static void init(char meth)
{
int i,j,ind;
for( i=0;i<nx;i++ ) {
*(x0+i)=i*hx;
*(t0+i)=0.0;
*(v+i)=(*(f+i));
*(s+i)=1/(*(f+i));
*(q+i)=1.0;
ind=i;
for( j=1;j<nz;j++ ) {
ind+=nx;
*(x0+ind)=0.0;
*(t0+ind)=INFTY;
*(v+ind)=0.0;
}
for( j=1;j<nt;j++ ){
ind=i+j*nx;
*(q+ind)=1.0;
}
}
if ('c'==meth) chebyshev_init();
fastmarch_init(nx,nz,nt,
hx,hz,ht,
x0,t0,v,s);
}
static gnm_float lgammacor(gnm_float x)
{
static const gnm_float algmcs[15] = {
GNM_const(+.1666389480451863247205729650822e+0),
GNM_const(-.1384948176067563840732986059135e-4),
GNM_const(+.9810825646924729426157171547487e-8),
GNM_const(-.1809129475572494194263306266719e-10),
GNM_const(+.6221098041892605227126015543416e-13),
GNM_const(-.3399615005417721944303330599666e-15),
GNM_const(+.2683181998482698748957538846666e-17),
GNM_const(-.2868042435334643284144622399999e-19),
GNM_const(+.3962837061046434803679306666666e-21),
GNM_const(-.6831888753985766870111999999999e-23),
GNM_const(+.1429227355942498147573333333333e-24),
GNM_const(-.3547598158101070547199999999999e-26),
GNM_const(+.1025680058010470912000000000000e-27),
GNM_const(-.3401102254316748799999999999999e-29),
GNM_const(+.1276642195630062933333333333333e-30)
};
gnm_float tmp;
#ifdef NOMORE_FOR_THREADS
static int nalgm = 0;
static gnm_float xbig = 0, xmax = 0;
/* Initialize machine dependent constants, the first time gamma() is called.
FIXME for threads ! */
if (nalgm == 0) {
/* For IEEE gnm_float precision : nalgm = 5 */
nalgm = chebyshev_init(algmcs, 15, GNM_EPSILON/2);/*was d1mach(3)*/
xbig = 1 / gnm_sqrt(GNM_EPSILON/2); /* ~ 94906265.6 for IEEE gnm_float */
xmax = gnm_exp(fmin2(gnm_log(GNM_MAX / 12), -gnm_log(12 * GNM_MIN)));
/* = GNM_MAX / 48 ~= 3.745e306 for IEEE gnm_float */
}
#else
/* For IEEE gnm_float precision GNM_EPSILON = 2^-52 = GNM_const(2.220446049250313e-16) :
* xbig = 2 ^ 26.5
* xmax = GNM_MAX / 48 = 2^1020 / 3 */
# define nalgm 5
# define xbig GNM_const(94906265.62425156)
# define xmax GNM_const(3.745194030963158e306)
#endif
if (x < 10)
ML_ERR_return_NAN
else if (x >= xmax) {
ML_ERROR(ME_UNDERFLOW);
return ML_UNDERFLOW;
}
else if (x < xbig) {
tmp = 10 / x;
return chebyshev_eval(tmp * tmp * 2 - 1, algmcs, nalgm) / x;
}
else return 1 / (x * 12);
}
int main (void)
{
int i;
float x, y, x1=1.0f, x2=2.0f, d[N];
for (i=0; i < N; i++) {
x = cosf(i*SF_PI/(N-1));
x = 0.5*x+1.5;
d[i] = x*x*x-x*x+1.0;
}
chebyshev_init(N,d,x1,x2);
x = 1.1;
y = x*x*x-x*x+1.0;
printf("Compare %g and %g\n",y,chebyshev(x));
}
double gammafn(double x)
{
const static double gamcs[42] = {
+.8571195590989331421920062399942e-2,
+.4415381324841006757191315771652e-2,
+.5685043681599363378632664588789e-1,
-.4219835396418560501012500186624e-2,
+.1326808181212460220584006796352e-2,
-.1893024529798880432523947023886e-3,
+.3606925327441245256578082217225e-4,
-.6056761904460864218485548290365e-5,
+.1055829546302283344731823509093e-5,
-.1811967365542384048291855891166e-6,
+.3117724964715322277790254593169e-7,
-.5354219639019687140874081024347e-8,
+.9193275519859588946887786825940e-9,
-.1577941280288339761767423273953e-9,
+.2707980622934954543266540433089e-10,
-.4646818653825730144081661058933e-11,
+.7973350192007419656460767175359e-12,
-.1368078209830916025799499172309e-12,
+.2347319486563800657233471771688e-13,
-.4027432614949066932766570534699e-14,
+.6910051747372100912138336975257e-15,
-.1185584500221992907052387126192e-15,
+.2034148542496373955201026051932e-16,
-.3490054341717405849274012949108e-17,
+.5987993856485305567135051066026e-18,
-.1027378057872228074490069778431e-18,
+.1762702816060529824942759660748e-19,
-.3024320653735306260958772112042e-20,
+.5188914660218397839717833550506e-21,
-.8902770842456576692449251601066e-22,
+.1527474068493342602274596891306e-22,
-.2620731256187362900257328332799e-23,
+.4496464047830538670331046570666e-24,
-.7714712731336877911703901525333e-25,
+.1323635453126044036486572714666e-25,
-.2270999412942928816702313813333e-26,
+.3896418998003991449320816639999e-27,
-.6685198115125953327792127999999e-28,
+.1146998663140024384347613866666e-28,
-.1967938586345134677295103999999e-29,
+.3376448816585338090334890666666e-30,
-.5793070335782135784625493333333e-31
};
int i, n;
double y;
double sinpiy, value;
#ifdef NOMORE_FOR_THREADS
static int ngam = 0;
static double xmin = 0, xmax = 0., xsml = 0., dxrel = 0.;
/* Initialize machine dependent constants, the first time gamma() is called.
FIXME for threads ! */
if (ngam == 0) {
ngam = chebyshev_init(gamcs, 42, DBL_EPSILON/20);/*was .1*d1mach(3)*/
gammalims(&xmin, &xmax);/*-> ./gammalims.c */
xsml = exp(fmax2(log(DBL_MIN), -log(DBL_MAX)) + 0.01);
/* = exp(.01)*DBL_MIN = 2.247e-308 for IEEE */
dxrel = sqrt(DBL_EPSILON);/*was sqrt(d1mach(4)) */
}
#else
/* For IEEE double precision DBL_EPSILON = 2^-52 = 2.220446049250313e-16 :
* (xmin, xmax) are non-trivial, see ./gammalims.c
* xsml = exp(.01)*DBL_MIN
* dxrel = sqrt(DBL_EPSILON) = 2 ^ -26
*/
# define ngam 22
# define xmin -170.5674972726612
# define xmax 171.61447887182298
# define xsml 2.2474362225598545e-308
# define dxrel 1.490116119384765696e-8
#endif
if(ISNAN(x)) return x;
/* If the argument is exactly zero or a negative integer
* then return NaN. */
if (x == 0 || (x < 0 && x == (long)x)) {
ML_ERROR(ME_DOMAIN, "gammafn");
return ML_NAN;
}
y = fabs(x);
if (y <= 10) {
/* Compute gamma(x) for -10 <= x <= 10
* Reduce the interval and find gamma(1 + y) for 0 <= y < 1
* first of all. */
n = (int) x;
if(x < 0) --n;
y = x - n;/* n = floor(x) ==> y in [ 0, 1 ) */
--n;
value = chebyshev_eval(y * 2 - 1, gamcs, ngam) + .9375;
if (n == 0)
return value;/* x = 1.dddd = 1+y */
if (n < 0) {
/* compute gamma(x) for -10 <= x < 1 */
/* exact 0 or "-n" checked already above */
/* The answer is less than half precision */
/* because x too near a negative integer. */
if (x < -0.5 && fabs(x - (int)(x - 0.5) / x) < dxrel) {
ML_ERROR(ME_PRECISION, "gammafn");
}
/* The argument is so close to 0 that the result would overflow. */
if (y < xsml) {
ML_ERROR(ME_RANGE, "gammafn");
if(x > 0) return ML_POSINF;
else return ML_NEGINF;
}
n = -n;
for (i = 0; i < n; i++) {
value /= (x + i);
}
return value;
}
else {
/* gamma(x) for 2 <= x <= 10 */
for (i = 1; i <= n; i++) {
value *= (y + i);
}
return value;
}
}
else {
/* gamma(x) for y = |x| > 10. */
if (x > xmax) { /* Overflow */
ML_ERROR(ME_RANGE, "gammafn");
return ML_POSINF;
}
if (x < xmin) { /* Underflow */
ML_ERROR(ME_UNDERFLOW, "gammafn");
return 0.;
}
if(y <= 50 && y == (int)y) { /* compute (n - 1)! */
value = 1.;
for (i = 2; i < y; i++) value *= i;
}
else { /* normal case */
value = exp((y - 0.5) * log(y) - y + M_LN_SQRT_2PI +
((2*y == (int)2*y)? stirlerr(y) : lgammacor(y)));
}
if (x > 0)
return value;
if (fabs((x - (int)(x - 0.5))/x) < dxrel){
/* The answer is less than half precision because */
/* the argument is too near a negative integer. */
ML_ERROR(ME_PRECISION, "gammafn");
}
sinpiy = sin(M_PI * y);
if (sinpiy == 0) { /* Negative integer arg - overflow */
ML_ERROR(ME_RANGE, "gammafn");
return ML_POSINF;
}
return -M_PI / (y * sinpiy * value);
}
}
double log1p(double x)
{
/* series for log1p on the interval -.375 to .375
* with weighted error 6.35e-32
* log weighted error 31.20
* significant figures required 30.93
* decimal places required 32.01
*/
const static double alnrcs[43] = {
+.10378693562743769800686267719098e+1,
-.13364301504908918098766041553133e+0,
+.19408249135520563357926199374750e-1,
-.30107551127535777690376537776592e-2,
+.48694614797154850090456366509137e-3,
-.81054881893175356066809943008622e-4,
+.13778847799559524782938251496059e-4,
-.23802210894358970251369992914935e-5,
+.41640416213865183476391859901989e-6,
-.73595828378075994984266837031998e-7,
+.13117611876241674949152294345011e-7,
-.23546709317742425136696092330175e-8,
+.42522773276034997775638052962567e-9,
-.77190894134840796826108107493300e-10,
+.14075746481359069909215356472191e-10,
-.25769072058024680627537078627584e-11,
+.47342406666294421849154395005938e-12,
-.87249012674742641745301263292675e-13,
+.16124614902740551465739833119115e-13,
-.29875652015665773006710792416815e-14,
+.55480701209082887983041321697279e-15,
-.10324619158271569595141333961932e-15,
+.19250239203049851177878503244868e-16,
-.35955073465265150011189707844266e-17,
+.67264542537876857892194574226773e-18,
-.12602624168735219252082425637546e-18,
+.23644884408606210044916158955519e-19,
-.44419377050807936898878389179733e-20,
+.83546594464034259016241293994666e-21,
-.15731559416479562574899253521066e-21,
+.29653128740247422686154369706666e-22,
-.55949583481815947292156013226666e-23,
+.10566354268835681048187284138666e-23,
-.19972483680670204548314999466666e-24,
+.37782977818839361421049855999999e-25,
-.71531586889081740345038165333333e-26,
+.13552488463674213646502024533333e-26,
-.25694673048487567430079829333333e-27,
+.48747756066216949076459519999999e-28,
-.92542112530849715321132373333333e-29,
+.17578597841760239233269760000000e-29,
-.33410026677731010351377066666666e-30,
+.63533936180236187354180266666666e-31,
};
#ifdef NOMORE_FOR_THREADS
static int nlnrel = 0;
static double xmin = 0.0;
if (xmin == 0.0) xmin = -1 + sqrt(DBL_EPSILON);/*was sqrt(d1mach(4)); */
if (nlnrel == 0) /* initialize chebychev coefficients */
nlnrel = chebyshev_init(alnrcs, 43, DBL_EPSILON/20);/*was .1*d1mach(3)*/
#else
# define nlnrel 22
const static double xmin = -0.999999985;
/* 22: for IEEE double precision where DBL_EPSILON = 2.22044604925031e-16 */
#endif
if (x == 0.) return 0.;/* speed */
if (x == -1) return(ML_NEGINF);
if (x < -1) ML_ERR_return_NAN;
if (fabs(x) <= .375) {
/* Improve on speed (only);
again give result accurate to IEEE double precision: */
if(fabs(x) < .5 * DBL_EPSILON)
return x;
if( (0 < x && x < 1e-8) || (-1e-9 < x && x < 0))
return x * (1 - .5 * x);
/* else */
return x * (1 - x * chebyshev_eval(x / .375, alnrcs, nlnrel));
}
/* else */
if (x < xmin) {
/* answer less than half precision because x too near -1 */
ML_ERROR(ME_PRECISION, "log1p");
}
return log(1 + x);
}
