void HSItoRGB(double H, double S, double I, int *r, int *g, int *b)
{
double T,Rv,Gv,Bv;
Rv=1+S*sin(H-2*M_PI/3);
Gv=1+S*sin(H);
Bv=1+S*sin(H+2*M_PI/3);
T=255.999*I/2;
*r=itrunc(Rv*T);
*g=itrunc(Gv*T);
*b=itrunc(Bv*T);
}
T cos_pi_imp(T x, const Policy& pol)
{
BOOST_MATH_STD_USING // ADL of std names
// cos of pi*x:
bool invert = false;
if(x < 0.5)
return cos(constants::pi<T>() * x);
if(x < 1)
{
x = -x;
}
T rem = floor(x);
if(itrunc(rem, pol) & 1)
invert = !invert;
rem = x - rem;
if(rem > 0.5f)
{
rem = 1 - rem;
invert = !invert;
}
if(rem == 0.5f)
return 0;
rem = cos(constants::pi<T>() * rem);
return invert ? T(-rem) : rem;
}
/*
* release an inode.
* decrease the reference count, write updates to disk if nessary.
* also check the link count, if zero, trucate it.
* */
void iput(struct inode *ip){
ushort dev;
if(ip==NULL)
panic("bad struct inode*");
ip->i_flag |= I_LOCK;
if (ip->i_count > 0) {
ip->i_count--;
}
if (ip->i_count==0){
if (ip->i_nlink==0) {
itrunc(ip);
ifree(ip->i_dev, ip->i_num);
}
// if it's a device file, the dev number is stored in zone[0].
dev = ip->i_zone[0];
switch (ip->i_mode & S_IFMT) {
case S_IFBLK:
(*bdevsw[MAJOR(dev)].d_close)(dev);
break;
case S_IFCHR:
(*cdevsw[MAJOR(dev)].d_close)(dev);
break;
}
iupdate(ip);
ip->i_flag = 0;
ip->i_num = 0;
}
unlk_ino(ip);
}
inline T falling_factorial_imp(T x, unsigned n, const Policy& pol)
{
BOOST_STATIC_ASSERT(!boost::is_integral<T>::value);
BOOST_MATH_STD_USING // ADL of std names
if((x == 0) && (n >= 0))
return 0;
if(x < 0)
{
//
// For x < 0 we really have a rising factorial
// modulo a possible change of sign:
//
return (n&1 ? -1 : 1) * rising_factorial(-x, n, pol);
}
if(n == 0)
return 1;
if(x < 0.5f)
{
//
// 1 + x below will throw away digits, so split up calculation:
//
if(n > max_factorial<T>::value - 2)
{
// If the two end of the range are far apart we have a ratio of two very large
// numbers, split the calculation up into two blocks:
T t1 = x * boost::math::falling_factorial(x - 1, max_factorial<T>::value - 2);
T t2 = boost::math::falling_factorial(x - max_factorial<T>::value + 1, n - max_factorial<T>::value + 1);
if(tools::max_value<T>() / fabs(t1) < fabs(t2))
return boost::math::sign(t1) * boost::math::sign(t2) * policies::raise_overflow_error<T>("boost::math::falling_factorial<%1%>", 0, pol);
return t1 * t2;
}
return x * boost::math::falling_factorial(x - 1, n - 1);
}
if(x <= n - 1)
{
//
// x+1-n will be negative and tgamma_delta_ratio won't
// handle it, split the product up into three parts:
//
T xp1 = x + 1;
unsigned n2 = itrunc((T)floor(xp1), pol);
if(n2 == xp1)
return 0;
T result = boost::math::tgamma_delta_ratio(xp1, -static_cast<T>(n2), pol);
x -= n2;
result *= x;
++n2;
if(n2 < n)
result *= falling_factorial(x - 1, n - n2, pol);
return result;
}
//
// Simple case: just the ratio of two
// (positive argument) gamma functions.
// Note that we don't optimise this for small n,
// because tgamma_delta_ratio is alreay optimised
// for that use case:
//
return boost::math::tgamma_delta_ratio(x + 1, -static_cast<T>(n), pol);
}
inline T cyl_bessel_j_prime_imp(T v, T x, const Policy& pol)
{
static const char* const function = "boost::math::cyl_bessel_j_prime<%1%>(%1%,%1%)";
BOOST_MATH_STD_USING
//
// Prevent complex result:
//
if (x < 0 && floor(v) != v)
return boost::math::policies::raise_domain_error<T>(
function,
"Got x = %1%, but function requires x >= 0", x, pol);
//
// Special cases for x == 0:
//
if (x == 0)
{
if (v == 1)
return 0.5;
else if (v == -1)
return -0.5;
else if (floor(v) == v || v > 1)
return 0;
else return boost::math::policies::raise_domain_error<T>(
function,
"Got x = %1%, but function is indeterminate for this order", x, pol);
}
//
// Special case for large x: use asymptotic expansion:
//
if (boost::math::detail::asymptotic_bessel_derivative_large_x_limit(v, x))
return boost::math::detail::asymptotic_bessel_j_derivative_large_x_2(v, x);
//
// Special case for small x: use Taylor series:
//
if ((abs(x) < 5) || (abs(v) > x * x / 4))
{
bool inversed = false;
if (floor(v) == v && v < 0)
{
v = -v;
if (itrunc(v, pol) & 1)
inversed = true;
}
T r = boost::math::detail::bessel_j_derivative_small_z_series(v, x, pol);
return inversed ? T(-r) : r;
}
//
// Special case for v == 0:
//
if (v == 0)
return -boost::math::detail::cyl_bessel_j_imp<T>(1, x, Tag(), pol);
//
// Default case:
//
return boost::math::detail::bessel_j_derivative_linear(v, x, Tag(), pol);
}
T float_advance(T val, int distance, const Policy& pol)
{
//
// Error handling:
//
static const char* function = "float_advance<%1%>(%1%, int)";
if(!(boost::math::isfinite)(val))
return policies::raise_domain_error<T>(
function,
"Argument val must be finite, but got %1%", val, pol);
if(val < 0)
return -float_advance(-val, -distance, pol);
if(distance == 0)
return val;
if(distance == 1)
return float_next(val, pol);
if(distance == -1)
return float_prior(val, pol);
BOOST_MATH_STD_USING
int expon;
frexp(val, &expon);
T limit = ldexp((distance < 0 ? T(0.5f) : T(1)), expon);
if(val <= tools::min_value<T>())
{
limit = sign(T(distance)) * tools::min_value<T>();
}
T limit_distance = float_distance(val, limit);
while(fabs(limit_distance) < abs(distance))
{
distance -= itrunc(limit_distance);
val = limit;
if(distance < 0)
{
limit /= 2;
expon--;
}
else
{
limit *= 2;
expon++;
}
limit_distance = float_distance(val, limit);
}
if((0.5f == frexp(val, &expon)) && (distance < 0))
--expon;
T diff = 0;
if(val != 0)
diff = distance * ldexp(T(1), expon - tools::digits<T>());
if(diff == 0)
diff = distance * detail::get_smallest_value<T>();
return val += diff;
}
inline RealType cdf(const complemented2_type<hypergeometric_distribution<RealType, Policy>, U>& c)
{
BOOST_MATH_STD_USING
static const char* function = "boost::math::cdf(const hypergeometric_distribution<%1%>&, const %1%&)";
RealType r = static_cast<RealType>(c.param);
unsigned u = itrunc(r, typename policies::normalise<Policy, policies::rounding_error<policies::ignore_error> >::type());
if(u != r)
{
return boost::math::policies::raise_domain_error<RealType>(
function, "Random variable out of range: must be an integer but got %1%", r, Policy());
}
return cdf(complement(c.dist, u));
}
/*
* open a file. flag indicated opened type like O_RDONLY, O_TRUNC, O_CREAT and blah. And
* mode only used in the O_CREAT scenary, indicated the file (inode) type.
*
* each proc has got one user file table(p_ofile[NOFILE]), it's each entry is also a number,
* indicated the number in the system file table(file[NFILE]). when user opened a file, it
* first allocate a user file table entry(aka. file descriptor), then attach it with a system
* file table entry. It's reference count is increased in fork() or dup().
* */
int do_open(char *path, uint flag, uint mode){
struct inode *ip;
struct file *fp;
ushort dev;
int fd;
// on create a new file.
if (flag & O_CREAT){
ip = namei(path, 1);
// if file is not existing yet.
if (ip->i_nlink==0) {
ip->i_mode = mode;
ip->i_uid = cu->p_euid;
ip->i_gid = cu->p_egid;
ip->i_mtime = time();
ip->i_nlink = 1;
iupdate(ip);
}
}
// an existing file.
else {
ip = namei(path, 0);
if (ip == NULL){
syserr(ENFILE);
return -1;
}
// TODO: check access
// if it's a device file, the dev number is stored in zone[0].
dev = ip->i_zone[0];
switch(ip->i_mode & S_IFMT) {
case S_IFBLK:
(*bdevsw[MAJOR(dev)].d_open)(dev);
break;
case S_IFCHR:
(*cdevsw[MAJOR(dev)].d_open)(dev);
break;
}
}
if (((fd=ufalloc())<0) || (fp=falloc(fd))==NULL) {
iput(ip);
return -1;
}
if (flag & O_TRUNC){
itrunc(ip);
}
unlk_ino(ip);
fp->f_oflag = flag;
fp->f_ino = ip;
cu->p_fdflag[fd] = FD_CLOEXEC;
return fd;
}
/* reference of ip - 1
* if it is the last ref, this node can be recycle (ref = 1) (?)
* and if this inode have no link to it (nlinks = 0)
* free this inode in the disk
*/
void iput(struct inode *ip) {
if (ip->ref == 1 && ip->flags & I_VALID && ip->nlinks == 0) {
/* can not free a locked inode */
ip->flags |= I_BUSY;
itrunc(ip);
_ifree(ip->dev, ip->ino);
// ip-> ref == 0
// ip->flags = 0;
}
ip->ref--;
}
T gamma_imp(T z, const Policy& pol, const lanczos::undefined_lanczos& l)
{
static const char* function = "boost::math::tgamma<%1%>(%1%)";
BOOST_MATH_STD_USING
if((z <= 0) && (floor(z) == z))
return policies::raise_pole_error<T>(function, "Evaluation of tgamma at a negative integer %1%.", z, pol);
if(z <= -20)
{
T result = gamma_imp(-z, pol, l) * sinpx(z);
if((fabs(result) < 1) && (tools::max_value<T>() * fabs(result) < boost::math::constants::pi<T>()))
return policies::raise_overflow_error<T>(function, "Result of tgamma is too large to represent.", pol);
result = -boost::math::constants::pi<T>() / result;
if(result == 0)
return policies::raise_underflow_error<T>(function, "Result of tgamma is too small to represent.", pol);
if((boost::math::fpclassify)(result) == (int)FP_SUBNORMAL)
return policies::raise_denorm_error<T>(function, "Result of tgamma is denormalized.", result, pol);
return result;
}
//
// The upper gamma fraction is *very* slow for z < 6, actually it's very
// slow to converge everywhere but recursing until z > 6 gets rid of the
// worst of it's behaviour.
//
T prefix = 1;
while(z < 6)
{
prefix /= z;
z += 1;
}
BOOST_MATH_INSTRUMENT_CODE(prefix);
if((floor(z) == z) && (z < max_factorial<T>::value))
{
prefix *= unchecked_factorial<T>(itrunc(z, pol) - 1);
}
else
{
prefix = prefix * pow(z / boost::math::constants::e<T>(), z);
BOOST_MATH_INSTRUMENT_CODE(prefix);
T sum = detail::lower_gamma_series(z, z, pol) / z;
BOOST_MATH_INSTRUMENT_CODE(sum);
sum += detail::upper_gamma_fraction(z, z, ::boost::math::policies::digits<T, Policy>());
BOOST_MATH_INSTRUMENT_CODE(sum);
if(fabs(tools::max_value<T>() / prefix) < fabs(sum))
return policies::raise_overflow_error<T>(function, "Result of tgamma is too large to represent.", pol);
BOOST_MATH_INSTRUMENT_CODE((sum * prefix));
return sum * prefix;
}
return prefix;
}
/*
* Drop a reference to an in-memory inode. If that was the last reference, the
* inode cache entry can be recycled.
*
* If that was the last reference and the inode has no links to it, free the
* inode (and its content) on disk.
*/
void iput(struct inode *ip)
{
acquire(&icache.lock);
if (ip->ref == 1 && (ip->flags & I_VALID) && ip->nlink == 0) {
/* inode has no links: truncate and free inode. */
if (ip->flags & I_BUSY)
panic("iput busy");
ip->flags |= I_BUSY;
release(&icache.lock);
itrunc(ip);
ip->type = 0;
iupdate(ip);
acquire(&icache.lock);
ip->flags = 0;
wakeup(ip);
}
ip->ref--;
release(&icache.lock);
}
inline T falling_factorial_imp(T x, unsigned n, const Policy& pol)
{
BOOST_STATIC_ASSERT(!lslboost::is_integral<T>::value);
BOOST_MATH_STD_USING // ADL of std names
if(x == 0)
return 0;
if(x < 0)
{
//
// For x < 0 we really have a rising factorial
// modulo a possible change of sign:
//
return (n&1 ? -1 : 1) * rising_factorial(-x, n, pol);
}
if(n == 0)
return 1;
if(x < n-1)
{
//
// x+1-n will be negative and tgamma_delta_ratio won't
// handle it, split the product up into three parts:
//
T xp1 = x + 1;
unsigned n2 = itrunc((T)floor(xp1), pol);
if(n2 == xp1)
return 0;
T result = lslboost::math::tgamma_delta_ratio(xp1, -static_cast<T>(n2), pol);
x -= n2;
result *= x;
++n2;
if(n2 < n)
result *= falling_factorial(x - 1, n - n2, pol);
return result;
}
//
// Simple case: just the ratio of two
// (positive argument) gamma functions.
// Note that we don't optimise this for small n,
// because tgamma_delta_ratio is alreay optimised
// for that use case:
//
return lslboost::math::tgamma_delta_ratio(x + 1, -static_cast<T>(n), pol);
}
// Drop a reference to an in-memory inode.
// If that was the last reference, the inode cache entry can
// be recycled.
// If that was the last reference and the inode has no links
// to it, free the inode (and its content) on disk.
// All calls to iput() must be inside a transaction in
// case it has to free the inode.
void iput(struct inode* ip)
{
// cprintf("iput %d \n",ip->inum);
acquire(&icache.lock);
if (ip->ref == 1 && (ip->flags & I_VALID) && ip->nlink == 0) {
// inode has no links and no other references: truncate and free.
if (ip->flags & I_BUSY)
panic("iput busy");
ip->flags |= I_BUSY;
release(&icache.lock);
itrunc(ip);
ip->type = 0;
iupdate(ip);
acquire(&icache.lock);
ip->flags = 0;
wakeup(ip);
}
ip->ref--;
release(&icache.lock);
}
T non_central_t2_p(T v, T delta, T x, T y, const Policy& pol, T init_val)
{
BOOST_MATH_STD_USING
//
// Variables come first:
//
boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
T errtol = policies::get_epsilon<T, Policy>();
T d2 = delta * delta / 2;
//
// k is the starting point for iteration, and is the
// maximum of the poisson weighting term, we don't
// ever allow k == 0 as this can lead to catastrophic
// cancellation errors later (test case is v = 1621286869049072.3
// delta = 0.16212868690490723, x = 0.86987415482475994).
//
int k = itrunc(d2);
T pois;
if(k == 0) k = 1;
// Starting Poisson weight:
pois = gamma_p_derivative(T(k+1), d2, pol)
* tgamma_delta_ratio(T(k + 1), T(0.5f))
* delta / constants::root_two<T>();
if(pois == 0)
return init_val;
T xterm, beta;
// Recurrance & starting beta terms:
beta = x < y
? detail::ibeta_imp(T(k + 1), T(v / 2), x, pol, false, true, &xterm)
: detail::ibeta_imp(T(v / 2), T(k + 1), y, pol, true, true, &xterm);
xterm *= y / (v / 2 + k);
T poisf(pois), betaf(beta), xtermf(xterm);
T sum = init_val;
if((xterm == 0) && (beta == 0))
return init_val;
//
// Backwards recursion first, this is the stable
// direction for recursion:
//
boost::uintmax_t count = 0;
T last_term = 0;
for(int i = k; i >= 0; --i)
{
T term = beta * pois;
sum += term;
// Don't terminate on first term in case we "fixed" k above:
if((fabs(last_term) > fabs(term)) && fabs(term/sum) < errtol)
break;
last_term = term;
pois *= (i + 0.5f) / d2;
beta += xterm;
xterm *= (i) / (x * (v / 2 + i - 1));
++count;
}
last_term = 0;
for(int i = k + 1; ; ++i)
{
poisf *= d2 / (i + 0.5f);
xtermf *= (x * (v / 2 + i - 1)) / (i);
betaf -= xtermf;
T term = poisf * betaf;
sum += term;
if((fabs(last_term) > fabs(term)) && (fabs(term/sum) < errtol))
break;
last_term = term;
++count;
if(count > max_iter)
{
return policies::raise_evaluation_error(
"cdf(non_central_t_distribution<%1%>, %1%)",
"Series did not converge, closest value was %1%", sum, pol);
}
}
return sum;
}
T non_central_t2_q(T v, T delta, T x, T y, const Policy& pol, T init_val)
{
BOOST_MATH_STD_USING
//
// Variables come first:
//
boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
T errtol = boost::math::policies::get_epsilon<T, Policy>();
T d2 = delta * delta / 2;
//
// k is the starting point for iteration, and is the
// maximum of the poisson weighting term, we don't allow
// k == 0 as this can cause catastrophic cancellation errors
// (test case is v = 561908036470413.25, delta = 0.056190803647041321,
// x = 1.6155232703966216):
//
int k = itrunc(d2);
if(k == 0) k = 1;
// Starting Poisson weight:
T pois;
if((k < (int)(max_factorial<T>::value)) && (d2 < tools::log_max_value<T>()) && (log(d2) * k < tools::log_max_value<T>()))
{
//
// For small k we can optimise this calculation by using
// a simpler reduced formula:
//
pois = exp(-d2);
pois *= pow(d2, static_cast<T>(k));
pois /= boost::math::tgamma(T(k + 1 + 0.5), pol);
pois *= delta / constants::root_two<T>();
}
else
{
pois = gamma_p_derivative(T(k+1), d2, pol)
* tgamma_delta_ratio(T(k + 1), T(0.5f))
* delta / constants::root_two<T>();
}
if(pois == 0)
return init_val;
// Recurance term:
T xterm;
T beta;
// Starting beta term:
if(k != 0)
{
beta = x < y
? detail::ibeta_imp(T(k + 1), T(v / 2), x, pol, true, true, &xterm)
: detail::ibeta_imp(T(v / 2), T(k + 1), y, pol, false, true, &xterm);
xterm *= y / (v / 2 + k);
}
else
{
beta = pow(y, v / 2);
xterm = beta;
}
T poisf(pois), betaf(beta), xtermf(xterm);
T sum = init_val;
if((xterm == 0) && (beta == 0))
return init_val;
//
// Fused forward and backwards recursion:
//
boost::uintmax_t count = 0;
T last_term = 0;
for(int i = k + 1, j = k; ; ++i, --j)
{
poisf *= d2 / (i + 0.5f);
xtermf *= (x * (v / 2 + i - 1)) / (i);
betaf += xtermf;
T term = poisf * betaf;
if(j >= 0)
{
term += beta * pois;
pois *= (j + 0.5f) / d2;
beta -= xterm;
xterm *= (j) / (x * (v / 2 + j - 1));
}
sum += term;
// Don't terminate on first term in case we "fixed" the value of k above:
if((fabs(last_term) > fabs(term)) && fabs(term/sum) < errtol)
break;
last_term = term;
if(count > max_iter)
{
return policies::raise_evaluation_error(
"cdf(non_central_t_distribution<%1%>, %1%)",
"Series did not converge, closest value was %1%", sum, pol);
}
++count;
}
return sum;
}
inline T modf(const T& v, int* ipart, const Policy& pol)
{
*ipart = itrunc(v, pol);
return v - *ipart;
}
inline int itrunc(const T& v)
{
return itrunc(v, policies::policy<>());
}
inline int itrunc(__gmp_expr<T,U> const& x, const Policy& pol)
{
return itrunc(static_cast<mpfr_class>(x), pol);
}
T float_advance(T val, int distance, const Policy& pol)
{
BOOST_MATH_STD_USING
//
// Error handling:
//
static const char* function = "float_advance<%1%>(%1%, int)";
int fpclass = (pdalboost::math::fpclassify)(val);
if((fpclass == FP_NAN) || (fpclass == FP_INFINITE))
return policies::raise_domain_error<T>(
function,
"Argument val must be finite, but got %1%", val, pol);
if(val < 0)
return -float_advance(-val, -distance, pol);
if(distance == 0)
return val;
if(distance == 1)
return float_next(val, pol);
if(distance == -1)
return float_prior(val, pol);
if(fabs(val) < detail::get_min_shift_value<T>())
{
//
// Special case: if the value of the least significant bit is a denorm,
// implement in terms of float_next/float_prior.
// This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set.
//
if(distance > 0)
{
do{ val = float_next(val, pol); } while(--distance);
}
else
{
do{ val = float_prior(val, pol); } while(++distance);
}
return val;
}
int expon;
frexp(val, &expon);
T limit = ldexp((distance < 0 ? T(0.5f) : T(1)), expon);
if(val <= tools::min_value<T>())
{
limit = sign(T(distance)) * tools::min_value<T>();
}
T limit_distance = float_distance(val, limit);
while(fabs(limit_distance) < abs(distance))
{
distance -= itrunc(limit_distance);
val = limit;
if(distance < 0)
{
limit /= 2;
expon--;
}
else
{
limit *= 2;
expon++;
}
limit_distance = float_distance(val, limit);
if(distance && (limit_distance == 0))
{
policies::raise_evaluation_error<T>(function, "Internal logic failed while trying to increment floating point value %1%: most likely your FPU is in non-IEEE conforming mode.", val, pol);
}
}
if((0.5f == frexp(val, &expon)) && (distance < 0))
--expon;
T diff = 0;
if(val != 0)
diff = distance * ldexp(T(1), expon - tools::digits<T>());
if(diff == 0)
diff = distance * detail::get_smallest_value<T>();
return val += diff;
}
T gamma_imp(T z, const Policy& pol, const L& l)
{
BOOST_MATH_STD_USING
T result = 1;
#ifdef BOOST_MATH_INSTRUMENT
static bool b = false;
if(!b)
{
std::cout << "tgamma_imp called with " << typeid(z).name() << " " << typeid(l).name() << std::endl;
b = true;
}
#endif
static const char* function = "boost::math::tgamma<%1%>(%1%)";
if(z <= 0)
{
if(floor(z) == z)
return policies::raise_pole_error<T>(function, "Evaluation of tgamma at a negative integer %1%.", z, pol);
if(z <= -20)
{
result = gamma_imp(-z, pol, l) * sinpx(z);
if((fabs(result) < 1) && (tools::max_value<T>() * fabs(result) < boost::math::constants::pi<T>()))
return policies::raise_overflow_error<T>(function, "Result of tgamma is too large to represent.", pol);
result = -boost::math::constants::pi<T>() / result;
if(result == 0)
return policies::raise_underflow_error<T>(function, "Result of tgamma is too small to represent.", pol);
if((boost::math::fpclassify)(result) == (int)FP_SUBNORMAL)
return policies::raise_denorm_error<T>(function, "Result of tgamma is denormalized.", result, pol);
return result;
}
// shift z to > 1:
while(z < 0)
{
result /= z;
z += 1;
}
}
if((floor(z) == z) && (z < max_factorial<T>::value))
{
result *= unchecked_factorial<T>(itrunc(z, pol) - 1);
}
else
{
result *= L::lanczos_sum(z);
if(z * log(z) > tools::log_max_value<T>())
{
// we're going to overflow unless this is done with care:
T zgh = (z + static_cast<T>(L::g()) - boost::math::constants::half<T>());
if(log(zgh) * z / 2 > tools::log_max_value<T>())
return policies::raise_overflow_error<T>(function, "Result of tgamma is too large to represent.", pol);
T hp = pow(zgh, (z / 2) - T(0.25));
result *= hp / exp(zgh);
if(tools::max_value<T>() / hp < result)
return policies::raise_overflow_error<T>(function, "Result of tgamma is too large to represent.", pol);
result *= hp;
}
else
{
T zgh = (z + static_cast<T>(L::g()) - boost::math::constants::half<T>());
result *= pow(zgh, z - boost::math::constants::half<T>()) / exp(zgh);
}
}
return result;
}