Normalize to speed up distance calculation

bruteforce.go

@@ -4,6 +4,7 @@
 package search
 
 import (
+	"math"
 	"sort"
 
 	"github.com/kelindar/search/internal/cosine/simd"
@@ -36,6 +37,8 @@ func NewIndex[T any]() *Index[T] {
 
 // Add adds a new vector to the search index.
 func (b *Index[T]) Add(vx Vector, item T) {
+	normalize(vx)
+
 	b.arr = append(b.arr, entry[T]{
 		Vector: vx,
 		Value:  item,
@@ -48,10 +51,13 @@ func (b *Index[T]) Search(query Vector, k int) []Result[T] {
 		return nil
 	}
 
+	// Normalize and quantize the query vector
+	normalize(query)
+
 	var relevance float64
 	dst := make(minheap[T], 0, k)
 	for _, v := range b.arr {
-		simd.Cosine(&relevance, v.Vector, query)
+		simd.DotProduct(&relevance, query, v.Vector)
 		result := Result[T]{
 			entry:     v,
 			Relevance: relevance,
@@ -73,6 +79,21 @@ func (b *Index[T]) Search(query Vector, k int) []Result[T] {
 	return dst
 }
 
+// Normalize normalizes the vector, resulting in a unit vector. This allows us
+// to do a simple dot product to calculate the cosine similarity instead of
+// the full cosine distance.
+func normalize(v []float32) {
+	norm := float32(0)
+	for _, x := range v {
+		norm += x * x
+	}
+
+	norm = float32(math.Sqrt(float64(norm)))
+	for i := range v {
+		v[i] /= norm
+	}
+}
+
 // --------------------------------- Heap ---------------------------------
 
 // minheap is a min-heap of top values, ordered by relevance.

bruteforce_test.go

@@ -13,7 +13,7 @@ import (
 
 /*
 cpu: 13th Gen Intel(R) Core(TM) i7-13700K
-BenchmarkIndex/search-24         	    4029	    298055 ns/op	     272 B/op	       3 allocs/op
+BenchmarkIndex/search-24         	    5366	    217116 ns/op	     272 B/op	       3 allocs/op
 */
 func BenchmarkIndex(b *testing.B) {
 	data, err := loadDataset()

internal/cosine/cosine_apple.c

@@ -26,4 +26,15 @@ void f32_cosine_distance(const float *x, const float *y, double *result, const u
 
     double cosine_similarity = (double)sum_xy / (double)denominator;
     *result = cosine_similarity;
-}
+}
+
+void f32_dot_product(const float *x, const float *y, double *result, const uint64_t size) {
+    float sum = 0.0f;
+
+    #pragma clang loop vectorize(enable) interleave(enable)
+    for (uint64_t i = 0; i < size; i++) {
+        sum += x[i] * y[i];
+    }
+
+    *result = (double)sum;
+}

internal/cosine/cosine_avx.c

@@ -13,8 +13,8 @@ void f32_cosine_distance(const float *x, const float *y, double *result, const u
     #pragma clang loop vectorize(enable) interleave_count(2)
     for (uint64_t i = 0; i < size; i++) {
         sum_xy += x[i] * y[i];    // Sum of x * y
-        sum_xx += x[i] * x[i];     // Sum of x * x
-        sum_yy += y[i] * y[i];     // Sum of y * y
+        sum_xx += x[i] * x[i];    // Sum of x * x
+        sum_yy += y[i] * y[i];    // Sum of y * y
     }
 
     // Calculate the final result
@@ -26,4 +26,15 @@ void f32_cosine_distance(const float *x, const float *y, double *result, const u
 
     double cosine_similarity = (double)sum_xy / (double)denominator;
     *result = cosine_similarity;
-}
+}
+
+void f32_dot_product(const float *x, const float *y, double *result, const uint64_t size) {
+    float sum = 0.0f;
+
+    #pragma clang loop vectorize(enable) interleave(enable)
+    for (uint64_t i = 0; i < size; i++) {
+        sum += x[i] * y[i];
+    }
+
+    *result = (double)sum;
+}

internal/cosine/cosine_neon.c

@@ -26,4 +26,15 @@ void f32_cosine_distance(const float *x, const float *y, double *result, const u
 
     double cosine_similarity = (double)sum_xy / (double)denominator;
     *result = cosine_similarity;
-}
+}
+
+void f32_dot_product(const float *x, const float *y, double *result, const uint64_t size) {
+    float sum = 0.0f;
+
+    #pragma clang loop vectorize(enable) interleave(enable)
+    for (uint64_t i = 0; i < size; i++) {
+        sum += x[i] * y[i];
+    }
+
+    *result = (double)sum;
+}

internal/cosine/simd/cosine_apple.go

@@ -7,3 +7,6 @@ import "unsafe"
 
 //go:noescape,nosplit
 func f32_cosine_distance(x unsafe.Pointer, y unsafe.Pointer, result unsafe.Pointer, size uint64)
+
+//go:noescape,nosplit
+func f32_dot_product(x unsafe.Pointer, y unsafe.Pointer, result unsafe.Pointer, size uint64)

internal/cosine/simd/cosine_apple.s

@@ -114,3 +114,65 @@ BB0_11:
 	WORD $0xfd000040 // str	d0, [x2]
 	WORD $0xa8c17bfd // ldp	x29, x30, [sp], #16             ; 16-byte Folded Reload
 	WORD $0xd65f03c0 // ret
+
+TEXT ·f32_dot_product(SB), $0-32
+	MOVD x+0(FP), R0
+	MOVD y+8(FP), R1
+	MOVD result+16(FP), R2
+	MOVD size+24(FP), R3
+	WORD $0xa9bf7bfd       // stp	x29, x30, [sp, #-16]!           ; 16-byte Folded Spill
+	WORD $0x910003fd       // mov	x29, sp
+	WORD $0xb40000c3       // cbz	x3, LBB1_3
+	WORD $0xf100207f       // cmp	x3, #8
+	WORD $0x54000102       // b.hs	LBB1_4
+	WORD $0xd2800008       // mov	x8, #0
+	WORD $0x2f00e400       // movi	d0, #0000000000000000
+	WORD $0x14000018       // b	LBB1_7
+
+BB1_3:
+	WORD $0x2f00e400 // movi	d0, #0000000000000000
+	WORD $0xfd000040 // str	d0, [x2]
+	WORD $0xa8c17bfd // ldp	x29, x30, [sp], #16             ; 16-byte Folded Reload
+	WORD $0xd65f03c0 // ret
+
+BB1_4:
+	WORD $0x927df068 // and	x8, x3, #0xfffffffffffffff8
+	WORD $0x91004009 // add	x9, x0, #16
+	WORD $0x9100402a // add	x10, x1, #16
+	WORD $0x6f00e400 // movi.2d	v0, #0000000000000000
+	WORD $0xaa0803eb // mov	x11, x8
+	WORD $0x6f00e401 // movi.2d	v1, #0000000000000000
+
+BB1_5:
+	WORD $0xad7f8d22 // ldp	q2, q3, [x9, #-16]
+	WORD $0xad7f9544 // ldp	q4, q5, [x10, #-16]
+	WORD $0x4e22cc80 // fmla.4s	v0, v4, v2
+	WORD $0x4e23cca1 // fmla.4s	v1, v5, v3
+	WORD $0x91008129 // add	x9, x9, #32
+	WORD $0x9100814a // add	x10, x10, #32
+	WORD $0xf100216b // subs	x11, x11, #8
+	WORD $0x54ffff21 // b.ne	LBB1_5
+	WORD $0x4e20d420 // fadd.4s	v0, v1, v0
+	WORD $0x6e20d400 // faddp.4s	v0, v0, v0
+	WORD $0x7e30d800 // faddp.2s	s0, v0
+	WORD $0xeb03011f // cmp	x8, x3
+	WORD $0x54000140 // b.eq	LBB1_9
+
+BB1_7:
+	WORD $0xcb080069 // sub	x9, x3, x8
+	WORD $0xd37ef50a // lsl	x10, x8, #2
+	WORD $0x8b0a0028 // add	x8, x1, x10
+	WORD $0x8b0a000a // add	x10, x0, x10
+
+BB1_8:
+	WORD $0xbc404541 // ldr	s1, [x10], #4
+	WORD $0xbc404502 // ldr	s2, [x8], #4
+	WORD $0x1f010040 // fmadd	s0, s2, s1, s0
+	WORD $0xf1000529 // subs	x9, x9, #1
+	WORD $0x54ffff81 // b.ne	LBB1_8
+
+BB1_9:
+	WORD $0x1e22c000 // fcvt	d0, s0
+	WORD $0xfd000040 // str	d0, [x2]
+	WORD $0xa8c17bfd // ldp	x29, x30, [sp], #16             ; 16-byte Folded Reload
+	WORD $0xd65f03c0 // ret

internal/cosine/simd/cosine_avx.go

@@ -7,3 +7,6 @@ import "unsafe"
 
 //go:noescape,nosplit
 func f32_cosine_distance(x unsafe.Pointer, y unsafe.Pointer, result unsafe.Pointer, size uint64)
+
+//go:noescape,nosplit
+func f32_dot_product(x unsafe.Pointer, y unsafe.Pointer, result unsafe.Pointer, size uint64)

internal/cosine/simd/cosine_avx.s

@@ -104,3 +104,74 @@ LBB0_9:
 	BYTE $0x5d               // pop	rbp
 	WORD $0xf8c5; BYTE $0x77 // vzeroupper
 	BYTE $0xc3               // ret
+
+TEXT ·f32_dot_product(SB), $0-32
+	MOVQ x+0(FP), DI
+	MOVQ y+8(FP), SI
+	MOVQ result+16(FP), DX
+	MOVQ size+24(FP), CX
+	BYTE $0x55               // push	rbp
+	WORD $0x8948; BYTE $0xe5 // mov	rbp, rsp
+	LONG $0xf8e48348         // and	rsp, -8
+	WORD $0x8548; BYTE $0xc9 // test	rcx, rcx
+	JE   LBB1_1
+	LONG $0x20f98348         // cmp	rcx, 32
+	JAE  LBB1_5
+	LONG $0xc057f8c5         // vxorps	xmm0, xmm0, xmm0
+	WORD $0x3145; BYTE $0xc0 // xor	r8d, r8d
+	JMP  LBB1_4
+
+LBB1_1:
+	LONG $0xc057f8c5         // vxorps	xmm0, xmm0, xmm0
+	LONG $0x0211fbc5         // vmovsd	qword ptr [rdx], xmm0
+	WORD $0x8948; BYTE $0xec // mov	rsp, rbp
+	BYTE $0x5d               // pop	rbp
+	BYTE $0xc3               // ret
+
+LBB1_5:
+	WORD $0x8949; BYTE $0xc8 // mov	r8, rcx
+	LONG $0xe0e08349         // and	r8, -32
+	LONG $0xc057f8c5         // vxorps	xmm0, xmm0, xmm0
+	WORD $0xc031             // xor	eax, eax
+	LONG $0xc957f0c5         // vxorps	xmm1, xmm1, xmm1
+	LONG $0xd257e8c5         // vxorps	xmm2, xmm2, xmm2
+	LONG $0xdb57e0c5         // vxorps	xmm3, xmm3, xmm3
+
+LBB1_6:
+	LONG $0x2410fcc5; BYTE $0x86               // vmovups	ymm4, ymmword ptr [rsi + 4*rax]
+	LONG $0x6c10fcc5; WORD $0x2086             // vmovups	ymm5, ymmword ptr [rsi + 4*rax + 32]
+	LONG $0x7410fcc5; WORD $0x4086             // vmovups	ymm6, ymmword ptr [rsi + 4*rax + 64]
+	LONG $0x7c10fcc5; WORD $0x6086             // vmovups	ymm7, ymmword ptr [rsi + 4*rax + 96]
+	LONG $0xb85de2c4; WORD $0x8704             // vfmadd231ps	ymm0, ymm4, ymmword ptr [rdi + 4*rax]
+	LONG $0xb855e2c4; WORD $0x874c; BYTE $0x20 // vfmadd231ps	ymm1, ymm5, ymmword ptr [rdi + 4*rax + 32]
+	LONG $0xb84de2c4; WORD $0x8754; BYTE $0x40 // vfmadd231ps	ymm2, ymm6, ymmword ptr [rdi + 4*rax + 64]
+	LONG $0xb845e2c4; WORD $0x875c; BYTE $0x60 // vfmadd231ps	ymm3, ymm7, ymmword ptr [rdi + 4*rax + 96]
+	LONG $0x20c08348                           // add	rax, 32
+	WORD $0x3949; BYTE $0xc0                   // cmp	r8, rax
+	JNE  LBB1_6
+	LONG $0xc058f4c5                           // vaddps	ymm0, ymm1, ymm0
+	LONG $0xc058ecc5                           // vaddps	ymm0, ymm2, ymm0
+	LONG $0xc058e4c5                           // vaddps	ymm0, ymm3, ymm0
+	LONG $0x197de3c4; WORD $0x01c1             // vextractf128	xmm1, ymm0, 1
+	LONG $0xc158f8c5                           // vaddps	xmm0, xmm0, xmm1
+	LONG $0x0579e3c4; WORD $0x01c8             // vpermilpd	xmm1, xmm0, 1
+	LONG $0xc158f8c5                           // vaddps	xmm0, xmm0, xmm1
+	LONG $0xc816fac5                           // vmovshdup	xmm1, xmm0
+	LONG $0xc158fac5                           // vaddss	xmm0, xmm0, xmm1
+	WORD $0x3949; BYTE $0xc8                   // cmp	r8, rcx
+	JE   LBB1_8
+
+LBB1_4:
+	LONG $0x107aa1c4; WORD $0x860c // vmovss	xmm1, dword ptr [rsi + 4*r8]
+	LONG $0xb971a2c4; WORD $0x8704 // vfmadd231ss	xmm0, xmm1, dword ptr [rdi + 4*r8]
+	WORD $0xff49; BYTE $0xc0       // inc	r8
+	WORD $0x394c; BYTE $0xc1       // cmp	rcx, r8
+	JNE  LBB1_4
+
+LBB1_8:
+	LONG $0xc05afac5         // vcvtss2sd	xmm0, xmm0, xmm0
+	LONG $0x0211fbc5         // vmovsd	qword ptr [rdx], xmm0
+	WORD $0x8948; BYTE $0xec // mov	rsp, rbp
+	BYTE $0x5d               // pop	rbp
+	WORD $0xf8c5; BYTE $0x77 // vzeroupper
+	BYTE $0xc3               // ret

internal/cosine/simd/cosine_neon.go

@@ -7,3 +7,6 @@ import "unsafe"
 
 //go:noescape,nosplit
 func f32_cosine_distance(x unsafe.Pointer, y unsafe.Pointer, result unsafe.Pointer, size uint64)
+
+//go:noescape,nosplit
+func f32_dot_product(x unsafe.Pointer, y unsafe.Pointer, result unsafe.Pointer, size uint64)

internal/cosine/simd/cosine_neon.s

@@ -114,3 +114,65 @@ LBB0_11:
 	WORD $0xfd000040 // str	d0, [x2]
 	WORD $0xa8c17bfd // ldp	x29, x30, [sp], #16
 	WORD $0xd65f03c0 // ret
+
+TEXT ·f32_dot_product(SB), $0-32
+	MOVD x+0(FP), R0
+	MOVD y+8(FP), R1
+	MOVD result+16(FP), R2
+	MOVD size+24(FP), R3
+	WORD $0xa9bf7bfd       // stp	x29, x30, [sp, #-16]!
+	WORD $0x910003fd       // mov	x29, sp
+	WORD $0xb40000c3       // cbz	x3, .LBB1_3
+	WORD $0xf100207f       // cmp	x3, #8
+	WORD $0x54000102       // b.hs	.LBB1_4
+	WORD $0x2f00e400       // movi	d0, #0000000000000000
+	WORD $0xaa1f03e8       // mov	x8, xzr
+	WORD $0x14000018       // b	.LBB1_7
+
+LBB1_3:
+	WORD $0x2f00e400 // movi	d0, #0000000000000000
+	WORD $0xfd000040 // str	d0, [x2]
+	WORD $0xa8c17bfd // ldp	x29, x30, [sp], #16
+	WORD $0xd65f03c0 // ret
+
+LBB1_4:
+	WORD $0x927df068 // and	x8, x3, #0xfffffffffffffff8
+	WORD $0x91004009 // add	x9, x0, #16
+	WORD $0x6f00e400 // movi	v0.2d, #0000000000000000
+	WORD $0x9100402a // add	x10, x1, #16
+	WORD $0x6f00e401 // movi	v1.2d, #0000000000000000
+	WORD $0xaa0803eb // mov	x11, x8
+
+LBB1_5:
+	WORD $0xad7f8d22 // ldp	q2, q3, [x9, #-16]
+	WORD $0x91008129 // add	x9, x9, #32
+	WORD $0xf100216b // subs	x11, x11, #8
+	WORD $0xad7f9544 // ldp	q4, q5, [x10, #-16]
+	WORD $0x9100814a // add	x10, x10, #32
+	WORD $0x4e22cc80 // fmla	v0.4s, v4.4s, v2.4s
+	WORD $0x4e23cca1 // fmla	v1.4s, v5.4s, v3.4s
+	WORD $0x54ffff21 // b.ne	.LBB1_5
+	WORD $0x4e20d420 // fadd	v0.4s, v1.4s, v0.4s
+	WORD $0xeb03011f // cmp	x8, x3
+	WORD $0x6e20d400 // faddp	v0.4s, v0.4s, v0.4s
+	WORD $0x7e30d800 // faddp	s0, v0.2s
+	WORD $0x54000140 // b.eq	.LBB1_9
+
+LBB1_7:
+	WORD $0xd37ef50a // lsl	x10, x8, #2
+	WORD $0xcb080069 // sub	x9, x3, x8
+	WORD $0x8b0a0028 // add	x8, x1, x10
+	WORD $0x8b0a000a // add	x10, x0, x10
+
+LBB1_8:
+	WORD $0xbc404541 // ldr	s1, [x10], #4
+	WORD $0xbc404502 // ldr	s2, [x8], #4
+	WORD $0xf1000529 // subs	x9, x9, #1
+	WORD $0x1f010040 // fmadd	s0, s2, s1, s0
+	WORD $0x54ffff81 // b.ne	.LBB1_8
+
+LBB1_9:
+	WORD $0x1e22c000 // fcvt	d0, s0
+	WORD $0xfd000040 // str	d0, [x2]
+	WORD $0xa8c17bfd // ldp	x29, x30, [sp], #16
+	WORD $0xd65f03c0 // ret

internal/cosine/simd/cosine_stub.go

@@ -4,7 +4,10 @@ package simd
 
 import "unsafe"
 
-// stub
 func f32_cosine_distance(x unsafe.Pointer, y unsafe.Pointer, result unsafe.Pointer, size uint64) {
 	panic("not implemented")
 }
+
+func f32_dot_product(x unsafe.Pointer, y unsafe.Pointer, result unsafe.Pointer, size uint64) {
+	panic("not implemented")
+}