| sqrt(x) | square root | |
| exp(x) | ||
| log(x) | ln, base e | |
| log10(x) | lg, base 10 | |
| sin(x) | ||
| cos(x) | ||
| tan(x) | ||
| asin(x) | arc sine | |
| acos(x) | ||
| atan(x) | ||
| sinh(x) | hyperbolic sine | |
| cosh(x) | ||
| tanh(x) |
| abs(a) | integer, real | absolute |
| int(a) | integer | truncation |
| nint(a) | integer | nearest |
| floor(a) | integer | |
| ceiling(a) | integer | |
| real(a) | real | |
| aint(a) | real | truncation |
| anint(a) | real | nearest |
| aimag(z) | real | imaginary part |
| cmplx(a) cmplx(a, b) |
complex | |
| conjg(z) | complex | conjugate |
| max(a1, a2, ...) | integer, real | maximum |
| min(a1, a2, ...) | integer, real | minimum |
| mod(a, p) | integer, real | remainder |
| modulo(a, p) | integer, real | remainder |
| sign(a, b) | integer, real | abs(a) with sign of b |
| index(string, substring) | integer | starting position or 0 |
| len(string) | integer | length |
| len_trim(string) | integer | length w/o trailing blanks |
| trim(string) | character | trailing blanks removed |
| dot_product(vector_a, vector_b) | ||
| matmul(matrix_a, matrix_b) | ||
| maxval(array) | ||
| minval(array) | ||
| sum(array) | ||
| product(array) |
p(x) = a0 + a1x + a2x2 + ... + an-1xn-1 + anxn
1 + 2 + ... + (n-1) + n = n(n+1)/2 multiplications
p(x) = (((anx + an-1)x + ... + a2)x + a1)x + a0
Only n multiplications, better accuracy
1. Compute the coefficients of the Hermite polynomials up to H11(z).
2. Compute Hn(z) for given n and z using Horner's rule.
3. Compute ex using the series 1 + x + x2/2 + x3/6 + ... and compare with the intrinsic function.
4. Compute the complex numbers eix for angles x from 0 to 360 degrees in steps of 15.