irrMath.h

// Copyright (C) 2002-2012 Nikolaus Gebhardt
// This file is part of the "Irrlicht Engine".
// For conditions of distribution and use, see copyright notice in irrlicht.h
 
#ifndef __IRR_MATH_H_INCLUDED__
#define __IRR_MATH_H_INCLUDED__
 
#include "IrrCompileConfig.h"
#include "irrTypes.h"
#include <math.h>
#include <float.h>
#include <stdlib.h> // for abs() etc.
#include <limits.h> // For INT_MAX / UINT_MAX
 
#if defined(_IRR_SOLARIS_PLATFORM_) || defined(__BORLANDC__) || defined (__BCPLUSPLUS__)
    #define sqrtf(X) (irr::f32)sqrt((irr::f64)(X))
    #define sinf(X) (irr::f32)sin((irr::f64)(X))
    #define cosf(X) (irr::f32)cos((irr::f64)(X))
    #define asinf(X) (irr::f32)asin((irr::f64)(X))
    #define acosf(X) (irr::f32)acos((irr::f64)(X))
    #define atan2f(X,Y) (irr::f32)atan2((irr::f64)(X),(irr::f64)(Y))
    #define ceilf(X) (irr::f32)ceil((irr::f64)(X))
    #define floorf(X) (irr::f32)floor((irr::f64)(X))
    #define powf(X,Y) (irr::f32)pow((irr::f64)(X),(irr::f64)(Y))
    #define fmodf(X,Y) (irr::f32)fmod((irr::f64)(X),(irr::f64)(Y))
    #define fabsf(X) (irr::f32)fabs((irr::f64)(X))
    #define logf(X) (irr::f32)log((irr::f64)(X))
#endif
 
#ifndef FLT_MAX
#define FLT_MAX 3.402823466E+38F
#endif
 
#ifndef FLT_MIN
#define FLT_MIN 1.17549435e-38F
#endif
 
namespace irr
{
namespace core
{

 
    const s32 ROUNDING_ERROR_S32 = 0;
#ifdef __IRR_HAS_S64
    const s64 ROUNDING_ERROR_S64 = 0;
#endif
    const f32 ROUNDING_ERROR_f32 = 0.000001f;
    const f64 ROUNDING_ERROR_f64 = 0.00000001;
 
#ifdef PI // make sure we don't collide with a define
#undef PI
#endif
    const f32 PI = 3.14159265359f;

    const f32 RECIPROCAL_PI = 1.0f/PI;

    const f32 HALF_PI = PI/2.0f;
 
#ifdef PI64 // make sure we don't collide with a define
#undef PI64
#endif
    const f64 PI64 = 3.1415926535897932384626433832795028841971693993751;

    const f64 RECIPROCAL_PI64 = 1.0/PI64;

    const f32 DEGTORAD = PI / 180.0f;

    const f32 RADTODEG   = 180.0f / PI;

    const f64 DEGTORAD64 = PI64 / 180.0;

    const f64 RADTODEG64 = 180.0 / PI64;


    inline f32 radToDeg(f32 radians)
    {
        return RADTODEG * radians;
    }


    inline f64 radToDeg(f64 radians)
    {
        return RADTODEG64 * radians;
    }


    inline f32 degToRad(f32 degrees)
    {
        return DEGTORAD * degrees;
    }


    inline f64 degToRad(f64 degrees)
    {
        return DEGTORAD64 * degrees;
    }

    template<class T>
    inline const T& min_(const T& a, const T& b)
    {
        return a < b ? a : b;
    }

    template<class T>
    inline const T& min_(const T& a, const T& b, const T& c)
    {
        return a < b ? min_(a, c) : min_(b, c);
    }

    template<class T>
    inline const T& max_(const T& a, const T& b)
    {
        return a < b ? b : a;
    }

    template<class T>
    inline const T& max_(const T& a, const T& b, const T& c)
    {
        return a < b ? max_(b, c) : max_(a, c);
    }

    template<class T>
    inline T abs_(const T& a)
    {
        return a < (T)0 ? -a : a;
    }

    template<class T>
    inline T lerp(const T& a, const T& b, const f32 t)
    {
        return (T)(a*(1.f-t)) + (b*t);
    }

    template <class T>
    inline const T clamp (const T& value, const T& low, const T& high)
    {
        return min_ (max_(value,low), high);
    }

    // Note: We use the same trick as boost and use two template arguments to
    // avoid ambiguity when swapping objects of an Irrlicht type that has not
    // it's own swap overload. Otherwise we get conflicts with some compilers
    // in combination with stl.
    template <class T1, class T2>
    inline void swap(T1& a, T2& b)
    {
        T1 c(a);
        a = b;
        b = c;
    }

    inline bool equals(const f64 a, const f64 b, const f64 tolerance = ROUNDING_ERROR_f64)
    {
        return (a + tolerance >= b) && (a - tolerance <= b);
    }

    inline bool equals(const f32 a, const f32 b, const f32 tolerance = ROUNDING_ERROR_f32)
    {
        return (a + tolerance >= b) && (a - tolerance <= b);
    }
 
    union FloatIntUnion32
    {
        FloatIntUnion32(float f1 = 0.0f) : f(f1) {}
        // Portable sign-extraction
        bool sign() const { return (i >> 31) != 0; }
 
        irr::s32 i;
        irr::f32 f;
    };

    //\result true when numbers have a ULP <= maxUlpDiff AND have the same sign.
    inline bool equalsByUlp(f32 a, f32 b, int maxUlpDiff)
    {
        // Based on the ideas and code from Bruce Dawson on
        // http://www.altdevblogaday.com/2012/02/22/comparing-floating-point-numbers-2012-edition/
        // When floats are interpreted as integers the two nearest possible float numbers differ just
        // by one integer number. Also works the other way round, an integer of 1 interpreted as float
        // is for example the smallest possible float number.
 
        FloatIntUnion32 fa(a);
        FloatIntUnion32 fb(b);
 
        // Different signs, we could maybe get difference to 0, but so close to 0 using epsilons is better.
        if ( fa.sign() != fb.sign() )
        {
            // Check for equality to make sure +0==-0
            if (fa.i == fb.i)
                return true;
            return false;
        }
 
        // Find the difference in ULPs.
        int ulpsDiff = abs_(fa.i- fb.i);
        if (ulpsDiff <= maxUlpDiff)
            return true;
 
        return false;
    }
 
#if 0
    inline bool equals(const s32 a, const s32 b)
    {
        return (a == b);
    }

    inline bool equals(const u32 a, const u32 b)
    {
        return (a == b);
    }
#endif
    inline bool equals(const s32 a, const s32 b, const s32 tolerance = ROUNDING_ERROR_S32)
    {
        return (a + tolerance >= b) && (a - tolerance <= b);
    }

    inline bool equals(const u32 a, const u32 b, const s32 tolerance = ROUNDING_ERROR_S32)
    {
        return (a + tolerance >= b) && (a - tolerance <= b);
    }
 
#ifdef __IRR_HAS_S64
    inline bool equals(const s64 a, const s64 b, const s64 tolerance = ROUNDING_ERROR_S64)
    {
        return (a + tolerance >= b) && (a - tolerance <= b);
    }
#endif

    inline bool iszero(const f64 a, const f64 tolerance = ROUNDING_ERROR_f64)
    {
        return fabs(a) <= tolerance;
    }

    inline bool iszero(const f32 a, const f32 tolerance = ROUNDING_ERROR_f32)
    {
        return fabsf(a) <= tolerance;
    }

    inline bool isnotzero(const f32 a, const f32 tolerance = ROUNDING_ERROR_f32)
    {
        return fabsf(a) > tolerance;
    }

    inline bool iszero(const s32 a, const s32 tolerance = 0)
    {
        return ( a & 0x7ffffff ) <= tolerance;
    }

    inline bool iszero(const u32 a, const u32 tolerance = 0)
    {
        return a <= tolerance;
    }
 
#ifdef __IRR_HAS_S64
    inline bool iszero(const s64 a, const s64 tolerance = 0)
    {
        return abs_(a) <= tolerance;
    }
#endif
 
    inline s32 s32_min(s32 a, s32 b)
    {
        const s32 mask = (a - b) >> 31;
        return (a & mask) | (b & ~mask);
    }
 
    inline s32 s32_max(s32 a, s32 b)
    {
        const s32 mask = (a - b) >> 31;
        return (b & mask) | (a & ~mask);
    }
 
    inline s32 s32_clamp (s32 value, s32 low, s32 high)
    {
        return s32_min(s32_max(value,low), high);
    }
 
    /*
        float IEEE-754 bit represenation
 
        0      0x00000000
        1.0    0x3f800000
        0.5    0x3f000000
        3      0x40400000
        +inf   0x7f800000
        -inf   0xff800000
        +NaN   0x7fc00000 or 0x7ff00000
        in general: number = (sign ? -1:1) * 2^(exponent) * 1.(mantissa bits)
    */
 
    typedef union { u32 u; s32 s; f32 f; } inttofloat;
 
    #define F32_AS_S32(f)       (*((s32 *) &(f)))
    #define F32_AS_U32(f)       (*((u32 *) &(f)))
    #define F32_AS_U32_POINTER(f)   ( ((u32 *) &(f)))
 
    #define F32_VALUE_0     0x00000000
    #define F32_VALUE_1     0x3f800000
    #define F32_SIGN_BIT        0x80000000U
    #define F32_EXPON_MANTISSA  0x7FFFFFFFU

#ifdef IRRLICHT_FAST_MATH
    #define IR(x)           ((u32&)(x))
#else
    inline u32 IR(f32 x) {inttofloat tmp; tmp.f=x; return tmp.u;}
#endif

    #define AIR(x)          (IR(x)&0x7fffffff)

#ifdef IRRLICHT_FAST_MATH
    #define FR(x)           ((f32&)(x))
#else
    inline f32 FR(u32 x) {inttofloat tmp; tmp.u=x; return tmp.f;}
    inline f32 FR(s32 x) {inttofloat tmp; tmp.s=x; return tmp.f;}
#endif

    #define IEEE_1_0        0x3f800000
    #define IEEE_255_0      0x437f0000
 
#ifdef IRRLICHT_FAST_MATH
    #define F32_LOWER_0(f)      (F32_AS_U32(f) >  F32_SIGN_BIT)
    #define F32_LOWER_EQUAL_0(f)    (F32_AS_S32(f) <= F32_VALUE_0)
    #define F32_GREATER_0(f)    (F32_AS_S32(f) >  F32_VALUE_0)
    #define F32_GREATER_EQUAL_0(f)  (F32_AS_U32(f) <= F32_SIGN_BIT)
    #define F32_EQUAL_1(f)      (F32_AS_U32(f) == F32_VALUE_1)
    #define F32_EQUAL_0(f)      ( (F32_AS_U32(f) & F32_EXPON_MANTISSA ) == F32_VALUE_0)
 
    // only same sign
    #define F32_A_GREATER_B(a,b)    (F32_AS_S32((a)) > F32_AS_S32((b)))
 
#else
 
    #define F32_LOWER_0(n)      ((n) <  0.0f)
    #define F32_LOWER_EQUAL_0(n)    ((n) <= 0.0f)
    #define F32_GREATER_0(n)    ((n) >  0.0f)
    #define F32_GREATER_EQUAL_0(n)  ((n) >= 0.0f)
    #define F32_EQUAL_1(n)      ((n) == 1.0f)
    #define F32_EQUAL_0(n)      ((n) == 0.0f)
    #define F32_A_GREATER_B(a,b)    ((a) > (b))
#endif
 
 
#ifndef REALINLINE
    #ifdef _MSC_VER
        #define REALINLINE __forceinline
    #else
        #define REALINLINE inline
    #endif
#endif
 
#if defined(__BORLANDC__) || defined (__BCPLUSPLUS__)
 
    // 8-bit bools in borland builder

    REALINLINE u32 if_c_a_else_b ( const c8 condition, const u32 a, const u32 b )
    {
        return ( ( -condition >> 7 ) & ( a ^ b ) ) ^ b;
    }

    REALINLINE u32 if_c_a_else_0 ( const c8 condition, const u32 a )
    {
        return ( -condition >> 31 ) & a;
    }
#else

    REALINLINE u32 if_c_a_else_b ( const s32 condition, const u32 a, const u32 b )
    {
        return ( ( -condition >> 31 ) & ( a ^ b ) ) ^ b;
    }

    REALINLINE u16 if_c_a_else_b ( const s16 condition, const u16 a, const u16 b )
    {
        return ( ( -condition >> 15 ) & ( a ^ b ) ) ^ b;
    }

    REALINLINE u32 if_c_a_else_0 ( const s32 condition, const u32 a )
    {
        return ( -condition >> 31 ) & a;
    }
#endif
 
    /*
        if (condition) state |= m; else state &= ~m;
    */
    REALINLINE void setbit_cond ( u32 &state, s32 condition, u32 mask )
    {
        // 0, or any postive to mask
        //s32 conmask = -condition >> 31;
        state ^= ( ( -condition >> 31 ) ^ state ) & mask;
    }
 
    inline f32 round_( f32 x )
    {
        return floorf( x + 0.5f );
    }
 
    REALINLINE void clearFPUException ()
    {
#ifdef IRRLICHT_FAST_MATH
        return;
    #ifdef feclearexcept
        feclearexcept(FE_ALL_EXCEPT);
    #elif defined(_MSC_VER)
        __asm fnclex;
    #elif defined(__GNUC__) && defined(__x86__)
        __asm__ __volatile__ ("fclex \n\t");
    #endif
#endif
    }
 
    // calculate: sqrt ( x )
    REALINLINE f32 squareroot(const f32 f)
    {
        return sqrtf(f);
    }
 
    // calculate: sqrt ( x )
    REALINLINE f64 squareroot(const f64 f)
    {
        return sqrt(f);
    }
 
    // calculate: sqrt ( x )
    REALINLINE s32 squareroot(const s32 f)
    {
        return static_cast<s32>(squareroot(static_cast<f32>(f)));
    }
 
#ifdef __IRR_HAS_S64
    // calculate: sqrt ( x )
    REALINLINE s64 squareroot(const s64 f)
    {
        return static_cast<s64>(squareroot(static_cast<f64>(f)));
    }
#endif
 
    // calculate: 1 / sqrt ( x )
    REALINLINE f64 reciprocal_squareroot(const f64 x)
    {
        return 1.0 / sqrt(x);
    }
 
    // calculate: 1 / sqrtf ( x )
    REALINLINE f32 reciprocal_squareroot(const f32 f)
    {
#if defined ( IRRLICHT_FAST_MATH )
    #if defined(_MSC_VER)
        // SSE reciprocal square root estimate, accurate to 12 significant
        // bits of the mantissa
        f32 recsqrt;
        __asm rsqrtss xmm0, f           // xmm0 = rsqrtss(f)
        __asm movss recsqrt, xmm0       // return xmm0
        return recsqrt;
 
/*
        // comes from Nvidia
        u32 tmp = (u32(IEEE_1_0 << 1) + IEEE_1_0 - *(u32*)&x) >> 1;
        f32 y = *(f32*)&tmp;
        return y * (1.47f - 0.47f * x * y * y);
*/
    #else
        return 1.f / sqrtf(f);
    #endif
#else // no fast math
        return 1.f / sqrtf(f);
#endif
    }
 
    // calculate: 1 / sqrtf( x )
    REALINLINE s32 reciprocal_squareroot(const s32 x)
    {
        return static_cast<s32>(reciprocal_squareroot(static_cast<f32>(x)));
    }
 
    // calculate: 1 / x
    REALINLINE f32 reciprocal( const f32 f )
    {
#if defined (IRRLICHT_FAST_MATH)
 
        // SSE Newton-Raphson reciprocal estimate, accurate to 23 significant
        // bi ts of the mantissa
        // One Newtown-Raphson Iteration:
        // f(i+1) = 2 * rcpss(f) - f * rcpss(f) * rcpss(f)
#if defined(_MSC_VER)               
        f32 rec;
        __asm rcpss xmm0, f               // xmm0 = rcpss(f)
        __asm movss xmm1, f               // xmm1 = f
        __asm mulss xmm1, xmm0            // xmm1 = f * rcpss(f)
        __asm mulss xmm1, xmm0            // xmm2 = f * rcpss(f) * rcpss(f)
        __asm addss xmm0, xmm0            // xmm0 = 2 * rcpss(f)
        __asm subss xmm0, xmm1            // xmm0 = 2 * rcpss(f)
                                          //        - f * rcpss(f) * rcpss(f)
        __asm movss rec, xmm0             // return xmm0
        return rec;
#else // no support yet for other compilers
        return 1.f / f;
#endif
        // instead set f to a high value to get a return value near zero..
        // -1000000000000.f.. is use minus to stay negative..
        // must test's here (plane.normal dot anything ) checks on <= 0.f
        //u32 x = (-(AIR(f) != 0 ) >> 31 ) & ( IR(f) ^ 0xd368d4a5 ) ^ 0xd368d4a5;
        //return 1.f / FR ( x );
 
#else // no fast math
        return 1.f / f;
#endif
    }
 
    // calculate: 1 / x
    REALINLINE f64 reciprocal ( const f64 f )
    {
        return 1.0 / f;
    }
 
 
    // calculate: 1 / x, low precision allowed
    REALINLINE f32 reciprocal_approxim ( const f32 f )
    {
#if defined( IRRLICHT_FAST_MATH)
 
        // SSE Newton-Raphson reciprocal estimate, accurate to 23 significant
        // bi ts of the mantissa
        // One Newtown-Raphson Iteration:
        // f(i+1) = 2 * rcpss(f) - f * rcpss(f) * rcpss(f)
#if defined(_MSC_VER)       
        f32 rec;
        __asm rcpss xmm0, f               // xmm0 = rcpss(f)
        __asm movss xmm1, f               // xmm1 = f
        __asm mulss xmm1, xmm0            // xmm1 = f * rcpss(f)
        __asm mulss xmm1, xmm0            // xmm2 = f * rcpss(f) * rcpss(f)
        __asm addss xmm0, xmm0            // xmm0 = 2 * rcpss(f)
        __asm subss xmm0, xmm1            // xmm0 = 2 * rcpss(f)
                                          //        - f * rcpss(f) * rcpss(f)
        __asm movss rec, xmm0             // return xmm0
        return rec;
#else // no support yet for other compilers
        return 1.f / f;
#endif
 
/*
        // SSE reciprocal estimate, accurate to 12 significant bits of
        f32 rec;
        __asm rcpss xmm0, f             // xmm0 = rcpss(f)
        __asm movss rec , xmm0          // return xmm0
        return rec;
*/
/*
        register u32 x = 0x7F000000 - IR ( p );
        const f32 r = FR ( x );
        return r * (2.0f - p * r);
*/
#else // no fast math
        return 1.f / f;
#endif
    }
 
 
    REALINLINE s32 floor32(f32 x)
    {
#ifdef IRRLICHT_FAST_MATH
        const f32 h = 0.5f;
 
        s32 t;
 
#if defined(_MSC_VER)
        __asm
        {
            fld x
            fsub    h
            fistp   t
        }
#elif defined(__GNUC__)
        __asm__ __volatile__ (
            "fsub %2 \n\t"
            "fistpl %0"
            : "=m" (t)
            : "t" (x), "f" (h)
            : "st"
            );
#else
        return (s32) floorf ( x );
#endif
        return t;
#else // no fast math
        return (s32) floorf ( x );
#endif
    }
 
 
    REALINLINE s32 ceil32 ( f32 x )
    {
#ifdef IRRLICHT_FAST_MATH
        const f32 h = 0.5f;
 
        s32 t;
 
#if defined(_MSC_VER)
        __asm
        {
            fld x
            fadd    h
            fistp   t
        }
#elif defined(__GNUC__)
        __asm__ __volatile__ (
            "fadd %2 \n\t"
            "fistpl %0 \n\t"
            : "=m"(t)
            : "t"(x), "f"(h)
            : "st"
            );
#else
        return (s32) ceilf ( x );
#endif
        return t;
#else // not fast math
        return (s32) ceilf ( x );
#endif
    }
 
 
 
    REALINLINE s32 round32(f32 x)
    {
#if defined(IRRLICHT_FAST_MATH)
        s32 t;
 
#if defined(_MSC_VER)
        __asm
        {
            fld   x
            fistp t
        }
#elif defined(__GNUC__)
        __asm__ __volatile__ (
            "fistpl %0 \n\t"
            : "=m"(t)
            : "t"(x)
            : "st"
            );
#else
        return (s32) round_(x);
#endif
        return t;
#else // no fast math
        return (s32) round_(x);
#endif
    }
 
    inline f32 f32_max3(const f32 a, const f32 b, const f32 c)
    {
        return a > b ? (a > c ? a : c) : (b > c ? b : c);
    }
 
    inline f32 f32_min3(const f32 a, const f32 b, const f32 c)
    {
        return a < b ? (a < c ? a : c) : (b < c ? b : c);
    }
 
    inline f32 fract ( f32 x )
    {
        return x - floorf ( x );
    }
 
} // end namespace core
} // end namespace irr
 
#ifndef IRRLICHT_FAST_MATH
    using irr::core::IR;
    using irr::core::FR;
#endif
 
#endif