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chealpix.c
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chealpix.c
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/* -----------------------------------------------------------------------------
*
* Copyright (C) 1997-2016 Krzysztof M. Gorski, Eric Hivon, Martin Reinecke,
* Benjamin D. Wandelt, Anthony J. Banday,
* Matthias Bartelmann,
* Reza Ansari & Kenneth M. Ganga
*
*
* This file is part of HEALPix.
*
* HEALPix is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* HEALPix 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with HEALPix; if not, write to the Free Software
* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*
* For more information about HEALPix see http://healpix.sourceforge.net
*
*---------------------------------------------------------------------------*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "chealpix.h"
static const double twothird=2.0/3.0;
static const double pi=3.141592653589793238462643383279502884197;
static const double twopi=6.283185307179586476925286766559005768394;
static const double halfpi=1.570796326794896619231321691639751442099;
static const double inv_halfpi=0.6366197723675813430755350534900574;
static void util_fail_ (const char *file, int line, const char *func,
const char *msg)
{
fprintf(stderr,"%s, %i (%s):\n%s\n",file,line,func,msg);
exit(1);
}
#if defined (__GNUC__)
#define UTIL_FUNC_NAME__ __func__
#else
#define UTIL_FUNC_NAME__ "unknown"
#endif
#define UTIL_ASSERT(cond,msg) \
if(!(cond)) util_fail_(__FILE__,__LINE__,UTIL_FUNC_NAME__,msg)
#define UTIL_FAIL(msg) \
util_fail_(__FILE__,__LINE__,UTIL_FUNC_NAME__,msg)
/*! Returns the remainder of the division \a v1/v2.
The result is non-negative.
\a v1 can be positive or negative; \a v2 must be positive. */
static double fmodulo (double v1, double v2)
{
if (v1>=0)
return (v1<v2) ? v1 : fmod(v1,v2);
double tmp=fmod(v1,v2)+v2;
return (tmp==v2) ? 0. : tmp;
}
/*! Returns the remainder of the division \a v1/v2.
The result is non-negative.
\a v1 can be positive or negative; \a v2 must be positive. */
static int imodulo (int v1, int v2)
{ int v=v1%v2; return (v>=0) ? v : v+v2; }
static int isqrt(int v)
{ return (int)(sqrt(v+0.5)); }
/* ctab[m] = (short)(
(m&0x1 ) | ((m&0x2 ) << 7) | ((m&0x4 ) >> 1) | ((m&0x8 ) << 6)
| ((m&0x10) >> 2) | ((m&0x20) << 5) | ((m&0x40) >> 3) | ((m&0x80) << 4)); */
static const short ctab[]={
#define Z(a) a,a+1,a+256,a+257
#define Y(a) Z(a),Z(a+2),Z(a+512),Z(a+514)
#define X(a) Y(a),Y(a+4),Y(a+1024),Y(a+1028)
X(0),X(8),X(2048),X(2056)
#undef X
#undef Y
#undef Z
};
/* utab[m] = (short)(
(m&0x1 ) | ((m&0x2 ) << 1) | ((m&0x4 ) << 2) | ((m&0x8 ) << 3)
| ((m&0x10) << 4) | ((m&0x20) << 5) | ((m&0x40) << 6) | ((m&0x80) << 7)); */
static const short utab[]={
#define Z(a) 0x##a##0, 0x##a##1, 0x##a##4, 0x##a##5
#define Y(a) Z(a##0), Z(a##1), Z(a##4), Z(a##5)
#define X(a) Y(a##0), Y(a##1), Y(a##4), Y(a##5)
X(0),X(1),X(4),X(5)
#undef X
#undef Y
#undef Z
};
static const int jrll[] = { 2,2,2,2,3,3,3,3,4,4,4,4 };
static const int jpll[] = { 1,3,5,7,0,2,4,6,1,3,5,7 };
#ifndef __BMI2__
static int xyf2nest (int nside, int ix, int iy, int face_num)
{
return (face_num*nside*nside) +
(utab[ix&0xff] | (utab[ix>>8]<<16)
| (utab[iy&0xff]<<1) | (utab[iy>>8]<<17));
}
static void nest2xyf (int nside, int pix, int *ix, int *iy, int *face_num)
{
int npface_=nside*nside, raw;
*face_num = pix/npface_;
pix &= (npface_-1);
raw = (pix&0x5555) | ((pix&0x55550000)>>15);
*ix = ctab[raw&0xff] | (ctab[raw>>8]<<4);
pix >>= 1;
raw = (pix&0x5555) | ((pix&0x55550000)>>15);
*iy = ctab[raw&0xff] | (ctab[raw>>8]<<4);
}
#else
#include <x86intrin.h>
static int xyf2nest (int nside, int ix, int iy, int face_num)
{
return (face_num*nside*nside) +
(_pdep_u32(ix,0x55555555u) | _pdep_u32(iy,0xaaaaaaaau));
}
static void nest2xyf (int nside, int pix, int *ix, int *iy, int *face_num)
{
int npface_=nside*nside, raw;
*face_num = pix/npface_;
pix &= (npface_-1);
*ix=_pext_u32(pix,0x55555555u);
*iy=_pext_u32(pix,0xaaaaaaaau);
}
#endif
static inline int special_div (int a, int b)
{
int t=(a>=(b<<1));
a-=t*(b<<1);
return (t<<1)+(a>=b);
}
static int xyf2ring (int nside_, int ix, int iy, int face_num)
{
int nl4 = 4*nside_;
int jr = (jrll[face_num]*nside_) - ix - iy - 1, jp;
int nr, kshift, n_before;
if (jr<nside_)
{
nr = jr;
n_before = 2*nr*(nr-1);
kshift = 0;
}
else if (jr > 3*nside_)
{
nr = nl4-jr;
n_before = 12*nside_*nside_ - 2*(nr+1)*nr;
kshift = 0;
}
else
{
int ncap_=2*nside_*(nside_-1);
nr = nside_;
n_before = ncap_ + (jr-nside_)*nl4;
kshift = (jr-nside_)&1;
}
jp = (jpll[face_num]*nr + ix - iy + 1 + kshift) / 2;
if (jp>nl4)
jp-=nl4;
else
if (jp<1) jp+=nl4;
return n_before + jp - 1;
}
static void ring2xyf (int nside_, int pix, int *ix, int *iy, int *face_num)
{
int iring, iphi, kshift, nr;
int ncap_=2*nside_*(nside_-1);
int npix_=12*nside_*nside_;
int nl2 = 2*nside_;
if (pix<ncap_) /* North Polar cap */
{
iring = (1+isqrt(1+2*pix))>>1; /* counted from North pole */
iphi = (pix+1) - 2*iring*(iring-1);
kshift = 0;
nr = iring;
*face_num = special_div(iphi-1,nr);
}
else if (pix<(npix_-ncap_)) /* Equatorial region */
{
int ip = pix - ncap_;
iring = (ip/(4*nside_)) + nside_; /* counted from North pole */
iphi = (ip%(4*nside_)) + 1;
kshift = (iring+nside_)&1;
nr = nside_;
unsigned int ire = iring-nside_+1;
unsigned int irm = nl2+2-ire;
int ifm = (iphi - ire/2 + nside_ -1) / nside_;
int ifp = (iphi - irm/2 + nside_ -1) / nside_;
*face_num = (ifp==ifm) ? (ifp|4) : ((ifp<ifm) ? ifp : (ifm+8));
}
else /* South Polar cap */
{
int ip = npix_ - pix;
iring = (1+isqrt(2*ip-1))>>1; /* counted from South pole */
iphi = 4*iring + 1 - (ip - 2*iring*(iring-1));
kshift = 0;
nr = iring;
iring = 2*nl2-iring;
*face_num=8+special_div(iphi-1,nr);
}
int irt = iring - (jrll[*face_num]*nside_) + 1;
int ipt = 2*iphi- jpll[*face_num]*nr - kshift -1;
if (ipt>=nl2) ipt-=8*nside_;
*ix = (ipt-irt) >>1;
*iy =(-(ipt+irt))>>1;
}
static int ang2pix_nest_z_phi (long nside_, double z, double phi)
{
double za = fabs(z);
double tt = fmodulo(phi,twopi) * inv_halfpi; /* in [0,4) */
int face_num, ix, iy;
if (za<=twothird) /* Equatorial region */
{
double temp1 = nside_*(0.5+tt);
double temp2 = nside_*(z*0.75);
int jp = (int)(temp1-temp2); /* index of ascending edge line */
int jm = (int)(temp1+temp2); /* index of descending edge line */
int ifp = jp/nside_; /* in {0,4} */
int ifm = jm/nside_;
face_num = (ifp==ifm) ? (ifp|4) : ((ifp<ifm) ? ifp : (ifm+8));
ix = jm & (nside_-1);
iy = nside_ - (jp & (nside_-1)) - 1;
}
else /* polar region, za > 2/3 */
{
int ntt = (int)tt, jp, jm;
double tp, tmp;
if (ntt>=4) ntt=3;
tp = tt-ntt;
tmp = nside_*sqrt(3*(1-za));
jp = (int)(tp*tmp); /* increasing edge line index */
jm = (int)((1.0-tp)*tmp); /* decreasing edge line index */
if (jp>=nside_) jp = nside_-1; /* for points too close to the boundary */
if (jm>=nside_) jm = nside_-1;
if (z >= 0)
{
face_num = ntt; /* in {0,3} */
ix = nside_ - jm - 1;
iy = nside_ - jp - 1;
}
else
{
face_num = ntt + 8; /* in {8,11} */
ix = jp;
iy = jm;
}
}
return xyf2nest(nside_,ix,iy,face_num);
}
static int ang2pix_ring_z_phi (long nside_, double z, double phi)
{
double za = fabs(z);
double tt = fmodulo(phi,twopi) * inv_halfpi; /* in [0,4) */
if (za<=twothird) /* Equatorial region */
{
double temp1 = nside_*(0.5+tt);
double temp2 = nside_*z*0.75;
int jp = (int)(temp1-temp2); /* index of ascending edge line */
int jm = (int)(temp1+temp2); /* index of descending edge line */
/* ring number counted from z=2/3 */
int ir = nside_ + 1 + jp - jm; /* in {1,2n+1} */
int kshift = 1-(ir&1); /* kshift=1 if ir even, 0 otherwise */
int ip = (jp+jm-nside_+kshift+1)/2; /* in {0,4n-1} */
ip = imodulo(ip,4*nside_);
return nside_*(nside_-1)*2 + (ir-1)*4*nside_ + ip;
}
else /* North & South polar caps */
{
double tp = tt-(int)(tt);
double tmp = nside_*sqrt(3*(1-za));
int jp = (int)(tp*tmp); /* increasing edge line index */
int jm = (int)((1.0-tp)*tmp); /* decreasing edge line index */
int ir = jp+jm+1; /* ring number counted from the closest pole */
int ip = (int)(tt*ir); /* in {0,4*ir-1} */
ip = imodulo(ip,4*ir);
if (z>0)
return 2*ir*(ir-1) + ip;
else
return 12*nside_*nside_ - 2*ir*(ir+1) + ip;
}
}
static void pix2ang_ring_z_phi (int nside_, int pix, double *z, double *phi)
{
long ncap_=nside_*(nside_-1)*2;
long npix_=12*nside_*nside_;
double fact2_ = 4./npix_;
if (pix<ncap_) /* North Polar cap */
{
int iring = (1+isqrt(1+2*pix))>>1; /* counted from North pole */
int iphi = (pix+1) - 2*iring*(iring-1);
*z = 1.0 - (iring*iring)*fact2_;
*phi = (iphi-0.5) * halfpi/iring;
}
else if (pix<(npix_-ncap_)) /* Equatorial region */
{
double fact1_ = (nside_<<1)*fact2_;
int ip = pix - ncap_;
int iring = ip/(4*nside_) + nside_; /* counted from North pole */
int iphi = ip%(4*nside_) + 1;
/* 1 if iring+nside is odd, 1/2 otherwise */
double fodd = ((iring+nside_)&1) ? 1 : 0.5;
int nl2 = 2*nside_;
*z = (nl2-iring)*fact1_;
*phi = (iphi-fodd) * pi/nl2;
}
else /* South Polar cap */
{
int ip = npix_ - pix;
int iring = (1+isqrt(2*ip-1))>>1; /* counted from South pole */
int iphi = 4*iring + 1 - (ip - 2*iring*(iring-1));
*z = -1.0 + (iring*iring)*fact2_;
*phi = (iphi-0.5) * halfpi/iring;
}
}
static void pix2ang_nest_z_phi (int nside_, int pix, double *z, double *phi)
{
int nl4 = nside_*4;
int npix_=12*nside_*nside_;
double fact2_ = 4./npix_;
int face_num, ix, iy, nr, kshift;
nest2xyf(nside_,pix,&ix,&iy,&face_num);
int jr = (jrll[face_num]*nside_) - ix - iy - 1;
if (jr<nside_)
{
nr = jr;
*z = 1 - nr*nr*fact2_;
kshift = 0;
}
else if (jr > 3*nside_)
{
nr = nl4-jr;
*z = nr*nr*fact2_ - 1;
kshift = 0;
}
else
{
double fact1_ = (nside_<<1)*fact2_;
nr = nside_;
*z = (2*nside_-jr)*fact1_;
kshift = (jr-nside_)&1;
}
int jp = (jpll[face_num]*nr + ix -iy + 1 + kshift) / 2;
if (jp>nl4) jp-=nl4;
if (jp<1) jp+=nl4;
*phi = (jp-(kshift+1)*0.5)*(halfpi/nr);
}
void ang2vec(double theta, double phi, double *vec)
{
double sz = sin(theta);
vec[0] = sz * cos(phi);
vec[1] = sz * sin(phi);
vec[2] = cos(theta);
}
void vec2ang(const double *vec, double *theta, double *phi)
{
*theta = atan2(sqrt(vec[0]*vec[0]+vec[1]*vec[1]),vec[2]);
*phi = atan2 (vec[1],vec[0]);
if (*phi<0.) *phi += twopi;
}
long npix2nside(long npix)
{
long res = isqrt(npix/12);
return (res*res*12==npix) ? res : -1;
}
long nside2npix(const long nside)
{ return 12*nside*nside; }
void ang2pix_ring(long nside, double theta, double phi, long *ipix)
{
UTIL_ASSERT((theta>=0)&&(theta<=pi),"theta out of range");
*ipix=ang2pix_ring_z_phi (nside,cos(theta),phi);
}
void ang2pix_nest(long nside, double theta, double phi, long *ipix)
{
UTIL_ASSERT((theta>=0)&&(theta<=pi),"theta out of range");
*ipix=ang2pix_nest_z_phi (nside,cos(theta),phi);
}
void vec2pix_ring(long nside, const double *vec, long *ipix)
{
double vlen=sqrt(vec[0]*vec[0]+vec[1]*vec[1]+vec[2]*vec[2]);
*ipix=ang2pix_ring_z_phi (nside,vec[2]/vlen, atan2(vec[1],vec[0]));
}
void vec2pix_nest(long nside, const double *vec, long *ipix)
{
double vlen=sqrt(vec[0]*vec[0]+vec[1]*vec[1]+vec[2]*vec[2]);
*ipix=ang2pix_nest_z_phi (nside,vec[2]/vlen, atan2(vec[1],vec[0]));
}
void pix2ang_ring(long nside, long ipix, double *theta, double *phi)
{
double z;
pix2ang_ring_z_phi (nside,ipix,&z,phi);
*theta=acos(z);
}
void pix2ang_nest(long nside, long ipix, double *theta, double *phi)
{
double z;
pix2ang_nest_z_phi (nside,ipix,&z,phi);
*theta=acos(z);
}
void pix2vec_ring(long nside, long ipix, double *vec)
{
double z, phi;
pix2ang_ring_z_phi (nside,ipix,&z,&phi);
double stheta=sqrt((1.-z)*(1.+z));
vec[0]=stheta*cos(phi);
vec[1]=stheta*sin(phi);
vec[2]=z;
}
void pix2vec_nest(long nside, long ipix, double *vec)
{
double z, phi;
pix2ang_nest_z_phi (nside,ipix,&z,&phi);
double stheta=sqrt((1.-z)*(1.+z));
vec[0]=stheta*cos(phi);
vec[1]=stheta*sin(phi);
vec[2]=z;
}
void nest2ring(long nside, long ipnest, long *ipring)
{
int ix, iy, face_num;
if ((nside&(nside-1))!=0) { *ipring=-1; return; }
nest2xyf (nside, ipnest, &ix, &iy, &face_num);
*ipring = xyf2ring (nside, ix, iy, face_num);
}
void ring2nest(long nside, long ipring, long *ipnest)
{
int ix, iy, face_num;
if ((nside&(nside-1))!=0) { *ipnest=-1; return; }
ring2xyf (nside, ipring, &ix, &iy, &face_num);
*ipnest = xyf2nest (nside, ix, iy, face_num);
}
/* 64bit functions */
static int64_t imodulo64 (int64_t v1, int64_t v2)
{ int64_t v=v1%v2; return (v>=0) ? v : v+v2; }
static long isqrt64(int64_t v)
{
int64_t res = sqrt(v+0.5);
if (v<((int64_t)(1)<<50)) return (long)res;
if (res*res>v)
--res;
else if ((res+1)*(res+1)<=v)
++res;
return (long)res;
}
#ifndef __BMI2__
static int64_t spread_bits64 (int v)
{
return (int64_t)(utab[ v &0xff])
| ((int64_t)(utab[(v>> 8)&0xff])<<16)
| ((int64_t)(utab[(v>>16)&0xff])<<32)
| ((int64_t)(utab[(v>>24)&0xff])<<48);
}
static int64_t compress_bits64 (int64_t v)
{
int64_t raw = v&0x5555555555555555ull;
raw|=raw>>15;
return ctab[ raw &0xff] | (ctab[(raw>> 8)&0xff]<< 4)
| (ctab[(raw>>32)&0xff]<<16) | (ctab[(raw>>40)&0xff]<<20);
}
static int64_t xyf2nest64 (int64_t nside, int ix, int iy, int face_num)
{
return (face_num*nside*nside) + spread_bits64(ix) + (spread_bits64(iy)<<1);
}
static void nest2xyf64 (int64_t nside, int64_t pix, int *ix, int *iy,
int *face_num)
{
int64_t npface_=nside*nside;
*face_num = pix/npface_;
pix &= (npface_-1);
*ix = compress_bits64(pix);
*iy = compress_bits64(pix>>1);
}
#else
static int64_t xyf2nest64 (int64_t nside, int ix, int iy, int face_num)
{
return (face_num*nside*nside)
+ _pdep_u64(ix,0x5555555555555555ull) + _pdep_u64(iy,0xaaaaaaaaaaaaaaaaull);
}
static void nest2xyf64 (int64_t nside, int64_t pix, int *ix, int *iy,
int *face_num)
{
int64_t npface_=nside*nside;
*face_num = pix/npface_;
pix &= (npface_-1);
*ix = _pext_u64(pix,0x5555555555555555ull);
*iy = _pext_u64(pix,0xaaaaaaaaaaaaaaaaull);
}
#endif
static inline int64_t special_div64 (int64_t a, int64_t b)
{
int64_t t=(a>=(b<<1));
a-=t*(b<<1);
return (t<<1)+(a>=b);
}
static int64_t xyf2ring64 (int64_t nside_, int ix, int iy, int face_num)
{
int64_t nl4 = 4*nside_;
int64_t jr = (jrll[face_num]*nside_) - ix - iy - 1, jp;
int64_t nr, kshift, n_before;
if (jr<nside_)
{
nr = jr;
n_before = 2*nr*(nr-1);
kshift = 0;
}
else if (jr > 3*nside_)
{
nr = nl4-jr;
n_before = 12*nside_*nside_ - 2*(nr+1)*nr;
kshift = 0;
}
else
{
int64_t ncap_=2*nside_*(nside_-1);
nr = nside_;
n_before = ncap_ + (jr-nside_)*nl4;
kshift = (jr-nside_)&1;
}
jp = (jpll[face_num]*nr + ix - iy + 1 + kshift) / 2;
if (jp>nl4)
jp-=nl4;
else
if (jp<1) jp+=nl4;
return n_before + jp - 1;
}
static void ring2xyf64 (int64_t nside_, int64_t pix, int *ix, int *iy,
int *face_num)
{
int64_t iring, iphi, kshift, nr;
int64_t ncap_=2*nside_*(nside_-1);
int64_t npix_=12*nside_*nside_;
int64_t nl2 = 2*nside_;
if (pix<ncap_) /* North Polar cap */
{
iring = (1+isqrt64(1+2*pix))>>1; /* counted from North pole */
iphi = (pix+1) - 2*iring*(iring-1);
kshift = 0;
nr = iring;
*face_num=special_div64(iphi-1,nr);
}
else if (pix<(npix_-ncap_)) /* Equatorial region */
{
int64_t ip = pix - ncap_;
iring = (ip/(4*nside_)) + nside_; /* counted from North pole */
iphi = (ip%(4*nside_)) + 1;
kshift = (iring+nside_)&1;
nr = nside_;
int64_t ire = iring-nside_+1;
int64_t irm = nl2+2-ire;
int64_t ifm = (iphi - ire/2 + nside_ -1) / nside_;
int64_t ifp = (iphi - irm/2 + nside_ -1) / nside_;
*face_num = (ifp==ifm) ? (ifp|4) : ((ifp<ifm) ? ifp : (ifm+8));
}
else /* South Polar cap */
{
int64_t ip = npix_ - pix;
iring = (1+isqrt64(2*ip-1))>>1; /* counted from South pole */
iphi = 4*iring + 1 - (ip - 2*iring*(iring-1));
kshift = 0;
nr = iring;
iring = 2*nl2-iring;
*face_num=8+special_div64(iphi-1,nr);
}
int64_t irt = iring - (jrll[*face_num]*nside_) + 1;
int64_t ipt = 2*iphi- jpll[*face_num]*nr - kshift -1;
if (ipt>=nl2) ipt-=8*nside_;
*ix = (ipt-irt) >>1;
*iy =(-(ipt+irt))>>1;
}
static int64_t ang2pix_nest_z_phi64 (int64_t nside_, double z, double s,
double phi)
{
double za = fabs(z);
double tt = fmodulo(phi,twopi) * inv_halfpi; /* in [0,4) */
int face_num, ix, iy;
if (za<=twothird) /* Equatorial region */
{
double temp1 = nside_*(0.5+tt);
double temp2 = nside_*(z*0.75);
int64_t jp = (int64_t)(temp1-temp2); /* index of ascending edge line */
int64_t jm = (int64_t)(temp1+temp2); /* index of descending edge line */
int64_t ifp = jp/nside_; /* in {0,4} */
int64_t ifm = jm/nside_;
face_num = (ifp==ifm) ? (ifp|4) : ((ifp<ifm) ? ifp : (ifm+8));
ix = jm & (nside_-1);
iy = nside_ - (jp & (nside_-1)) - 1;
}
else /* polar region, za > 2/3 */
{
int ntt = (int)tt, jp, jm;
double tp, tmp;
if (ntt>=4) ntt=3;
tp = tt-ntt;
if (s>-2.)
tmp = nside_*s/sqrt((1.+za)/3.);
else
tmp = nside_*sqrt(3*(1-za));
jp = (int64_t)(tp*tmp); /* increasing edge line index */
jm = (int64_t)((1.0-tp)*tmp); /* decreasing edge line index */
if (jp>=nside_) jp = nside_-1; /* for points too close to the boundary */
if (jm>=nside_) jm = nside_-1;
if (z >= 0)
{
face_num = ntt; /* in {0,3} */
ix = nside_ - jm - 1;
iy = nside_ - jp - 1;
}
else
{
face_num = ntt + 8; /* in {8,11} */
ix = jp;
iy = jm;
}
}
return xyf2nest64(nside_,ix,iy,face_num);
}
static int64_t ang2pix_ring_z_phi64 (int64_t nside_, double z, double s,
double phi)
{
double za = fabs(z);
double tt = fmodulo(phi,twopi) * inv_halfpi; /* in [0,4) */
if (za<=twothird) /* Equatorial region */
{
double temp1 = nside_*(0.5+tt);
double temp2 = nside_*z*0.75;
int64_t jp = (int64_t)(temp1-temp2); /* index of ascending edge line */
int64_t jm = (int64_t)(temp1+temp2); /* index of descending edge line */
/* ring number counted from z=2/3 */
int64_t ir = nside_ + 1 + jp - jm; /* in {1,2n+1} */
int kshift = 1-(ir&1); /* kshift=1 if ir even, 0 otherwise */
int64_t ip = (jp+jm-nside_+kshift+1)/2; /* in {0,4n-1} */
ip = imodulo64(ip,4*nside_);
return nside_*(nside_-1)*2 + (ir-1)*4*nside_ + ip;
}
else /* North & South polar caps */
{
double tp = tt-(int)(tt);
double tmp = (s>-2.) ? nside_*s/sqrt((1.+za)/3.) : nside_*sqrt(3*(1-za));
int64_t jp = (int64_t)(tp*tmp); /* increasing edge line index */
int64_t jm = (int64_t)((1.0-tp)*tmp); /* decreasing edge line index */
int64_t ir = jp+jm+1; /* ring number counted from the closest pole */
int64_t ip = (int64_t)(tt*ir); /* in {0,4*ir-1} */
ip = imodulo64(ip,4*ir);
if (z>0)
return 2*ir*(ir-1) + ip;
else
return 12*nside_*nside_ - 2*ir*(ir+1) + ip;
}
}
static void pix2ang_ring_z_phi64 (int64_t nside_, int64_t pix,
double *z, double *s, double *phi)
{
int64_t ncap_=nside_*(nside_-1)*2;
int64_t npix_=12*nside_*nside_;
double fact2_ = 4./npix_;
*s=-5;
if (pix<ncap_) /* North Polar cap */
{
int64_t iring = (1+isqrt64(1+2*pix))>>1; /* from N pole */
int64_t iphi = (pix+1) - 2*iring*(iring-1);
double tmp=(iring*iring)*fact2_;
*z = 1.0 - tmp;
if (*z>0.99) *s=sqrt(tmp*(2.-tmp));
*phi = (iphi-0.5) * halfpi/iring;
}
else if (pix<(npix_-ncap_)) /* Equatorial region */
{
double fact1_ = (nside_<<1)*fact2_;
int64_t ip = pix - ncap_;
int64_t iring = ip/(4*nside_) + nside_; /* counted from North pole */
int64_t iphi = ip%(4*nside_) + 1;
/* 1 if iring+nside is odd, 1/2 otherwise */
double fodd = ((iring+nside_)&1) ? 1 : 0.5;
int64_t nl2 = 2*nside_;
*z = (nl2-iring)*fact1_;
*phi = (iphi-fodd) * pi/nl2;
}
else /* South Polar cap */
{
int64_t ip = npix_ - pix;
int64_t iring = (1+isqrt64(2*ip-1))>>1; /* from S pole */
int64_t iphi = 4*iring + 1 - (ip - 2*iring*(iring-1));
double tmp=(iring*iring)*fact2_;
*z = tmp - 1.0;
if (*z<-0.99) *s=sqrt(tmp*(2.-tmp));
*phi = (iphi-0.5) * halfpi/iring;
}
}
static void pix2ang_nest_z_phi64 (int64_t nside_, int64_t pix, double *z,
double *s, double *phi)
{
int64_t nl4 = nside_*4;
int64_t npix_=12*nside_*nside_;
double fact2_ = 4./npix_;
int face_num, ix, iy;
int64_t jr, nr, kshift, jp;
*s=-5;
nest2xyf64(nside_,pix,&ix,&iy,&face_num);
jr = (jrll[face_num]*nside_) - ix - iy - 1;
if (jr<nside_)
{
double tmp;
nr = jr;
tmp=(nr*nr)*fact2_;
*z = 1 - tmp;
if (*z>0.99) *s=sqrt(tmp*(2.-tmp));
kshift = 0;
}
else if (jr > 3*nside_)
{
double tmp;
nr = nl4-jr;
tmp=(nr*nr)*fact2_;
*z = tmp - 1;
if (*z<-0.99) *s=sqrt(tmp*(2.-tmp));
kshift = 0;
}
else
{
double fact1_ = (nside_<<1)*fact2_;
nr = nside_;
*z = (2*nside_-jr)*fact1_;
kshift = (jr-nside_)&1;
}
jp = (jpll[face_num]*nr + ix -iy + 1 + kshift) / 2;
if (jp>nl4) jp-=nl4;
if (jp<1) jp+=nl4;
*phi = (jp-(kshift+1)*0.5)*(halfpi/nr);
}
long npix2nside64(int64_t npix)
{
int64_t res = isqrt64(npix/12.);
return (res*res*12==npix) ? (long)res : -1;
}
int64_t nside2npix64(int64_t nside)
{ return 12*nside*nside; }
void ang2pix_ring64(int64_t nside, double theta, double phi, int64_t *ipix)
{
UTIL_ASSERT((theta>=0)&&(theta<=pi),"theta out of range");
double cth=cos(theta), sth=(fabs(cth)>0.99) ? sin(theta) : -5;
*ipix=ang2pix_ring_z_phi64 (nside,cth,sth,phi);
}
void ang2pix_nest64(int64_t nside, double theta, double phi, int64_t *ipix)
{
UTIL_ASSERT((theta>=0)&&(theta<=pi),"theta out of range");
double cth=cos(theta), sth=(fabs(cth)>0.99) ? sin(theta) : -5;
*ipix=ang2pix_nest_z_phi64 (nside,cth,sth,phi);
}
void vec2pix_ring64(int64_t nside, const double *vec, int64_t *ipix)
{
double vlen=sqrt(vec[0]*vec[0]+vec[1]*vec[1]+vec[2]*vec[2]);
double cth = vec[2]/vlen;
double sth=(fabs(cth)>0.99) ? sqrt(vec[0]*vec[0]+vec[1]*vec[1])/vlen : -5;
*ipix=ang2pix_ring_z_phi64 (nside,cth,sth,atan2(vec[1],vec[0]));
}
void vec2pix_nest64(int64_t nside, const double *vec, int64_t *ipix)
{
double vlen=sqrt(vec[0]*vec[0]+vec[1]*vec[1]+vec[2]*vec[2]);
double cth = vec[2]/vlen;
double sth=(fabs(cth)>0.99) ? sqrt(vec[0]*vec[0]+vec[1]*vec[1])/vlen : -5;
*ipix=ang2pix_nest_z_phi64 (nside,cth,sth,atan2(vec[1],vec[0]));
}
void pix2ang_ring64(int64_t nside, int64_t ipix, double *theta, double *phi)
{
double z,s;
pix2ang_ring_z_phi64 (nside,ipix,&z,&s,phi);
*theta= (s<-2) ? acos(z) : atan2(s,z);
}
void pix2ang_nest64(int64_t nside, int64_t ipix, double *theta, double *phi)
{
double z,s;
pix2ang_nest_z_phi64 (nside,ipix,&z,&s,phi);
*theta= (s<-2) ? acos(z) : atan2(s,z);
}
void pix2vec_ring64(int64_t nside, int64_t ipix, double *vec)
{
double z, phi, stheta;
pix2ang_ring_z_phi64 (nside,ipix,&z,&stheta,&phi);
if (stheta<-2) stheta=sqrt((1.-z)*(1.+z));
vec[0]=stheta*cos(phi);
vec[1]=stheta*sin(phi);
vec[2]=z;
}
void pix2vec_nest64(int64_t nside, int64_t ipix, double *vec)
{
double z, phi, stheta;
pix2ang_nest_z_phi64 (nside,ipix,&z,&stheta,&phi);
if (stheta<-2) stheta=sqrt((1.-z)*(1.+z));
vec[0]=stheta*cos(phi);
vec[1]=stheta*sin(phi);
vec[2]=z;
}
void nest2ring64(int64_t nside, int64_t ipnest, int64_t *ipring)
{
int ix, iy, face_num;
if ((nside&(nside-1))!=0) { *ipring=-1; return; }
nest2xyf64 (nside, ipnest, &ix, &iy, &face_num);
*ipring = xyf2ring64 (nside, ix, iy, face_num);
}
void ring2nest64(int64_t nside, int64_t ipring, int64_t *ipnest)
{
int ix, iy, face_num;
if ((nside&(nside-1))!=0) { *ipnest=-1; return; }
ring2xyf64 (nside, ipring, &ix, &iy, &face_num);
*ipnest = xyf2nest64 (nside, ix, iy, face_num);
}
#ifdef ENABLE_FITSIO
#include "fitsio.h"
#define RALLOC(type,num) \
((type *)util_malloc_((num)*sizeof(type)))
#define DEALLOC(ptr) \
do { util_free_(ptr); (ptr)=NULL; } while(0)
static void *util_malloc_ (size_t sz)
{
if (sz==0) return NULL;
void *res = malloc(sz);
UTIL_ASSERT(res,"malloc() failed");
return res;
}
static void util_free_ (void *ptr)
{ if ((ptr)!=NULL) free(ptr); }
static void printerror (int status)
{
if (status==0) return;
fits_report_error(stderr, status);
UTIL_FAIL("FITS error");
}
static void setCoordSysHP(char coordsys,char *coordsys9)
{
strcpy(coordsys9,"C ");
if (coordsys=='G')
strcpy (coordsys9,"G ");
else if (coordsys=='E')
strcpy (coordsys9,"E ");
else if ((coordsys!='C')&&(coordsys!='Q'))
fprintf(stderr, "%s (%d): System Cordinates are not correct"
"(Galactic,Ecliptic,Celestial=Equatorial). "
" Celestial system was set.\n", __FILE__, __LINE__);
}
float *read_healpix_map(const char *infile, long *nside, char *coordsys,
char *ordering)
{
/* Local Declarations */
long naxes, *naxis, npix;
int status=0, hdutype, nfound, anynul;
float nulval, *map;
fitsfile *fptr;
fits_open_file(&fptr, infile, READONLY, &status);
fits_movabs_hdu(fptr, 2, &hdutype, &status);
printerror(status);
UTIL_ASSERT(hdutype==BINARY_TBL,"Extension is not binary!");
/* Read the sizes of the array */
fits_read_key_lng(fptr, "NAXIS", &naxes, NULL, &status);
printerror(status);
naxis = RALLOC(long,naxes);
fits_read_keys_lng(fptr, "NAXIS", 1, naxes, naxis, &nfound, &status);
printerror(status);
UTIL_ASSERT(nfound==naxes,"nfound!=naxes");
fits_read_key_lng(fptr, "NSIDE", nside, NULL, &status);
printerror(status);
npix = 12*(*nside)*(*nside);
UTIL_ASSERT((npix%naxis[1])==0,"Problem with npix.");
if (fits_read_key(fptr, TSTRING, "COORDSYS",coordsys, NULL, &status)) {
fprintf(stderr, "WARNING: Could not find %s keyword in in file %s\n",
"COORDSYS",infile);
status = 0;
}
if (fits_read_key(fptr, TSTRING, "ORDERING", ordering, NULL, &status)) {
fprintf(stderr, "WARNING: Could not find %s keyword in in file %s\n",
"ORDERING",infile);
status = 0;
}
/* Read the array */
map = RALLOC(float,npix);
nulval = HEALPIX_NULLVAL;
fits_read_col(fptr, TFLOAT, 1, 1, 1, npix, &nulval, map, &anynul, &status);
printerror(status);
DEALLOC(naxis);
fits_close_file(fptr, &status);
printerror(status);
return map;
}
long get_fits_size(const char *filename, long *nside, char *ordering)
{
fitsfile *fptr; /* pointer to the FITS file, defined in fitsio.h */
int status=0, hdutype;