## 25 August, 2018

### C++ Autovectorization - Part 1

This is a first part of my autovectorization experiments. As a part of my refactoring work I did some cleanup in a Blend2D's internal algebra module and I finally tried how compilers optimize some of its features. I would like to highlight that the performance of this code is very important as essentially all vectors passed to Blend2D's rendering context are processed before the rasterizer can do its work. The processing depends on what you want to do with them - if it's just for filling then the input is transformed, clipped, and passed to edge builder. If you intend to stroke a 2D path then the processing is much heavier and a lot of approximations come into the scene.

Today's post contains more code than usual, however, the code solves real problems so people can seriously consider which compiler would optimize their code the most. Spoiler alert - Clang is superior!

## Preparation

Instead of using one huge code section I decided to provide a utility code first and then functions that I would compare. Some code is directly from Blend2D and some was added just for simplicity to make the code compile:

``````#include <algorithm>
#include <cmath>
#include <stdint.h>

// Point structure [x, y]
struct BLPoint {
double x;
double y;

inline BLPoint() noexcept = default;
constexpr BLPoint(const BLPoint&) noexcept = default;

constexpr BLPoint(double x, double y) noexcept
: x(x), y(y) {}

inline void reset() noexcept { reset(0, 0); }
inline void reset(double x, double y) noexcept {
this->x = x;
this->y = y;
}
};

// Box structure [x0, y0, x1, y1]
struct BLBox {
double x0;
double y0;
double x1;
double y1;

inline BLBox() noexcept = default;
constexpr BLBox(const BLBox&) noexcept = default;

constexpr BLBox(double x0, double y0, double x1, double y1) noexcept
: x0(x0), y0(y0), x1(x1), y1(y1) {}

inline void reset() noexcept { reset(0.0, 0.0, 0.0, 0.0); }
inline void reset(double x0, double y0, double x1, double y1) noexcept {
this->x0 = x0;
this->y0 = y0;
this->x1 = x1;
this->y1 = y1;
}
};

// Overloads to make vector processing simpler.
static constexpr BLPoint operator-(const BLPoint& a) noexcept { return BLPoint(-a.x, -a.y); }

static constexpr BLPoint operator+(const BLPoint& a, double b) noexcept { return BLPoint(a.x + b, a.y + b); }
static constexpr BLPoint operator-(const BLPoint& a, double b) noexcept { return BLPoint(a.x - b, a.y - b); }
static constexpr BLPoint operator*(const BLPoint& a, double b) noexcept { return BLPoint(a.x * b, a.y * b); }
static constexpr BLPoint operator/(const BLPoint& a, double b) noexcept { return BLPoint(a.x / b, a.y / b); }

static constexpr BLPoint operator+(const BLPoint& a, const BLPoint& b) noexcept { return BLPoint(a.x + b.x, a.y + b.y); }
static constexpr BLPoint operator-(const BLPoint& a, const BLPoint& b) noexcept { return BLPoint(a.x - b.x, a.y - b.y); }
static constexpr BLPoint operator*(const BLPoint& a, const BLPoint& b) noexcept { return BLPoint(a.x * b.x, a.y * b.y); }
static constexpr BLPoint operator/(const BLPoint& a, const BLPoint& b) noexcept { return BLPoint(a.x / b.x, a.y / b.y); }

static constexpr BLPoint operator+(double a, const BLPoint& b) noexcept { return BLPoint(a + b.x, a + b.y); }
static constexpr BLPoint operator-(double a, const BLPoint& b) noexcept { return BLPoint(a - b.x, a - b.y); }
static constexpr BLPoint operator*(double a, const BLPoint& b) noexcept { return BLPoint(a * b.x, a * b.y); }
static constexpr BLPoint operator/(double a, const BLPoint& b) noexcept { return BLPoint(a / b.x, a / b.y); }

static inline BLPoint& operator+=(BLPoint& a, double b) noexcept { a.x += b; a.y += b; return a; }
static inline BLPoint& operator-=(BLPoint& a, double b) noexcept { a.x -= b; a.y -= b; return a; }
static inline BLPoint& operator*=(BLPoint& a, double b) noexcept { a.x *= b; a.y *= b; return a; }
static inline BLPoint& operator/=(BLPoint& a, double b) noexcept { a.x /= b; a.y /= b; return a; }

static inline BLPoint& operator+=(BLPoint& a, const BLPoint& b) noexcept { a.x += b.x; a.y += b.y; return a; }
static inline BLPoint& operator-=(BLPoint& a, const BLPoint& b) noexcept { a.x -= b.x; a.y -= b.y; return a; }
static inline BLPoint& operator*=(BLPoint& a, const BLPoint& b) noexcept { a.x *= b.x; a.y *= b.y; return a; }
static inline BLPoint& operator/=(BLPoint& a, const BLPoint& b) noexcept { a.x /= b.x; a.y /= b.y; return a; }

// Min/Max - different semantics compared to std.
template<typename T> constexpr T blMin(const T& a, const T& b) noexcept { return b < a ? b : a; }
template<typename T> constexpr T blMax(const T& a, const T& b) noexcept { return a < b ? b : a; }

// Linear interpolation, works with points as well.
template<typename V, typename T = double>
inline V blLerp(const V& a, const V& b, const T& t) noexcept {
return (a * (1.0 - t)) + (b * t);
}

// Merge a point into a box by possibly increasing its size.
inline void blBoxMergePoint(BLBox& box, const BLPoint& p) noexcept {
box.x0 = blMin(box.x0, p.x);
box.y0 = blMin(box.y0, p.y);
box.x1 = blMax(box.x1, p.x);
box.y1 = blMax(box.y1, p.y);
}

// Quadratic Bezier Coefficients and Derivative.
inline void blQuadExtractCoefficients(const BLPoint bez[3], BLPoint& a, BLPoint& b, BLPoint& c) noexcept {
a = bez[0] - bez[1] * 2.0 + bez[2];
b = (bez[1] - bez[0]) * 2.0;
c = bez[0];
}

inline void blQuadExtractDerivative(const BLPoint bez[3], BLPoint& a, BLPoint& b) noexcept {
a = (bez[2] - bez[1] * 2.0 + bez[0]) * 2.0;
b = (bez[1] - bez[0]) * 2.0;
}

// Cubic Bezier Coefficients and Derivative.
inline void blCubicExtractCoefficients(const BLPoint bez[4], BLPoint& a, BLPoint& b, BLPoint& c, BLPoint& d) noexcept {
d = bez[0];
a = (bez[1] - bez[2]) * 3.0 + bez[3] - d;
b = (bez[0] - bez[1]  * 2.0 + bez[2]) * 3.0;
c = (bez[1] - bez[0]) * 3.0;
}

inline void blCubicExtractDerivative(const BLPoint bez[4], BLPoint& a, BLPoint& b, BLPoint& c) noexcept {
a = ((bez[1] - bez[2]) * 3.0 + bez[3] - bez[0]) * 3.0;
b = (bez[2] - bez[1] * 2.0 + bez[0]) * 6.0;
c = (bez[1] - bez[0]) * 3.0;
}``````

I don't know whether to comment it - it's pretty simple code that provides Point, Box, and some utility functions we rely on.

## Quadratic Bezier Evaluation

These functions return a point of quadratic Bezier at the given `t`:

``````// Quadratic Bezier Evaluation.
BLPoint blQuadEvaluateAtT(const BLPoint bez[3], double t) noexcept {
BLPoint a, b, c;
blQuadExtractCoefficients(bez, a, b, c);
return (a * t + b) * t + c;
}

BLPoint blQuadPreciseEvaluateAtT(const BLPoint bez[3], double t) noexcept {
return blLerp(blLerp(bez[0], bez[1], t),
blLerp(bez[1], bez[2], t), t);
}``````

### GCC [-std=c++17 -O3 -fno-math-errno -mavx2]

``````blQuadEvaluateAtT(BLPoint const*, double):
vmovupd  xmm2, XMMWORD PTR [rdi+16]
vmovupd  xmm4, XMMWORD PTR [rdi]
vmovddup xmm3, xmm0
vaddpd   xmm1, xmm2, xmm2
vsubpd   xmm2, xmm2, xmm4
vsubpd   xmm1, xmm4, xmm1
vaddpd   xmm0, xmm1, XMMWORD PTR [rdi+32]
vaddpd   xmm2, xmm2, xmm2
vmulpd   xmm1, xmm0, xmm3
vaddpd   xmm0, xmm1, xmm2
vmulpd   xmm0, xmm0, xmm3
vaddpd   xmm5, xmm0, xmm4
vmovaps  XMMWORD PTR [rsp-24], xmm5
vmovsd   xmm1, QWORD PTR [rsp-16]
vmovsd   xmm0, QWORD PTR [rsp-24]
ret

vmovapd  xmm3, XMMWORD PTR .LC0[rip]
vmovddup xmm0, xmm0
vmovupd  xmm4, XMMWORD PTR [rdi+16]
vmulpd   xmm2, xmm0, XMMWORD PTR [rdi+32]
vsubpd   xmm3, xmm3, xmm0
vmulpd   xmm1, xmm3, xmm4
vaddpd   xmm2, xmm2, xmm1
vmulpd   xmm1, xmm3, XMMWORD PTR [rdi]
vmulpd   xmm2, xmm2, xmm0
vmulpd   xmm0, xmm4, xmm0
vaddpd   xmm0, xmm1, xmm0
vmulpd   xmm0, xmm0, xmm3
vaddpd   xmm5, xmm2, xmm0
vmovaps  XMMWORD PTR [rsp-24], xmm5
vmovsd   xmm1, QWORD PTR [rsp-16]
vmovsd   xmm0, QWORD PTR [rsp-24]
ret
``````

### Clang [-std=c++17 -O3 -fno-math-errno -mavx2]

``````blQuadEvaluateAtT(BLPoint const*, double):
vmovupd  xmm1, xmmword ptr [rdi]
vmovupd  xmm2, xmmword ptr [rdi + 16]
vaddpd   xmm3, xmm2, xmm2
vsubpd   xmm3, xmm1, xmm3
vaddpd   xmm3, xmm3, xmmword ptr [rdi + 32]
vsubpd   xmm2, xmm2, xmm1
vaddpd   xmm2, xmm2, xmm2
vmovddup xmm0, xmm0      # xmm0 = xmm0[0,0]
vmulpd   xmm3, xmm0, xmm3
vaddpd   xmm2, xmm2, xmm3
vmulpd   xmm0, xmm0, xmm2
vaddpd   xmm0, xmm1, xmm0
vpermilpd xmm1, xmm0, 1   # xmm1 = xmm0[1,0]
ret

.LCPI1_0:
.quad    4607182418800017408     # double 1

vmovsd   xmm1, qword ptr [rip + .LCPI1_0] # xmm1 = mem[0],zero
vsubsd   xmm1, xmm1, xmm0
vmovddup xmm1, xmm1      # xmm1 = xmm1[0,0]
vmulpd   xmm2, xmm1, xmmword ptr [rdi]
vmovupd  xmm3, xmmword ptr [rdi + 16]
vmovddup xmm0, xmm0      # xmm0 = xmm0[0,0]
vmulpd   xmm4, xmm0, xmm3
vaddpd   xmm2, xmm2, xmm4
vmulpd   xmm3, xmm1, xmm3
vmulpd   xmm4, xmm0, xmmword ptr [rdi + 32]
vaddpd   xmm3, xmm3, xmm4
vmulpd   xmm1, xmm1, xmm2
vmulpd   xmm0, xmm0, xmm3
vaddpd   xmm0, xmm1, xmm0
vpermilpd xmm1, xmm0, 1   # xmm1 = xmm0[1,0]
ret
``````

### MSVC [/O2 /Qpar /arch:AVX2]

``````; NOT VECTORIZED!
__\$ReturnUdt\$ = 80
bez\$ = 88
t\$ = 96
BLPoint blQuadEvaluateAtT(BLPoint const * __ptr64 const,double) PROC
\$LN42:
sub     rsp, 72                             ; 00000048H
vmovsd  xmm0, QWORD PTR [rdx+16]
vmovsd  xmm1, QWORD PTR [rdx+24]
vmovsd  xmm5, QWORD PTR [rdx]
vmovaps XMMWORD PTR [rsp+48], xmm6
mov     rax, rcx
vmovsd  xmm6, QWORD PTR [rdx+8]
vmovaps XMMWORD PTR [rsp+32], xmm7
vaddsd  xmm3, xmm0, xmm0
vsubsd  xmm0, xmm5, xmm3
vmovaps XMMWORD PTR [rsp+16], xmm8
vaddsd  xmm8, xmm0, QWORD PTR [rdx+32]
vmovsd  xmm0, QWORD PTR [rdx+16]
vsubsd  xmm3, xmm0, xmm5
vmovaps XMMWORD PTR [rsp], xmm9
vmovaps xmm9, xmm2
vaddsd  xmm4, xmm1, xmm1
vsubsd  xmm1, xmm6, xmm4
vaddsd  xmm7, xmm1, QWORD PTR [rdx+40]
vmulsd  xmm4, xmm3, QWORD PTR __real@4000000000000000
vmovsd  xmm1, QWORD PTR [rdx+24]
vsubsd  xmm2, xmm1, xmm6
vmulsd  xmm5, xmm2, QWORD PTR __real@4000000000000000
vmovups xmm6, XMMWORD PTR [rdx]
vmulsd  xmm2, xmm7, xmm9
vmovaps xmm7, XMMWORD PTR [rsp+32]
vmulsd  xmm1, xmm8, xmm9
vmovaps xmm8, XMMWORD PTR [rsp+16]
vaddsd  xmm0, xmm4, xmm1
vmulsd  xmm4, xmm0, xmm9
vaddsd  xmm0, xmm4, xmm6
vaddsd  xmm3, xmm2, xmm5
vmulsd  xmm5, xmm3, xmm9
vmovaps xmm9, XMMWORD PTR [rsp]
vunpckhpd xmm2, xmm6, xmm6
vmovaps xmm6, XMMWORD PTR [rsp+48]
vmovsd  QWORD PTR [rcx], xmm0
vaddsd  xmm0, xmm5, xmm2
vmovsd  QWORD PTR [rcx+8], xmm0
add     rsp, 72                             ; 00000048H
ret     0
BLPoint blQuadEvaluateAtT(BLPoint const * __ptr64 const,double) ENDP

; NOT VECTORIZED!
__\$ReturnUdt\$ = 64
bez\$ = 72
t\$ = 80
BLPoint blQuadPreciseEvaluateAtT(BLPoint const * __ptr64 const,double) PROC
\$LN46:
sub     rsp, 56                             ; 00000038H
vmulsd  xmm4, xmm2, QWORD PTR [rdx+32]
vmulsd  xmm3, xmm2, QWORD PTR [rdx+40]
vmovsd  xmm0, QWORD PTR __real@3ff0000000000000
vmovaps XMMWORD PTR [rsp+32], xmm6
mov     rax, rcx
vmovaps XMMWORD PTR [rsp+16], xmm7
vsubsd  xmm7, xmm0, xmm2
vmulsd  xmm1, xmm7, QWORD PTR [rdx+16]
vmulsd  xmm0, xmm7, QWORD PTR [rdx+24]
vaddsd  xmm6, xmm3, xmm0
vmulsd  xmm0, xmm7, QWORD PTR [rdx+8]
vaddsd  xmm5, xmm4, xmm1
vmulsd  xmm1, xmm7, QWORD PTR [rdx]
vmovaps XMMWORD PTR [rsp], xmm8
vmovaps xmm8, xmm2
vmulsd  xmm3, xmm8, QWORD PTR [rdx+24]
vmulsd  xmm2, xmm2, QWORD PTR [rdx+16]
vaddsd  xmm2, xmm2, xmm1
vaddsd  xmm3, xmm0, xmm3
vmulsd  xmm4, xmm5, xmm8
vmulsd  xmm5, xmm6, xmm8
vmovaps xmm6, XMMWORD PTR [rsp+32]
vmovaps xmm8, XMMWORD PTR [rsp]
vmulsd  xmm0, xmm2, xmm7
vmulsd  xmm1, xmm3, xmm7
vmovaps xmm7, XMMWORD PTR [rsp+16]
vaddsd  xmm0, xmm0, xmm4
vaddsd  xmm1, xmm1, xmm5
vmovsd  QWORD PTR [rcx], xmm0
vmovsd  QWORD PTR [rcx+8], xmm1
add     rsp, 56                             ; 00000038H
ret     0
BLPoint blQuadPreciseEvaluateAtT(BLPoint const * __ptr64 const,double) ENDP
``````

### Interpreting the Results

GCC and Clang okay, MSVC didn't use SIMD.

## Cubic Bezier Evaluation

These functions return a point of cubic Bezier at the given `t`:

``````// Cubic Bezier Evaluation.
BLPoint blCubicEvaluateAtT(const BLPoint bez[4], double t) noexcept {
BLPoint a, b, c, d;
blCubicExtractCoefficients(bez, a, b, c, d);
return ((a * t + b) * t + c) * t + c;
}

BLPoint blCubicPreciseEvaluateAtT(const BLPoint bez[4], double t) noexcept {
BLPoint p01(blLerp(bez[0], bez[1], t));
BLPoint p12(blLerp(bez[1], bez[2], t));
BLPoint p23(blLerp(bez[2], bez[3], t));
return blLerp(blLerp(p01, p12, t), blLerp(p12, p23, t), t);
}
``````

### GCC [-std=c++17 -O3 -fno-math-errno -mavx2]

``````blCubicEvaluateAtT(BLPoint const*, double):
vmovupd  xmm3, XMMWORD PTR [rdi+16]
vmovddup xmm4, xmm0
vmovupd  xmm1, XMMWORD PTR [rdi]
vmovupd  xmm6, XMMWORD PTR [rdi+32]
vmovapd  xmm5, XMMWORD PTR .LC1[rip]
vsubpd   xmm2, xmm3, xmm1
vsubpd   xmm0, xmm3, xmm6
vaddpd   xmm3, xmm3, xmm3
vmulpd   xmm2, xmm2, xmm5
vmulpd   xmm0, xmm0, xmm5
vaddpd   xmm0, xmm0, XMMWORD PTR [rdi+48]
vsubpd   xmm0, xmm0, xmm1
vsubpd   xmm1, xmm1, xmm3
vaddpd   xmm1, xmm1, xmm6
vmulpd   xmm0, xmm0, xmm4
vmulpd   xmm1, xmm1, xmm5
vaddpd   xmm0, xmm0, xmm1
vmulpd   xmm0, xmm0, xmm4
vaddpd   xmm0, xmm0, xmm2
vmulpd   xmm0, xmm0, xmm4
vaddpd   xmm7, xmm0, xmm2
vmovaps  XMMWORD PTR [rsp-24], xmm7
vmovsd   xmm1, QWORD PTR [rsp-16]
vmovsd   xmm0, QWORD PTR [rsp-24]
ret

blCubicPreciseEvaluateAtT(BLPoint const*, double):
vmovddup xmm2, xmm0
vmovapd  xmm0, XMMWORD PTR .LC0[rip]
vmovupd  xmm5, XMMWORD PTR [rdi+16]
vmulpd   xmm4, xmm2, XMMWORD PTR [rdi+32]
vsubpd   xmm3, xmm0, xmm2
vmulpd   xmm1, xmm2, XMMWORD PTR [rdi+48]
vmulpd   xmm0, xmm3, xmm5
vmulpd   xmm5, xmm5, xmm2
vaddpd   xmm4, xmm4, xmm0
vmulpd   xmm0, xmm3, XMMWORD PTR [rdi+32]
vaddpd   xmm1, xmm1, xmm0
vmulpd   xmm0, xmm3, xmm4
vmulpd   xmm1, xmm1, xmm2
vaddpd   xmm1, xmm1, xmm0
vmulpd   xmm0, xmm3, XMMWORD PTR [rdi]
vmulpd   xmm1, xmm1, xmm2
vmulpd   xmm2, xmm4, xmm2
vaddpd   xmm0, xmm0, xmm5
vmulpd   xmm0, xmm0, xmm3
vaddpd   xmm0, xmm0, xmm2
vmulpd   xmm0, xmm0, xmm3
vaddpd   xmm6, xmm1, xmm0
vmovaps  XMMWORD PTR [rsp-24], xmm6
vmovsd   xmm1, QWORD PTR [rsp-16]
vmovsd   xmm0, QWORD PTR [rsp-24]
ret
``````

### Clang [-std=c++17 -O3 -fno-math-errno -mavx2]

``````.LCPI2_0:
.quad    4613937818241073152     # double 3
.quad    4613937818241073152     # double 3

blCubicEvaluateAtT(BLPoint const*, double):
vmovupd  xmm1, xmmword ptr [rdi + 16]
vmovupd  xmm2, xmmword ptr [rdi + 32]
vsubpd   xmm3, xmm1, xmm2
vmovapd  xmm4, xmmword ptr [rip + .LCPI2_0] # xmm4 = [3.000000e+00,3.000000e+00]
vmulpd   xmm3, xmm3, xmm4
vaddpd   xmm3, xmm3, xmmword ptr [rdi + 48]
vmovupd  xmm5, xmmword ptr [rdi]
vsubpd   xmm3, xmm3, xmm5
vaddpd   xmm6, xmm1, xmm1
vsubpd   xmm6, xmm5, xmm6
vaddpd   xmm2, xmm6, xmm2
vmulpd   xmm2, xmm2, xmm4
vsubpd   xmm1, xmm1, xmm5
vmulpd   xmm1, xmm1, xmm4
vmovddup xmm0, xmm0      # xmm0 = xmm0[0,0]
vmulpd   xmm3, xmm0, xmm3
vaddpd   xmm2, xmm2, xmm3
vmulpd   xmm2, xmm0, xmm2
vaddpd   xmm2, xmm1, xmm2
vmulpd   xmm0, xmm0, xmm2
vaddpd   xmm0, xmm1, xmm0
vpermilpd xmm1, xmm0, 1   # xmm1 = xmm0[1,0]
ret

.LCPI3_0:
.quad    4607182418800017408     # double 1

blCubicPreciseEvaluateAtT(BLPoint const*, double):
vmovsd   xmm1, qword ptr [rip + .LCPI3_0] # xmm1 = mem[0],zero
vsubsd   xmm1, xmm1, xmm0
vmovddup xmm1, xmm1      # xmm1 = xmm1[0,0]
vmulpd   xmm2, xmm1, xmmword ptr [rdi]
vmovddup xmm0, xmm0      # xmm0 = xmm0[0,0]
vmovupd  xmm3, xmmword ptr [rdi + 16]
vmovupd  xmm4, xmmword ptr [rdi + 32]
vmulpd   xmm5, xmm0, xmm3
vaddpd   xmm2, xmm2, xmm5
vmulpd   xmm3, xmm1, xmm3
vmulpd   xmm5, xmm0, xmm4
vaddpd   xmm3, xmm3, xmm5
vmulpd   xmm5, xmm0, xmmword ptr [rdi + 48]
vmulpd   xmm4, xmm1, xmm4
vaddpd   xmm4, xmm4, xmm5
vmulpd   xmm2, xmm1, xmm2
vmulpd   xmm5, xmm0, xmm3
vaddpd   xmm2, xmm2, xmm5
vmulpd   xmm3, xmm1, xmm3
vmulpd   xmm4, xmm0, xmm4
vaddpd   xmm3, xmm3, xmm4
vmulpd   xmm1, xmm1, xmm2
vmulpd   xmm0, xmm0, xmm3
vaddpd   xmm0, xmm1, xmm0
vpermilpd xmm1, xmm0, 1   # xmm1 = xmm0[1,0]
ret
``````

### MSVC [/O2 /Qpar /arch:AVX2]

``````; NOT VECTORIZED!
__\$ReturnUdt\$ = 96
bez\$ = 104
t\$ = 112
BLPoint blCubicEvaluateAtT(BLPoint const * __ptr64 const,double) PROC
\$LN70:
sub     rsp, 88                             ; 00000058H
vmovsd  xmm0, QWORD PTR [rdx+16]
vsubsd  xmm3, xmm0, QWORD PTR [rdx+32]
vmovsd  xmm1, QWORD PTR [rdx+24]
vmovups xmm5, XMMWORD PTR [rdx]
vmovaps XMMWORD PTR [rsp+64], xmm6
mov     rax, rcx
vmovaps XMMWORD PTR [rsp+48], xmm7
vmovsd  xmm7, QWORD PTR __real@4008000000000000
vmovaps XMMWORD PTR [rsp+32], xmm8
vmulsd  xmm0, xmm3, xmm7
vmovaps XMMWORD PTR [rsp+16], xmm9
vmovaps XMMWORD PTR [rsp], xmm10
vmovaps xmm10, xmm2
vsubsd  xmm2, xmm1, QWORD PTR [rdx+40]
vaddsd  xmm1, xmm0, QWORD PTR [rdx+48]
vmovsd  xmm0, QWORD PTR [rdx+16]
vsubsd  xmm9, xmm1, xmm5
vmulsd  xmm4, xmm2, xmm7
vaddsd  xmm2, xmm4, QWORD PTR [rdx+56]
vunpckhpd xmm1, xmm5, xmm5
vmovsd  xmm5, QWORD PTR [rdx]
vsubsd  xmm8, xmm2, xmm1
vmovsd  xmm1, QWORD PTR [rdx+24]
vaddsd  xmm2, xmm0, xmm0
vsubsd  xmm0, xmm5, xmm2
vmovsd  xmm2, QWORD PTR [rdx+8]
vaddsd  xmm3, xmm1, xmm1
vaddsd  xmm1, xmm0, QWORD PTR [rdx+32]
vsubsd  xmm4, xmm2, xmm3
vaddsd  xmm0, xmm4, QWORD PTR [rdx+40]
vmulsd  xmm6, xmm0, xmm7
vmovsd  xmm0, QWORD PTR [rdx+16]
vmulsd  xmm4, xmm1, xmm7
vmovsd  xmm1, QWORD PTR [rdx+24]
vsubsd  xmm2, xmm1, xmm2
vsubsd  xmm3, xmm0, xmm5
vmulsd  xmm5, xmm3, xmm7
vmulsd  xmm0, xmm9, xmm10
vmovaps xmm9, XMMWORD PTR [rsp+16]
vmulsd  xmm1, xmm8, xmm10
vmovaps xmm8, XMMWORD PTR [rsp+32]
vaddsd  xmm3, xmm1, xmm6
vmovaps xmm6, XMMWORD PTR [rsp+64]
vmulsd  xmm7, xmm2, xmm7
vaddsd  xmm2, xmm0, xmm4
vmulsd  xmm4, xmm2, xmm10
vmulsd  xmm0, xmm3, xmm10
vaddsd  xmm1, xmm4, xmm5
vaddsd  xmm2, xmm0, xmm7
vmulsd  xmm3, xmm1, xmm10
vmulsd  xmm4, xmm2, xmm10
vmovaps xmm10, XMMWORD PTR [rsp]
vaddsd  xmm1, xmm4, xmm7
vmovaps xmm7, XMMWORD PTR [rsp+48]
vaddsd  xmm0, xmm3, xmm5
vmovsd  QWORD PTR [rcx], xmm0
vmovsd  QWORD PTR [rcx+8], xmm1
add     rsp, 88                             ; 00000058H
ret     0
BLPoint blCubicEvaluateAtT(BLPoint const * __ptr64 const,double) ENDP

; NOT VECTORIZED!
__\$ReturnUdt\$ = 128
bez\$ = 136
t\$ = 144
BLPoint blCubicPreciseEvaluateAtT(BLPoint const * __ptr64 const,double) PROC
\$LN88:
mov     r11, rsp
sub     rsp, 120                      ; 00000078H
vmulsd  xmm4, xmm2, QWORD PTR [rdx+16]
vmulsd  xmm3, xmm2, QWORD PTR [rdx+24]
vmovsd  xmm0, QWORD PTR __real@3ff0000000000000
vmovaps XMMWORD PTR [rsp+96], xmm6
mov     rax, rcx
vmovaps XMMWORD PTR [rsp+80], xmm7
vmovaps XMMWORD PTR [r11-56], xmm8
vmovaps XMMWORD PTR [r11-72], xmm9
vmovaps XMMWORD PTR [r11-88], xmm10
vmovaps XMMWORD PTR [r11-104], xmm11
vsubsd  xmm11, xmm0, xmm2
vmulsd  xmm1, xmm11, QWORD PTR [rdx]
vmulsd  xmm0, xmm11, QWORD PTR [rdx+8]
vaddsd  xmm10, xmm3, xmm0
vmulsd  xmm3, xmm2, QWORD PTR [rdx+32]
vmulsd  xmm0, xmm11, QWORD PTR [rdx+24]
vaddsd  xmm9, xmm4, xmm1
vmulsd  xmm1, xmm11, QWORD PTR [rdx+16]
vaddsd  xmm5, xmm3, xmm1
vmulsd  xmm1, xmm11, QWORD PTR [rdx+32]
vmovaps XMMWORD PTR [rsp], xmm12
vmovaps xmm12, xmm2
vmulsd  xmm2, xmm2, QWORD PTR [rdx+40]
vmulsd  xmm3, xmm12, QWORD PTR [rdx+48]
vaddsd  xmm8, xmm2, xmm0
vmulsd  xmm0, xmm11, QWORD PTR [rdx+40]
vmulsd  xmm2, xmm12, QWORD PTR [rdx+56]
vaddsd  xmm1, xmm1, xmm3
vaddsd  xmm2, xmm2, xmm0
vmulsd  xmm3, xmm1, xmm12
vmulsd  xmm4, xmm2, xmm12
vmulsd  xmm1, xmm8, xmm11
vaddsd  xmm7, xmm1, xmm4
vmulsd  xmm0, xmm5, xmm11
vaddsd  xmm6, xmm0, xmm3
vmulsd  xmm1, xmm10, xmm11
vmovaps xmm10, XMMWORD PTR [r11-88]
vmulsd  xmm2, xmm5, xmm12
vmulsd  xmm3, xmm8, xmm12
vmovaps xmm8, XMMWORD PTR [r11-56]
vmulsd  xmm0, xmm9, xmm11
vmovaps xmm9, XMMWORD PTR [r11-72]
vaddsd  xmm5, xmm1, xmm3
vaddsd  xmm4, xmm0, xmm2
vmulsd  xmm2, xmm6, xmm12
vmovaps xmm6, XMMWORD PTR [rsp+96]
vmulsd  xmm3, xmm7, xmm12
vmovaps xmm7, XMMWORD PTR [rsp+80]
vmovaps xmm12, XMMWORD PTR [rsp]
vmulsd  xmm1, xmm5, xmm11
vmulsd  xmm0, xmm4, xmm11
vmovaps xmm11, XMMWORD PTR [r11-104]
vaddsd  xmm1, xmm1, xmm3
vaddsd  xmm0, xmm0, xmm2
vmovsd  QWORD PTR [rcx+8], xmm1
vmovsd  QWORD PTR [rcx], xmm0
add     rsp, 120                      ; 00000078H
ret     0
BLPoint blCubicPreciseEvaluateAtT(BLPoint const * __ptr64 const,double) ENDP
``````

### Interpreting the Results

GCC and Clang okay, MSVC didn't use SIMD and generated so much code again.

## Quadratic Bezier Bounding Box

Calculating bounding box of a quadratic Bezier curve is quite common. I wrote two solutions - the first version (V1) uses scalar code that only merges possible extremas when they are found. The second version (V2) doesn't bother and always calculates both extremas even if they are outside of the domain (they would be clamped in such case). The second version is SIMD friendly and that was the intention:

``````// Scalar version - not good for SIMD.
inline void blQuadCoefficientsAtT(double t, double& a, double& b, double& c) noexcept {
double tInv = 1.0 - t;
a = tInv * tInv;
b = 2.0 * (t - tInv);
c = t * t;
}

void blQuadBoundingBoxV1(const BLPoint bez[3], BLBox& bBox) noexcept {
// Get bounding box of start and end points.
bBox.reset(blMin(bez[0].x, bez[2].x), blMin(bez[0].y, bez[2].y),
blMax(bez[0].x, bez[2].x), blMax(bez[0].y, bez[2].y));

// Merge X extrema.
if (bez[1].x < bBox.x0 || bez[1].x > bBox.x1) {
double t = (bez[0].x - bez[1].x) / (bez[0].x - 2.0 * bez[1].x + bez[2].x);
double a, b, c;

blQuadCoefficientsAtT(t, a, b, c);
double coord = a * bez[0].x + b * bez[1].x + c * bez[2].x;
bBox.x0 = blMin(bBox.x0, coord);
bBox.x1 = blMax(bBox.x1, coord);
}

// Merge Y extrema.
if (bez[1].y < bBox.y0 || bez[1].y > bBox.y1) {
double t = (bez[0].y - bez[1].y) / (bez[0].y - 2.0 * bez[1].y + bez[2].y);
double a, b, c;

blQuadCoefficientsAtT(t, a, b, c);
double coord = a * bez[0].y + b * bez[1].y + c * bez[2].y;
bBox.y0 = blMin(bBox.y0, coord);
bBox.y1 = blMax(bBox.y1, coord);
}
}

// SIMD friendly (branchless).
void blQuadBoundingBoxV2(const BLPoint bez[3], BLBox& bBox) noexcept {
// Bounding box of start and end points.
bBox.reset(blMin(bez[0].x, bez[2].x), blMin(bez[0].y, bez[2].y),
blMax(bez[0].x, bez[2].x), blMax(bez[0].y, bez[2].y));

BLPoint t = (bez[0] - bez[1]) / (bez[0] - bez[1] * 2.0 + bez[2]);
t.x = blMax(t.x, 0.0);
t.y = blMax(t.y, 0.0);
t.x = blMin(t.x, 1.0);
t.y = blMin(t.y, 1.0);

blBoxMergePoint(bBox, blLerp(blLerp(bez[0], bez[1], t),
blLerp(bez[1], bez[2], t), t));
}
``````

### GCC [-std=c++17 -O3 -fno-math-errno -mavx2]

``````# NOT VECTORIZED!
vmovsd  xmm7, QWORD PTR [rdi+8]
vmovsd  xmm6, QWORD PTR [rdi+40]
vmovsd  xmm11, QWORD PTR [rdi]
vmovsd  xmm10, QWORD PTR [rdi+32]
vmaxsd  xmm4, xmm6, xmm7
vminsd  xmm3, xmm6, xmm7
vminsd  xmm8, xmm10, xmm11
vmaxsd  xmm9, xmm10, xmm11
vunpcklpd       xmm1, xmm8, xmm3
vunpcklpd       xmm0, xmm9, xmm4
vmovups XMMWORD PTR [rsi], xmm1
vmovups XMMWORD PTR [rsi+16], xmm0
vmovsd  xmm1, QWORD PTR [rdi+16]
vcomisd xmm8, xmm1
ja      .L11
vcomisd xmm1, xmm9
ja      .L11
.L12:
vmovsd  xmm0, QWORD PTR [rdi+24]
vcomisd xmm3, xmm0
ja      .L16
vcomisd xmm0, xmm4
jbe     .L27
.L16:
vaddsd  xmm1, xmm0, xmm0
vsubsd  xmm2, xmm7, xmm0
vmovsd  xmm5, QWORD PTR .LC2[rip]
vsubsd  xmm1, xmm7, xmm1
vaddsd  xmm1, xmm1, xmm6
vdivsd  xmm2, xmm2, xmm1
vsubsd  xmm5, xmm5, xmm2
vsubsd  xmm1, xmm2, xmm5
vmulsd  xmm5, xmm5, xmm5
vmulsd  xmm2, xmm2, xmm2
vaddsd  xmm1, xmm1, xmm1
vmulsd  xmm5, xmm5, xmm7
vmulsd  xmm0, xmm1, xmm0
vmulsd  xmm2, xmm2, xmm6
vaddsd  xmm0, xmm0, xmm5
vaddsd  xmm0, xmm0, xmm2
vminsd  xmm3, xmm0, xmm3
vmaxsd  xmm0, xmm0, xmm4
vmovsd  QWORD PTR [rsi+8], xmm3
vmovsd  QWORD PTR [rsi+24], xmm0
.L27:
ret
.L11:
vaddsd  xmm0, xmm1, xmm1
vsubsd  xmm5, xmm11, xmm1
vsubsd  xmm0, xmm11, xmm0
vaddsd  xmm0, xmm0, xmm10
vdivsd  xmm5, xmm5, xmm0
vmovsd  xmm0, QWORD PTR .LC2[rip]
vsubsd  xmm0, xmm0, xmm5
vsubsd  xmm2, xmm5, xmm0
vmulsd  xmm0, xmm0, xmm0
vmulsd  xmm5, xmm5, xmm5
vaddsd  xmm2, xmm2, xmm2
vmulsd  xmm0, xmm0, xmm11
vmulsd  xmm1, xmm2, xmm1
vmulsd  xmm5, xmm5, xmm10
vaddsd  xmm1, xmm1, xmm0
vaddsd  xmm1, xmm1, xmm5
vminsd  xmm8, xmm1, xmm8
vmaxsd  xmm1, xmm1, xmm9
vmovsd  QWORD PTR [rsi], xmm8
vmovsd  QWORD PTR [rsi+16], xmm1
jmp     .L12

# NOT VECTORIZED!
push    rbp
mov     rbp, rsp
and     rsp, -32
vmovsd  xmm1, QWORD PTR [rdi+8]
vmovsd  xmm0, QWORD PTR [rdi]
vmovsd  xmm5, QWORD PTR [rdi+40]
vmovsd  xmm6, QWORD PTR [rdi+32]
vmaxsd  xmm13, xmm5, xmm1
vmaxsd  xmm12, xmm6, xmm0
vminsd  xmm5, xmm5, xmm1
vminsd  xmm6, xmm6, xmm0
vunpcklpd       xmm0, xmm12, xmm13
vunpcklpd       xmm1, xmm6, xmm5
vmovups XMMWORD PTR [rsi+16], xmm0
vmovups XMMWORD PTR [rsi], xmm1
vmovsd  xmm2, QWORD PTR [rdi+24]
vmovsd  xmm10, QWORD PTR [rdi+8]
vmovsd  xmm1, QWORD PTR [rdi+40]
vmovsd  xmm7, QWORD PTR [rdi+16]
vaddsd  xmm4, xmm2, xmm2
vsubsd  xmm9, xmm10, xmm2
vmovsd  xmm3, QWORD PTR [rdi]
vmovsd  xmm0, QWORD PTR [rdi+32]
vsubsd  xmm8, xmm3, xmm7
vsubsd  xmm4, xmm10, xmm4
vaddsd  xmm4, xmm4, xmm1
vdivsd  xmm9, xmm9, xmm4
vaddsd  xmm4, xmm7, xmm7
vsubsd  xmm4, xmm3, xmm4
vaddsd  xmm4, xmm4, xmm0
vdivsd  xmm8, xmm8, xmm4
vxorpd  xmm4, xmm4, xmm4
vcomisd xmm4, xmm8
ja      .L33
vcomisd xmm4, xmm9
jbe     .L62
vmovsd  xmm11, QWORD PTR .LC2[rip]
vmulsd  xmm14, xmm1, xmm4
vmulsd  xmm9, xmm2, xmm4
vcomisd xmm8, xmm11
jbe     .L63
vmovsd  QWORD PTR [rsp-16], xmm2
vmovapd xmm1, xmm14
vmovapd xmm2, xmm9
vxorpd  xmm14, xmm14, xmm14
vmovsd  QWORD PTR [rsp-8], xmm7
vmulsd  xmm3, xmm3, xmm4
vmovapd xmm15, xmm11
vmovapd xmm8, xmm11
vmulsd  xmm7, xmm7, xmm4
vxorpd  xmm9, xmm9, xmm9
jmp     .L40
.L33:
vmulsd  xmm11, xmm7, xmm4
vcomisd xmm4, xmm9
vxorpd  xmm8, xmm8, xmm8
vmulsd  xmm0, xmm0, xmm4
vmovsd  QWORD PTR [rsp-8], xmm11
vmovsd  xmm11, QWORD PTR .LC2[rip]
vmovapd xmm14, xmm11
jbe     .L37
.L46:
vmovsd  QWORD PTR [rsp-16], xmm2
vmulsd  xmm1, xmm1, xmm4
vmovapd xmm15, xmm11
vxorpd  xmm9, xmm9, xmm9
vmulsd  xmm2, xmm2, xmm4
jmp     .L40
.L62:
vmovsd  xmm11, QWORD PTR .LC2[rip]
vcomisd xmm8, xmm11
jbe     .L56
vmovsd  QWORD PTR [rsp-8], xmm7
vmulsd  xmm3, xmm3, xmm4
vxorpd  xmm14, xmm14, xmm14
vmovapd xmm8, xmm11
vmulsd  xmm7, xmm7, xmm4
.L37:
vcomisd xmm9, xmm11
jbe     .L57
vmulsd  xmm15, xmm2, xmm4
vmovapd xmm9, xmm11
vmulsd  xmm10, xmm10, xmm4
vmovsd  QWORD PTR [rsp-16], xmm15
vxorpd  xmm15, xmm15, xmm15
.L40:
vaddsd  xmm1, xmm1, QWORD PTR [rsp-16]
vaddsd  xmm3, xmm3, QWORD PTR [rsp-8]
vaddsd  xmm2, xmm2, xmm10
vaddsd  xmm0, xmm0, xmm7
vmulsd  xmm9, xmm1, xmm9
vmulsd  xmm15, xmm2, xmm15
vmulsd  xmm8, xmm0, xmm8
vmulsd  xmm14, xmm3, xmm14
vaddsd  xmm9, xmm9, xmm15
vaddsd  xmm14, xmm8, xmm14
vminsd  xmm5, xmm9, xmm5
vmaxsd  xmm9, xmm9, xmm13
vminsd  xmm6, xmm14, xmm6
vmaxsd  xmm14, xmm14, xmm12
vmovsd  QWORD PTR [rsi+8], xmm5
vmovsd  QWORD PTR [rsi+24], xmm9
vmovsd  QWORD PTR [rsi], xmm6
vmovsd  QWORD PTR [rsi+16], xmm14
leave
ret
.L56:
vmulsd  xmm15, xmm7, xmm8
vsubsd  xmm14, xmm11, xmm8
vmulsd  xmm0, xmm0, xmm8
vmulsd  xmm3, xmm3, xmm14
vmulsd  xmm7, xmm7, xmm14
vmovsd  QWORD PTR [rsp-8], xmm15
jmp     .L37
.L63:
vmulsd  xmm15, xmm7, xmm8
vsubsd  xmm14, xmm11, xmm8
vmulsd  xmm0, xmm0, xmm8
vmulsd  xmm3, xmm3, xmm14
vmulsd  xmm7, xmm7, xmm14
vmovsd  QWORD PTR [rsp-8], xmm15
jmp     .L46
.L57:
vsubsd  xmm15, xmm11, xmm9
vmulsd  xmm1, xmm1, xmm9
vmulsd  xmm4, xmm2, xmm15
vmulsd  xmm10, xmm10, xmm15
vmulsd  xmm2, xmm2, xmm9
vmovsd  QWORD PTR [rsp-16], xmm4
jmp     .L40
.LC0:
.long   0
.long   1072693248
.long   0
.long   1072693248
.LC1:
.long   0
.long   1074266112
.long   0
.long   1074266112
.LC2:
.long   0
.long   1072693248
``````

### Clang [-std=c++17 -O3 -fno-math-errno -mavx2]

``````# NOT VECTORIZED!
.LCPI4_0:
.quad   4607182418800017408     # double 1

blQuadBoundingBoxV1(BLPoint const*, BLBox&): # @blQuadBoundingBoxV1(BLPoint const*, BLBox&)
vmovupd xmm1, xmmword ptr [rdi]
vmovupd xmm0, xmmword ptr [rdi + 32]
vminpd  xmm3, xmm0, xmm1
vmaxpd  xmm2, xmm0, xmm1
vmovupd xmmword ptr [rsi], xmm3
vmovupd xmmword ptr [rsi + 16], xmm2
vmovsd  xmm4, qword ptr [rdi + 16] # xmm4 = mem[0],zero
vucomisd        xmm3, xmm4
ja      .LBB4_2
vucomisd        xmm4, xmm2
jbe     .LBB4_3
.LBB4_2:
vsubsd  xmm5, xmm1, xmm4
vaddsd  xmm6, xmm4, xmm4
vsubsd  xmm6, xmm1, xmm6
vaddsd  xmm6, xmm0, xmm6
vdivsd  xmm5, xmm5, xmm6
vmovsd  xmm6, qword ptr [rip + .LCPI4_0] # xmm6 = mem[0],zero
vsubsd  xmm6, xmm6, xmm5
vmulsd  xmm7, xmm6, xmm6
vsubsd  xmm6, xmm5, xmm6
vaddsd  xmm6, xmm6, xmm6
vmulsd  xmm5, xmm5, xmm5
vmulsd  xmm7, xmm1, xmm7
vmulsd  xmm4, xmm4, xmm6
vaddsd  xmm4, xmm7, xmm4
vmulsd  xmm5, xmm0, xmm5
vaddsd  xmm4, xmm5, xmm4
vminsd  xmm5, xmm4, xmm3
vmovsd  qword ptr [rsi], xmm5
vmaxsd  xmm4, xmm4, xmm2
vmovsd  qword ptr [rsi + 16], xmm4
.LBB4_3:
vmovsd  xmm4, qword ptr [rdi + 24] # xmm4 = mem[0],zero
vpermilpd       xmm3, xmm3, 1   # xmm3 = xmm3[1,0]
vucomisd        xmm3, xmm4
vpermilpd       xmm2, xmm2, 1   # xmm2 = xmm2[1,0]
ja      .LBB4_5
vucomisd        xmm4, xmm2
ja      .LBB4_5
ret
.LBB4_5:
vpermilpd       xmm1, xmm1, 1   # xmm1 = xmm1[1,0]
vsubsd  xmm5, xmm1, xmm4
vaddsd  xmm6, xmm4, xmm4
vsubsd  xmm6, xmm1, xmm6
vpermilpd       xmm0, xmm0, 1   # xmm0 = xmm0[1,0]
vaddsd  xmm6, xmm0, xmm6
vdivsd  xmm5, xmm5, xmm6
vmovsd  xmm6, qword ptr [rip + .LCPI4_0] # xmm6 = mem[0],zero
vsubsd  xmm6, xmm6, xmm5
vmulsd  xmm7, xmm6, xmm6
vsubsd  xmm6, xmm5, xmm6
vaddsd  xmm6, xmm6, xmm6
vmulsd  xmm5, xmm5, xmm5
vmulsd  xmm1, xmm1, xmm7
vmulsd  xmm4, xmm4, xmm6
vaddsd  xmm1, xmm1, xmm4
vmulsd  xmm0, xmm0, xmm5
vaddsd  xmm0, xmm0, xmm1
vminsd  xmm1, xmm0, xmm3
vmovsd  qword ptr [rsi + 8], xmm1
vmaxsd  xmm0, xmm0, xmm2
vmovsd  qword ptr [rsi + 24], xmm0
ret
.LCPI5_0:
.quad   4607182418800017408     # double 1
.quad   4607182418800017408     # double 1

# Vectorized
blQuadBoundingBoxV2(BLPoint const*, BLBox&): # @blQuadBoundingBoxV2(BLPoint const*, BLBox&)
vmovupd xmm0, xmmword ptr [rdi]
vmovupd xmm1, xmmword ptr [rdi + 16]
vmovupd xmm2, xmmword ptr [rdi + 32]
vminpd  xmm3, xmm2, xmm0
vmaxpd  xmm4, xmm2, xmm0
vsubpd  xmm5, xmm0, xmm1
vaddpd  xmm6, xmm1, xmm1
vsubpd  xmm6, xmm0, xmm6
vaddpd  xmm6, xmm2, xmm6
vdivpd  xmm5, xmm5, xmm6
vxorpd  xmm6, xmm6, xmm6
vmaxpd  xmm5, xmm6, xmm5
vmovapd xmm6, xmmword ptr [rip + .LCPI5_0] # xmm6 = [1.000000e+00,1.000000e+00]
vminpd  xmm5, xmm6, xmm5
vsubpd  xmm6, xmm6, xmm5
vmulpd  xmm0, xmm0, xmm6
vmulpd  xmm7, xmm1, xmm5
vaddpd  xmm0, xmm7, xmm0
vmulpd  xmm1, xmm1, xmm6
vmulpd  xmm2, xmm2, xmm5
vaddpd  xmm1, xmm2, xmm1
vmulpd  xmm0, xmm6, xmm0
vmulpd  xmm1, xmm5, xmm1
vaddpd  xmm0, xmm0, xmm1
vminpd  xmm1, xmm0, xmm3
vmovupd xmmword ptr [rsi], xmm1
vmaxpd  xmm0, xmm0, xmm4
vmovupd xmmword ptr [rsi + 16], xmm0
ret
``````

### MSVC [/O2 /Qpar /arch:AVX2]

``````; NOT VECTORIZED!
bez\$ = 128
bBox\$ = 136
void blQuadBoundingBoxV1(BLPoint const * __ptr64 const,BLBox & __ptr64) PROC
\$LN46:
sub     rsp, 120                      ; 00000078H
vmovsd  xmm3, QWORD PTR [rcx+40]
vmovsd  xmm1, QWORD PTR [rcx+32]
vminsd  xmm0, xmm1, QWORD PTR [rcx]
vmovaps XMMWORD PTR [rsp+96], xmm6
vmovaps XMMWORD PTR [rsp+80], xmm8
vmovaps XMMWORD PTR [rsp+64], xmm9
vmaxsd  xmm9, xmm3, QWORD PTR [rcx+8]
vmovaps XMMWORD PTR [rsp+48], xmm10
vminsd  xmm10, xmm3, QWORD PTR [rcx+8]
vmovaps XMMWORD PTR [rsp], xmm13
vmovsd  xmm13, QWORD PTR __real@3ff0000000000000
vmovaps XMMWORD PTR [rsp+32], xmm11
vmaxsd  xmm11, xmm1, QWORD PTR [rcx]
vmovsd  QWORD PTR [rdx+16], xmm11
vmovsd  QWORD PTR [rdx], xmm0
vmovsd  QWORD PTR [rdx+8], xmm10
vmovsd  QWORD PTR [rdx+24], xmm9
vmovsd  xmm8, QWORD PTR [rcx+16]
vmovaps XMMWORD PTR [rsp+16], xmm12
vmovaps xmm12, xmm0
vcomisd xmm12, xmm8
vcomisd xmm8, xmm11
vmovsd  xmm6, QWORD PTR [rcx]
vaddsd  xmm0, xmm8, xmm8
vsubsd  xmm1, xmm6, xmm0
vaddsd  xmm2, xmm1, QWORD PTR [rcx+32]
vsubsd  xmm3, xmm6, xmm8
vdivsd  xmm5, xmm3, xmm2
vsubsd  xmm4, xmm13, xmm5
vsubsd  xmm0, xmm5, xmm4
vaddsd  xmm1, xmm0, xmm0
vmulsd  xmm3, xmm1, xmm8
vmulsd  xmm2, xmm4, xmm4
vmulsd  xmm0, xmm2, xmm6
vmulsd  xmm1, xmm5, xmm5
vmulsd  xmm2, xmm1, QWORD PTR [rcx+32]
vaddsd  xmm4, xmm3, xmm0
vaddsd  xmm3, xmm4, xmm2
vminsd  xmm0, xmm3, xmm12
vmaxsd  xmm1, xmm3, xmm11
vmovsd  QWORD PTR [rdx], xmm0
vmovsd  QWORD PTR [rdx+16], xmm1
vmovsd  xmm8, QWORD PTR [rcx+24]
vcomisd xmm10, xmm8
vmovaps xmm12, XMMWORD PTR [rsp+16]
vmovaps xmm11, XMMWORD PTR [rsp+32]
vcomisd xmm8, xmm9
vmovsd  xmm6, QWORD PTR [rcx+8]
vaddsd  xmm0, xmm8, xmm8
vsubsd  xmm1, xmm6, xmm0
vaddsd  xmm2, xmm1, QWORD PTR [rcx+40]
vsubsd  xmm3, xmm6, xmm8
vdivsd  xmm5, xmm3, xmm2
vsubsd  xmm4, xmm13, xmm5
vsubsd  xmm0, xmm5, xmm4
vaddsd  xmm1, xmm0, xmm0
vmulsd  xmm3, xmm1, xmm8
vmulsd  xmm2, xmm4, xmm4
vmulsd  xmm0, xmm2, xmm6
vmulsd  xmm1, xmm5, xmm5
vmulsd  xmm2, xmm1, QWORD PTR [rcx+40]
vaddsd  xmm4, xmm3, xmm0
vaddsd  xmm3, xmm4, xmm2
vminsd  xmm0, xmm3, xmm10
vmaxsd  xmm1, xmm3, xmm9
vmovsd  QWORD PTR [rdx+8], xmm0
vmovsd  QWORD PTR [rdx+24], xmm1
vmovaps xmm6, XMMWORD PTR [rsp+96]
vmovaps xmm8, XMMWORD PTR [rsp+80]
vmovaps xmm9, XMMWORD PTR [rsp+64]
vmovaps xmm10, XMMWORD PTR [rsp+48]
vmovaps xmm13, XMMWORD PTR [rsp]
add     rsp, 120                      ; 00000078H
ret     0
void blQuadBoundingBoxV1(BLPoint const * __ptr64 const,BLBox & __ptr64) ENDP

; NOT VECTORIZED!
bez\$ = 176
bBox\$ = 184
void blQuadBoundingBoxV2(BLPoint const * __ptr64 const,BLBox & __ptr64) PROC
\$LN130:
mov     rax, rsp
sub     rsp, 168                      ; 000000a8H
vmovsd  xmm3, QWORD PTR [rcx+40]
vmovsd  xmm1, QWORD PTR [rcx+32]
vminsd  xmm0, xmm1, QWORD PTR [rcx]
vmovaps XMMWORD PTR [rax-24], xmm6
lea     r11, QWORD PTR [rax]
vmovaps XMMWORD PTR [rax-40], xmm7
vmovaps XMMWORD PTR [rax-56], xmm8
vmovaps XMMWORD PTR [rax-72], xmm9
vmovaps XMMWORD PTR [rax-88], xmm10
vmovaps XMMWORD PTR [rax-104], xmm11
vmovaps XMMWORD PTR [rax-120], xmm12
vmovaps XMMWORD PTR [rsp+32], xmm13
vminsd  xmm13, xmm3, QWORD PTR [rcx+8]
vmovaps XMMWORD PTR [rsp+16], xmm14
vmaxsd  xmm14, xmm1, QWORD PTR [rcx]
vmovaps XMMWORD PTR [rsp], xmm15
vmaxsd  xmm15, xmm3, QWORD PTR [rcx+8]
vmovsd  QWORD PTR [rdx], xmm0
vmovsd  QWORD PTR [rdx+24], xmm15
vmovsd  QWORD PTR [rdx+8], xmm13
vmovsd  QWORD PTR [rdx+16], xmm14
vmovsd  xmm12, QWORD PTR [rcx]
vmovsd  xmm11, QWORD PTR [rcx+8]
vmovsd  xmm0, QWORD PTR [rcx+16]
vmovsd  xmm1, QWORD PTR [rcx+24]
vaddsd  xmm2, xmm0, xmm0
vaddsd  xmm3, xmm1, xmm1
vsubsd  xmm0, xmm12, xmm2
vaddsd  xmm2, xmm0, QWORD PTR [rcx+32]
vsubsd  xmm0, xmm12, QWORD PTR [rcx+16]
vdivsd  xmm2, xmm0, xmm2
vsubsd  xmm1, xmm11, xmm3
vaddsd  xmm3, xmm1, QWORD PTR [rcx+40]
vsubsd  xmm1, xmm11, QWORD PTR [rcx+24]
vdivsd  xmm5, xmm1, xmm3
vxorpd  xmm4, xmm4, xmm4
vmaxsd  xmm0, xmm4, xmm2
vmaxsd  xmm1, xmm4, xmm5
vmovsd  xmm4, QWORD PTR __real@3ff0000000000000
vminsd  xmm10, xmm4, xmm0
vmulsd  xmm3, xmm10, QWORD PTR [rcx+32]
vminsd  xmm9, xmm4, xmm1
vmulsd  xmm2, xmm9, QWORD PTR [rcx+40]
vsubsd  xmm8, xmm4, xmm10
vmulsd  xmm1, xmm8, QWORD PTR [rcx+16]
vaddsd  xmm5, xmm1, xmm3
vmulsd  xmm3, xmm10, QWORD PTR [rcx+16]
vsubsd  xmm7, xmm4, xmm9
vmulsd  xmm0, xmm7, QWORD PTR [rcx+24]
vaddsd  xmm6, xmm2, xmm0
vmulsd  xmm2, xmm9, QWORD PTR [rcx+24]
vmulsd  xmm0, xmm8, xmm12
vmovaps xmm12, XMMWORD PTR [r11-120]
vmulsd  xmm1, xmm7, xmm11
vmovaps xmm11, XMMWORD PTR [r11-104]
vaddsd  xmm4, xmm2, xmm1
vaddsd  xmm3, xmm3, xmm0
vmulsd  xmm0, xmm3, xmm8
vmovaps xmm8, XMMWORD PTR [r11-56]
vmulsd  xmm1, xmm4, xmm7
vmovaps xmm7, XMMWORD PTR [r11-40]
vmulsd  xmm2, xmm6, xmm9
vmovaps xmm6, XMMWORD PTR [r11-24]
vmovaps xmm9, XMMWORD PTR [r11-72]
vmulsd  xmm5, xmm5, xmm10
vmovaps xmm10, XMMWORD PTR [r11-88]
vaddsd  xmm3, xmm0, xmm5
vminsd  xmm0, xmm3, QWORD PTR [rdx]
vaddsd  xmm4, xmm1, xmm2
vminsd  xmm1, xmm4, xmm13
vmovaps xmm13, XMMWORD PTR [rsp+32]
vmovsd  QWORD PTR [rdx], xmm0
vmaxsd  xmm0, xmm3, xmm14
vmovaps xmm14, XMMWORD PTR [rsp+16]
vmovsd  QWORD PTR [rdx+8], xmm1
vmaxsd  xmm1, xmm4, xmm15
vmovaps xmm15, XMMWORD PTR [rsp]
vmovsd  QWORD PTR [rdx+16], xmm0
vmovsd  QWORD PTR [rdx+24], xmm1
mov     rsp, r11
ret     0
void blQuadBoundingBoxV2(BLPoint const * __ptr64 const,BLBox & __ptr64) ENDP
``````

### Interpreting the Results

Only Clang was able to use SIMD in the second version. The rest was uninteresting scalar asm.

## Quadratic Bezier Bounding Box - Clang Experiments

I did a bit of experimenting and I would like to show how sensitive compilers are when it comes to certain expressions. I created my own version of some basic functions like `blMin(a, b)` and `blMax(a, b)`. The main reason was to have these constexpr and to return a copy instead of a reference to either `a` or `b`, which is useful when the type is not primitive and it's some structure like `BLPoint`. Let's take a look what would happen if we used standard `std::min` and `std::max` functions:

``````// Experiment, use std::min and std::max instead of our own.
void blQuadBoundingBoxV3(const BLPoint bez[3], BLBox& bBox) noexcept {
// Bounding box of start and end points.
bBox.reset(std::min(bez[0].x, bez[2].x), std::min(bez[0].y, bez[2].y),
std::max(bez[0].x, bez[2].x), std::max(bez[0].y, bez[2].y));

BLPoint t = (bez[0] - bez[1]) / (bez[0] - bez[1] * 2.0 + bez[2]);
t.x = std::max(t.x, 0.0);
t.y = std::max(t.y, 0.0);
t.x = std::min(t.x, 1.0);
t.y = std::min(t.y, 1.0);

blBoxMergePoint(bBox, blLerp(blLerp(bez[0], bez[1], t),
blLerp(bez[1], bez[2], t), t));
}
``````

And the output:

``````# The code becomes a mixture of scalar and SIMD, much worse than the previous one.
vmovupd  xmm3, xmmword ptr [rdi]
vmovupd  xmm2, xmmword ptr [rdi + 32]
vminpd   xmm9, xmm2, xmm3
vmaxpd   xmm8, xmm2, xmm3
vmovupd  xmm4, xmmword ptr [rdi + 16]
vsubsd   xmm5, xmm3, xmm4
vpermilpd xmm6, xmm4, 1   # xmm6 = xmm4[1,0]
vpermilpd xmm7, xmm3, 1   # xmm7 = xmm3[1,0]
vsubsd   xmm0, xmm7, xmm6
vaddsd   xmm1, xmm4, xmm4
vaddsd   xmm6, xmm6, xmm6
vsubsd   xmm1, xmm3, xmm1
vsubsd   xmm6, xmm7, xmm6
vaddsd   xmm1, xmm2, xmm1
vdivsd   xmm1, xmm5, xmm1
vpermilpd xmm5, xmm2, 1   # xmm5 = xmm2[1,0]
vaddsd   xmm5, xmm5, xmm6
vdivsd   xmm0, xmm0, xmm5
vmovsd   qword ptr [rsp - 16], xmm1
vmovsd   qword ptr [rsp - 24], xmm0
vxorpd   xmm5, xmm5, xmm5
vucomisd xmm5, xmm1
lea      rax, [rsp - 8]
lea      rcx, [rsp - 16]
cmova    rcx, rax
mov      qword ptr [rsp - 8], 0
mov      rcx, qword ptr [rcx]
vucomisd xmm5, xmm0
lea      rdx, [rsp - 24]
cmova    rdx, rax
mov      qword ptr [rsp - 16], rcx
mov      qword ptr [rsp - 8], 0
mov      rax, qword ptr [rdx]
mov      qword ptr [rsp - 24], rax
vmovsd   xmm0, qword ptr [rsp - 16] # xmm0 = mem[0],zero
vmovq    xmm1, rcx
vmovq    xmm5, rax
vpunpcklqdq xmm1, xmm1, xmm5 # xmm1 = xmm1[0],xmm5[0]
vmovapd  xmm5, xmmword ptr [rip + .LCPI6_0] # xmm5 = [1.000000e+00,1.000000e+00]
vcmpltpd xmm1, xmm5, xmm1
vmovhpd  xmm0, xmm0, qword ptr [rsp - 24] # xmm0 = xmm0[0],mem[0]
vblendvpd xmm0, xmm0, xmm5, xmm1
vsubpd   xmm1, xmm5, xmm0
vmulpd   xmm3, xmm3, xmm1
vmulpd   xmm5, xmm4, xmm0
vaddpd   xmm3, xmm5, xmm3
vmulpd   xmm4, xmm4, xmm1
vmulpd   xmm2, xmm2, xmm0
vaddpd   xmm2, xmm2, xmm4
vmulpd   xmm1, xmm1, xmm3
vmulpd   xmm0, xmm2, xmm0
vaddpd   xmm0, xmm1, xmm0
vminpd   xmm1, xmm0, xmm9
vmovupd  xmmword ptr [rsi], xmm1
vmaxpd   xmm0, xmm0, xmm8
vmovupd  xmmword ptr [rsi + 16], xmm0
ret
``````

As you can see a slight modification of the code resulted in disaster. That nicely vectorized code is gone and instead we've got a mixture scalar and SIMD code that is still better than scalar-only version, but it's much longer than the previous fully autovectorized one.

## Conclusion

I initially planned to show more snippets, but I think this was enough for a single post. I'm planning to continue with these experiments to show how code that I use in production compiles and possibly how to improve or rethink what you do to make it more likely to be optimized the way you want. I think that the best compiler at the moment is Clang as it's able to autovectorize well written code really easily, however, as the last snippet shows even Clang can be picky about the constructs you use and sometimes it's pure gambling.

In next posts I would like to focus moslty on GCC and Clang as these compilers are not shy to use SIMD. I tried also ICC before publishing this post, but since it produced similar output as MSVC it doesn't deserve my focus at all - one shitty compiler that makes this post longer is enough :)

You can try it yourself in Compiler Exporer.

## Update

I reported a GCC Bug #87105 and clang bug #38705 as I think fixing these would help other code-bases as well.