Supported Special Functions

The following special functions (with some duplicates of the intrinsic versions, but with different names) are defined within the Phoenix PML language. The detailed C language code implementing each can be found in <Phoenix_install_dir>\application\lib\NLME\Executables\mutil.c.

Name	Usage	Definition
CalcTMax	CalcTMax(A, a, B, b, C, c);	obtain Tmax for a macro-parameter model
ilogit iloglog icloglog iprobit	ilogit(x); iloglog(x); icloglog(x); iprobit(x);	exp(x)/(exp(x)+1) inverse log-log link function inverse complementary log-log link function inverse probit (same as phi(x))
lambertw	lambertw(const z);	inverse of x(y)=y*exp(y)
lgamm factorial	lgamm(x); factorial(x);	gamma function x!=x(x – 1)…*1
lnegbin_rp megnin_rp	lnegbin_rp(r, p, y); rnegbin_rp(r, p);	neg. binomial, parameterized by r, p (LL) (sample)
lnegbin pnegbin rnegbin	lnegbin(mean, beta, power, y); pnegbin(mean, beta, power, y); rnegbin(mean, beta, power);	neg. binom., param. by mean, beta (= log(alpha)), power (LL) (exp(LL)) (sample)
lnorm	lnorm(x, std);	log of probability density function of normal distribution with mean (m)=0. Since probability density of the normal distribution is f(x)=1/(v(2p)s)e^–((x–m)^2/(2s^2)), then assuming that m=0, log f(x)= – 0.5*(log2p+log(s^2) +(x/s)^2).
lphi phi probit erfunc	lphi(x, v); phi(x); probit(p); erfunc(x);	log(phi(x/stdev)) normal(0,1) cum. dist. function inverse N(0,1) cum.dist. function error function
lpois ppois rpois	lpois(mean, int _x); ppois(mean, int _x); int rpois(lambda);	log(mean^n*exp(–mean)/n!) (LL) (exp(LL)) (sample)
min max log10 abs ln	min(x, y); max(x, y); log10(x); abs(x); ln(x);	minimum maximum log base10 absolute natural log
unifToPoisson	unifToPoisson(mean, r);	convert uniform distribution to poisson
vfwt	vfwt(f, p);	make an observation variance function

Math functions

Phoenix PML supports a majority of the intrinsic math functions in the Cmath.h library. See the following tables for a list of supported functions. (Refer to http://www.cplusplus.com/reference/cmath/ for more information on the Cmath.h library.)

•Trigonometric functions 928

•Hyperbolic functions 928

•Exponential and logarithmic functions 928

•Power functions 929

•Error and gamma functions 929

•Rounding and remainder functions 929

•Floating-point manipulation functions 930

•Minimum, maximum, difference functions 930

•Other functions available in math.h 930

•Classification macro/functions 930

•Comparison macro/functions 931

Trigonometric functions
Function	Description
cos	Compute cosine
sin	Compute sine
tan	Compute tangent
acos	Compute arc cosine
asin	Compute arc sine
atan	Compute arc tangent
atan2	Compute arc tangent with two parameters

Hyperbolic functions
Function	Description
cosh	Compute hyperbolic cosine
sinh	Compute hyperbolic sine
tanh	Compute hyperbolic tangent
acosh	Compute arc hyperbolic cosine
asinh	Compute arc hyperbolic sine
atanh	Compute arc hyperbolic tangent

Exponential and logarithmic functions
Function	Description
exp	Compute exponential function
ldexp	Generate value from significand and exponent
log	Compute natural logarithm
log10	Compute common logarithm
exp2	Compute binary exponential function
expm1	Compute exponential minus one
ilogb	Integer binary logarithm
log1p	Compute logarithm plus one
log2	Compute binary logarithm
logb	Compute floating-point base logarithm
scalbn	Scale significand using floating-point base exponent
scalbln	Scale significand using floating-point base exponent (long)

Power functions
Function	Description
pow	Raise to power
sqrt	Compute square root
cbrt	Compute cubic root
hypot	Compute hypotenuse

Error and gamma functions
Function	Description
erf	Compute error function
erfc	Compute complementary error function
tgamma	Compute gamma function
lgamma	Compute log-gamma function

Rounding and remainder functions
Function	Description
ceil	Round up value
floor	Round down value
fmod	Compute remainder of division
trunc	Truncate value
round	Round to nearest
lround	Round to nearest and cast to long integer
llround	Round to nearest and cast to long long integer
rint	Round to integral value
lrint	Round and cast to long integer
llrint	Round and cast to long long integer
nearbyint	Round to nearby integral value
remainder	Compute remainder

Floating-point manipulation functions
Function	Description
copysign	Copy sign
nextafter	Next representable value
nextforward	Next representable value toward precise value

Minimum, maximum, difference functions
Function	Description
fdim	Positive difference
fmax	Maximum value
fmin	Minimum value

Other functions available in math.h
Function	Description
fabs	Compute absolute value
abs	Compute absolute value
fma	Multiply-add

Classification macro/functions
Function	Description
isfinite	Is a finite value
isinf	Is infinity
isnormal	Is normal
signbit	Sign bit (whether the sign of x is negative)

Comparison macro/functions
Function	Description
isgreater	Is greater
isgreaterequal	Is greater or equal
isless	Is less
islessequal	Is less or equal
islessgreater	Is less or greater
isunordered	Is unordered