2.1 Floating Point Reals

There are 3 floating point real types: float, double, and {long double} real and complex numbers. All support these base functions: Felix provides 3 floating point types.

  Felix name     C name       Suffix
  ----------------------------------
  float         float         f
  double        double        d (default)
  ldouble       long double   l

Floating literals roughly follow ISO C99, except underscores are allowed between digits. The mantissa radix can either be decimal (default) or hexadecimal with a 0x or 0X prefix. The exponent is always decimal radix but can either be a power of 10 with an E or e separator or binary, with a P or p separator.

There is also an additional constraint: decimal radix floating literals which include a decimal point, must include at least one digit before and after the decimal point.

2.1.1 Exact rule for literals

  let decimal_string = digit (underscore? digit) *
  let hexadecimal_string = hexdigit (underscore? hexdigit) *

  let decimal_fractional_constant =
    decimal_string '.' decimal_string?

  let hexadecimal_fractional_constant =
    ("0x" |"0X")
    (hexadecimal_string '.' hexadecimal_string?
    | '.' hexadecimal_string) /* leading . allowed here because of prefix */

  let decimal_exponent = ('E'|'e') ('+'|'-')? decimal_string
  let binary_exponent = ('P'|'p') ('+'|'-')? decimal_string

  let floating_suffix = 'L' | 'l' | 'F' | 'f' | 'D' | 'd'
  let floating_literal =
    (
      decimal_fractional_constant decimal_exponent? |
      hexadecimal_fractional_constant binary_exponent?
    )
    floating_suffix?

2.1.2 Real Functions

Felix provides these base functions:

  neg: t -> t;
  add: t * t -> t;
  sub: t * t -> t;
  mul: t * t -> t;
  div: t * t -> t;

and these trigonometric functions:

  sin: t -> t;
  cos: t -> t;
  tan: t -> t;
  asin: t -> t;
  acos: t -> t;
  atan: t -> t;
  sinh: t -> t;
  cosh: t -> t;
  tanh: t -> t;
  asinh: t -> t;
  acosh: t -> t;
  atanh: t -> t;
  exp: t -> t;
  log: t -> t;
  pow: t * t -> t;

In addition to the trigonometric functions, reals support these functions:

  log10: t -> t;
  abs: t -> t;
  sqrt: t -> t;
  ceil: t -> t;
  floor: t -> t;
  trunc: t -> t;