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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 and license were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/12.2.0/lib/msun/src/e_powf.c}. The implementation follows the original, but has been modified for JavaScript.
*
* ```text
* Copyright (C) 2004 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 isnanf = require( '@stdlib/math/base/assert/is-nanf' );
var isOddf = require( '@stdlib/math/base/assert/is-oddf' );
var isInfinitef = require( '@stdlib/math/base/assert/is-infinitef' );
var isIntegerf = require( '@stdlib/math/base/assert/is-integerf' );
var sqrtf = require( '@stdlib/math/base/special/sqrtf' );
var absf = require( '@stdlib/math/base/special/absf' );
var fromWordf = require( '@stdlib/number/float32/base/from-word' );
var toWordf = require( '@stdlib/number/float32/base/to-word' );
var f32 = require( '@stdlib/number/float64/base/to-float32' );
var NINF = require( '@stdlib/constants/float32/ninf' );
var PINF = require( '@stdlib/constants/float32/pinf' );
var ABS_MASK = require( '@stdlib/constants/float32/abs-mask' );
var xIsZerof = require( './x_is_zerof.js' );
var yIsInfinitef = require( './y_is_infinitef.js' );
var log2axf = require( './log2axf.js' );
var logxf = require( './logxf.js' );
var pow2f = require( './pow2f.js' );
// VARIABLES //
var ZERO = f32( 0.0 );
var HALF = f32( 0.5 );
var ONE = f32( 1.0 );
var TWO = f32( 2.0 );
var THREE = f32( 3.0 );
var NEG_ZERO = f32( -0.0 );
var NEG_HALF = f32( -0.5 );
var NEG_ONE = f32( -1.0 );
var HUGE = f32( 1.0e30 );
var TINY = f32( 1.0e-30 );
// -(128-log2(ovfl+.5ulp))
var OVT = f32( 4.2995665694e-08 );
// 2^27 = 134217728.0 => 1 0011010 00000000000000000000000 => 0x4d000000 = 1291845632
var Y_LARGE_WORD = 0x4d000000|0; // asm type annotation
// 0.9999994039535522 => 0 01111110 11111111111111111110110 => 0x3f7ffff6 = 1065353206
var X_BELOW_ONE_WORD = 0x3f7ffff6|0; // asm type annotation
// 1.0000008344650269 => 0 01111111 00000000000000000000111 => 0x3f800007 = 1065353223
var X_ABOVE_ONE_WORD = 0x3f800007|0; // asm type annotation
// Mask to clear lower 12 significand bits:
var TRUNC_MASK_12 = 0xfffff000|0; // asm type annotation
// 128 => 0 10000110 00000000000000000000000 => 0x43000000 = 1124073472
var Z_OVF_WORD = 0x43000000|0; // asm type annotation
// 150 => 0 10000110 00101100000000000000000 => 0x43160000 = 1125515264
var Z_UNF_WORD = 0x43160000|0; // asm type annotation
// -150 => 1 10000110 00101100000000000000000 => 0xc3160000 = 3272998912
var Z_NEG_UNF_WORD = 0xc3160000|0; // asm type annotation
// Log workspace:
var LOG_WORKSPACE = [ 0.0, 0.0 ];
// MAIN //
/**
* Evaluates the exponential function for a single-precision floating-point number.
*
* @param {number} x - base
* @param {number} y - exponent
* @returns {number} function value
*
* @example
* var v = powf( 2.0, 3.0 );
* // returns 8.0
*
* @example
* var v = powf( 4.0, 0.5 );
* // returns 2.0
*
* @example
* var v = powf( 100.0, 0.0 );
* // returns 1.0
*
* @example
* var v = powf( 3.1415927410125732, 5.0 );
* // returns ~306.0197
*
* @example
* var v = powf( 3.1415927410125732, -0.2 );
* // returns ~0.7954
*
* @example
* var v = powf( NaN, 3.0 );
* // returns NaN
*
* @example
* var v = powf( 5.0, NaN );
* // returns NaN
*
* @example
* var v = powf( NaN, NaN );
* // returns NaN
*/
function powf( x, y ) {
var tmp;
var ahx; // absolute value word `x`
var ahy; // absolute value word `y`
var ax; // absolute value `x`
var hx; // word representation of `x`
var hy; // word representation of `y`
var sn; // sign of the result
var y1;
var hp;
var lp;
var t;
var z; // y prime
var j;
x = f32( x );
y = f32( y );
if ( y === ZERO ) {
return ONE;
}
if ( x === ONE ) {
return ONE;
}
if ( isnanf( x ) || isnanf( y ) ) {
return NaN;
}
// Other special cases `y`...
if ( y === ONE ) {
return x;
}
if ( y === NEG_ONE ) {
return f32( ONE / x );
}
if ( y === HALF ) {
return sqrtf( x );
}
if ( y === NEG_HALF ) {
return f32( ONE / sqrtf( x ) );
}
if ( y === TWO ) {
return f32( x * x );
}
if ( y === THREE ) {
return f32( f32( x * x ) * x );
}
if ( isInfinitef( y ) ) { // y is +-inf
return yIsInfinitef( x, y );
}
// Other special cases `x`...
if ( x === ZERO ) {
return xIsZerof( x, y );
}
if ( x === NEG_ONE ) {
if ( isIntegerf( y ) ) {
return ( isOddf( y ) ) ? NEG_ONE : ONE;
}
}
if ( isInfinitef( x ) ) {
if ( x === NINF ) {
// `pow( 1/x, -y )`
return powf( NEG_ZERO, f32( -y ) );
}
if ( y < ZERO ) {
return ZERO;
}
return PINF;
}
if (
x < ZERO &&
isIntegerf( y ) === false
) {
// Signal NaN...
return NaN; // (-1)**non-int is NaN
}
ax = absf( x );
hx = toWordf( x ) | 0; // asm type annotation
hy = toWordf( y ) | 0; // asm type annotation
// Remove the sign bits (i.e., get absolute values):
ahx = (hx & ABS_MASK) | 0; // asm type annotation
ahy = (hy & ABS_MASK) | 0; // asm type annotation
// Determine the sign of the result...
if ( x < ZERO && isOddf( y ) ) {
sn = NEG_ONE;
} else {
sn = ONE;
}
// Case 1: `|y|` is huge
// If |y| > 2^27
if ( ahy > Y_LARGE_WORD ) {
// Over- or underflow if `x` is not close to unity...
if ( ahx < X_BELOW_ONE_WORD ) {
// y < 0
if ( y < ZERO ) {
// Signal overflow...
return f32( f32( sn * HUGE ) * HUGE );
}
// Signal underflow...
return f32( f32( sn * TINY ) * TINY );
}
if ( ahx > X_ABOVE_ONE_WORD ) {
// y > 0
if ( y > ZERO ) {
// Signal overflow...
return f32( f32( sn * HUGE ) * HUGE );
}
// Signal underflow...
return f32( f32( sn * TINY ) * TINY );
}
// At this point, `|1-x|` is tiny (`<= 2^-20`). Suffice to compute `log(x)` by `x - x^2/2 + x^3/3 - x^4/4`.
t = logxf( LOG_WORKSPACE, ax );
}
// Case 2: `|y|` is not huge...
else {
t = log2axf( LOG_WORKSPACE, ax, ahx );
}
// Split `y` into `y1 + y2` and compute `(y1+y2) * (t1+t2)`...
tmp = toWordf( y ) | 0; // asm type annotation
y1 = fromWordf( tmp & TRUNC_MASK_12 );
lp = f32( f32( f32( y-y1 ) * t[0] ) + f32( y * t[1] ) );
hp = f32( y1 * t[0] );
z = f32( lp + hp );
j = toWordf( z ) | 0; // asm type annotation
// z > 128
if ( j > Z_OVF_WORD ) {
// Signal overflow...
return f32( f32( sn * HUGE ) * HUGE );
}
// z == 128
if ( j === Z_OVF_WORD ) {
if ( f32( lp+OVT ) > f32( z-hp ) ) {
// Signal overflow...
return f32( f32( sn * HUGE ) * HUGE );
}
}
// z < -150
if ( (j&ABS_MASK) > Z_UNF_WORD ) {
// Signal underflow...
return f32( f32( sn * TINY ) * TINY );
}
// z == -150
if ( j === Z_NEG_UNF_WORD ) {
if ( lp <= f32( z-hp ) ) {
// Signal underflow...
return f32( f32( sn * TINY ) * TINY );
}
}
// Compute `2^(hp+lp)`...
z = pow2f( j, hp, lp );
return f32( sn * z );
}
// EXPORTS //
module.exports = powf;
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