feat: add number/float16/base/normalize

lib/node_modules/@stdlib/number/float16/base/normalize/README.md

@@ -0,0 +1,271 @@
+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 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.
+
+-->
+
+# normalize
+
+> Return a normal number `y` and exponent `exp` satisfying `x = y * 2^exp`.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var normalize = require( '@stdlib/number/float16/base/normalize' );
+```
+
+#### normalize( x )
+
+Returns a normal number `y` and exponent `exp` satisfying `x = y * 2^exp`.
+
+```javascript
+var toFloat16 = require( '@stdlib/number/float64/base/to-float16' );
+
+var out = normalize( toFloat16( 1.401e-6 ) );
+// returns [ 0.00146484375, -10 ]
+```
+
+By default, the function returns `y` and `exp` as a two-element `array`.
+
+```javascript
+var toFloat16 = require( '@stdlib/number/float64/base/to-float16' );
+var pow = require( '@stdlib/math/base/special/pow' );
+
+var out = normalize( toFloat16( 1.401e-6 ) );
+// returns [ 0.00146484375, -10 ]
+
+var y = out[ 0 ];
+var exp = out[ 1 ];
+
+var bool = ( y*pow(2, exp) === toFloat16(1.401e-6) );
+// returns true
+```
+
+The function expects a finite, non-zero [half-precision floating-point number][ieee754] `x`. If `x == 0`,
+
+```javascript
+var out = normalize( 0.0 );
+// returns [ 0.0, 0 ];
+```
+
+If `x` is either positive or negative `infinity` or `NaN`,
+
+```javascript
+var PINF = require( '@stdlib/constants/float16/pinf' );
+var NINF = require( '@stdlib/constants/float16/ninf' );
+
+var out = normalize( PINF );
+// returns [ Infinity, 0 ]
+
+out = normalize( NINF );
+// returns [ -Infinity, 0 ]
+
+out = normalize( NaN );
+// returns [ NaN, 0 ]
+```
+
+#### normalize( x, out, stride, offset )
+
+Returns a normal number `y` and exponent `exp` satisfying `x = y * 2^exp` and assigns results to a provided output array.
+
+```javascript
+var toFloat16 = require( '@stdlib/number/float64/base/to-float16' );
+var Float16Array = require( '@stdlib/array/float16' );
+
+var out = new Float16Array( 2 );
+
+var v = normalize.assign( toFloat16( 1.401e-6 ), out, 1, 0 );
+// returns <Float16Array>[ 0.00146484375, -10 ]
+
+var bool = ( v === out );
+// returns true
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   While the function accepts higher precision [floating-point numbers][ieee754], beware that providing such numbers can be a source of subtle bugs as the relation `x = y * 2^exp` may **not** hold.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var round = require( '@stdlib/math/base/special/round' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var toFloat16 = require( '@stdlib/number/float64/base/to-float16' );
+var normalize = require( '@stdlib/number/float16/base/normalize' );
+
+var frac;
+var exp;
+var x;
+var v;
+var i;
+
+// Generate denormalized half-precision floating-point numbers and then normalize them...
+for ( i = 0; i < 100; i++ ) {
+    frac = 0.26 + (randu()*10.0);
+    exp = 5 + round( randu()*4.0 );
+    x = frac * pow( 10.0, -exp );
+    x = toFloat16( x );
+    v = normalize( x );
+    console.log( '%d = %d * 2^%d = %d', x, v[0], v[1], v[0]*pow(2.0, v[1]) );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/number/float16/base/normalize.h"
+```
+
+#### stdlib_base_float16_normalize( x, \*y, \*exp )
+
+Returns a normal number `y` and exponent `exp` satisfying `x = y * 2^exp`.
+
+```c
+#include "stdlib/number/float16/ctor.h"
+#include <stdint.h>
+
+stdlib_float16_t x;
+stdlib_float16_t y;
+int16_t exp;
+
+x = stdlib_float16_from_bits( 51648 ); // => -11.5
+
+stdlib_base_float16_normalize( x, &y, &exp );
+```
+
+The function accepts the following arguments:
+
+-   **x**: `[in] stdlib_float16_t` input value.
+-   **y**: `[out] stdlib_float16_t*` destination for normal number.
+-   **exp**: `[out] int16_t*` destination for exponent.
+
+```c
+void stdlib_base_float16_normalize( const stdlib_float16_t x, stdlib_float16_t *y, int16_t *exp );
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+#include "stdlib/number/float16/ctor.h"
+#include "stdlib/number/float16/base/normalize.h"
+#include "stdlib/number/float32/base/to_float16.h"
+#include "stdlib/number/float16/base/to_float32.h"
+#include <stdint.h>
+#include <inttypes.h>
+#include <stdio.h>
+
+int main( void ) {
+    float x[] = { 4.0f, 0.0f, -0.0f, 1.0f, -1.0f, 3.14f, -3.14f, 1.0e-6f, -1.0e-6f, 1.0f/0.0f, -1.0f/0.0f, 0.0f/0.0f };
+
+    stdlib_float16_t v;
+    stdlib_float16_t y;
+    int16_t exp;
+    int i;
+    for ( i = 0; i < 12; i++ ) {
+        v = stdlib_base_float32_to_float16( x[ i ] );
+        stdlib_base_float16_normalize( v, &y, &exp );
+        printf( "%f => y: %f, exp: %" PRId16 "\n", v, stdlib_base_float16_to_float32( y ), exp );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/number/float16/base/normalize/benchmark/benchmark.js

@@ -0,0 +1,79 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var toFloat16 = require( '@stdlib/number/float64/base/to-float16' );
+var map = require( '@stdlib/array/base/map' );
+var naryFunction = require( '@stdlib/utils/nary-function' );
+var isArray = require( '@stdlib/assert/is-array' );
+var pkg = require( './../package.json' ).name;
+var normalize = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	x = map( uniform( 100, -5.0e4, 5.0e4 ), naryFunction( toFloat16, 1 ) );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = normalize( x[ i%x.length ] );
+		if ( typeof y !== 'object' ) {
+			b.fail( 'should return an array' );
+		}
+	}
+	b.toc();
+	if ( !isArray( y ) ) {
+		b.fail( 'should return an array' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+':assign', function benchmark( b ) {
+	var out;
+	var x;
+	var y;
+	var i;
+
+	out = [ 0.0, 0.0 ];
+	x = map( uniform( 100, -5.0e4, 5.0e4 ), naryFunction( toFloat16, 1 ) );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = normalize.assign( x[ i%x.length ], out, 1, 0 );
+		if ( typeof y !== 'object' ) {
+			b.fail( 'should return an array' );
+		}
+	}
+	b.toc();
+	if ( !isArray( y ) || y !== out ) {
+		b.fail( 'should return the output array' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});