ai_math.h

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// Copyright 2021 Autodesk, Inc.  All rights reserved.
//
// Use of this software is subject to the terms of the Autodesk license
// agreement provided at the time of installation or download, or which
// otherwise accompanies this software in either electronic or hard copy form.
 
#pragma once
#include "ai_api.h"
#include "ai_constants.h"
#include <cmath>
#include <cstdlib> // for int abs(int)
#include <cstring> // for memcpy
 
template <typename T>
AI_DEVICE inline constexpr T AiMin(T a, T b)
{
#ifdef AI_CPU_COMPILER
   return (a < b) ? a : b;
#else
   return min(a,b);
#endif
}
 
template <typename T>
AI_DEVICE inline constexpr T AiMax(T a, T b)
{
#ifdef AI_CPU_COMPILER
   return (a > b) ? a : b;
#else
   return max(a,b);
#endif
}
 
template <typename T>
AI_DEVICE inline constexpr T AiMin(T a, T b, T c)
{
   return AiMin(AiMin(a, b), c);
}
 
template <typename T>
AI_DEVICE inline constexpr T AiMax(T a, T b, T c)
{
   return AiMax(AiMax(a, b), c);
}
 
template <typename T>
AI_DEVICE inline constexpr T AiMin(T a, T b, T c, T d)
{
   return AiMin(AiMin(a, b), AiMin(c, d));
}
 
template <typename T>
AI_DEVICE inline constexpr T AiMax(T a, T b, T c, T d)
{
   return AiMax(AiMax(a, b), AiMax(c, d));
}
 
template <typename T>
AI_DEVICE inline constexpr T AiSqr(T a)
{
   return (a * a);
}
 
template <typename T>
AI_DEVICE inline constexpr T AiClamp(T v, T lo, T hi)
{
   return AiMax(lo, AiMin(v, hi));
}
 
template <typename T>
AI_DEVICE inline constexpr T AiSafeAcos(T x)
{
   return (x >= 1) ? 0 : ((x <= -1) ? static_cast<T>(AI_PI) : std::acos(x));
}
 
template <typename T1, typename T2>
AI_DEVICE inline constexpr T1 AiLerp(T2 t, T1 a, T1 b)
{
   return ((T2(1) - t) * a) + (b * t);
}
 
template <typename T>
AI_DEVICE inline constexpr T AiHerp01(T t)
{
   return t * t * ((T) 3 - (T) 2 * t);
}
 
template <typename T1, typename T2>
AI_DEVICE inline constexpr T1 AiHerp(T2 t, T1 a, T1 b)
{
   return AiLerp(AiHerp01(t), a, b);
}
 
template <typename T1, typename T2>
AI_DEVICE inline T1 AiBiLerp(T2 s, T2 t, T1 c00, T1 c10, T1 c01, T1 c11)
{
   T1 c0x = AiLerp(t, c00, c01);
   T1 c1x = AiLerp(t, c10, c11);
   return AiLerp(s, c0x, c1x);
}
 
template <typename T>
AI_DEVICE inline constexpr T AiBias(T a, T b)
{
   return (a > 0) ? ((b == (T) 0.5) ? a : std::pow(a, (std::log(b) * (T)-1.442695041))) : 0;
}
 
template <typename T>
AI_DEVICE inline constexpr T AiGain(T a, T g)
{
   return (g == (T) 0.5) ? a : ((a < (T) 0.5) ? (AiBias(a + a, (T) 1 - g) * (T) 0.5) : ((T) 1 - AiBias((T) 2 - a - a, (T) 1 - g) * (T) 0.5));
}
 
template <typename T>
AI_DEVICE inline constexpr T AiStep(T x, T e)
{
   return (x < e) ? (T) 0 : (T) 1;
}
 
template <typename T>
AI_DEVICE inline constexpr T AiFilterStep(T x, T e, T w)
{
   return AiClamp((x + w * (T) 0.5 - e) / w, (T) 0, (T) 1);
}
#ifdef AI_GPU_COMPILER
AI_DEVICE inline float AiFilterStep(float x, float e, float w)
{
   return __saturatef((x + w * 0.5f - e) / w);
}
#endif
 
 
template <typename T>
AI_DEVICE inline constexpr T AiLinearStep(T lo, T hi, T t)
{
   return AiClamp((t - lo) / (hi - lo), (T) 0, (T) 1);
}
#ifdef AI_GPU_COMPILER
AI_DEVICE inline float AiLinearStep(float lo, float hi, float t)
{
   return __saturatef((t - lo) / (hi - lo));
}
#endif
 
template <typename T>
AI_DEVICE inline constexpr T AiSmoothStep(T e0, T e1, T t)
{
   return AiHerp01(AiClamp((t - e0) / (e1 - e0), (T) 0, (T) 1));
}
#ifdef AI_GPU_COMPILER
AI_DEVICE inline float AiSmoothStep(float e0, float e1, float t)
{
   return AiHerp01(__saturatef((t - e0) / (e1 - e0)));
}
#endif
 
template <typename OUT_T, typename IN_T>
AI_DEVICE inline OUT_T reinterpret_type(const IN_T in)
{
   OUT_T out;
   std::memcpy(&out, &in, sizeof(OUT_T));
   return out;
}
 
AI_API AI_DEVICE AI_CONST bool AiIsFinite(float x);
AI_API AI_CONST float AiFastExp(float x);
AI_API AI_DEVICE AI_CONST float AiFastPow(float x, float y);
 
/*\}*/