User: rhaas
Date: 2010/04/29 05:20 PM
Modified:
/trunk/src/
CoordTransf.c, TP_utilities.c, TP_utilities.h
Log:
TwoPunctures: remove NR memory management and complex arithmetic code
File Changes:
Directory: /trunk/src/
======================
File [modified]: CoordTransf.c
Delta lines: +24 -27
===================================================================
--- trunk/src/CoordTransf.c 2010-03-24 00:48:53 UTC (rev 100)
+++ trunk/src/CoordTransf.c 2010-04-29 22:20:36 UTC (rev 101)
@@ -6,6 +6,8 @@
#include <math.h>
#include <ctype.h>
#include <time.h>
+#include <gsl/gsl_complex.h>
+#include <gsl/gsl_complex_math.h>
#include "cctk_Parameters.h"
#include "TP_utilities.h"
#include "TwoPunctures.h"
@@ -58,59 +60,54 @@
{
DECLARE_CCTK_PARAMETERS;
CCTK_REAL C_c2, U_cb, U_CB;
- dcomplex C, C_c, C_cc, c, c_C, c_CC, U_c, U_cc, U_C, U_CC, One =
- Complex (1., 0.);
+ gsl_complex C, C_c, C_cc, c, c_C, c_CC, U_c, U_cc, U_C, U_CC;
int ivar;
- C.r = X;
- C.i = R;
+ C = gsl_complex_rect (X, R);
- c = RCmul (par_b, Ccosh (C)); /* c=b*cosh(C)*/
- c_C = RCmul (par_b, Csinh (C));
+ c = gsl_complex_mul_real (gsl_complex_cosh (C), par_b); /* c=b*cosh(C)*/
+ c_C = gsl_complex_mul_real (gsl_complex_sinh (C), par_b);
c_CC = c;
- C_c = Cdiv (One, c_C);
- C_cc = RCmul (-1., Cmul (Cmul (C_c, C_c), Cmul (C_c, c_CC)));
- C_c2 = C_c.r * C_c.r + C_c.i * C_c.i;
+ C_c = gsl_complex_inverse (c_C);
+ C_cc = gsl_complex_negative (gsl_complex_mul (gsl_complex_mul (C_c, C_c), gsl_complex_mul (C_c, c_CC)));
+ C_c2 = gsl_complex_abs2 (C_c);
for (ivar = 0; ivar < nvar; ivar++)
{
/* U_C = 0.5*(U_X3-i*U_R3)*/
/* U_c = U_C*C_c = 0.5*(U_x3-i*U_r3)*/
- U_C.r = 0.5 * U.d13[ivar];
- U_C.i = -0.5 * U.d23[ivar];
- U_c = Cmul (U_C, C_c);
- U.d13[ivar] = 2. * U_c.r;
- U.d23[ivar] = -2. * U_c.i;
+ U_C = gsl_complex_rect (0.5 * U.d13[ivar], -0.5 * U.d23[ivar]);
+ U_c = gsl_complex_mul (U_C, C_c);
+ U.d13[ivar] = 2. * GSL_REAL(U_c);
+ U.d23[ivar] = -2. * GSL_IMAG(U_c);
/* U_C = 0.5*(U_X-i*U_R)*/
/* U_c = U_C*C_c = 0.5*(U_x-i*U_r)*/
- U_C.r = 0.5 * U.d1[ivar];
- U_C.i = -0.5 * U.d2[ivar];
- U_c = Cmul (U_C, C_c);
- U.d1[ivar] = 2. * U_c.r;
- U.d2[ivar] = -2. * U_c.i;
+ U_C = gsl_complex_rect (0.5 * U.d1[ivar], -0.5 * U.d2[ivar]);
+ U_c = gsl_complex_mul (U_C, C_c);
+ U.d1[ivar] = 2. * GSL_REAL(U_c);
+ U.d2[ivar] = -2. * GSL_IMAG(U_c);
/* U_CC = 0.25*(U_XX-U_RR-2*i*U_XR)*/
/* U_CB = d^2(U)/(dC*d\bar{C}) = 0.25*(U_XX+U_RR)*/
- U_CC.r = 0.25 * (U.d11[ivar] - U.d22[ivar]);
- U_CC.i = -0.5 * U.d12[ivar];
+ U_CC = gsl_complex_rect (0.25 * (U.d11[ivar] - U.d22[ivar]), -0.5 * U.d12[ivar]);
U_CB = 0.25 * (U.d11[ivar] + U.d22[ivar]);
/* U_cc = C_cc*U_C+(C_c)^2*U_CC*/
U_cb = U_CB * C_c2;
- U_cc = Cadd (Cmul (C_cc, U_C), Cmul (Cmul (C_c, C_c), U_CC));
+ U_cc = gsl_complex_add (gsl_complex_mul (C_cc, U_C), gsl_complex_mul (gsl_complex_mul (C_c, C_c), U_CC));
/* U_xx = 2*(U_cb+Re[U_cc])*/
/* U_rr = 2*(U_cb-Re[U_cc])*/
/* U_rx = -2*Im[U_cc]*/
- U.d11[ivar] = 2 * (U_cb + U_cc.r);
- U.d22[ivar] = 2 * (U_cb - U_cc.r);
- U.d12[ivar] = -2 * U_cc.i;
+ U.d11[ivar] = 2 * (U_cb + GSL_REAL(U_cc));
+ U.d22[ivar] = 2 * (U_cb - GSL_REAL(U_cc));
+ U.d12[ivar] = -2 * GSL_IMAG(U_cc);
}
- *x = c.r;
- *r = c.i;
+ *x = GSL_REAL(c);
+ *r = GSL_IMAG(c);
}
/*-----------------------------------------------------------*/
File [modified]: TP_utilities.c
Delta lines: +87 -361
===================================================================
--- trunk/src/TP_utilities.c 2010-03-24 00:48:53 UTC (rev 100)
+++ trunk/src/TP_utilities.c 2010-04-29 22:20:36 UTC (rev 101)
@@ -4,6 +4,7 @@
#include <stdio.h>
#include <stddef.h>
#include <stdlib.h>
+#include <assert.h>
#include "TP_utilities.h"
#include "cctk_Functions.h"
@@ -13,12 +14,13 @@
ivector (long nl, long nh)
/* allocate an int vector with subscript range v[nl..nh] */
{
- int *v;
+ int *retval;
- v = (int *) malloc ((size_t) ((nh - nl + 1 + NR_END) * sizeof (int)));
- if (!v)
+ retval = malloc(sizeof(int)*(nh-nl+1));
+ if(retval == NULL)
CCTK_WARN (CCTK_WARN_ABORT, "allocation failure in ivector()");
- return v - nl + NR_END;
+
+ return retval - nl;
}
/*---------------------------------------------------------------------------*/
@@ -26,12 +28,13 @@
dvector (long nl, long nh)
/* allocate a CCTK_REAL vector with subscript range v[nl..nh] */
{
- CCTK_REAL *v;
+ CCTK_REAL *retval;
- v = (CCTK_REAL *) malloc ((size_t) ((nh - nl + 1 + NR_END) * sizeof (CCTK_REAL)));
- if (!v)
+ retval = malloc(sizeof(CCTK_REAL)*(nh-nl+1));
+ if(retval == NULL)
CCTK_WARN (CCTK_WARN_ABORT, "allocation failure in dvector()");
- return v - nl + NR_END;
+
+ return retval - nl;
}
/*---------------------------------------------------------------------------*/
@@ -39,59 +42,57 @@
imatrix (long nrl, long nrh, long ncl, long nch)
/* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */
{
- long i, nrow = nrh - nrl + 1, ncol = nch - ncl + 1;
- int **m;
+ int **retval;
- /* allocate pointers to rows */
- m = (int **) malloc ((size_t) ((nrow + NR_END) * sizeof (int *)));
- if (!m)
- CCTK_WARN (CCTK_WARN_ABORT, "allocation failure 1 in matrix()");
- m += NR_END;
- m -= nrl;
+ retval = malloc(sizeof(int *)*(nrh-nrl+1));
+ if(retval == NULL)
+ CCTK_WARN (CCTK_WARN_ABORT, "allocation failure (1) in imatrix()");
+ /* get all memory for the matrix in on chunk */
+ retval[0] = malloc(sizeof(int)*(nrh-nrl+1)*(nch-ncl+1));
+ if(retval[0] == NULL)
+ CCTK_WARN (CCTK_WARN_ABORT, "allocation failure (2) in imatrix()");
- /* allocate rows and set pointers to them */
- m[nrl] = (int *) malloc ((size_t) ((nrow * ncol + NR_END) * sizeof (int)));
- if (!m[nrl])
- CCTK_WARN (CCTK_WARN_ABORT, "allocation failure 2 in matrix()");
- m[nrl] += NR_END;
- m[nrl] -= ncl;
+ /* apply column and row offsets */
+ retval[0] -= ncl;
+ retval -= nrl;
- for (i = nrl + 1; i <= nrh; i++)
- m[i] = m[i - 1] + ncol;
+ /* slice chunk into rows */
+ long width = (nch-ncl+1);
+ for(long i = nrl+1 ; i <= nrh ; i++)
+ retval[i] = retval[i-1] + width;
+ assert(retval[nrh]-retval[nrl] == (nrh-nrl)*width);
- /* return pointer to array of pointers to rows */
- return m;
+ return retval;
}
/*---------------------------------------------------------------------------*/
CCTK_REAL **
dmatrix (long nrl, long nrh, long ncl, long nch)
-/* allocate a CCTK_REAL matrix with subscript range m[nrl..nrh][ncl..nch] */
+/* allocate a double matrix with subscript range m[nrl..nrh][ncl..nch] */
{
- long i, nrow = nrh - nrl + 1, ncol = nch - ncl + 1;
- CCTK_REAL **m;
+ CCTK_REAL **retval;
- /* allocate pointers to rows */
- m = (CCTK_REAL **) malloc ((size_t) ((nrow + NR_END) * sizeof (CCTK_REAL *)));
- if (!m)
- CCTK_WARN (CCTK_WARN_ABORT, "allocation failure 1 in matrix()");
- m += NR_END;
- m -= nrl;
+ retval = malloc(sizeof(CCTK_REAL *)*(nrh-nrl+1));
+ if(retval == NULL)
+ CCTK_WARN (CCTK_WARN_ABORT, "allocation failure (1) in dmatrix()");
- /* allocate rows and set pointers to them */
- m[nrl] =
- (CCTK_REAL *) malloc ((size_t) ((nrow * ncol + NR_END) * sizeof (CCTK_REAL)));
- if (!m[nrl])
- CCTK_WARN (CCTK_WARN_ABORT, "allocation failure 2 in matrix()");
- m[nrl] += NR_END;
- m[nrl] -= ncl;
+ /* get all memory for the matrix in on chunk */
+ retval[0] = malloc(sizeof(CCTK_REAL)*(nrh-nrl+1)*(nch-ncl+1));
+ if(retval[0] == NULL)
+ CCTK_WARN (CCTK_WARN_ABORT, "allocation failure (2) in dmatrix()");
- for (i = nrl + 1; i <= nrh; i++)
- m[i] = m[i - 1] + ncol;
+ /* apply column and row offsets */
+ retval[0] -= ncl;
+ retval -= nrl;
- /* return pointer to array of pointers to rows */
- return m;
+ /* slice chunk into rows */
+ long width = (nch-ncl+1);
+ for(long i = nrl+1 ; i <= nrh ; i++)
+ retval[i] = retval[i-1] + width;
+ assert(retval[nrh]-retval[nrl] == (nrh-nrl)*width);
+
+ return retval;
}
/*---------------------------------------------------------------------------*/
@@ -99,46 +100,42 @@
d3tensor (long nrl, long nrh, long ncl, long nch, long ndl, long ndh)
/* allocate a CCTK_REAL 3tensor with range t[nrl..nrh][ncl..nch][ndl..ndh] */
{
- long i, j, nrow = nrh - nrl + 1, ncol = nch - ncl + 1, ndep = ndh - ndl + 1;
- CCTK_REAL ***t;
+ CCTK_REAL ***retval;
- /* allocate pointers to pointers to rows */
- t = (CCTK_REAL ***) malloc ((size_t) ((nrow + NR_END) * sizeof (CCTK_REAL **)));
- if (!t)
- CCTK_WARN (CCTK_WARN_ABORT, "allocation failure 1 in f3tensor()");
- t += NR_END;
- t -= nrl;
+ /* get memory for index structures */
+ retval = malloc(sizeof(CCTK_REAL **)*(nrh-nrl+1));
+ if(retval == NULL)
+ CCTK_WARN (CCTK_WARN_ABORT, "allocation failure (1) in dmatrix()");
- /* allocate pointers to rows and set pointers to them */
- t[nrl] =
- (CCTK_REAL **)
- malloc ((size_t) ((nrow * ncol + NR_END) * sizeof (CCTK_REAL *)));
- if (!t[nrl])
- CCTK_WARN (CCTK_WARN_ABORT, "allocation failure 2 in f3tensor()");
- t[nrl] += NR_END;
- t[nrl] -= ncl;
+ retval[0] = malloc(sizeof(CCTK_REAL *)*(nrh-nrl+1)*(nch-ncl+1));
+ if(retval[0] == NULL)
+ CCTK_WARN (CCTK_WARN_ABORT, "allocation failure (2) in dmatrix()");
- /* allocate rows and set pointers to them */
- t[nrl][ncl] =
- (CCTK_REAL *)
- malloc ((size_t) ((nrow * ncol * ndep + NR_END) * sizeof (CCTK_REAL)));
- if (!t[nrl][ncl])
- CCTK_WARN (CCTK_WARN_ABORT, "allocation failure 3 in f3tensor()");
- t[nrl][ncl] += NR_END;
- t[nrl][ncl] -= ndl;
+ /* get all memory for the tensor in on chunk */
+ retval[0][0] = malloc(sizeof(CCTK_REAL)*(nrh-nrl+1)*(nch-ncl+1)*(nrh-nrl+1));
+ if(retval[0][0] == NULL)
+ CCTK_WARN (CCTK_WARN_ABORT, "allocation failure (3) in dmatrix()");
- for (j = ncl + 1; j <= nch; j++)
- t[nrl][j] = t[nrl][j - 1] + ndep;
- for (i = nrl + 1; i <= nrh; i++)
- {
- t[i] = t[i - 1] + ncol;
- t[i][ncl] = t[i - 1][ncl] + ncol * ndep;
- for (j = ncl + 1; j <= nch; j++)
- t[i][j] = t[i][j - 1] + ndep;
+ /* apply all offsets */
+ retval[0][0] -= ndl;
+ retval[0] -= ncl;
+ retval -= nrl;
+
+ /* slice chunk into rows and columns */
+ long width = (nch-ncl+1);
+ long depth = (ndh-ndl+1);
+ for(long i = nrl+1 ; i <= nrh ; i++) {
+ retval[i] = retval[i-1] + width;
+ retval[i][0] = retval[i-1][0] + width*depth;
+ for(long j = ncl+1 ; j <= nch ; j++) {
+ retval[i][j] = retval[i][j-1] + depth;
+ }
+ assert(retval[i][nch]-retval[i][ncl] == (ndh-ndl)*depth);
}
+ assert(retval[nrh]-retval[nrl] == (nrh-nrl)*width);
+ assert(retval[nrh][nch]-retval[nrl][ncl] == (nrh-nrl)*(nch-ncl)*depth);
- /* return pointer to array of pointers to rows */
- return t;
+ return retval;
}
/*--------------------------------------------------------------------------*/
@@ -146,15 +143,15 @@
free_ivector (int *v, long nl, long nh)
/* free an int vector allocated with ivector() */
{
- free ((FREE_ARG) (v + nl - NR_END));
+ free(v+nl);
}
/*--------------------------------------------------------------------------*/
void
free_dvector (CCTK_REAL *v, long nl, long nh)
-/* free a CCTK_REAL vector allocated with dvector() */
+/* free an double vector allocated with dvector() */
{
- free ((FREE_ARG) (v + nl - NR_END));
+ free(v+nl);
}
/*--------------------------------------------------------------------------*/
@@ -162,8 +159,8 @@
free_imatrix (int **m, long nrl, long nrh, long ncl, long nch)
/* free an int matrix allocated by imatrix() */
{
- free ((FREE_ARG) (m[nrl] + ncl - NR_END));
- free ((FREE_ARG) (m + nrl - NR_END));
+ free(m[nrl]+ncl);
+ free(m+nrl);
}
/*--------------------------------------------------------------------------*/
@@ -171,8 +168,8 @@
free_dmatrix (CCTK_REAL **m, long nrl, long nrh, long ncl, long nch)
/* free a CCTK_REAL matrix allocated by dmatrix() */
{
- free ((FREE_ARG) (m[nrl] + ncl - NR_END));
- free ((FREE_ARG) (m + nrl - NR_END));
+ free(m[nrl]+ncl);
+ free(m+nrl);
}
/*--------------------------------------------------------------------------*/
@@ -181,9 +178,9 @@
long ndl, long ndh)
/* free a CCTK_REAL f3tensor allocated by f3tensor() */
{
- free ((FREE_ARG) (t[nrl][ncl] + ndl - NR_END));
- free ((FREE_ARG) (t[nrl] + ncl - NR_END));
- free ((FREE_ARG) (t + nrl - NR_END));
+ free(t[nrl][ncl]+ndl);
+ free(t[nrl]+ncl);
+ free(t+nrl);
}
/*--------------------------------------------------------------------------*/
@@ -243,277 +240,6 @@
}
/*--------------------------------------------------------------------------*/
-#if 0
-CCTK_REAL
-atanh (CCTK_REAL x)
-{
- return 0.5 * log ((1 + x) / (1 - x));
-}
-
-/*--------------------------------------------------------------------------*/
-CCTK_REAL
-asinh (CCTK_REAL x)
-{
- return log (x + sqrt (1 + x * x));
-}
-
-/*--------------------------------------------------------------------------*/
-CCTK_REAL
-acosh (CCTK_REAL x)
-{
- return log (x + sqrt (x * x - 1));
-}
-#endif
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Cadd (dcomplex a, dcomplex b)
-{
- dcomplex c;
- c.r = a.r + b.r;
- c.i = a.i + b.i;
- return c;
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Csub (dcomplex a, dcomplex b)
-{
- dcomplex c;
- c.r = a.r - b.r;
- c.i = a.i - b.i;
- return c;
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Cmul (dcomplex a, dcomplex b)
-{
- dcomplex c;
- c.r = a.r * b.r - a.i * b.i;
- c.i = a.i * b.r + a.r * b.i;
- return c;
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-RCmul (CCTK_REAL x, dcomplex a)
-{
- dcomplex c;
- c.r = x * a.r;
- c.i = x * a.i;
- return c;
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Cdiv (dcomplex a, dcomplex b)
-{
- dcomplex c;
- CCTK_REAL r, den;
- if (fabs (b.r) >= fabs (b.i))
- {
- r = b.i / b.r;
- den = b.r + r * b.i;
- c.r = (a.r + r * a.i) / den;
- c.i = (a.i - r * a.r) / den;
- }
- else
- {
- r = b.r / b.i;
- den = b.i + r * b.r;
- c.r = (a.r * r + a.i) / den;
- c.i = (a.i * r - a.r) / den;
- }
- return c;
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Complex (CCTK_REAL re, CCTK_REAL im)
-{
- dcomplex c;
- c.r = re;
- c.i = im;
- return c;
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Conjg (dcomplex z)
-{
- dcomplex c;
- c.r = z.r;
- c.i = -z.i;
- return c;
-}
-
-/*--------------------------------------------------------------------------*/
-CCTK_REAL
-Cabs (dcomplex z)
-{
- CCTK_REAL x, y, ans, temp;
- x = fabs (z.r);
- y = fabs (z.i);
- if (x == 0.0)
- ans = y;
- else if (y == 0.0)
- ans = x;
- else if (x > y)
- {
- temp = y / x;
- ans = x * sqrt (1.0 + temp * temp);
- }
- else
- {
- temp = x / y;
- ans = y * sqrt (1.0 + temp * temp);
- }
- return ans;
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Csqrt (dcomplex z)
-{
- dcomplex c;
- CCTK_REAL x, y, w, r;
- if ((z.r == 0.0) && (z.i == 0.0))
- {
- c.r = 0.0;
- c.i = 0.0;
- return c;
- }
- else
- {
- x = fabs (z.r);
- y = fabs (z.i);
- if (x >= y)
- {
- r = y / x;
- w = sqrt (x) * sqrt (0.5 * (1.0 + sqrt (1.0 + r * r)));
- }
- else
- {
- r = x / y;
- w = sqrt (y) * sqrt (0.5 * (r + sqrt (1.0 + r * r)));
- }
- if (z.r >= 0.0)
- {
- c.r = w;
- c.i = z.i / (2.0 * w);
- }
- else
- {
- c.i = (z.i >= 0) ? w : -w;
- c.r = z.i / (2.0 * c.i);
- }
- return c;
- }
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Cexp (dcomplex z)
-{
- dcomplex c;
- CCTK_REAL exp_r = exp (z.r);
-
- c.r = exp_r * cos (z.i);
- c.i = exp_r * sin (z.i);
-
- return c;
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Clog (dcomplex z)
-{
- dcomplex c;
-
- c.r = 0.5 * log (z.r * z.r + z.i * z.i);
- c.i = atan2 (z.i, z.r);
-
- return c;
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Csin (dcomplex z)
-{
- dcomplex c;
-
- c.r = sin (z.r) * cosh (z.i);
- c.i = cos (z.r) * sinh (z.i);
-
- return c;
-}
-/*--------------------------------------------------------------------------*/
-
-dcomplex
-Ccos (dcomplex z)
-{
- dcomplex c;
-
- c.r = cos (z.r) * cosh (z.i);
- c.i = -sin (z.r) * sinh (z.i);
-
- return c;
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Ctan (dcomplex z)
-{
- return Cdiv (Csin (z), Ccos (z));
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Ccot (dcomplex z)
-{
- return Cdiv (Ccos (z), Csin (z));
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Csinh (dcomplex z)
-{
- dcomplex c;
-
- c.r = sinh (z.r) * cos (z.i);
- c.i = cosh (z.r) * sin (z.i);
-
- return c;
-}
-/*--------------------------------------------------------------------------*/
-
-dcomplex
-Ccosh (dcomplex z)
-{
- dcomplex c;
-
- c.r = cosh (z.r) * cos (z.i);
- c.i = sinh (z.r) * sin (z.i);
-
- return c;
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Ctanh (dcomplex z)
-{
- return Cdiv (Csinh (z), Ccosh (z));
-}
-
-/*--------------------------------------------------------------------------*/
-dcomplex
-Ccoth (dcomplex z)
-{
- return Cdiv (Ccosh (z), Csinh (z));
-}
-
-/*--------------------------------------------------------------------------*/
void
chebft_Zeros (CCTK_REAL u[], int n, int inv)
/* eq. 5.8.7 and 5.8.8 at x = (5.8.4) of 2nd edition C++ NR */
File [modified]: TP_utilities.h
Delta lines: +0 -33
===================================================================
--- trunk/src/TP_utilities.h 2010-03-24 00:48:53 UTC (rev 100)
+++ trunk/src/TP_utilities.h 2010-04-29 22:20:36 UTC (rev 101)
@@ -10,14 +10,7 @@
#define TINY 1.0e-20
#define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}
-#define NR_END 1
-#define FREE_ARG char*
-typedef struct DCOMPLEX
-{
- CCTK_REAL r, i;
-} dcomplex;
-
#define nrerror TP_nrerror
#define ivector TP_ivector
#define dvector TP_dvector
@@ -49,33 +42,7 @@
int maximum2 (int i, int j);
int maximum3 (int i, int j, int k);
int pow_int (int mantisse, int exponent);
-#if 0
-CCTK_REAL atanh (CCTK_REAL x);
-CCTK_REAL asinh (CCTK_REAL x);
-CCTK_REAL acosh (CCTK_REAL x);
-#endif
-dcomplex Cadd (dcomplex a, dcomplex b);
-dcomplex Csub (dcomplex a, dcomplex b);
-dcomplex Cmul (dcomplex a, dcomplex b);
-dcomplex RCmul (CCTK_REAL x, dcomplex a);
-dcomplex Cdiv (dcomplex a, dcomplex b);
-dcomplex Complex (CCTK_REAL re, CCTK_REAL im);
-dcomplex Conjg (dcomplex z);
-CCTK_REAL Cabs (dcomplex z);
-
-dcomplex Csqrt (dcomplex z);
-dcomplex Cexp (dcomplex z);
-dcomplex Clog (dcomplex z);
-dcomplex Csin (dcomplex z);
-dcomplex Ccos (dcomplex z);
-dcomplex Ctan (dcomplex z);
-dcomplex Ccot (dcomplex z);
-dcomplex Csinh (dcomplex z);
-dcomplex Ccosh (dcomplex z);
-dcomplex Ctanh (dcomplex z);
-dcomplex Ccoth (dcomplex z);
-
void chebft_Zeros (CCTK_REAL u[], int n, int inv);
void chebft_Extremes (CCTK_REAL u[], int n, int inv);
void chder (CCTK_REAL *c, CCTK_REAL *cder, int n);
