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refactor: optimize number/uint32/base/muldw implementation for better performance #11702

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Merged
kgryte merged 5 commits into from
Apr 22, 2026
Merged

refactor: optimize number/uint32/base/muldw implementation for better performance #11702

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2b1e266
bench: update random number generation in `number/uint32/base/muldw`
impawstarlight Apr 21, 2026
e8bffef
refactor: move `isnan` check from assign.js into main.js and utilize …
impawstarlight Apr 21, 2026
311d2e2
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kgryte Apr 21, 2026
acec498
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kgryte Apr 22, 2026
16574b5
test: remove isnan checks from test.main.js
impawstarlight Apr 22, 2026
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22 changes: 16 additions & 6 deletions lib/node_modules/@stdlib/number/uint32/base/muldw/benchmark/benchmark.js
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Original file line number Diff line number Diff line change
Expand Up @@ -21,7 +21,7 @@
// MODULES //

var bench = require( '@stdlib/bench' );
var minstd = require( '@stdlib/random/base/minstd' );
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var format = require( '@stdlib/string/format' );
var pkg = require( './../package.json' ).name;
Expand All @@ -33,12 +33,17 @@ var umuldw = require( './../lib' );
bench( pkg, function benchmark( b ) {
var x;
var y;
var z;
var i;

x = discreteUniform( 100, 0x10000, 0x10000000, {
'dtype': 'uint32'
});

b.tic();
for ( i = 0; i < b.iterations; i++ ) {
x = minstd();
y = umuldw( x, x );
z = x[ i%x.length ];
y = umuldw( z, z );
if ( isnan( y[0] ) ) {
b.fail( 'should not return NaN' );
}
Expand All @@ -55,14 +60,19 @@ bench( format( '%s:assign', pkg ), function benchmark( b ) {
var out;
var x;
var y;
var z;
var i;

out = [ 0.0, 0.0];
x = discreteUniform( 100, 0x10000, 0x10000000, {
'dtype': 'uint32'
});

out = [ 0.0, 0.0 ];

b.tic();
for ( i = 0; i < b.iterations; i++ ) {
x = minstd();
y = umuldw.assign( x, x, out, 1, 0 );
z = x[ i%x.length ];
y = umuldw.assign( z, z, out, 1, 0 );
if ( isnan( y[0] ) ) {
b.fail( 'should not return NaN' );
}
Expand Down
11 changes: 2 additions & 9 deletions lib/node_modules/@stdlib/number/uint32/base/muldw/lib/assign.js
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Expand Up @@ -20,7 +20,7 @@

// MODULES //

var isnan = require( '@stdlib/math/base/assert/is-nan' );
var umul = require( '@stdlib/number/uint32/base/mul' );


// VARIABLES //
Expand Down Expand Up @@ -49,19 +49,13 @@ var LOW_WORD_MASK = 0x0000ffff>>>0; // asm type annotation
function umuldw(a, b, out, stride, offset ) {
var w1;
var w2;
var w3;
var ha;
var hb;
var la;
var lb;
var t;
var k;

if ( isnan( a ) || isnan( b ) ) {
out[ offset ] = NaN;
out[ offset + stride ] = NaN;
return out;
}
a >>>= 0; // asm type annotation
b >>>= 0; // asm type annotation

Expand All @@ -72,7 +66,6 @@ function umuldw(a, b, out, stride, offset ) {
lb = ( b & LOW_WORD_MASK ) >>> 0;

t = ( la*lb ) >>> 0;
w3 = ( t & LOW_WORD_MASK ) >>> 0;
k = ( t >>> 16 ) >>> 0;

t = ( ( ha*lb ) + k ) >>> 0;
Expand All @@ -83,7 +76,7 @@ function umuldw(a, b, out, stride, offset ) {
k = ( t >>> 16 ) >>> 0;

out[ offset ] = ( ( ha*hb ) + w1 + k ) >>> 0; // compute the higher 32 bits and cast to an unsigned 32-bit integer
out[ offset + stride ] = ( ( t << 16 ) + w3) >>> 0; // compute the lower 32 bits and cast to an unsigned 32-bit integer
out[ offset + stride ] = umul( a, b ) >>> 0; // compute the lower 32 bits and cast to an unsigned 32-bit integer
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@kgryte kgryte Apr 21, 2026

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@impawstarlight I am a bit dense, but how does this manage to produce the same result? Previously, the logic for computing the lower 32 bits doesn't exceed the max uint32, but, here, a*b could, resulting in wraparound, which is a bit counterintuitive to me that it achieves the same result.

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@kgryte kgryte Apr 21, 2026

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Ultimately, this boils down to a call to imul, but not obvious to me why imul is faster than a bit shift plus addition.

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@impawstarlight impawstarlight Apr 22, 2026 •
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Previously, the logic for computing the lower 32 bits doesn't exceed the max uint32, but, here, a*b could, resulting in wraparound, which is a bit counterintuitive to me that it achieves the same result.

Actually, the way it avoids overflow is a clever engineering trick for extracting those bits that would normally overflow outside the lower 32 bits. This is done because these overflow bits contribute to the higher 32 bits and hence necessary for that calculation.

But for the lower 32 bits, we could very well make do with allowing overflow if we didn't have to calculate the higher 32 bits, like here in our imul polyfill.

Ultimately, it is fully equivalent to imul because of what its purpose is - calculate the low 32-bit of a 32x32 mult - which is basically the definition of imul.

So the wrap around behavour of imul is also happening in the shift-add approach, just not very obvious because they are handled through the 16-bit splitting logic while eliminating any intermediate overflow.

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@impawstarlight impawstarlight Apr 22, 2026 •
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Ultimately, this boils down to a call to imul, but not obvious to me why imul is faster than a bit shift plus addition.

imul is probably faster here because otherwise we were doing 3 operations before:

w3 = ( t & LOW_WORD_MASK ) >>> 0;
...
out[ offset + stride ] = ( ( t << 16 ) + w3) >>> 0;

So we're comparing AND + SHIFT + ADD vs IMUL. Although individual add and bitwise instructions are very fast, the combination is probably slower than a single IMUL instruction because of various other factors like intermediate moving around around between registers. Just my guess, but the benchmark approves.

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@kgryte kgryte Apr 22, 2026

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Okay, sounds good.


return out;
}
Expand Down
26 changes: 0 additions & 26 deletions lib/node_modules/@stdlib/number/uint32/base/muldw/test/test.assign.js
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Original file line number Diff line number Diff line change
Expand Up @@ -21,7 +21,6 @@
// MODULES //

var tape = require( 'tape' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var Float64Array = require( '@stdlib/array/float64' );
var umuldw = require( './../lib/assign.js' );

Expand All @@ -39,31 +38,6 @@ tape( 'main export is a function', function test( t ) {
t.end();
});

tape( 'the function returns `NaN` if provided `NaN`', function test( t ) {
var out;
var v;

out = [ 0, 0 ];
v = umuldw( NaN, 1, out, 1, 0 );
t.strictEqual( v, out, 'returns output array' );
t.strictEqual( isnan( v[0] ), true, 'returns expected value' );
t.strictEqual( isnan( v[1] ), true, 'returns expected value' );

out = [ 0, 0 ];
v = umuldw( 1, NaN, out, 1, 0 );
t.strictEqual( v, out, 'returns output array' );
t.strictEqual( isnan( v[0] ), true, 'returns expected value' );
t.strictEqual( isnan( v[1] ), true, 'returns expected value' );

out = [ 0, 0 ];
v = umuldw( NaN, NaN, out, 1, 0 );
t.strictEqual( v, out, 'returns output array' );
t.strictEqual( isnan( v[0] ), true, 'returns expected value' );
t.strictEqual( isnan( v[1] ), true, 'returns expected value' );

t.end();
});

tape( 'the function computes the double word product of two (unsigned) words', function test( t ) {
var expected;
var actual;
Expand Down
19 changes: 0 additions & 19 deletions lib/node_modules/@stdlib/number/uint32/base/muldw/test/test.main.js
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Original file line number Diff line number Diff line change
Expand Up @@ -21,7 +21,6 @@
// MODULES //

var tape = require( 'tape' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var umuldw = require( './../lib/main.js' );


Expand All @@ -38,24 +37,6 @@ tape( 'main export is a function', function test( t ) {
t.end();
});

tape( 'the function returns `NaN` if provided `NaN`', function test( t ) {
var v;

v = umuldw( NaN, 1 );
t.strictEqual( isnan( v[0] ), true, 'returns expected value' );
t.strictEqual( isnan( v[1] ), true, 'returns expected value' );

v = umuldw( 1, NaN );
t.strictEqual( isnan( v[0] ), true, 'returns expected value' );
t.strictEqual( isnan( v[1] ), true, 'returns expected value' );

v = umuldw( NaN, NaN );
t.strictEqual( isnan( v[0] ), true, 'returns expected value' );
t.strictEqual( isnan( v[1] ), true, 'returns expected value' );

t.end();
});

tape( 'the function computes the double word product of two (unsigned) words', function test( t ) {
var expected;
var actual;
Expand Down