4.1.25 Intrinsic mathematical methods
ncap2 supports the standard mathematical functions supplied with
most operating systems.
Standard calculator notation is used for addition +, subtraction
-, multiplication *, division /, exponentiation
^, and modulus %.
The available elementary mathematical functions are:
abs(x)
- Absolute value
Absolute value of x.
Example:
abs(-1) = 1
acos(x)
- Arc-cosine
Arc-cosine of x where x is specified in radians.
Example:
acos(1.0) = 0.0
acosh(x)
- Hyperbolic arc-cosine
Hyperbolic arc-cosine of x where x is specified in radians.
Example:
acosh(1.0) = 0.0
asin(x)
- Arc-sine
Arc-sine of x where x is specified in radians.
Example:
asin(1.0) = 1.57079632679489661922
asinh(x)
- Hyperbolic arc-sine
Hyperbolic arc-sine of x where x is specified in radians.
Example:
asinh(1.0) = 0.88137358702
atan(x)
- Arc-tangent
Arc-tangent of x where x is specified in radians between
-pi/2 and pi/2.
Example:
atan(1.0) = 0.78539816339744830961
atan2(y,x)
- Arc-tangent2
Arc-tangent of y/x
:Example atan2(1,3) = 0.321689857
atanh(x)
- Hyperbolic arc-tangent
Hyperbolic arc-tangent of x where x is specified in radians between
-pi/2 and pi/2.
Example:
atanh(3.14159265358979323844) = 1.0
ceil(x)
- Ceil
Ceiling of x. Smallest integral value not less than argument.
Example:
ceil(0.1) = 1.0
cos(x)
- Cosine
Cosine of x where x is specified in radians.
Example:
cos(0.0) = 1.0
cosh(x)
- Hyperbolic cosine
Hyperbolic cosine of x where x is specified in radians.
Example:
cosh(0.0) = 1.0
erf(x)
- Error function
Error function of x where x is specified between
-1 and 1.
Example:
erf(1.0) = 0.842701
erfc(x)
- Complementary error function
Complementary error function of x where x is specified between
-1 and 1.
Example:
erfc(1.0) = 0.15729920705
exp(x)
- Exponential
Exponential of x,
e^x.
Example:
exp(1.0) = 2.71828182845904523536
floor(x)
- Floor
Floor of x. Largest integral value not greater than argument.
Example:
floor(1.9) = 1
gamma(x)
- Gamma function
Gamma function of x,
Gamma(x).
The well-known and loved continuous factorial function.
Example:
gamma(0.5) = sqrt(pi)
gamma_inc_P(x)
- Incomplete Gamma function
Incomplete Gamma function of parameter a and variable x,
gamma_inc_P(a,x).
One of the four incomplete gamma functions.
Example:
gamma_inc_P(1,1) = 1-1/e
ln(x)
- Natural Logarithm
Natural logarithm of x,
ln(x).
Example:
ln(2.71828182845904523536) = 1.0
log(x)
- Natural Logarithm
Exact synonym for
ln(x)
.
log10(x)
- Base 10 Logarithm
Base 10 logarithm of x,
log10(x).
Example:
log(10.0) = 1.0
nearbyint(x)
- Round inexactly
Nearest integer to x is returned in floating point format.
No exceptions are raised for inexact conversions.
Example:
nearbyint(0.1) = 0.0
pow(x,y)
- Power
Value of x is raised to the power of y.
Exceptions are raised for domain errors.
Due to type-limitations in the C language
pow
function,
integer arguments are promoted (see Type Conversion) to type
NC_FLOAT
before evaluation.
Example:
pow(2,3) = 8
rint(x)
- Round exactly
Nearest integer to x is returned in floating point format.
Exceptions are raised for inexact conversions.
Example:
rint(0.1) = 0
round(x)
- Round
Nearest integer to x is returned in floating point format.
Round halfway cases away from zero, regardless of current IEEE rounding direction.
Example:
round(0.5) = 1.0
sin(x)
- Sine
Sine of x where x is specified in radians.
Example:
sin(1.57079632679489661922) = 1.0
sinh(x)
- Hyperbolic sine
Hyperbolic sine of x where x is specified in radians.
Example:
sinh(1.0) = 1.1752
sqrt(x)
- Square Root
Square Root of x,
sqrt(x).
Example:
sqrt(4.0) = 2.0
tan(x)
- Tangent
Tangent of x where x is specified in radians.
Example:
tan(0.78539816339744830961) = 1.0
tanh(x)
- Hyperbolic tangent
Hyperbolic tangent of x where x is specified in radians.
Example:
tanh(1.0) = 0.761594155956
trunc(x)
- Truncate
Nearest integer to x is returned in floating point format.
Round halfway cases toward zero, regardless of current IEEE rounding direction.
Example:
trunc(0.5) = 0.0
The complete list of mathematical functions supported is
platform-specific.
Functions mandated by ANSI C are guaranteed to be present
and are indicated with an asterisk
1.
and are indicated with an asterisk.
Use the ‘-f’ (or ‘fnc_tbl’ or ‘prn_fnc_tbl’) switch
to print a complete list of functions supported on your platform.
2