maths.lib
Mathematic library for Faust. Its official prefix is ma.
References
Functions Reference
(ma.)SR
Current sampling rate given at init time. Constant during program execution.
Usage
SR : _
(ma.)T
Current sample duration in seconds computed from the sampling rate given at init time. Constant during program execution.
Usage
T : _
(ma.)BS
Current block-size. Can change during the execution at each block.
Usage
BS : _
(ma.)PI
Constant PI in double precision.
Usage
PI : _
(ma.)deg2rad
Convert degrees to radians.
Usage
45. : deg2rad
(ma.)rad2deg
Convert radians to degrees.
Usage
ma.PI : rad2deg
(ma.)E
Constant e in double precision.
Usage
E : _
(ma.)EPSILON
Constant EPSILON available in simple/double/quad precision,
as defined in the floating-point standard
and machine epsilon,
that is smallest positive number such that 1.0 + EPSILON != 1.0.
Usage
EPSILON : _
(ma.)MIN
Constant MIN available in simple/double/quad precision (minimal positive value).
Usage
MIN : _
(ma.)MAX
Constant MAX available in simple/double/quad precision (maximal positive value).
Usage
MAX : _
(ma.)FTZ
Flush to zero: force samples under the "maximum subnormal number" to be zero. Usually not needed in C++ because the architecture file take care of this, but can be useful in JavaScript for instance.
Usage
_ : FTZ : _
Reference
(ma.)copysign
Changes the sign of x (first input) to that of y (second input).
Usage
_,_ : copysign : _
(ma.)neg
Invert the sign (-x) of a signal.
Usage
_ : neg : _
(ma.)not
Bitwise not implemented with xor as not(x) = x xor -1;.
So working regardless of the size of the integer, assuming negative numbers in two's complement.
Usage
_ : not : _
(ma.)sub(x,y)
Subtract x and y.
Usage
_,_ : sub : _
(ma.)inv
Compute the inverse (1/x) of the input signal.
Usage
_ : inv : _
(ma.)cbrt
Computes the cube root of of the input signal.
Usage
_ : cbrt : _
(ma.)hypot
Computes the euclidian distance of the two input signals sqrt(xx+yy) without undue overflow or underflow.
Usage
_,_ : hypot : _
(ma.)ldexp
Takes two input signals: x and n, and multiplies x by 2 to the power n.
Usage
_,_ : ldexp : _
(ma.)scalb
Takes two input signals: x and n, and multiplies x by 2 to the power n.
Usage
_,_ : scalb : _
(ma.)log1p
Computes log(1 + x) without undue loss of accuracy when x is nearly zero.
Usage
_ : log1p : _
(ma.)logb
Return exponent of the input signal as a floating-point number.
Usage
_ : logb : _
(ma.)ilogb
Return exponent of the input signal as an integer number.
Usage
_ : ilogb : _
(ma.)log2
Returns the base 2 logarithm of x.
Usage
_ : log2 : _
(ma.)expm1
Return exponent of the input signal minus 1 with better precision.
Usage
_ : expm1 : _
(ma.)acosh
Computes the principle value of the inverse hyperbolic cosine of the input signal.
Usage
_ : acosh : _
(ma.)asinh
Computes the inverse hyperbolic sine of the input signal.
Usage
_ : asinh : _
(ma.)atanh
Computes the inverse hyperbolic tangent of the input signal.
Usage
_ : atanh : _
(ma.)sinh
Computes the hyperbolic sine of the input signal.
Usage
_ : sinh : _
(ma.)cosh
Computes the hyperbolic cosine of the input signal.
Usage
_ : cosh : _
(ma.)tanh
Computes the hyperbolic tangent of the input signal.
Usage
_ : tanh : _
(ma.)erf
Computes the error function of the input signal.
Usage
_ : erf : _
(ma.)erfc
Computes the complementary error function of the input signal.
Usage
_ : erfc : _
(ma.)gamma
Computes the gamma function of the input signal.
Usage
_ : gamma : _
(ma.)lgamma
Calculates the natural logorithm of the absolute value of the gamma function of the input signal.
Usage
_ : lgamma : _
(ma.)J0
Computes the Bessel function of the first kind of order 0 of the input signal.
Usage
_ : J0 : _
(ma.)J1
Computes the Bessel function of the first kind of order 1 of the input signal.
Usage
_ : J1 : _
(ma.)Jn
Computes the Bessel function of the first kind of order n (first input signal) of the second input signal.
Usage
_,_ : Jn : _
(ma.)Y0
Computes the linearly independent Bessel function of the second kind of order 0 of the input signal.
Usage
_ : Y0 : _
(ma.)Y1
Computes the linearly independent Bessel function of the second kind of order 1 of the input signal.
Usage
_ : Y0 : _
(ma.)Yn
Computes the linearly independent Bessel function of the second kind of order n (first input signal) of the second input signal.
Usage
_,_ : Yn : _
(ma.)fabs, (ma.)fmax, (ma.)fmin
Just for compatibility...
fabs = abs
fmax = max
fmin = min
(ma.)np2
Gives the next power of 2 of x.
Usage
np2(n) : _
Where:
n: an integer
(ma.)frac
Gives the fractional part of n.
Usage
frac(n) : _
Where:
n: a decimal number
(ma.)modulo
Modulus operation using the (x%y+y)%y formula to ensures the result is always non-negative, even if x is negative.
Usage
modulo(x,y) : _
Where:
x: the numeratory: the denominator
(ma.)isnan
Return non-zero if x is a NaN.
Usage
isnan(x)
_ : isnan : _
Where:
x: signal to analyse
(ma.)isinf
Return non-zero if x is a positive or negative infinity.
Usage
isinf(x)
_ : isinf : _
Where:
x: signal to analyse
(ma.)chebychev
Chebychev transformation of order N.
Usage
_ : chebychev(N) : _
Where:
N: the order of the polynomial, a constant numerical expression
Semantics
T[0](x) = 1,
T[1](x) = x,
T[n](x) = 2x*T[n-1](x) - T[n-2](x)
Reference
(ma.)chebychevpoly
Linear combination of the first Chebyshev polynomials.
Usage
_ : chebychevpoly((c0,c1,...,cn)) : _
Where:
cn: the different Chebychevs polynomials such that: chebychevpoly((c0,c1,...,cn)) = Sum of chebychev(i)*ci
Reference
(ma.)diffn
Negated first-order difference.
Usage
_ : diffn : _
(ma.)signum
The signum function signum(x) is defined as -1 for x<0, 0 for x==0, and 1 for x>0.
Usage
_ : signum : _
(ma.)nextpow2
The nextpow2(x) returns the lowest integer m such that 2^m >= x.
Usage
2^nextpow2(n) : _
Useful for allocating delay lines, e.g.,
delay(2^nextpow2(maxDelayNeeded), currentDelay);
(ma.)zc
Indicator function for zero-crossing: it returns 1 if a zero-crossing occurs, 0 otherwise.
Usage
_ : zc : _
(ma.)primes
Return the n-th prime using a waveform primitive. Note that primes(0) is 2, primes(1) is 3, and so on. The waveform is length 2048, so the largest precomputed prime is primes(2047) which is 17863.
Usage
_ : primes : _