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* @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.
*
*
* ## Notice
*
* The following copyright and license were part of the original implementation available as part of [FreeBSD][freebsd-src]. The implementation has been modified for JavaScript.
*
* ```text
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ```
*
* [freebsd-src]: https://svnweb.freebsd.org/base/release/12.2.0/lib/msun/src/s_erff.c
*/
'use strict';
// MODULES //
var float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
var exp = require( '@stdlib/math/base/special/exp' );
var PINF = require( '@stdlib/constants/float32/pinf' );
var NINF = require( '@stdlib/constants/float32/ninf' );
var polyvalPP = require( './polyval_pp.js' );
var polyvalQQ = require( './polyval_qq.js' );
var polyvalPA = require( './polyval_pa.js' );
var polyvalQA = require( './polyval_qa.js' );
var polyvalRA = require( './polyval_ra.js' );
var polyvalSA = require( './polyval_sa.js' );
var polyvalRB = require( './polyval_rb.js' );
var polyvalSB = require( './polyval_sb.js' );
// VARIABLES //
var TINY = float64ToFloat32( 1.0e-30 );
var ONE = float64ToFloat32( 1.0 );
var ERX = float64ToFloat32( 8.4506291151e-01 ); // 0x3f58560b
var EFX = float64ToFloat32( 1.2837916613e-01 ); // 0x3e0375d4
var EFX8 = float64ToFloat32( 1.0270333290e+00 ); // 0x3f8375d4
var PP0 = float64ToFloat32( 1.2837916613e-01 ); // 0x3e0375d4
var PA0 = float64ToFloat32( -2.3621185683e-03 ); // 0xbb1acdc6
var RA0 = float64ToFloat32( -9.8649440333e-03 ); // 0xbc21a093
var RB0 = float64ToFloat32( -9.86496918e-03 ); // 0xbc21a0ae
// MAIN //
/**
* Evaluates the error function for a single-precision floating-point number.
*
* ## Method
*
* 1. For `|x|` in `[0, 0.84375]`
*
* ```tex
* \operatorname{erf}(x) = x + x \cdot R(x^2)
* ```
*
* For very small `x`, a linear approximation is used to avoid underflow.
*
* 2. For `|x|` in `[0.84375,1.25]`
*
* ```tex
* \operatorname{erf}(x) = \operatorname{sign}(x) \cdot (erx + P(|x| - 1) / Q(|x| - 1))
* ```
*
* 3. For `x` in `[1.25,1/0.35 ~ 2.857143]`
*
* ```tex
* \operatorname{erf}(x) = 1 - (1/x) \cdot \exp(-x \cdot x - 0.5625 + R/S)
* ```
*
* 4. For `x >= 1/0.35 ~ 2.857143`
*
* ```tex
* \operatorname{erf}(x) = \operatorname{sign}(x) \cdot (1 - tiny)
* ```
*
* @param {number} x - input value
* @returns {number} function value
*
* @example
* var y = erff( 2.0 );
* // returns ~0.9953
*
* @example
* var y = erff( -1.0 );
* // returns ~-0.8427
*
* @example
* var y = erff( 0.0 );
* // returns 0.0
*
* @example
* var y = erff( NaN );
* // returns NaN
*/
function erff( x ) {
var sign;
var ax;
var z;
var r;
var s;
var y;
var p;
var q;
// Special case: NaN
if ( isnanf( x ) ) {
return NaN;
}
// Special case: +infinity
if ( x === PINF ) {
return ONE;
}
// Special case: -infinity
if ( x === NINF ) {
return -ONE;
}
// Special case: +-0
if ( x === 0.0 ) {
return x;
}
if ( x < 0.0 ) {
sign = true;
ax = float64ToFloat32( -x );
} else {
sign = false;
ax = float64ToFloat32( x );
}
// |x| < 0.84375
if ( ax < float64ToFloat32( 0.84375 ) ) {
if ( ax < float64ToFloat32( 1.0e-4 ) ) {
if ( ax < float64ToFloat32( 1.0e-30 ) ) {
// Avoid underflow:
return float64ToFloat32( float64ToFloat32( 0.125 * float64ToFloat32( float64ToFloat32( 8.0*x ) + float64ToFloat32( EFX8*x ) ) ) ); // eslint-disable-line max-len
}
return float64ToFloat32( x + float64ToFloat32( EFX * x ) );
}
z = float64ToFloat32( x * x );
r = float64ToFloat32( PP0 + float64ToFloat32( z*polyvalPP( z ) ) );
s = float64ToFloat32( ONE + float64ToFloat32( z*polyvalQQ( z ) ) );
y = float64ToFloat32( r / s );
return float64ToFloat32( x + float64ToFloat32( x*y ) );
}
// 0.84375 <= |x| < 1.25
if ( ax < float64ToFloat32( 1.25 ) ) {
s = float64ToFloat32( ax - ONE );
p = float64ToFloat32( PA0 + float64ToFloat32( s * polyvalPA( s ) ) );
q = float64ToFloat32( ONE + float64ToFloat32( s * polyvalQA( s ) ) );
if (sign) {
return float64ToFloat32( float64ToFloat32( -ERX ) - float64ToFloat32( p / q ) ); // eslint-disable-line max-len
}
return float64ToFloat32( ERX + float64ToFloat32( p / q ) );
}
// |x| >= 4
if ( ax >= float64ToFloat32( 4.0 ) ) {
if ( sign ) {
return float64ToFloat32( TINY - ONE );
}
return float64ToFloat32( ONE - TINY );
}
s = float64ToFloat32( ONE / float64ToFloat32( ax * ax ) );
// |x| < 1/0.35 ~ 2.857143
if ( ax < float64ToFloat32( 2.857142857142857 ) ) {
r = float64ToFloat32( RA0 + float64ToFloat32( s * polyvalRA( s ) ) );
s = float64ToFloat32( ONE + float64ToFloat32( s * polyvalSA( s ) ) );
}
// |x| >= 1/0.35 ~ 2.857143
else {
r = float64ToFloat32( RB0 + float64ToFloat32( s * polyvalRB( s ) ) );
s = float64ToFloat32( ONE + float64ToFloat32( s * polyvalSB( s ) ) );
}
z = ax;
r = float64ToFloat32(float64ToFloat32(exp(float64ToFloat32(float64ToFloat32(-z * z) - float64ToFloat32(0.5625)))) * float64ToFloat32(exp(float64ToFloat32((float64ToFloat32((z-x))*float64ToFloat32((z+x)))+float64ToFloat32(r / s))))); // eslint-disable-line max-len
if ( sign ) {
return float64ToFloat32( float64ToFloat32( r / ax ) - ONE );
}
return float64ToFloat32( ONE - float64ToFloat32( r / ax ) );
}
// EXPORTS //
module.exports = erff;
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