/*
* vdtcore_common.h
* Common functions for the vdt routines.
* The basic idea is to exploit Pade polynomials.
* A lot of ideas were inspired by the cephes math library (by Stephen L. Moshier
* moshier@na-net.ornl.gov) as well as actual code for the exp, log, sin, cos,
* tan, asin, acos and atan functions. The Cephes library can be found here:
* http://www.netlib.org/cephes/
*
* Created on: Jun 23, 2012
* Author: Danilo Piparo, Thomas Hauth, Vincenzo Innocente
*/
/*
* VDT is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser Public License for more details.
*
* You should have received a copy of the GNU Lesser Public License
* along with this program. If not, see .
*/
#ifndef VDTCOMMON_H_
#define VDTCOMMON_H_
#include
#include
namespace vdt{
namespace details{
// Constants
const double TWOPI = 2.*M_PI;
const double PI = M_PI;
const double PIO2 = M_PI_2;
const double PIO4 = M_PI_4;
const double ONEOPIO4 = 4./M_PI;
const float TWOPIF = 2.*M_PI;
const float PIF = M_PI;
const float PIO2F = M_PI_2;
const float PIO4F = M_PI_4;
const float ONEOPIO4F = 4./M_PI;
const double MOREBITS = 6.123233995736765886130E-17;
const float MAXNUMF = 3.4028234663852885981170418348451692544e38f;
//------------------------------------------------------------------------------
/// Used to switch between different type of interpretations of the data (64 bits)
union ieee754{
inline ieee754 () {};
inline ieee754 (double thed) {d=thed;};
inline ieee754 (uint64_t thell) {ll=thell;};
inline ieee754 (float thef) {f[0]=thef;};
inline ieee754 (uint32_t thei) {i[0]=thei;};
double d;
float f[2];
uint32_t i[2];
uint64_t ll;
uint16_t s[4];
};
//------------------------------------------------------------------------------
/// Converts an unsigned long long to a double
inline double uint642dp(uint64_t ll) {
ieee754 tmp;
tmp.ll=ll;
return tmp.d;
}
//------------------------------------------------------------------------------
/// Converts a double to an unsigned long long
inline uint64_t dp2uint64(double x) {
ieee754 tmp;
tmp.d=x;
return tmp.ll;
}
//------------------------------------------------------------------------------
/// Makes an AND of a double and a unsigned long long
inline double dpANDuint64(const double x, const uint64_t i ){
return uint642dp(dp2uint64(x) & i);
}
//------------------------------------------------------------------------------
/// Makes an OR of a double and a unsigned long long
inline double dpORuint64(const double x, const uint64_t i ){
return uint642dp(dp2uint64(x) | i);
}
/// Makes a XOR of a double and a unsigned long long
inline double dpXORuint64(const double x, const uint64_t i ){
return uint642dp(dp2uint64(x) ^ i);
}
//------------------------------------------------------------------------------
inline uint64_t getSignMask(const double x){
const uint64_t mask=0x8000000000000000ULL;
return dp2uint64(x) & mask;
}
//------------------------------------------------------------------------------
/// Converts an int to a float
inline float uint322sp(int x) {
ieee754 tmp;
tmp.i[0]=x;
return tmp.f[0];
}
//------------------------------------------------------------------------------
/// Converts a float to an int
inline uint32_t sp2uint32(float x) {
ieee754 tmp;
tmp.f[0]=x;
return tmp.i[0];
}
//------------------------------------------------------------------------------
/// Makes an AND of a float and a unsigned long
inline float spANDuint32(const float x, const uint32_t i ){
return uint322sp(sp2uint32(x) & i);
}
//------------------------------------------------------------------------------
/// Makes an OR of a float and a unsigned long
inline float spORuint32(const float x, const uint32_t i ){
return uint322sp(sp2uint32(x) | i);
}
//------------------------------------------------------------------------------
/// Makes an OR of a float and a unsigned long
inline float spXORuint32(const float x, const uint32_t i ){
return uint322sp(sp2uint32(x) ^ i);
}
//------------------------------------------------------------------------------
/// Get the sign mask
inline uint32_t getSignMask(const float x){
const uint32_t mask=0x80000000;
return sp2uint32(x) & mask;
}
//------------------------------------------------------------------------------
/// Like frexp but vectorising and the exponent is a double.
inline double getMantExponent(const double x, double & fe){
uint64_t n = dp2uint64(x);
// Shift to the right up to the beginning of the exponent.
// Then with a mask, cut off the sign bit
uint64_t le = (n >> 52);
// chop the head of the number: an int contains more than 11 bits (32)
int32_t e = le; // This is important since sums on uint64_t do not vectorise
fe = e-1023 ;
// This puts to 11 zeroes the exponent
n &=0x800FFFFFFFFFFFFFULL;
// build a mask which is 0.5, i.e. an exponent equal to 1022
// which means *2, see the above +1.
const uint64_t p05 = 0x3FE0000000000000ULL; //dp2uint64(0.5);
n |= p05;
return uint642dp(n);
}
//------------------------------------------------------------------------------
/// Like frexp but vectorising and the exponent is a float.
inline float getMantExponentf(const float x, float & fe){
uint32_t n = sp2uint32(x);
int32_t e = (n >> 23)-127;
fe = e;
// fractional part
const uint32_t p05f = 0x3f000000; // //sp2uint32(0.5);
n &= 0x807fffff;// ~0x7f800000;
n |= p05f;
return uint322sp(n);
}
//------------------------------------------------------------------------------
/// Converts a fp to an int
inline uint32_t fp2uint(float x) {
return sp2uint32(x);
}
/// Converts a fp to an int
inline uint64_t fp2uint(double x) {
return dp2uint64(x);
}
/// Converts an int to fp
inline float int2fp(uint32_t i) {
return uint322sp(i);
}
/// Converts an int to fp
inline double int2fp(uint64_t i) {
return uint642dp(i);
}
//------------------------------------------------------------------------------
/**
* A vectorisable floor implementation, not only triggered by fast-math.
* These functions do not distinguish between -0.0 and 0.0, so are not IEC6509
* compliant for argument -0.0
**/
inline double fpfloor(const double x){
// no problem since exp is defined between -708 and 708. Int is enough for it!
int32_t ret = int32_t (x);
ret-=(sp2uint32(x)>>31);
return ret;
}
//------------------------------------------------------------------------------
/**
* A vectorisable floor implementation, not only triggered by fast-math.
* These functions do not distinguish between -0.0 and 0.0, so are not IEC6509
* compliant for argument -0.0
**/
inline float fpfloor(const float x){
int32_t ret = int32_t (x);
ret-=(sp2uint32(x)>>31);
return ret;
}
//------------------------------------------------------------------------------
}
} // end of namespace vdt
#endif /* VDTCOMMON_H_ */