12. Numeric Functions

The numeric functions include all of the functions from the C90 standard library math.h, all of the non-complex functions from C99 tgmath.h (i.e. all except carg, cimag, conj, cproj, and creal), as well as rand from stdlib.h, time from time.h, and the scaled pseudo-random number generators drand, irand, and nrand.

Most of the numeric functions take one expression argument and return one value. A few of the functions take no arguments (drand, nrand, rand, time, row, col), and some take two or three arguments. frexp, modf, and remquo can return two values.

The numeric functions are:

  acos          arc cosine
  acosh         inverse hyperbolic cosine
  asin          arc sine
  asinh         inverse hyperbolic sine
  atan          two-quadrant arctangent
  atan2         four-quadrant arctangent, atan2(y,x) ~= atan(y/x)
  atanh         inverse hyperbolic tangent
  cbrt          cube root
  ceil          ceiling
  cell          cell(c,r) == value of cell from column c row r
  col           cell column number
  copysign      copy sign of a number
  cos           cosine
  cosh          hyperbolic cosine
  drand         pseudo-random double, 0.0 <= drand() < 1.0
  erf           error function
  erfc          complementary error function
  exp           exponential
  exp2          base-2 exponential
  expm1         exponential minus 1, expm1(x) == exp(x) - 1
  fabs          absolute value
  fdim          positive difference
  floor         floor
  fma           floating-point multiply and add
  fmax          maximum of two values
  fmin          minimum of two values
  fmod          mod, x%y == fmod(x,y)
  frexp         extract fraction and exponent, {f,e} = frexp(x)
  hypot         Euclidean distance
  ilogb         extract exponent
  irand         pseudo-random integer, 0 <= irand(i) <= i-1
  ldexp         ldexp(x,e) produces x * (2**e)
  lgamma        log gamma function
  llrint        round to nearest integer
  llround       round to nearest integer
  log           natural logarithm
  log10         base 10 logarithm
  log1p         logarithm of 1 plus argument, log1p(x) == log(1+x)
  log2          base 2 logarithm
  logb          extract exponent
  lrint         round to nearest integer
  lround        round to nearest integer
  modf          extract fraction and integral parts, {f,i} = modf(x)
  nearbyint     round to nearest integer
  nextafter     nextafter(x,y) == next value following x in the direction of y
  nexttoward    nexttoward(x,y) == next value following x in the direction of y
  nrand         pseudo-random normal (Gaussian) -6.0 <= nrand() < 6.0
  pow           exponentiation, x**y == pow(x,y)
  rand          pseudo-random integer, 0 <= rand() <= RAND_MAX
  remainder     remainder(x,y) == remainder of dividing x by y
  remquo        remainder and part of quotient, {r,q} = remquo(x,y)
  rint          round to nearest integer
  round         round to nearest integer
  row           cell row number
  scalbln       scalbln(x,e) produces x * (FLT_RADIX**e)
  scalbn        scalbn(x,e) produces x * (FLT_RADIX**e)
  sin           sine
  sinh          hyperbolic sine
  sqrt          square root
  tan           tangent
  tanh          hyperbolic tangent
  tgamma        gamma function
  time          time in seconds since 00:00:00 UTC, January 1, 1970
  trunc         round to integer, towards zero

Notes:

The pseudo-random number generator functions are initialized using srand(time()) when the program is run, but you can reinitialize using the srand command.

nrand is a simple approximate truncated Gaussian distribution computed as the sum of 12 uniform samples minus 6.

cell enables run-time evaluation of cell locations using expressions for the column and row. The column is specified as a numeric expression, or as a literal string, or as a cell or symbol containing a string, so the following three examples are equivalent:

  a0 = cell( "b", c0+2);  // e.g. a0 = b3, if c0 == 1

  a0 = cell( a1, c0+2); a1 = "b";

  a0 = cell( 1, c0+2); // "b" is column 1