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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, license, and long comment were part of the original implementation available as part of [FreeBSD]{@link https://github.com/freebsd/freebsd-src/blob/main/lib/msun/src/s_exp2f.c}. The implementation follows the original, but has been modified for JavaScript.
*
* ```text
* Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
* ```
*/
'use strict';
// MODULES //
var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
var toWordf = require( '@stdlib/number/float32/base/to-word' );
var fromWords = require( '@stdlib/number/float64/base/from-words' );
var f32 = require( '@stdlib/number/float64/base/to-float32' );
var PINF = require( '@stdlib/constants/float32/pinf' );
var NINF = require( '@stdlib/constants/float32/ninf' );
// VARIABLES //
// Table size: 2^4 = 16
var TBLSIZE = 16;
// Number of bits used to index into the table:
var TBLBITS = 4;
// 2^(i/16) for i = -8, -7, ..., 7 (in double-precision, offset by 8):
var TBL = [
0.7071067811865476, // 0x1.6a09e667f3bcdp-1
0.7384130729697497, // 0x1.7a11473eb0187p-1
0.7711054127039704, // 0x1.8ace5422aa0dbp-1
0.8052451659746271, // 0x1.9c49182a3f090p-1
0.8408964152537145, // 0x1.ae89f995ad3adp-1
0.8781260801866497, // 0x1.c199bdd85529cp-1
0.9170040432046712, // 0x1.d5818dcfba487p-1
0.9576032806985737, // 0x1.ea4afa2a490dap-1
1.0, // 0x1.0000000000000p+0
1.0442737824274138, // 0x1.0b5586cf9890fp+0
1.0905077326652577, // 0x1.172b83c7d517bp+0
1.1387886347566916, // 0x1.2387a6e756238p+0
1.189207115002721, // 0x1.306fe0a31b715p+0
1.241857812073484, // 0x1.3dea64c123422p+0
1.2968395546510096, // 0x1.4bfdad5362a27p+0
1.3542555469368927 // 0x1.5ab07dd485429p+0
];
// Reduction constant: 1.5*2^23/16 = 786432 => 0 10010010 10000000000000000000000 => 0x49400000 = 1228931072
var REDUX = f32( 786432.0 );
// Polynomial coefficient: ~ln(2) => 0 01111110 01100010111001000011000 => 0x3f317218 = 1060205080
var P1 = 0.6931471824645996;
// Polynomial coefficient => 0 01111100 11101011111110111110000 => 0x3e75fdf0 = 1047920112
var P2 = 0.24022650718688965;
// Polynomial coefficient => 0 01111010 11000110101100110100100 => 0x3d6359a4 = 1029921188
var P3 = 0.055505409836769104;
// Polynomial coefficient => 0 01111000 00111011001011001001110 => 0x3c1d964e = 1008571982
var P4 = 0.009618354961276054;
// Overflow threshold: 2^x overflows for x >= 128
var OVERFLOW = 128.0;
// Underflow threshold: 2^x underflows to 0 for x <= -150
var UNDERFLOW = -150.0;
// Near-zero threshold: 2^-25 => 0 01100110 00000000000000000000000 => 0x33000000 = 855638016
var NEARZERO = f32( 1.0 / ( 1 << 25 ) );
var NEG_NEARZERO = f32( -NEARZERO );
// High word of 1.0 => 0 01111111111 0000000000000000000 => 0x3ff00000 = 1072693248
var ONE_HIGH_WORD = 0x3ff00000|0; // asm type annotation
// MAIN //
/**
* Evaluates the base `2` exponential function in single-precision floating-point format.
*
* ## Method
*
* (equally-spaced tables)
*
* - Reduce \\( x \\):
*
* ```tex
* x = k + y
* ```
*
* for integer \\( k \\) and \\( |y| \leq 1/2 \\). Thus we have \\( \operatorname{exp2f}(x) = 2^k \cdot \operatorname{exp2}(y) \\).
*
* - Reduce \\( y \\):
*
* ```tex
* y = i/\mathrm{TBLSIZE} + z
* ```
*
* for integer \\( i \\) near \\( y \cdot \mathrm{TBLSIZE} \\). Thus we have \\( \operatorname{exp2}(y) = \operatorname{exp2}(i/\mathrm{TBLSIZE}) \cdot \operatorname{exp2}(z) \\), with \\( |z| \leq 2^{-(\mathrm{TBLBITS}+1)} \\).
*
* - We compute \\( \operatorname{exp2}(i/\mathrm{TBLSIZE}) \\) via table lookup and \\( \operatorname{exp2}(z) \\) via a degree-4 minimax polynomial with maximum error under \\( 1.4 \cdot 2^{-33} \\). Using double precision for everything except the reduction makes roundoff error insignificant and simplifies the scaling step.
*
* This method is due to Tang, but the implementation does not use his suggested parameters:
*
* > Tang, P. Table-driven Implementation of the Exponential Function in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989).
*
* ## Notes
*
* - Accuracy: peak error < 0.501 ulp.
*
* @param {number} x - input value
* @returns {number} function value
*
* @example
* var v = exp2f( 3.0 );
* // returns 8.0
*
* @example
* var v = exp2f( -9.0 );
* // returns ~0.002
*
* @example
* var v = exp2f( 0.0 );
* // returns 1.0
*
* @example
* var v = exp2f( NaN );
* // returns NaN
*/
function exp2f( x ) {
var twopk;
var i0;
var tv;
var hi;
var t;
var u;
var z;
x = f32( x );
if ( isnanf( x ) || x === PINF ) {
return x;
}
if ( x === NINF ) {
return 0.0;
}
if ( x >= OVERFLOW ) {
return PINF;
}
if ( x <= UNDERFLOW ) {
return 0.0;
}
if (
x > NEG_NEARZERO &&
x < NEARZERO
) {
return f32( 1.0 + x );
}
// Reduce `x`, computing `z`, `i0`, and `k` (the high word of 2^k)...
t = f32( x + REDUX );
i0 = toWordf( t ) >>> 0; // asm type annotation
i0 += TBLSIZE / 2;
hi = ( ONE_HIGH_WORD + ( ( i0 >>> TBLBITS ) << 20 ) ) >>> 0; // asm type annotation
i0 &= TBLSIZE - 1;
t = f32( t - REDUX );
z = x - t;
twopk = fromWords( hi, 0 );
// Compute r = exp2(y) = TBL[ i0 ] * p(z)...
tv = TBL[ i0 ];
u = tv * z;
tv = tv + ( u * ( P1 + ( z * P2 ) ) ) + ( u * ( z * z ) * ( P3 + ( z * P4 ) ) ); // eslint-disable-line max-len
// Scale by 2^k:
return f32( tv * twopk );
}
// EXPORTS //
module.exports = exp2f;
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