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284 lines
7.2 KiB
C++
284 lines
7.2 KiB
C++
// This code is in the public domain -- castanyo@yahoo.es
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#pragma once
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#ifndef NV_MATH_H
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#define NV_MATH_H
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#include "nvcore/nvcore.h"
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#include "nvcore/Debug.h" // nvDebugCheck
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#include "nvcore/Utils.h" // max, clamp
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#include <math.h>
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#if NV_OS_WIN32 || NV_OS_XBOX
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#include <float.h> // finite, isnan
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#endif
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// Function linkage
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#if NVMATH_SHARED
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#ifdef NVMATH_EXPORTS
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#define NVMATH_API DLL_EXPORT
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#define NVMATH_CLASS DLL_EXPORT_CLASS
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#else
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#define NVMATH_API DLL_IMPORT
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#define NVMATH_CLASS DLL_IMPORT
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#endif
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#else // NVMATH_SHARED
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#define NVMATH_API
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#define NVMATH_CLASS
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#endif // NVMATH_SHARED
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#ifndef PI
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#define PI float(3.1415926535897932384626433833)
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#endif
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#define NV_EPSILON (0.0001f)
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#define NV_NORMAL_EPSILON (0.001f)
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/*
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#define SQ(r) ((r)*(r))
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#define SIGN_BITMASK 0x80000000
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/// Integer representation of a floating-point value.
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#define IR(x) ((uint32 &)(x))
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/// Absolute integer representation of a floating-point value
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#define AIR(x) (IR(x) & 0x7fffffff)
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/// Floating-point representation of an integer value.
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#define FR(x) ((float&)(x))
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/// Integer-based comparison of a floating point value.
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/// Don't use it blindly, it can be faster or slower than the FPU comparison, depends on the context.
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#define IS_NEGATIVE_FLOAT(x) (IR(x)&SIGN_BITMASK)
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*/
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extern "C" inline double sqrt_assert(const double f)
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{
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nvDebugCheck(f >= 0.0f);
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return sqrt(f);
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}
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inline float sqrtf_assert(const float f)
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{
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nvDebugCheck(f >= 0.0f);
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return sqrtf(f);
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}
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extern "C" inline double acos_assert(const double f)
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{
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nvDebugCheck(f >= -1.0f && f <= 1.0f);
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return acos(f);
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}
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inline float acosf_assert(const float f)
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{
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nvDebugCheck(f >= -1.0f && f <= 1.0f);
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return acosf(f);
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}
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extern "C" inline double asin_assert(const double f)
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{
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nvDebugCheck(f >= -1.0f && f <= 1.0f);
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return asin(f);
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}
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inline float asinf_assert(const float f)
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{
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nvDebugCheck(f >= -1.0f && f <= 1.0f);
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return asinf(f);
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}
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// Replace default functions with asserting ones.
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#define sqrt sqrt_assert
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#define sqrtf sqrtf_assert
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#define acos acos_assert
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#define acosf acosf_assert
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#define asin asin_assert
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#define asinf asinf_assert
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#if NV_CC_MSVC
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NV_FORCEINLINE float log2f(float x)
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{
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nvCheck(x >= 0);
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return logf(x) / logf(2.0f);
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}
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NV_FORCEINLINE float exp2f(float x)
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{
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return powf(2.0f, x);
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}
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#endif
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namespace nv
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{
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inline float toRadian(float degree) { return degree * (PI / 180.0f); }
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inline float toDegree(float radian) { return radian * (180.0f / PI); }
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// Robust floating point comparisons:
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// http://realtimecollisiondetection.net/blog/?p=89
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inline bool equal(const float f0, const float f1, const float epsilon = NV_EPSILON)
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{
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//return fabs(f0-f1) <= epsilon;
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return fabs(f0-f1) <= epsilon * max3(1.0f, fabsf(f0), fabsf(f1));
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}
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inline bool isZero(const float f, const float epsilon = NV_EPSILON)
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{
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return fabs(f) <= epsilon;
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}
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inline bool isFinite(const float f)
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{
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#if NV_OS_WIN32 || NV_OS_XBOX
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return _finite(f) != 0;
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#elif NV_OS_DARWIN || NV_OS_FREEBSD || NV_OS_OPENBSD || NV_OS_ORBIS
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return isfinite(f);
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#elif NV_OS_LINUX
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return finitef(f);
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#else
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# error "isFinite not supported"
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#endif
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//return std::isfinite (f);
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//return finite (f);
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}
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inline bool isNan(const float f)
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{
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#if NV_OS_WIN32 || NV_OS_XBOX
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return _isnan(f) != 0;
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#elif NV_OS_DARWIN || NV_OS_FREEBSD || NV_OS_OPENBSD || NV_OS_ORBIS
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return isnan(f);
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#elif NV_OS_LINUX
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return isnanf(f);
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#else
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# error "isNan not supported"
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#endif
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}
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inline uint log2(uint i)
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{
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uint value = 0;
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while( i >>= 1 ) {
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value++;
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}
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return value;
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}
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inline float lerp(float f0, float f1, float t)
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{
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const float s = 1.0f - t;
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return f0 * s + f1 * t;
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}
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inline float square(float f) { return f * f; }
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inline int square(int i) { return i * i; }
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inline float cube(float f) { return f * f * f; }
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inline int cube(int i) { return i * i * i; }
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// @@ Float to int conversions to be optimized at some point. See:
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// http://cbloomrants.blogspot.com/2009/01/01-17-09-float-to-int.html
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// http://www.stereopsis.com/sree/fpu2006.html
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// http://assemblyrequired.crashworks.org/2009/01/12/why-you-should-never-cast-floats-to-ints/
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// http://chrishecker.com/Miscellaneous_Technical_Articles#Floating_Point
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inline int iround(float f)
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{
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return int(floorf(f + 0.5f));
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}
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inline int ifloor(float f)
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{
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return int(floorf(f));
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}
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inline int iceil(float f)
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{
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return int(ceilf(f));
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}
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inline float frac(float f)
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{
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return f - floor(f);
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}
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inline float floatRound(float f)
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{
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return floorf(f + 0.5f);
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}
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// Eliminates negative zeros from a float array.
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inline void floatCleanup(float * fp, int n)
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{
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for (int i = 0; i < n; i++) {
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//nvDebugCheck(isFinite(fp[i]));
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union { float f; uint32 i; } x = { fp[i] };
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if (x.i == 0x80000000) fp[i] = 0.0f;
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}
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}
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inline float saturate(float f) {
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return clamp(f, 0.0f, 1.0f);
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}
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inline float linearstep(float edge0, float edge1, float x) {
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// Scale, bias and saturate x to 0..1 range
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return saturate((x - edge0) / (edge1 - edge0));
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}
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inline float smoothstep(float edge0, float edge1, float x) {
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x = linearstep(edge0, edge1, x);
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// Evaluate polynomial
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return x*x*(3 - 2*x);
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}
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inline int sign(float a)
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{
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if (a > 0.0f) return 1;
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if (a < 0.0f) return -1;
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return 0;
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}
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// I'm always confused about which quantizer to use. I think we should choose a quantizer based on how the values are expanded later and this is generally using the 'exact endpoints' rule.
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// Quantize a float in the [0,1] range, using exact end points or uniform bins.
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inline float quantizeFloat(float x, uint bits, bool exactEndPoints = true) {
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nvDebugCheck(bits <= 16);
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float range = float(1 << bits);
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if (exactEndPoints) {
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return floorf(x * (range-1) + 0.5f) / (range-1);
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}
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else {
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return (floorf(x * range) + 0.5f) / range;
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}
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}
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union Float754 {
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unsigned int raw;
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float value;
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struct {
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#if NV_BIG_ENDIAN
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unsigned int negative:1;
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unsigned int biasedexponent:8;
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unsigned int mantissa:23;
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#else
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unsigned int mantissa:23;
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unsigned int biasedexponent:8;
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unsigned int negative:1;
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#endif
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} field;
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};
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// Return the exponent of x ~ Floor(Log2(x))
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inline int floatExponent(float x)
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{
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Float754 f;
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f.value = x;
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return (f.field.biasedexponent - 127);
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}
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} // nv
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#endif // NV_MATH_H
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