* IDSIA, Lugano, Switzerland
* http://www.inf.ethz.ch/~schraudo/pubs/exp.pdf
*
+ * Base-2 exp, Laurent de Soras
+ * http://www.musicdsp.org/archive.php?classid=5#106
+ *
* Fast log() Function, by Laurent de Soras:
* http://www.flipcode.com/cgi-bin/msg.cgi?showThread=Tip-Fastlogfunction&forum=totd&id=-1
*
+ * Sin, Cos, Tan approximation
+ * http://www.musicdsp.org/showArchiveComment.php?ArchiveID=115
+ *
+ * fast floating point power computation:
+ * http://playstation2-linux.com/download/adam/power.c
*/
/*
#include "fastmath.hxx"
+#define SGD_PI_2 1.57079632679489661923
/**
* This function is on avarage 9 times faster than the system exp() function
return _eco.d;
}
+/*
+ * Linear approx. between 2 integer values of val. Uses 32-bit integers.
+ * Not very efficient but faster than exp()
+ */
+double fast_exp2( const double val )
+{
+ int e;
+ double ret;
+
+ if (val >= 0) {
+ e = int (val);
+ ret = val - (e - 1);
+
+#if BYTE_ORDER == BIG_ENDIAN
+ ((*((int *) &ret)) &= ~(2047 << 20)) += (e + 1023) << 20;
+#else
+ ((*(1 + (int *) &ret)) &= ~(2047 << 20)) += (e + 1023) << 20;
+#endif
+ } else {
+ e = int (val + 1023);
+ ret = val - (e - 1024);
+
+#if BYTE_ORDER == BIG_ENDIAN
+ ((*((int *) &ret)) &= ~(2047 << 20)) += e << 20;
+#else
+ ((*(1 + (int *) &ret)) &= ~(2047 << 20)) += e << 20;
+#endif
+ }
+
+ return ret;
+}
+
+
+/*
+ *
+ */
+float _fast_log2(const float val)
+{
+ float result, tmp;
+ float mp = 0.346607f;
+
+ result = *(int*)&val;
+ result *= 1.0/(1<<23);
+ result = result - 127;
+
+ tmp = result - floor(result);
+ tmp = (tmp - tmp*tmp) * mp;
+ return tmp + result;
+}
+
+float _fast_pow2(const float val)
+{
+ float result;
+
+ float mp = 0.33971f;
+ float tmp = val - floor(val);
+ tmp = (tmp - tmp*tmp) * mp;
+
+ result = val + 127 - tmp;
+ result *= (1<<23);
+ *(int*)&result = (int)result;
+ return result;
+}
+
+
/**
* While we're on the subject, someone might have use for these as well?
}
+
+/*
+ * fastpow(f,n) gives a rather *rough* estimate of a float number f to the
+ * power of an integer number n (y=f^n). It is fast but result can be quite a
+ * bit off, since we directly mess with the floating point exponent.
+ *
+ * Use it only for getting rough estimates of the values and where precision
+ * is not that important.
+ */
+float fast_pow(const float f, const int n)
+{
+ long *lp,l;
+ lp=(long*)(&f);
+ l=*lp;l-=0x3F800000l;l<<=(n-1);l+=0x3F800000l;
+ *lp=l;
+ return f;
+}
+
+float fast_root(const float f, const int n)
+{
+ long *lp,l;
+ lp=(long*)(&f);
+ l=*lp;l-=0x3F800000l;l>>=(n-1);l+=0x3F800000l;
+ *lp=l;
+ return f;
+}
+
+
+/*
+ * Code for approximation of cos, sin, tan and inv sin, etc.
+ * Surprisingly accurate and very usable.
+ *
+ * Domain:
+ * Sin/Cos [0, pi/2]
+ * Tan [0,pi/4]
+ * InvSin/Cos [0, 1]
+ * InvTan [-1, 1]
+ */
+
+float fast_sin(const float val)
+{
+ float fASqr = val*val;
+ float fResult = -2.39e-08f;
+ fResult *= fASqr;
+ fResult += 2.7526e-06f;
+ fResult *= fASqr;
+ fResult -= 1.98409e-04f;
+ fResult *= fASqr;
+ fResult += 8.3333315e-03f;
+ fResult *= fASqr;
+ fResult -= 1.666666664e-01f;
+ fResult *= fASqr;
+ fResult += 1.0f;
+ fResult *= val;
+
+ return fResult;
+}
+
+float fast_cos(const float val)
+{
+ float fASqr = val*val;
+ float fResult = -2.605e-07f;
+ fResult *= fASqr;
+ fResult += 2.47609e-05f;
+ fResult *= fASqr;
+ fResult -= 1.3888397e-03f;
+ fResult *= fASqr;
+ fResult += 4.16666418e-02f;
+ fResult *= fASqr;
+ fResult -= 4.999999963e-01f;
+ fResult *= fASqr;
+ fResult += 1.0f;
+
+ return fResult;
+}
+
+float fast_tan(const float val)
+{
+ float fASqr = val*val;
+ float fResult = 9.5168091e-03f;
+ fResult *= fASqr;
+ fResult += 2.900525e-03f;
+ fResult *= fASqr;
+ fResult += 2.45650893e-02f;
+ fResult *= fASqr;
+ fResult += 5.33740603e-02f;
+ fResult *= fASqr;
+ fResult += 1.333923995e-01f;
+ fResult *= fASqr;
+ fResult += 3.333314036e-01f;
+ fResult *= fASqr;
+ fResult += 1.0f;
+ fResult *= val;
+
+ return fResult;
+
+}
+
+float fast_asin(float val)
+{
+ float fRoot = sqrt(1.0f-val);
+ float fResult = -0.0187293f;
+ fResult *= val;
+ fResult += 0.0742610f;
+ fResult *= val;
+ fResult -= 0.2121144f;
+ fResult *= val;
+ fResult += 1.5707288f;
+ fResult = SGD_PI_2 - fRoot*fResult;
+
+ return fResult;
+}
+
+float fast_acos(float val)
+{
+ float fRoot = sqrt(1.0f-val);
+ float fResult = -0.0187293f;
+ fResult *= val;
+ fResult += 0.0742610f;
+ fResult *= val;
+ fResult -= 0.2121144f;
+ fResult *= val;
+ fResult += 1.5707288f;
+ fResult *= fRoot;
+
+ return fResult;
+}
+
+float fast_atan(float val)
+{
+ float fVSqr = val*val;
+ float fResult = 0.0028662257f;
+ fResult *= fVSqr;
+ fResult -= 0.0161657367f;
+ fResult *= fVSqr;
+ fResult += 0.0429096138f;
+ fResult *= fVSqr;
+ fResult -= 0.0752896400f;
+ fResult *= fVSqr;
+ fResult += 0.1065626393f;
+ fResult *= fVSqr;
+ fResult -= 0.1420889944f;
+ fResult *= fVSqr;
+ fResult += 0.1999355085f;
+ fResult *= fVSqr;
+ fResult -= 0.3333314528f;
+ fResult *= fVSqr;
+ fResult += 1.0f;
+ fResult *= val;
+
+ return fResult;
+}
double fast_exp(double val);
+double fast_exp2(const double val);
+
+float fast_pow(const float val1, const float val2);
+float fast_log2(const float cal);
+float fast_root(const float f, const int n);
+
+float _fast_pow2(const float cal);
+float _fast_log2(const float val);
+
+float fast_sin(const float val);
+float fast_cos(const float val);
+float fast_tan(const float val);
+float fast_asin(const float val);
+float fast_acos(const float val);
+float fast_atan(const float val);
void fast_BSL(float &x, register unsigned long shiftAmount);
void fast_BSR(float &x, register unsigned long shiftAmount);
+
inline float fast_log2 (float val)
{
- int * const exp_ptr = reinterpret_cast <int *> (&val);
- int x = *exp_ptr;
- const int log_2 = ((x >> 23) & 255) - 128;
- x &= ~(255 << 23);
- x += 127 << 23;
- *exp_ptr = x;
+ int * const exp_ptr = reinterpret_cast <int *> (&val);
+ int x = *exp_ptr;
+ const int log_2 = ((x >> 23) & 255) - 128;
+ x &= ~(255 << 23);
+ x += 127 << 23;
+ *exp_ptr = x;
- val = ((-1.0f/3) * val + 2) * val - 2.0f/3; // (1)
+ val = ((-1.0f/3) * val + 2) * val - 2.0f/3; // (1)
- return (val + log_2);
+ return (val + log_2);
}
+
/**
* This function is about 3 times faster than the system log() function
* and has an error of about 0.01%
}
+/**
+ * This function is about twice as fast as the system pow(x,y) function
+ */
+inline float fast_pow(const float val1, const float val2)
+{
+ return _fast_pow2(val2 * _fast_log2(val1));
+}
+
+
+/*
+ * Haven't seen this elsewhere, probably because it is too obvious?
+ * Anyway, these functions are intended for 32-bit floating point numbers
+ * only and should work a bit faster than the regular ones.
+ */
+inline float fast_abs(float f)
+{
+ int i=((*(int*)&f)&0x7fffffff);
+ return (*(float*)&i);
+}
+
+inline float fast_neg(float f)
+{
+ int i=((*(int*)&f)^0x80000000);
+ return (*(float*)&i);
+}
+
+inline int fast_sgn(float f)
+{
+ return 1+(((*(int*)&f)>>31)<<1);
+}
+
#endif // !_SG_FMATH_HXX
projects / simgear.git / commitdiff