8 Bit LERP with SSE - x86-64

Question

I have been trying to figure out the best way to use AMD64 SIMD instructions to implement a lerp to be used with large sets of u8 values but I can't seem to figure out the correct instructions without requiring all the SIMD extensions.
The formula I am working with right now is
u8* a;
u8* b;
u8* result;
size_t count;
u16 total;
u16 progress;
u32 invertedProgress = total - progress;
for(size_t i = 0; i < count; i++){
result[i] = (u8)((b[i] * progress + a[i] * invertedProgress) / total);
}
I am thinking it would look something like:
u8* a;
u8* b;
u8* result;
size_t count;
u16 total;
u16 progress;
__m128i mmxZero;
__m128i mmxProgress;
__m128i mmxInvertedProgress;
__m128i mmxProductA;
__m128i mmxProductB;
mmxZero = _mm_xor_ps(zero, zero); // Is there a clear?
mmxProgress = Fill with progress;
mmxTotal = Fill with total;
mmxInvertedProgress = mmxTotal;
mmxInvertedProgress = _mm_unpacklo_epi8(mmxInvertedProgres, mmxZero);
mmxInvertedProgress = _mm_sub_epi8(mmxTotal, progress);
for(size_t i = 0; i < count; i += 8){
mmxProductA = load A;
// u8 -> u16
mmxProductA = _mm_unpacklo_epi8(mmxProductA, mmxZero);
mmxProductB = load B;
// u8 -> u16
mmxProductB = _mm_unpacklo_epi8(mmxProductB, mmxZero);
// a * (total - progress)
mmxProductA = _mm_mullo_epi16(mmxProductA, mmxInvertedProgress);
// b * progress
mmxProductB = _mm_mullo_epi16(mmxProductB, mmxProgress);
// a * (total - progress) + b * progress
mmxProductA = _mm_add_epi16(mmxProductA, mmxProductB);
// (a * (total - progress) + b * progress) / total
mmxProductA = _mm_div_epi16(mmxProductA, mmxTotal);
mmxProductA = saturated u16 -> u8;
store result = maxProductA;
}
There are a couple of things here that I just could not seem to find digging around in the guide, mostly related to loading and storing values.
I know there are some newer instructions that can do larger amounts at the same time, this initial implementation is supposed to work on older chips.
For this example I am also ignoring alignment and the potential for a buffer overrun, I figured that was a little out of scope for the question.

Answer 1

Good question. As you found out, SSE has no integer divide instruction, and (unlike ARM NEON) it doesn’t have multiplication or FMA for bytes.
Here’s what I usually do instead. The code below splits vectors into even/odd bytes, uses 16-bit multiplication instructions to scale separately, then merges them back into bytes.
// Linear interpolation is based on the following formula: x*(1-s) + y*s which can equivalently be written as x + s(y-x).
class LerpBytes
{
// Multipliers are fixed point numbers in 16-bit lanes of these vectors, in 1.8 format
__m128i mulX, mulY;
public:
LerpBytes( uint16_t progress, uint16_t total )
{
// The source and result are bytes.
// Multipliers only need 1.8 fixed point format, anything above that is wasteful.
assert( total > 0 );
assert( progress >= 0 );
assert( progress <= total );
const uint32_t fp = (uint32_t)progress * 0x100 / total;
mulY = _mm_set1_epi16( (short)fp );
mulX = _mm_set1_epi16( (short)( 0x100 - fp ) );
}
__m128i lerp( __m128i x, __m128i y ) const
{
const __m128i lowMask = _mm_set1_epi16( 0xFF );
// Split both vectors into even/odd bytes in 16-bit lanes
__m128i lowX = _mm_and_si128( x, lowMask );
__m128i highX = _mm_srli_epi16( x, 8 );
__m128i lowY = _mm_and_si128( y, lowMask );
__m128i highY = _mm_srli_epi16( y, 8 );
// That multiply instruction has relatively high latency, 3-5 cycles.
// We're lucky to have 4 vectors to handle.
lowX = _mm_mullo_epi16( lowX, mulX );
lowY = _mm_mullo_epi16( lowY, mulY );
highX = _mm_mullo_epi16( highX, mulX );
highY = _mm_mullo_epi16( highY, mulY );
// Add the products
__m128i low = _mm_adds_epu16( lowX, lowY );
__m128i high = _mm_adds_epu16( highX, highY );
// Pack them back into bytes.
// The multiplier was 1.8 fixed point, trimming the lowest byte off both vectors.
low = _mm_srli_epi16( low, 8 );
high = _mm_andnot_si128( lowMask, high );
return _mm_or_si128( low, high );
}
};
static void print( const char* what, __m128i v )
{
printf( "%s:\t", what );
alignas( 16 ) std::array<uint8_t, 16> arr;
_mm_store_si128( ( __m128i * )arr.data(), v );
for( uint8_t b : arr )
printf( " %02X", (int)b );
printf( "\n" );
}
int main()
{
const __m128i x = _mm_setr_epi32( 0x33221100, 0x77665544, 0xBBAA9988, 0xFFEEDDCC );
const __m128i y = _mm_setr_epi32( 0xCCDDEEFF, 0x8899AABB, 0x44556677, 0x00112233 );
LerpBytes test( 0, 1 );
print( "zero", test.lerp( x, y ) );
test = LerpBytes( 1, 1 );
print( "one", test.lerp( x, y ) );
test = LerpBytes( 1, 2 );
print( "half", test.lerp( x, y ) );
test = LerpBytes( 1, 3 );
print( "1/3", test.lerp( x, y ) );
test = LerpBytes( 1, 4 );
print( "1/4", test.lerp( x, y ) );
return 0;
}