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* @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 isnanf = require( '@stdlib/math/base/assert/is-nanf' );
var isInfinitef = require( '@stdlib/math/base/assert/is-infinitef' );
var roundf = require( '@stdlib/math/base/special/roundf' );
var powf = require( '@stdlib/math/base/special/powf' );
var absf = require( '@stdlib/math/base/special/absf' );
var f32 = require( '@stdlib/number/float64/base/to-float32' );
var MAX_SAFE_INTEGER = require( '@stdlib/constants/float32/max-safe-integer' );
var MAX_EXP = require( '@stdlib/constants/float32/max-base10-exponent' );
var MIN_EXP = require( '@stdlib/constants/float32/min-base10-exponent' );
var MIN_EXP_SUBNORMAL = require( '@stdlib/constants/float32/min-base10-exponent-subnormal' );
// VARIABLES //
var MAX_INT = MAX_SAFE_INTEGER + 1;
var HUGE = f32( 1.0e+38 );
// MAIN //
/**
* Rounds a single-precision floating-point number to the nearest multiple of \\(10^n\\).
*
* ## Method
*
* 1. If \\(|x| <= 2^{24}\\) and \\(|n| <= 38\\), we can use the formula
*
* ```tex
* \\operatorname{roundnf}(x,n) = \\frac{\\operatorname{roundf}(x \\cdot 10^{-n})}{10^{-n}}
* ```
*
* which shifts the decimal to the nearest multiple of \\(10^n\\), performs a standard \\(\\mathrm{roundf}\\) operation, and then shifts the decimal to its original position.
*
* <!-- <note> -->
*
* If \\(x \\cdot 10^{-n}\\) overflows, \\(x\\) lacks a sufficient number of decimal digits to have any effect when rounding. Accordingly, the rounded value is \\(x\\).
*
* <!-- </note> -->
*
* <!-- <note> -->
*
* Note that rescaling \\(x\\) can result in unexpected behavior. For instance, the result of \\(\\operatorname{roundnf}(0.2+0.1,-16)\\) is \\(0.30000001192092896\\) and not \\(0.3\\). While possibly unexpected, this is not a bug. The behavior stems from the fact that most decimal fractions cannot be exactly represented as floating-point numbers. And further, rescaling can lead to slightly different fractional values, which, in turn, affects the result of \\(\mathrm{roundf}\\).
*
* <!-- </note> -->
*
* 2. If \\(n > 38\\), we recognize that the maximum absolute single-precision floating-point number is \\(\\approx 3.4\\mbox{e}38\\) and, thus, the result of rounding any possible finite number \\(x\\) to the nearest \\(10^n\\) is \\(0.0\\). To ensure consistent behavior with \\(\\operatorname{roundf}(x)\\), the sign of \\(x\\) is preserved.
*
* 3. If \\(n < -45\\), \\(n\\) exceeds the maximum number of possible decimal places (such as with subnormal numbers), and, thus, the rounded value is \\(x\\).
*
* 4. If \\(x > 2^{24}\\), \\(x\\) is **always** an integer (i.e., \\(x\\) has no decimal digits). If \\(n <= 0\\), the rounded value is \\(x\\).
*
* 5. If \\(n < -38\\), we let \\(m = n + 38\\) and modify the above formula to avoid overflow.
*
* ```tex
* \\operatorname{roundnf}(x,n) = \\frac{\\biggl(\\frac{\\operatorname{roundf}( (x \\cdot 10^{38}) 10^{-m})}{10^{38}}\\biggr)}{10^{-m}}
* ```
*
* If overflow occurs, the rounded value is \\(x\\).
*
* ## Special Cases
*
* ```tex
* \\begin{align*}
* \\operatorname{roundnf}(\\mathrm{NaN}, n) &= \\mathrm{NaN} \\\\
* \\operatorname{roundnf}(x, \\mathrm{NaN}) &= \\mathrm{NaN} \\\\
* \\operatorname{roundnf}(x, \\pm\\infty) &= \\mathrm{NaN} \\\\
* \\operatorname{roundnf}(\\pm\\infty, n) &= \\pm\\infty \\\\
* \\operatorname{roundnf}(\\pm 0, n) &= \\pm 0
* \\end{align*}
* ```
*
* @param {number} x - input value
* @param {integer} n - integer power of `10`
* @returns {number} rounded value
*
* @example
* // Round a value to 2 decimal places:
* var v = roundnf( 3.1415927410125732, -2 );
* // returns ~3.14
*
* @example
* // If n = 0, `roundnf` behaves like `roundf`:
* var v = roundnf( 3.1415927410125732, 0 );
* // returns 3.0
*
* @example
* // Round a value to the nearest thousand:
* var v = roundnf( 12368.0, 3 );
* // returns ~12000.0
*/
function roundnf( x, n ) {
var s;
var y;
x = f32( x );
if (
isnanf( x ) ||
isnanf( n ) ||
isInfinitef( n )
) {
return NaN;
}
if (
// Handle infinities...
isInfinitef( x ) ||
// Handle +-0...
x === 0.0 ||
// If `n` exceeds the maximum number of feasible decimal places (such as with subnormal numbers), nothing to round...
n < MIN_EXP_SUBNORMAL ||
// If `|x|` is large enough, no decimals to round...
( absf( x ) > MAX_INT && n <= 0 )
) {
return x;
}
// The maximum absolute single-precision float is ~3.4e38. Accordingly, any possible finite `x` rounded to the nearest >=10^39 is 0.0.
if ( n > MAX_EXP ) {
return f32( f32( 0.0 ) * x ); // preserve the sign (same behavior as roundf)
}
// If we overflow, return `x`, as the number of digits to the right of the decimal is too small (i.e., `x` is too large / lacks sufficient fractional precision) for there to be any effect when rounding...
if ( n < MIN_EXP ) {
s = powf( f32( 10.0 ), -( n + MAX_EXP ) );
y = f32( f32( x * HUGE ) * s ); // order of operation matters!
if ( isInfinitef( y ) ) {
return x;
}
return f32( f32( roundf( y ) / HUGE ) / s );
}
s = powf( f32( 10.0 ), -n );
y = f32( x * s );
if ( isInfinitef( y ) ) {
return x;
}
return f32( roundf( y ) / s );
}
// EXPORTS //
module.exports = roundnf;
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