tracy/examples/ToyPathTracer/Source/Maths.cpp

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#include "Maths.h"
#include <stdlib.h>
#include <stdint.h>
static uint32_t XorShift32(uint32_t& state)
{
uint32_t x = state;
x ^= x << 13;
x ^= x >> 17;
x ^= x << 15;
state = x;
return x;
}
float RandomFloat01(uint32_t& state)
{
return (XorShift32(state) & 0xFFFFFF) / 16777216.0f;
}
float3 RandomInUnitDisk(uint32_t& state)
{
float3 p;
do
{
p = 2.0 * float3(RandomFloat01(state),RandomFloat01(state),0) - float3(1,1,0);
} while (dot(p,p) >= 1.0);
return p;
}
float3 RandomInUnitSphere(uint32_t& state)
{
float3 p;
do {
p = 2.0*float3(RandomFloat01(state),RandomFloat01(state),RandomFloat01(state)) - float3(1,1,1);
} while (sqLength(p) >= 1.0);
return p;
}
float3 RandomUnitVector(uint32_t& state)
{
float z = RandomFloat01(state) * 2.0f - 1.0f;
float a = RandomFloat01(state) * 2.0f * kPI;
float r = sqrtf(1.0f - z * z);
float x = r * cosf(a);
float y = r * sinf(a);
return float3(x, y, z);
}
int HitSpheres(const Ray& r, const SpheresSoA& spheres, float tMin, float tMax, Hit& outHit)
{
#if DO_HIT_SPHERES_SIMD
float4 hitT = float4(tMax);
#if USE_NEON
int32x4_t id = vdupq_n_s32(-1);
#else
__m128i id = _mm_set1_epi32(-1);
#endif
#if DO_FLOAT3_WITH_SIMD && !USE_NEON
float4 rOrigX = SHUFFLE4(r.orig, 0, 0, 0, 0);
float4 rOrigY = SHUFFLE4(r.orig, 1, 1, 1, 1);
float4 rOrigZ = SHUFFLE4(r.orig, 2, 2, 2, 2);
float4 rDirX = SHUFFLE4(r.dir, 0, 0, 0, 0);
float4 rDirY = SHUFFLE4(r.dir, 1, 1, 1, 1);
float4 rDirZ = SHUFFLE4(r.dir, 2, 2, 2, 2);
#elif DO_FLOAT3_WITH_SIMD
float4 rOrigX = splatX(r.orig.m);
float4 rOrigY = splatY(r.orig.m);
float4 rOrigZ = splatZ(r.orig.m);
float4 rDirX = splatX(r.dir.m);
float4 rDirY = splatY(r.dir.m);
float4 rDirZ = splatZ(r.dir.m);
#else
float4 rOrigX = float4(r.orig.x);
float4 rOrigY = float4(r.orig.y);
float4 rOrigZ = float4(r.orig.z);
float4 rDirX = float4(r.dir.x);
float4 rDirY = float4(r.dir.y);
float4 rDirZ = float4(r.dir.z);
#endif
float4 tMin4 = float4(tMin);
#if USE_NEON
int32x4_t curId = vcombine_u32(vcreate_u32(0ULL | (1ULL<<32)), vcreate_u32(2ULL | (3ULL<<32)));
#else
__m128i curId = _mm_set_epi32(3, 2, 1, 0);
#endif
// process 4 spheres at once
for (int i = 0; i < spheres.simdCount; i += kSimdWidth)
{
// load data for 4 spheres
float4 sCenterX = float4(spheres.centerX + i);
float4 sCenterY = float4(spheres.centerY + i);
float4 sCenterZ = float4(spheres.centerZ + i);
float4 sSqRadius = float4(spheres.sqRadius + i);
// note: we flip this vector and calculate -b (nb) since that happens to be slightly preferable computationally
float4 coX = sCenterX - rOrigX;
float4 coY = sCenterY - rOrigY;
float4 coZ = sCenterZ - rOrigZ;
float4 nb = coX * rDirX + coY * rDirY + coZ * rDirZ;
float4 c = coX * coX + coY * coY + coZ * coZ - sSqRadius;
float4 discr = nb * nb - c;
bool4 discrPos = discr > float4(0.0f);
// if ray hits any of the 4 spheres
if (any(discrPos))
{
float4 discrSq = sqrtf(discr);
// ray could hit spheres at t0 & t1
float4 t0 = nb - discrSq;
float4 t1 = nb + discrSq;
float4 t = select(t1, t0, t0 > tMin4); // if t0 is above min, take it (since it's the earlier hit); else try t1.
bool4 msk = discrPos & (t > tMin4) & (t < hitT);
// if hit, take it
id = select(id, curId, msk);
hitT = select(hitT, t, msk);
}
#if USE_NEON
curId = vaddq_s32(curId, vdupq_n_s32(kSimdWidth));
#else
curId = _mm_add_epi32(curId, _mm_set1_epi32(kSimdWidth));
#endif
}
// now we have up to 4 hits, find and return closest one
float minT = hmin(hitT);
if (minT < tMax) // any actual hits?
{
int minMask = mask(hitT == float4(minT));
if (minMask != 0)
{
int id_scalar[4];
float hitT_scalar[4];
#if USE_NEON
vst1q_s32(id_scalar, id);
vst1q_f32(hitT_scalar, hitT.m);
#else
_mm_storeu_si128((__m128i *)id_scalar, id);
_mm_storeu_ps(hitT_scalar, hitT.m);
#endif
// In general, you would do this with a bit scan (first set/trailing zero count).
// But who cares, it's only 16 options.
static const int laneId[16] =
{
0, 0, 1, 0, // 00xx
2, 0, 1, 0, // 01xx
3, 0, 1, 0, // 10xx
2, 0, 1, 0, // 11xx
};
int lane = laneId[minMask];
int hitId = id_scalar[lane];
float finalHitT = hitT_scalar[lane];
outHit.pos = r.pointAt(finalHitT);
outHit.normal = (outHit.pos - float3(spheres.centerX[hitId], spheres.centerY[hitId], spheres.centerZ[hitId])) * spheres.invRadius[hitId];
outHit.t = finalHitT;
return hitId;
}
}
return -1;
#else // #if DO_HIT_SPHERES_SIMD
float hitT = tMax;
int id = -1;
for (int i = 0; i < spheres.count; ++i)
{
float coX = spheres.centerX[i] - r.orig.getX();
float coY = spheres.centerY[i] - r.orig.getY();
float coZ = spheres.centerZ[i] - r.orig.getZ();
float nb = coX * r.dir.getX() + coY * r.dir.getY() + coZ * r.dir.getZ();
float c = coX * coX + coY * coY + coZ * coZ - spheres.sqRadius[i];
float discr = nb * nb - c;
if (discr > 0)
{
float discrSq = sqrtf(discr);
// Try earlier t
float t = nb - discrSq;
if (t <= tMin) // before min, try later t!
t = nb + discrSq;
if (t > tMin && t < hitT)
{
id = i;
hitT = t;
}
}
}
if (id != -1)
{
outHit.pos = r.pointAt(hitT);
outHit.normal = (outHit.pos - float3(spheres.centerX[id], spheres.centerY[id], spheres.centerZ[id])) * spheres.invRadius[id];
outHit.t = hitT;
return id;
}
else
return -1;
#endif // #else of #if DO_HIT_SPHERES_SIMD
}