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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 isnan = require( '@stdlib/math/base/assert/is-nan' );
var SIGN_MASK = require( '@stdlib/constants/float64/high-word-sign-mask' );
var toWords = require( '@stdlib/number/float64/base/to-words' ).assign;
var Uint32Array = require( '@stdlib/array/uint32' );
// VARIABLES //
var WX = new Uint32Array( 2 ); // WARNING: not thread safe
var WY = new Uint32Array( 2 );
var WZ = new Uint32Array( 2 );
// 2^32:
var TWO_32 = 4294967296;
// FUNCTIONS //
/**
* Converts the high and low words of a double-precision floating-point number to a lexicographically ordered integer.
*
* ## Notes
*
* - This function mutates the input array.
*
* @private
* @param {Array<integer>} words - high and low words
* @returns {Array<integer>} input array
*/
function monotoneKey( words ) {
if ( words[ 0 ]&SIGN_MASK ) { // x < 0
words = negate( words ); // maps -∞ to 0
} else { // x >= 0
words[ 0 ] |= SIGN_MASK; // push +0 to just above -0
}
return words;
}
/**
* Perform two's-complement negation.
*
* ## Notes
*
* - This function mutates the input array.
*
* @private
* @param {Array<integer>} words - high and low words
* @returns {Array<integer>} input array
*/
function negate( words ) {
words[ 0 ] = ~words[ 0 ];
words[ 1 ] = ~words[ 1 ];
words[ 1 ] += 1;
// Handle the carry into the high word...
if ( words[ 1 ] === 0 ) {
words[ 0 ] += 1;
}
return words;
}
/**
* Returns the ordering of two double-precision floating-point numbers according to their lexicographically ordered high and low words.
*
* @private
* @param {Array<integer>} wa - high and low words for first value
* @param {Array<integer>} wb - high and low words for second value
* @returns {integer} relative ordering
*/
function compare( wa, wb ) {
if ( wa[ 0 ] > wb[ 0 ] ) {
return 1;
}
if ( wa[ 0 ] < wb[ 0 ] ) {
return -1;
}
if ( wa[ 1 ] > wb[ 1 ] ) {
return 1;
}
if ( wa[ 1 ] < wb[ 1 ] ) {
return -1;
}
return 0;
}
/**
* Performs double-word subtraction.
*
* @private
* @param {Array<integer>} wa - high and low words for first value
* @param {Array<integer>} wb - high and low words for second value
* @param {Array<integer>} wc - output array
* @returns {Array<integer>} output array
*/
function subtract( wa, wb, wc ) {
var ha;
var hb;
var la;
var lb;
ha = wa[ 0 ];
la = wa[ 1 ];
hb = wb[ 0 ];
lb = wb[ 1 ];
if ( la >= lb ) {
wc[ 0 ] = ha - hb;
wc[ 1 ] = la - lb;
} else {
wc[ 0 ] = ( ha - hb - 1 ); // wrap
wc[ 1 ] = ( la + TWO_32 ) - lb; // borrow
}
return wc;
}
// MAIN //
/**
* Computes the number of representable double-precision floating-point values that separate two double-precision floating-point numbers along the real number line.
*
* ## Notes
*
* - Adjacent double-precision floating-point numbers differ by 1 ulp (unit in the last place).
* - Signed zeros differ only in the sign bit but are considered numerically equal, and thus their ULP difference is 0.
*
* @param {number} x - first value
* @param {number} y - second value
* @returns {number} result
*
* @example
* var EPS = require( '@stdlib/constants/float64/eps' );
*
* var d = ulpdiff( 1.0, 1.0+EPS );
* // returns 1.0
*
* d = ulpdiff( 1.0+EPS, 1.0 );
* // returns 1.0
*
* d = ulpdiff( 1.0, 1.0+EPS+EPS );
* // returns 2.0
*
* d = ulpdiff( 1.0, NaN );
* // returns NaN
*
* d = ulpdiff( NaN, 1.0 );
* // returns NaN
*
* d = ulpdiff( NaN, NaN );
* // returns NaN
*/
function ulpdiff( x, y ) {
var ord;
var wx;
var wy;
var wz;
if ( isnan( x ) || isnan( y ) ) {
return NaN;
}
// Convert input values to high and low words:
wx = toWords( x, WX, 1, 0 );
wy = toWords( y, WY, 1, 0 );
// Convert the values to lexicographically ordered integers:
wx = monotoneKey( wx );
wy = monotoneKey( wy );
// Determine the relative ordering of the two values so that we always subtract the smaller value from the larger value and ensure that the result is always >= 0:
ord = compare( wx, wy );
// Perform subtraction...
if ( ord === 0 ) {
// Identical encoding:
return 0;
}
if ( ord === 1 ) {
wz = subtract( wx, wy, WZ );
} else { // ord === -1
wz = subtract( wy, wx, WZ );
}
// Return a double as a result, which is fine for ≤2^53 ulps:
return ( wz[ 0 ]*TWO_32 ) + wz[ 1 ];
}
// EXPORTS //
module.exports = ulpdiff;
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