 2.0 ) .- 10.0; +re2 = ( rand( 500 ) .* 2.0 ) .- 10.0; +im1 = -rand( 500 ) .* 1.0e32; +im2 = -rand( 500 ) .* 1.0e32; +gen( re1, im1, re2, im2, "large_negative_imaginary_components.json" ); + +# Tiny positive real components: +re1 = rand( 500 ) .* 1.0e-34; +re2 = rand( 500 ) .* 1.0e-34; +im1 = ( rand( 500 ) .* 2.0 ) .- 10.0; +im2 = ( rand( 500 ) .* 2.0 ) .- 10.0; +gen( re1, im1, re2, im2, "tiny_positive_real_components.json" ); + +# Tiny negative real components: +re1 = -rand( 500 ) .* 1.0e-32; +re2 = -rand( 500 ) .* 1.0e-32; +im1 = ( rand( 500 ) .* 2.0 ) .- 10.0; +im2 = ( rand( 500 ) .* 2.0 ) .- 10.0; +gen( re1, im1, re2, im2, "tiny_negative_real_components.json" ); + +# Tiny positive imaginary components: +re1 = ( rand( 500 ) .* 2.0 ) .- 10.0; +re2 = ( rand( 500 ) .* 2.0 ) .- 10.0; +im1 = rand( 500 ) .* 1.0e-32; +im2 = rand( 500 ) .* 1.0e-32; +gen( re1, im1, re2, im2, "tiny_positive_imaginary_components.json" ); + +# Tiny negative imaginary components: +re1 = ( rand( 500 ) .* 2.0 ) .- 10.0; +re2 = ( rand( 500 ) .* 2.0 ) .- 10.0; +im1 = -rand( 500 ) .* 1.0e-34; +im2 = -rand( 500 ) .* 1.0e-34; +gen( re1, im1, re2, im2, "tiny_negative_imaginary_components.json" ); + +# Real components different scales: +re1 = rand( 500 ) .* 1.0e20; +re2 = rand( 500 ) .* 1.0e-10; +im1 = ( rand( 500 ) .* 2.0 ) .- 10.0; +im2 = ( rand( 500 ) .* 2.0 ) .- 10.0; +gen( re1, im1, re2, im2, "real_component_scales.json" ); + +# Imaginary components different scales: +re1 = ( rand( 500 ) .* 2.0 ) .- 10.0; +re2 = ( rand( 500 ) .* 2.0 ) .- 10.0; +im1 = rand( 500 ) .* 1.0e20; +im2 = rand( 500 ) .* 1.0e-10; +gen( re1, im1, re2, im2, "imaginary_component_scales.json" ); + +# Components different scales: +re1 = rand( 500 ) .* 1.0e15; +re2 = rand( 500 ) .* 1.0e15; +im1 = ( rand( 500 ) .* 1.0e-15 ) .- 0.5e-15; +im2 = ( rand( 500 ) .* 1.0e-15 ) .- 0.5e-15; +gen( re1, im1, re2, im2, "component_scales1.json" ); + +# Components different scales: +re1 = ( rand( 500 ) .* 1.0e-15 ) .- 0.5e-15; +re2 = ( rand( 500 ) .* 1.0e-15 ) .- 0.5e-15; +im1 = rand( 500 ) .* 1.0e15; +im2 = rand( 500 ) .* 1.0e15; +gen( re1, im1, re2, im2, "component_scales2.json" ); + +# Normal: +re1 = ( rand( 500 ) .* 10.0 ) .- 50.0; +re2 = ( rand( 500 ) .* 10.0 ) .- 50.0; +im1 = ( rand( 500 ) .* 10.0 ) .- 50.0; +im2 = ( rand( 500 ) .* 10.0 ) .- 50.0; +gen( re1, im1, re2, im2, "data.json" ); diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/tiny_negative_imaginary_components.json b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/tiny_negative_imaginary_components.json new file mode 100644 index 000000000000..6f8370236ea4 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/tiny_negative_imaginary_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/tiny_negative_real_components.json b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/tiny_negative_real_components.json new file mode 100644 index 000000000000..8d358b76b817 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/tiny_negative_real_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/tiny_positive_imaginary_components.json b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/tiny_positive_imaginary_components.json new file mode 100644 index 000000000000..e99bca8c5f33 --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/tiny_positive_imaginary_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/tiny_positive_real_components.json b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/tiny_positive_real_components.json new file mode 100644 index 000000000000..ac219e9644de --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/fixtures/julia/tiny_positive_real_components.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/complex/float32/base/div/test/test.js b/lib/node_modules/@stdlib/complex/float32/base/div/test/test.js new file mode 100644 index 000000000000..8f007cbda87e --- /dev/null +++ b/lib/node_modules/@stdlib/complex/float32/base/div/test/test.js @@ -0,0 +1,1056 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 pow = require( '@stdlib/math/base/special/pow' ); +var EPS = require( '@stdlib/constants/float32/eps' ); +var PINF = require( '@stdlib/constants/float32/pinf' ); +var NINF = require( '@stdlib/constants/float32/ninf' ); +var toBinaryString = require( '@stdlib/number/float32/base/to-binary-string' ); +var Complex64 = require( '@stdlib/complex/float32/ctor' ); +var realf = require( '@stdlib/complex/float32/real' ); +var imagf = require( '@stdlib/complex/float32/imag' ); +var div = require( './../lib' ); + + +// FIXTURES // + +var data = require( './fixtures/julia/data.json' ); +var componentScales1 = require( './fixtures/julia/component_scales1.json' ); +var componentScales2 = require( './fixtures/julia/component_scales2.json' ); +var imaginaryComponentScales = require( './fixtures/julia/imaginary_component_scales.json' ); +var realComponentScales = require( './fixtures/julia/real_component_scales.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' ); + + +// FUNCTIONS // + +/** +* Compares the binary representations of two single-precision floating-point numbers and returns the first index of a differing bit. If all bits match, the function returns `-1`. +* +* TODO: revisit once ULP distance fcn is written +* +* @private +* @param {number} a - first number +* @param {number} b - second number +* @returns {integer} index +*/ +function bitdiff( a, b ) { + var astr; + var bstr; + var i; + + astr = toBinaryString( a ); + bstr = toBinaryString( b ); + for ( i = 0; i < 32; i++ ) { + if ( astr[ i ] !== bstr[ i ] ) { + return i; + } + } + return -1; +} + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof div, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function computes a complex quotient (base behavior)', function test( t ) { + var z1; + var z2; + var v; + + z1 = new Complex64( 2.0, 4.0 ); + z2 = new Complex64( 1.0, 2.0 ); + + v = div( z1, z2 ); + + t.strictEqual( realf( v ), 2.0, 'returns expected value' ); + t.strictEqual( imagf( v ), 0.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function computes a complex quotient (difficult cases)', function test( t ) { + var idx; + var re1; + var im1; + var re2; + var im2; + var z1; + var z2; + var q; + + // Test case #1: + z1 = new Complex64( 1.0, 1.0 ); + z2 = new Complex64( 1.0, pow( 2.0, 103.0 ) ); + + q = div( z1, z2 ); + + idx = bitdiff( realf( q ), pow( 2.0, -103.0 ) ); + t.strictEqual( idx, -1, 'real component has expected binary representation' ); + + idx = bitdiff( imagf( q ), -pow( 2.0, -103.0 ) ); + t.strictEqual( idx, -1, 'imaginary component has expected binary representation' ); + + // Test case #2: + z1 = new Complex64( 1.0, 1.0 ); + z2 = new Complex64( pow( 2.0, -103.0 ), pow( 2.0, -103.0 ) ); + + q = div( z1, z2 ); + + idx = bitdiff( realf( q ), pow( 2.0, 103.0 ) ); + t.strictEqual( idx, -1, 'real component has expected binary representation' ); + + idx = bitdiff( imagf( q ), 0.0 ); + t.strictEqual( idx, -1, 'imaginary component has expected binary representation' ); + + // Test case #3: + re1 = pow( 2.0, 103.0 ); + im1 = pow( 2.0, -103.0 ); + re2 = pow( 2.0, 67.0 ); + im2 = pow( 2.0, -67.0 ); + + z1 = new Complex64( re1, im1 ); + z2 = new Complex64( re2, im2 ); + + q = div( z1, z2 ); + + idx = bitdiff( realf( q ), pow( 2.0, 36.0 ) ); + t.strictEqual( idx, -1, 'real component has expected binary representation' ); + + idx = bitdiff( imagf( q ), -pow( 2.0, -108.0 ) ); + t.strictEqual( idx, -1, 'imaginary component has expected binary representation' ); + + // Test case #4: + z1 = new Complex64( pow( 2.0, 103.0 ), pow( 2.0, 103.0 ) ); + z2 = new Complex64( 1.0, 1.0 ); + + q = div( z1, z2 ); + + idx = bitdiff( realf( q ), pow( 2.0, 103.0 ) ); + t.strictEqual( idx, -1, 'real component has expected binary representation' ); + + idx = bitdiff( imagf( q ), 0.0 ); + t.strictEqual( idx, -1, 'imaginary component has expected binary representation' ); + + // Test case #5: + re1 = pow( 2.0, 102.0 ); + im1 = pow( 2.0, -84.0 ); + re2 = pow( 2.0, 66.0 ); + im2 = pow( 2.0, -78.0 ); + + z1 = new Complex64( re1, im1 ); + z2 = new Complex64( re2, im2 ); + + q = div( z1, z2 ); + + idx = bitdiff( realf( q ), pow( 2.0, 36.0 ) ); + t.strictEqual( idx, -1, 'real component has expected binary representation' ); + + idx = bitdiff( imagf( q ), -pow( 2.0, -107.0 ) ); + t.strictEqual( idx, -1, 'imaginary component has expected binary representation' ); + + // Test case #6: + re1 = pow( 2.0, -7.0 ); + im1 = pow( 2.0, 101.0 ); + re2 = pow( 2.0, 100.0 ); + im2 = pow( 2.0, -33.0 ); + + z1 = new Complex64( re1, im1 ); + z2 = new Complex64( re2, im2 ); + + q = div( z1, z2 ); + + idx = bitdiff( realf( q ), pow( 2.0, -102.0 ) ); + t.strictEqual( idx, -1, 'real component has expected binary representation' ); + + idx = bitdiff( imagf( q ), pow( 2.0, 2.0 ) ); + t.strictEqual( idx, -1, 'imaginary component has expected binary representation' ); + + // Test case #7: + re1 = pow( 2.0, -37.0 ); + im1 = pow( 2.0, -5.0 ); + re2 = pow( 2.0, -103.0 ); + im2 = pow( 2.0, -108.0 ); + + z1 = new Complex64( re1, im1 ); + z2 = new Complex64( re2, im2 ); + + q = div( z1, z2 ); + + idx = bitdiff( realf( q ), 3.898125604559113300e29 ); + t.strictEqual( idx, -1, 'real component has expected binary representation' ); + + idx = bitdiff( imagf( q ), 8.174961907852353577e29 ); + t.strictEqual( idx, -1, 'imaginary component has expected binary representation' ); + + // Test case #8: + re1 = pow( 2.0, -107.0 ); + im1 = pow( 2.0, -107.0 ); + re2 = pow( 2.0, -107.0 ); + im2 = pow( 2.0, -107.0 ); + + z1 = new Complex64( re1, im1 ); + z2 = new Complex64( re2, im2 ); + + q = div( z1, z2 ); + + /* + * See section 3.6 in https://arxiv.org/pdf/1210.4539.pdf. + * + * ```text + * q[0]: 0011111111100011001100110011001100110011001100110011001100110100 + * 0.6: 0011111111100011001100110011001100110011001100110011001100110011 + * ``` + * + * If we add + * + * ```text + * 0000000000000000000000000000000000000000000000000000000000000001 + * ``` + * + * to `0.6`, we get `q[0]`; thus, the result is 1 bit off. + */ + idx = bitdiff( realf( q ), 0.6 ); + t.strictEqual( idx, 61, 'real component has expected binary representation' ); + + idx = bitdiff( imagf( q ), 0.2 ); + t.strictEqual( idx, -1, 'imaginary component has expected binary representation' ); + + // Test case #9: + re1 = pow( 2.0, 115.0 ); + im1 = pow( 2.0, -99.0 ); + re2 = pow( 2.0, 123.0 ); + im2 = pow( 2.0, 123.0 ); + + z1 = new Complex64( re1, im1 ); + z2 = new Complex64( re2, im2 ); + + q = div( z1, z2 ); + + idx = bitdiff( realf( q ), 0.001953125 ); + t.strictEqual( idx, -1, 'real component has expected binary representation' ); + + idx = bitdiff( imagf( q ), -0.001953125 ); + t.strictEqual( idx, -1, 'imaginary component has expected binary representation' ); + + // Test case #10: + re1 = pow( 2.0, -62.0 ); + im1 = pow( 2.0, -107.0 ); + re2 = pow( 2.0, -34.0 ); + im2 = pow( 2.0, -79.0 ); + + z1 = new Complex64( re1, im1 ); + z2 = new Complex64( re2, im2 ); + + q = div( z1, z2 ); + + idx = bitdiff( realf( q ), 1.02951151789360578e-8 ); + t.strictEqual( idx, -1, 'real component has expected binary representation' ); + + idx = bitdiff( imagf( q ), 6.97145987515076231e-22 ); + t.strictEqual( idx, -1, 'imaginary component has expected binary representation' ); + + t.end(); +}); + +tape( 'the function computes a complex quotient (tested against fixtures)', function test( t ) { + var delta; + var tol; + var re1; + var im1; + var re2; + var im2; + var qre; + var qim; + var z1; + var z2; + var i; + var q; + + re1 = data.re1; + im1 = data.im1; + re2 = data.re2; + im2 = data.im2; + qre = data.qre; + qim = data.qim; + + for ( i = 0; i < re1.length; i++ ) { + z1 = new Complex64( re1[ i ], im1[ i ] ); + z2 = new Complex64( re2[ i ], im2[ i ] ); + q = div( z1, z2 ); + + if ( realf( q ) === qre[ i ] ) { + t.strictEqual( realf( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( realf( q ) - qre[ i ] ); + tol = 3 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imagf( q ) === qim[ i ] ) { + t.strictEqual( imagf( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imagf( q ) - qim[ i ] ); + tol = 300 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex quotient (different component scales)', function test( t ) { + var delta; + var tol; + var re1; + var im1; + var re2; + var im2; + var qre; + var qim; + var z1; + var z2; + var i; + var q; + + re1 = componentScales1.re1; + im1 = componentScales1.im1; + re2 = componentScales1.re2; + im2 = componentScales1.im2; + qre = componentScales1.qre; + qim = componentScales1.qim; + + for ( i = 0; i < re1.length; i++ ) { + z1 = new Complex64( re1[ i ], im1[ i ] ); + z2 = new Complex64( re2[ i ], im2[ i ] ); + q = div( z1, z2 ); + + if ( realf( q ) === qre[ i ] ) { + t.strictEqual( realf( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( realf( q ) - qre[ i ] ); + tol = 2 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imagf( q ) === qim[ i ] ) { + t.strictEqual( imagf( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imagf( q ) - qim[ i ] ); + tol = 250 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex quotient (different component scales)', function test( t ) { + var delta; + var tol; + var re1; + var im1; + var re2; + var im2; + var qre; + var qim; + var z1; + var z2; + var i; + var q; + + re1 = componentScales2.re1; + im1 = componentScales2.im1; + re2 = componentScales2.re2; + im2 = componentScales2.im2; + qre = componentScales2.qre; + qim = componentScales2.qim; + + for ( i = 0; i < re1.length; i++ ) { + z1 = new Complex64( re1[ i ], im1[ i ] ); + z2 = new Complex64( re2[ i ], im2[ i ] ); + q = div( z1, z2 ); + + if ( realf( q ) === qre[ i ] ) { + t.strictEqual( realf( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( realf( q ) - qre[ i ] ); + tol = 2 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imagf( q ) === qim[ i ] ) { + t.strictEqual( imagf( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imagf( q ) - qim[ i ] ); + tol = 20 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex quotient (different imaginary component scales)', function test( t ) { + var delta; + var tol; + var re1; + var im1; + var re2; + var im2; + var qre; + var qim; + var z1; + var z2; + var i; + var q; + + re1 = imaginaryComponentScales.re1; + im1 = imaginaryComponentScales.im1; + re2 = imaginaryComponentScales.re2; + im2 = imaginaryComponentScales.im2; + qre = imaginaryComponentScales.qre; + qim = imaginaryComponentScales.qim; + + for ( i = 0; i < re1.length; i++ ) { + z1 = new Complex64( re1[ i ], im1[ i ] ); + z2 = new Complex64( re2[ i ], im2[ i ] ); + q = div( z1, z2 ); + + if ( realf( q ) === qre[ i ] ) { + t.strictEqual( realf( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( realf( q ) - qre[ i ] ); + tol = 2 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imagf( q ) === qim[ i ] ) { + t.strictEqual( imagf( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imagf( q ) - qim[ i ] ); + tol = 2 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex quotient (real imaginary component scales)', function test( t ) { + var delta; + var tol; + var re1; + var im1; + var re2; + var im2; + var qre; + var qim; + var z1; + var z2; + var i; + var q; + + re1 = realComponentScales.re1; + im1 = realComponentScales.im1; + re2 = realComponentScales.re2; + im2 = realComponentScales.im2; + qre = realComponentScales.qre; + qim = realComponentScales.qim; + + for ( i = 0; i < re1.length; i++ ) { + z1 = new Complex64( re1[ i ], im1[ i ] ); + z2 = new Complex64( re2[ i ], im2[ i ] ); + q = div( z1, z2 ); + + if ( realf( q ) === qre[ i ] ) { + t.strictEqual( realf( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( realf( q ) - qre[ i ] ); + tol = 2 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imagf( q ) === qim[ i ] ) { + t.strictEqual( imagf( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imagf( q ) - qim[ i ] ); + tol = 2 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex quotient (large negative imaginary components)', function test( t ) { + var delta; + var tol; + var re1; + var im1; + var re2; + var im2; + var qre; + var qim; + var z1; + var z2; + var i; + var q; + + re1 = largeNegativeImaginaryComponents.re1; + im1 = largeNegativeImaginaryComponents.im1; + re2 = largeNegativeImaginaryComponents.re2; + im2 = largeNegativeImaginaryComponents.im2; + qre = largeNegativeImaginaryComponents.qre; + qim = largeNegativeImaginaryComponents.qim; + + for ( i = 0; i < re1.length; i++ ) { + z1 = new Complex64( re1[ i ], im1[ i ] ); + z2 = new Complex64( re2[ i ], im2[ i ] ); + q = div( z1, z2 ); + + if ( realf( q ) === qre[ i ] ) { + t.strictEqual( realf( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( realf( q ) - qre[ i ] ); + tol = 2 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imagf( q ) === qim[ i ] ) { + t.strictEqual( imagf( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imagf( q ) - qim[ i ] ); + tol = 75 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex quotient (large negative real components)', function test( t ) { + var delta; + var tol; + var re1; + var im1; + var re2; + var im2; + var qre; + var qim; + var z1; + var z2; + var i; + var q; + + re1 = largeNegativeRealComponents.re1; + im1 = largeNegativeRealComponents.im1; + re2 = largeNegativeRealComponents.re2; + im2 = largeNegativeRealComponents.im2; + qre = largeNegativeRealComponents.qre; + qim = largeNegativeRealComponents.qim; + + for ( i = 0; i < re1.length; i++ ) { + z1 = new Complex64( re1[ i ], im1[ i ] ); + z2 = new Complex64( re2[ i ], im2[ i ] ); + q = div( z1, z2 ); + + if ( realf( q ) === qre[ i ] ) { + t.strictEqual( realf( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( realf( q ) - qre[ i ] ); + tol = 2 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imagf( q ) === qim[ i ] ) { + t.strictEqual( imagf( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imagf( q ) - qim[ i ] ); + tol = 300 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex quotient (large positive imaginary components)', function test( t ) { + var delta; + var tol; + var re1; + var im1; + var re2; + var im2; + var qre; + var qim; + var z1; + var z2; + var i; + var q; + + re1 = largePositiveImaginaryComponents.re1; + im1 = largePositiveImaginaryComponents.im1; + re2 = largePositiveImaginaryComponents.re2; + im2 = largePositiveImaginaryComponents.im2; + qre = largePositiveImaginaryComponents.qre; + qim = largePositiveImaginaryComponents.qim; + + for ( i = 0; i < re1.length; i++ ) { + z1 = new Complex64( re1[ i ], im1[ i ] ); + z2 = new Complex64( re2[ i ], im2[ i ] ); + q = div( z1, z2 ); + + if ( realf( q ) === qre[ i ] ) { + t.strictEqual( realf( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( realf( q ) - qre[ i ] ); + tol = 2 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imagf( q ) === qim[ i ] ) { + t.strictEqual( imagf( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = + absf( imagf( q ) - qim[ i ] ); + tol = 300 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex quotient (large positive real components)', function test( t ) { + var delta; + var tol; + var re1; + var im1; + var re2; + var im2; + var qre; + var qim; + var z1; + var z2; + var i; + var q; + + re1 = largePositiveRealComponents.re1; + im1 = largePositiveRealComponents.im1; + re2 = largePositiveRealComponents.re2; + im2 = largePositiveRealComponents.im2; + qre = largePositiveRealComponents.qre; + qim = largePositiveRealComponents.qim; + + for ( i = 0; i < re1.length; i++ ) { + z1 = new Complex64( re1[ i ], im1[ i ] ); + z2 = new Complex64( re2[ i ], im2[ i ] ); + q = div( z1, z2 ); + + if ( realf( q ) === qre[ i ] ) { + t.strictEqual( realf( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( realf( q ) - qre[ i ] ); + tol = 2 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imagf( q ) === qim[ i ] ) { + t.strictEqual( imagf( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imagf( q ) - qim[ i ] ); + tol = 325 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex quotient (tiny negative imaginary components)', function test( t ) { + var delta; + var tol; + var re1; + var im1; + var re2; + var im2; + var qre; + var qim; + var z1; + var z2; + var i; + var q; + + re1 = tinyNegativeImaginaryComponents.re1; + im1 = tinyNegativeImaginaryComponents.im1; + re2 = tinyNegativeImaginaryComponents.re2; + im2 = tinyNegativeImaginaryComponents.im2; + qre = tinyNegativeImaginaryComponents.qre; + qim = tinyNegativeImaginaryComponents.qim; + + for ( i = 0; i < re1.length; i++ ) { + z1 = new Complex64( re1[ i ], im1[ i ] ); + z2 = new Complex64( re2[ i ], im2[ i ] ); + q = div( z1, z2 ); + + if ( realf( q ) === qre[ i ] ) { + t.strictEqual( realf( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( realf( q ) - qre[ i ] ); + tol = 2 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imagf( q ) === qim[ i ] ) { + t.strictEqual( imagf( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imagf( q ) - qim[ i ] ); + tol = 450 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex quotient (tiny negative real components)', function test( t ) { + var delta; + var tol; + var re1; + var im1; + var re2; + var im2; + var qre; + var qim; + var z1; + var z2; + var i; + var q; + + re1 = tinyNegativeRealComponents.re1; + im1 = tinyNegativeRealComponents.im1; + re2 = tinyNegativeRealComponents.re2; + im2 = tinyNegativeRealComponents.im2; + qre = tinyNegativeRealComponents.qre; + qim = tinyNegativeRealComponents.qim; + + for ( i = 0; i < re1.length; i++ ) { + z1 = new Complex64( re1[ i ], im1[ i ] ); + z2 = new Complex64( re2[ i ], im2[ i ] ); + q = div( z1, z2 ); + + if ( realf( q ) === qre[ i ] ) { + t.strictEqual( realf( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( realf( q ) - qre[ i ] ); + tol = 2 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imagf( q ) === qim[ i ] ) { + t.strictEqual( imagf( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imagf( q ) - qim[ i ] ); + tol = 100 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex quotient (tiny positive imaginary components)', function test( t ) { + var delta; + var tol; + var re1; + var im1; + var re2; + var im2; + var qre; + var qim; + var z1; + var z2; + var i; + var q; + + re1 = tinyPositiveImaginaryComponents.re1; + im1 = tinyPositiveImaginaryComponents.im1; + re2 = tinyPositiveImaginaryComponents.re2; + im2 = tinyPositiveImaginaryComponents.im2; + qre = tinyPositiveImaginaryComponents.qre; + qim = tinyPositiveImaginaryComponents.qim; + + for ( i = 0; i < re1.length; i++ ) { + z1 = new Complex64( re1[ i ], im1[ i ] ); + z2 = new Complex64( re2[ i ], im2[ i ] ); + q = div( z1, z2 ); + + if ( realf( q ) === qre[ i ] ) { + t.strictEqual( realf( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( realf( q ) - qre[ i ] ); + tol = 2 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imagf( q ) === qim[ i ] ) { + t.strictEqual( imagf( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imagf( q ) - qim[ i ] ); + tol = 250 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex quotient (tiny positive real components)', function test( t ) { + var delta; + var tol; + var re1; + var im1; + var re2; + var im2; + var qre; + var qim; + var z1; + var z2; + var i; + var q; + + re1 = tinyPositiveRealComponents.re1; + im1 = tinyPositiveRealComponents.im1; + re2 = tinyPositiveRealComponents.re2; + im2 = tinyPositiveRealComponents.im2; + qre = tinyPositiveRealComponents.qre; + qim = tinyPositiveRealComponents.qim; + + for ( i = 0; i < re1.length; i++ ) { + z1 = new Complex64( re1[ i ], im1[ i ] ); + z2 = new Complex64( re2[ i ], im2[ i ] ); + q = div( z1, z2 ); + + if ( realf( q ) === qre[ i ] ) { + t.strictEqual( realf( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = absf( realf( q ) - qre[ i ] ); + tol = 2 * EPS * absf( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imagf( q ) === qim[ i ] ) { + t.strictEqual( imagf( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = absf( imagf( q ) - qim[ i ] ); + tol = 575 * EPS * absf( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re1[i]+' + '+im1[i]+'i. y: '+re2[i]+' + '+im2[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function handles large and small numbers', function test( t ) { + var expected; + var z1; + var z2; + var v; + + z1 = new Complex64( 1.0e38, 5.0e37 ); + z2 = new Complex64( 1.0, 0.5 ); + v = div( z1, z2 ); + expected = [ 1.0e38, 0.0 ]; + + t.strictEqual( realf( v ), expected[ 0 ], 'returns expected values' ); + t.strictEqual( imagf( v ), expected[ 1 ], 'returns expected values' ); + + z1 = new Complex64( 1.0, 0.5 ); + z2 = new Complex64( 1.0e38, 5.0e37 ); + v = div( z1, z2 ); + expected = [ 1.0e-38, 0.0 ]; + + t.strictEqual( realf( v ), expected[ 0 ], 'returns expected values' ); + t.strictEqual( imagf( v ), expected[ 1 ], 'returns expected values' ); + + z1 = new Complex64( 1.0e-34, 2.0e-34 ); + z2 = new Complex64( 1.0, 2.0 ); + v = div( z1, z2 ); + expected = [ 1.0e-34, 0.0 ]; + + t.strictEqual( realf( v ), expected[ 0 ], 'returns expected values' ); + t.strictEqual( imagf( v ), expected[ 1 ], 'returns expected values' ); + + z1 = new Complex64( 1.0, 2.0 ); + z2 = new Complex64( 1.0e-34, 2.0e-34 ); + v = div( z1, z2 ); + expected = [ 1.0e+34, 0.0 ]; + + t.strictEqual( realf( v ), expected[ 0 ], 'returns expected values' ); + t.strictEqual( imagf( v ), expected[ 1 ], 'returns expected values' ); + + z1 = new Complex64( 2.0, 4.0 ); + z2 = new Complex64( 0.0, 2.0 ); + v = div( z1, z2 ); + expected = [ 2.0, -1.0 ]; + + t.strictEqual( realf( v ), expected[ 0 ], 'returns expected values' ); + t.strictEqual( imagf( v ), expected[ 1 ], 'returns expected values' ); + + z1 = new Complex64( 1.0e-18, 1.0e-18 ); + z2 = new Complex64( 1.0, 1.0e-18 ); + v = div( z1, z2 ); + expected = [ 1.0e-18, 1.0e-18 ]; + + t.strictEqual( realf( v ), expected[ 0 ], 'returns expected values' ); + t.strictEqual( imagf( v ), expected[ 1 ], 'returns expected values' ); + + t.end(); +}); + +tape( 'the function may overflow during complex division', function test( t ) { + var z1; + var z2; + var v; + + z1 = new Complex64( 1.0e8, 1.0e8 ); + z2 = new Complex64( 5.0e-40, 5.0e-40 ); + v = div( z1, z2 ); + t.strictEqual( realf( v ), PINF, 'real component is +infinity' ); + t.strictEqual( imagf( v ), 0.0, 'imaginary component is 0' ); + + z1 = new Complex64( 1.0e8, 1.0e8 ); + z2 = new Complex64( -5.0e-40, 5.0e-40 ); + v = div( z1, z2 ); + t.strictEqual( realf( v ), 0.0, 'real component is 0' ); + t.strictEqual( imagf( v ), NINF, 'imaginary component is -infinity' ); + + z1 = new Complex64( 1.0e8, -1.0e8 ); + z2 = new Complex64( 5.0e-40, 5.0e-40 ); + v = div( z1, z2 ); + t.strictEqual( realf( v ), 0.0, 'real component is 0' ); + t.strictEqual( imagf( v ), NINF, 'imaginary component is -infinity' ); + + z1 = new Complex64( -1.0e8, 1.0e8 ); + z2 = new Complex64( 5.0e-40, 5.0e-40 ); + v = div( z1, z2 ); + t.strictEqual( realf( v ), 0.0, 'real component is 0' ); + t.strictEqual( imagf( v ), PINF, 'imaginary component is +infinity' ); + + z1 = new Complex64( 1.0e8, 1.0e8 ); + z2 = new Complex64( 5.0e-40, -5.0e-40 ); + v = div( z1, z2 ); + t.strictEqual( realf( v ), 0.0, 'real component is 0' ); + t.strictEqual( imagf( v ), PINF, 'imaginary component is +infinity' ); + + z1 = new Complex64( -1.0e8, 1.0e8 ); + z2 = new Complex64( -5.0e-40, 5.0e-40 ); + v = div( z1, z2 ); + t.strictEqual( realf( v ), PINF, 'real component is +infinity' ); + t.strictEqual( imagf( v ), 0.0, 'imaginary component is 0' ); + + z1 = new Complex64( 1.0e8, -1.0e8 ); + z2 = new Complex64( 5.0e-40, -5.0e-40 ); + v = div( z1, z2 ); + t.strictEqual( realf( v ), PINF, 'real component is +infinity' ); + t.strictEqual( imagf( v ), 0.0, 'imaginary component is 0' ); + + z1 = new Complex64( 1.0e8, -1.0e8 ); + z2 = new Complex64( -5.0e-40, 5.0e-40 ); + v = div( z1, z2 ); + t.strictEqual( realf( v ), NINF, 'real component is -infinity' ); + t.strictEqual( imagf( v ), 0.0, 'imaginary component is 0' ); + + z1 = new Complex64( -1.0e8, 1.0e8 ); + z2 = new Complex64( 5.0e-40, -5.0e-40 ); + v = div( z1, z2 ); + t.strictEqual( realf( v ), NINF, 'real component is -infinity' ); + t.strictEqual( imagf( v ), 0.0, 'imaginary component is 0' ); + + z1 = new Complex64( -1.0e8, -1.0e8 ); + z2 = new Complex64( -5.0e-40, 5.0e-40 ); + v = div( z1, z2 ); + t.strictEqual( realf( v ), 0.0, 'real component is 0' ); + t.strictEqual( imagf( v ), PINF, 'imaginary component is +infinity' ); + + z1 = new Complex64( 1.0e8, -1.0e8 ); + z2 = new Complex64( -5.0e-40, -5.0e-40 ); + v = div( z1, z2 ); + t.strictEqual( realf( v ), 0.0, 'real component is 0' ); + t.strictEqual( imagf( v ), PINF, 'imaginary component is +infinity' ); + + z1 = new Complex64( -1.0e8, 1.0e8 ); + z2 = new Complex64( -5.0e-40, -5.0e-40 ); + v = div( z1, z2 ); + t.strictEqual( realf( v ), 0.0, 'real component is 0' ); + t.strictEqual( imagf( v ), NINF, 'imaginary component is -infinity' ); + + z1 = new Complex64( -1.0e8, -1.0e8 ); + z2 = new Complex64( 5.0e-40, -5.0e-40 ); + v = div( z1, z2 ); + t.strictEqual( realf( v ), 0.0, 'real component is 0' ); + t.strictEqual( imagf( v ), NINF, 'imaginary component is -infinity' ); + + t.end(); +}); + +tape( 'if a real or imaginary component is `NaN`, all components are `NaN`', function test( t ) { + var z1; + var z2; + var v; + + z1 = new Complex64( NaN, 3.0 ); + z2 = new Complex64( -2.0, 1.0 ); + v = div( z1, z2 ); + t.strictEqual( isnanf( realf( v ) ), true, 'returns NaN' ); + t.strictEqual( isnanf( imagf( v ) ), true, 'returns NaN' ); + + z1 = new Complex64( 5.0, NaN ); + z2 = new Complex64( -2.0, 1.0 ); + v = div( z1, z2 ); + t.strictEqual( isnanf( realf( v ) ), true, 'returns NaN' ); + t.strictEqual( isnanf( imagf( v ) ), true, 'returns NaN' ); + + z1 = new Complex64( 5.0, 3.0 ); + z2 = new Complex64( NaN, 1.0 ); + v = div( z1, z2 ); + t.strictEqual( isnanf( realf( v ) ), true, 'returns NaN' ); + t.strictEqual( isnanf( imagf( v ) ), true, 'returns NaN' ); + + z1 = new Complex64( 5.0, 3.0 ); + z2 = new Complex64( -2.0, NaN ); + v = div( z1, z2 ); + t.strictEqual( isnanf( realf( v ) ), true, 'returns NaN' ); + t.strictEqual( isnanf( imagf( v ) ), true, 'returns NaN' ); + + z1 = new Complex64( 5.0, 3.0 ); + z2 = new Complex64( NaN, NaN ); + v = div( z1, z2 ); + t.strictEqual( isnanf( realf( v ) ), true, 'returns NaN' ); + t.strictEqual( isnanf( imagf( v ) ), true, 'returns NaN' ); + + z1 = new Complex64( NaN, NaN ); + z2 = new Complex64( -2.0, 1.0 ); + v = div( z1, z2 ); + t.strictEqual( isnanf( realf( v ) ), true, 'returns NaN' ); + t.strictEqual( isnanf( imagf( v ) ), true, 'returns NaN' ); + + z1 = new Complex64( NaN, NaN ); + z2 = new Complex64( NaN, NaN ); + v = div( z1, z2 ); + t.strictEqual( isnanf( realf( v ) ), true, 'returns NaN' ); + t.strictEqual( isnanf( imagf( v ) ), true, 'returns NaN' ); + + t.end(); +});