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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.
*
*
* ## Notice
*
* The following copyright, license, and long comment were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/12.2.0/lib/msun/src/s_log1pf.c}. The implementation follows the original, but 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.
* ```
*/
'use strict';
// MODULES //
var FLOAT32_NINF = require( '@stdlib/constants/float32/ninf' );
var FLOAT32_ABS_MASK = require( '@stdlib/constants/float32/abs-mask' );
var FLOAT32_PRECISION = require( '@stdlib/constants/float32/precision' );
var FLOAT32_EXPONENT_BIAS = require( '@stdlib/constants/float32/exponent-bias' );
var FLOAT32_SIGNIFICAND_MASK = require( '@stdlib/constants/float32/significand-mask' );
var toWord = require( '@stdlib/number/float32/base/to-word' );
var fromWord = require( '@stdlib/number/float32/base/from-word' );
var float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
var polyval = require( './polyval_lp.js' );
// VARIABLES //
// High and low words of ln(2):
var LN2_HI = 6.9313812256e-01; // 0x3f317180
var LN2_LO = 9.0580006145e-06; // 0x3717f7d1
// 2**25:
var TWO25 = 3.355443200e+07; // 0x4c000000
// 2/3:
var TWO_THIRDS = 6.666666865348816e-01;
// 2**-15:
var TWO_NEG_15 = 0x38000000;
// 2**-24:
var TWO_NEG_24 = 0x33800000;
// toWord( FLOAT32_PINF ):
var FLOAT32_PINF_WORD = 0x7f800000;
// toWord( 1.0 ):
var FLOAT32_ONE_WORD = 0x3f800000;
// toWord( 0.5 ):
var FLOAT32_HALF_WORD = 0x3f000000;
// MAIN //
/**
* Evaluates the natural logarithm of \\(1+x\\) as a single-precision floating-point number.
*
* @param {number} x - input value
* @returns {number} the natural logarithm of `1+x`
*
* @example
* var v = log1pf( 4.0 );
* // returns ~1.609
*
* @example
* var v = log1pf( -1.0 );
* // returns -Infinity
*
* @example
* var v = log1pf( 0.0 );
* // returns 0.0
*
* @example
* var v = log1pf( -0.0 );
* // returns -0.0
*
* @example
* var v = log1pf( -2.0 );
* // returns NaN
*
* @example
* var v = log1pf( NaN );
* // returns NaN
*/
function log1pf( x ) {
var hfsq;
var hx;
var ax;
var hu;
var f;
var c;
var s;
var z;
var R;
var u;
var k;
x = float64ToFloat32( x );
hx = toWord( x ) | 0;
ax = hx & FLOAT32_ABS_MASK;
k = 1;
if ( hx < 0x3ed413d0 ) { // 1+x < sqrt(2)+
if ( ax >= 0x3f800000 ) { // x <= -1.0
if ( x === -1.0 ) {
return FLOAT32_NINF; // log1p(-1)=+inf
}
return NaN; // log1p(x<-1)=NaN
}
if ( ax < TWO_NEG_15 ) { // |x| < 2**-15
if ( ( float64ToFloat32( TWO25 + x ) > 0.0 ) && ax < TWO_NEG_24 ) { // raise inexact, |x| < 2**-24
return x;
}
return float64ToFloat32( x - float64ToFloat32( x * float64ToFloat32( x * 0.5 ) ) ); // eslint-disable-line max-len
}
if ( ( hx > 0 ) || ( hx <= 0xbe95f619 ) ) {
// sqrt(2)/2- <= 1+x < sqrt(2)+:
k = 0;
f = x;
hu = 1;
}
}
if ( hx >= FLOAT32_PINF_WORD ) {
return float64ToFloat32( x + x );
}
if ( k !== 0 ) {
if ( hx < 0x5a000000 ) {
u = float64ToFloat32( 1.0 + x );
hu = toWord( u ) | 0;
k = ( hu >> ( FLOAT32_PRECISION - 1 ) ) - FLOAT32_EXPONENT_BIAS;
// Correction term:
c = ( k > 0 ) ? float64ToFloat32( 1.0 - float64ToFloat32( u - x ) ) : float64ToFloat32( x - float64ToFloat32( u - 1.0 ) ); // eslint-disable-line max-len
c = float64ToFloat32( c / u );
} else {
u = x;
hu = toWord( u ) | 0;
k = ( hu >> ( FLOAT32_PRECISION - 1 ) ) - FLOAT32_EXPONENT_BIAS;
c = 0;
}
hu &= FLOAT32_SIGNIFICAND_MASK;
// The approximation to sqrt(2) used in thresholds is not critical. However, the ones used above must give less strict bounds than the one here so that the k==0 case is never reached from here, since here we have committed to using the correction term but don't use it if k==0:
if ( hu < 0x3504f4 ) { // u < sqrt(2)
u = fromWord( ( hu | FLOAT32_ONE_WORD ) >>> 0 ); // normalize u
} else {
k += 1;
u = fromWord( ( hu | FLOAT32_HALF_WORD ) >>> 0 ); // normalize u/2
hu = ( 0x00800000 - hu ) >> 2;
}
f = float64ToFloat32( u - 1.0 );
}
hfsq = float64ToFloat32( 0.5 * float64ToFloat32( f * f ) );
if ( hu === 0 ) { // |f| < 2**-20
if ( f === 0.0 ) {
if ( k === 0 ) {
return 0.0;
}
c = float64ToFloat32( c + float64ToFloat32( k * LN2_LO ) );
return float64ToFloat32( float64ToFloat32( k * LN2_HI ) + c );
}
R = float64ToFloat32( hfsq * float64ToFloat32( 1.0 - float64ToFloat32( TWO_THIRDS * f ) ) ); // eslint-disable-line max-len
if ( k === 0 ) {
return float64ToFloat32( f - R );
}
return float64ToFloat32( float64ToFloat32( k * LN2_HI ) - float64ToFloat32( float64ToFloat32( R - float64ToFloat32( float64ToFloat32( k * LN2_LO ) + c ) ) - f ) ); // eslint-disable-line max-len
}
s = float64ToFloat32( f / float64ToFloat32( 2.0 + f ) );
z = float64ToFloat32( s * s );
R = float64ToFloat32( z * polyval( z ) );
if ( k === 0 ) {
return float64ToFloat32( f - float64ToFloat32( hfsq - float64ToFloat32( s * float64ToFloat32( hfsq + R ) ) ) ); // eslint-disable-line max-len
}
return float64ToFloat32( float64ToFloat32( k * LN2_HI ) - float64ToFloat32( float64ToFloat32( hfsq - float64ToFloat32( float64ToFloat32( s * float64ToFloat32( hfsq + R ) ) + float64ToFloat32( float64ToFloat32( k * LN2_LO ) + c ) ) ) - f ) ); // eslint-disable-line max-len
}
// EXPORTS //
module.exports = log1pf;
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