#include #include #include #include #include #ifndef _Standard_Stream_HeaderFile #include #endif #ifndef _Standard_OStream_HeaderFile #include #endif #if defined(WNT) && !defined(__CYGWIN32__) && !defined(__MINGW32__) Standard_Real PI = 3.14159265358979324; Standard_Real PI180 = 0.017453292519943296; Standard_Real Standard_PI = 3.14159265358979324; Standard_Real Standard_PI180 = 0.017453292519943296; #else const Standard_Real PI = 3.14159265358979324; const Standard_Real PI180 = 0.017453292519943296; const Standard_Real Standard_PI = 3.14159265358979324; const Standard_Real Standard_PI180 = 0.017453292519943296; #endif Handle_Standard_Type& Standard_Real_Type_() { static Handle_Standard_Type _aType = new Standard_Type("Standard_Real",sizeof(Standard_Real),0,NULL); return _aType; } // ------------------------------------------------------------------ // Hascode : Computes a hascoding value for a given real // ------------------------------------------------------------------ Standard_Integer HashCode(const Standard_Real me, const Standard_Integer Upper) { if (Upper < 1){ Standard_RangeError:: Raise("Try to apply HashCode method with negative or null argument."); } union { Standard_Real R; Standard_Integer I[2]; } U; // U.R = Abs(me); // Treat me = -0.0 ADN 27/11/97 U.R = me ; return HashCode( ( U.I[0] ^ U.I[1] ) , Upper ) ; } // ------------------------------------------------------------------ // ShallowCopy : Makes a copy of a real value // ------------------------------------------------------------------ Standard_Real ShallowCopy (const Standard_Real me) { return me; } //------------------------------------------------------------------- // ACos : Returns the value of the arc cosine of a real //------------------------------------------------------------------- Standard_Real ACos (const Standard_Real Value) { if ( (Value < -1.) || (Value > 1.) ){ Standard_RangeError::Raise(); } return acos(Value); } //------------------------------------------------------------------- // ACosApprox : Returns the approximate value of the arc cosine of a real. // The max error is about 1 degree near Value=0. //------------------------------------------------------------------- inline Standard_Real apx_for_ACosApprox (const Standard_Real x) { return (-0.000007239283986332 + x * (2.000291665285952400 + x * (0.163910606547823220 + x * (0.047654245891495528 - x * (0.005516443930088506 + 0.015098965761299077 * x))))) / sqrt(2*x); } Standard_Real ACosApprox (const Standard_Real Value) { double XX; if (Value < 0.) { XX = 1.+Value; if (XX < RealSmall()) return 0.; return PI - apx_for_ACosApprox(XX); } XX = 1.-Value; if (XX < RealSmall()) return 0.; return apx_for_ACosApprox(XX); // The code above is the same but includes 2 comparisons instead of 3 // Standard_Real xn = 1.+Value; // Standard_Real xp = 1.-Value; // if (xp < RealSmall() || xn < RealSmall()) // return 0.; // if (Value < 0.) // return PI - apx_for_ACosApprox (xn); // return apx_for_ACosApprox (xp); } //------------------------------------------------------------------- // ASin : Returns the value of the arc sine of a real //------------------------------------------------------------------- Standard_Real ASin (const Standard_Real Value) { if ( Value < -1 || Value > 1 ){ Standard_RangeError::Raise(); } return asin(Value); } //------------------------------------------------------------------- // ATan2 : Returns the arc tangent of a real divide by an another real //------------------------------------------------------------------- Standard_Real ATan2 (const Standard_Real Value, const Standard_Real Other) { if ( Value == 0. && Other == 0. ){ Standard_NullValue::Raise(); } return atan2(Value,Other); } //------------------------------------------------------------------- // Sign : Returns |a| if B >= 0; -|a| if b < 0. // from x in the direction y //------------------------------------------------------------------- Standard_Real Sign(const Standard_Real a, const Standard_Real b) { //==== We use the function "nextafter()" fom library "math.h" ============== if (b >= 0.0) { return Abs(a); } else { return (-1.0 * Abs(a)); } } //========================================================================== //===== The special routines for "IEEE" and differents hardwares =========== //========================================================================== union RealMap { double real; unsigned int map[2]; }; //-------------------------------------------------------------------- // HardwareHighBitsOfDouble : // Returns 1 if the low bits are at end. (exemple: decmips and ALPHA ) // Returns 0 if the low bits are at begin. (exemple: sun, sgi, ...) //-------------------------------------------------------------------- static int HardwareHighBitsOfDouble() { RealMap MaxDouble; MaxDouble.real = DBL_MAX; //========================================================= // reperesentation of the max double in IEEE is // "7fef ffff ffff ffff" for the big indiens. // "ffff ffff 7fef ffff" for the littel indiens. //========================================================= if(MaxDouble.map[1] != 0xffffffff){ return 1; } else { return 0; } } //-------------------------------------------------------------------- // HardwareLowBitsOfDouble : // Returns 0 if the low bits are at end. (exemple: decmips ) // Returns 1 if the low bits are at begin. (exemple: sun, sgi, ...) //-------------------------------------------------------------------- static int HardwareLowBitsOfDouble() { RealMap MaxDouble; MaxDouble.real = DBL_MAX; //========================================================= // reperesentation of the max double in IEEE is // "7fef ffff ffff ffff" for the big indiens. // "ffff ffff 7fef ffff" for the littel indiens. //========================================================= if(MaxDouble.map[1] != 0xffffffff){ return 0; } else { return 1; } } static int HighBitsOfDouble = HardwareHighBitsOfDouble(); static int LowBitsOfDouble = HardwareLowBitsOfDouble(); double NextAfter(const double x, const double y) { RealMap res; res.real=x; if (x == 0.0) { return DBL_MIN; } if(x==y) { //========================================= // -oo__________0___________+oo // x=y // The direction is "Null", so there is nothing after //========================================= } else if (((x=0.0)) || ((x>y) && (x<0.0))) { //========================================= // -oo__________0___________+oo // y <- x x -> y // //========================================= if (res.map[LowBitsOfDouble]==0xffffffff) { res.map[LowBitsOfDouble]=0; res.map[HighBitsOfDouble]++; } else { res.map[LowBitsOfDouble]++; } } else { //========================================= // -oo__________0___________+oo // x -> y y <- x // //========================================= if (res.map[LowBitsOfDouble]==0) { if (res.map[HighBitsOfDouble]==0) { res.map[HighBitsOfDouble]=0x80000000; res.map[LowBitsOfDouble]=0x00000001; } else { res.map[LowBitsOfDouble]=0xffffffff; res.map[HighBitsOfDouble]--; } } else { res.map[LowBitsOfDouble]--; } } return res.real; } // ------------------------------------------------------------------ // ShallowDump : Writes a real value // ------------------------------------------------------------------ Standard_EXPORT void ShallowDump(const Standard_Real Value, Standard_OStream& s) { s << Value << " Standard_Real" << "\n"; } //------------------------------------------------------------------- // ATanh : Returns the value of the hyperbolic arc tangent of a real //------------------------------------------------------------------- Standard_Real ATanh(const Standard_Real Value) { if ( (Value <= -1.) || (Value >= 1.) ){ Standard_NumericError::Raise("Illegal agument in ATanh"); cout << "Illegal agument in ATanh" << endl ; } return atanh(Value); } //------------------------------------------------------------------- // ACosh : Returns the hyperbolic Arc cosine of a real //------------------------------------------------------------------- Standard_Real ACosh (const Standard_Real Value) { if ( Value < 1. ){ Standard_NumericError::Raise("Illegal agument in ACosh"); cout << "Illegal agument in ACosh" << endl ; } return acosh(Value); } //------------------------------------------------------------------- // Log : Returns the naturaOPl logarithm of a real //------------------------------------------------------------------- Standard_Real Log (const Standard_Real Value) { if ( Value <= 0. ){ Standard_NumericError::Raise("Illegal agument in Log"); cout << "Illegal agument in Log" << endl ; } return log(Value); } //------------------------------------------------------------------- // Sqrt : Returns the square root of a real //------------------------------------------------------------------- Standard_Real Sqrt (const Standard_Real Value) { if ( Value < 0. ){ Standard_NumericError::Raise("Illegal agument in Sqrt"); cout << "Illegal agument in Sqrt" << endl ; } return sqrt(Value); }