(guile.info.gz) Primitive Numerics

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 21.2.13 Primitive Numeric Functions
 -----------------------------------
 
 Many of Guile's numeric procedures which accept any kind of numbers as
 arguments, including complex numbers, are implemented as Scheme
 procedures that use the following real number-based primitives.  These
 primitives signal an error if they are called with complex arguments.
 
  -- Scheme Procedure: $abs x
      Return the absolute value of X.
 
  -- Scheme Procedure: $sqrt x
      Return the square root of X.
 
  -- Scheme Procedure: $expt x y
  -- C Function: scm_sys_expt (x, y)
      Return X raised to the power of Y. This procedure does not accept
      complex arguments.
 
  -- Scheme Procedure: $sin x
      Return the sine of X.
 
  -- Scheme Procedure: $cos x
      Return the cosine of X.
 
  -- Scheme Procedure: $tan x
      Return the tangent of X.
 
  -- Scheme Procedure: $asin x
      Return the arcsine of X.
 
  -- Scheme Procedure: $acos x
      Return the arccosine of X.
 
  -- Scheme Procedure: $atan x
      Return the arctangent of X in the range -PI/2 to PI/2.
 
  -- Scheme Procedure: $atan2 x y
  -- C Function: scm_sys_atan2 (x, y)
      Return the arc tangent of the two arguments X and Y. This is
      similar to calculating the arc tangent of X / Y, except that the
      signs of both arguments are used to determine the quadrant of the
      result. This procedure does not accept complex arguments.
 
  -- Scheme Procedure: $exp x
      Return e to the power of X, where e is the base of natural
      logarithms (2.71828...).
 
  -- Scheme Procedure: $log x
      Return the natural logarithm of X.
 
  -- Scheme Procedure: $sinh x
      Return the hyperbolic sine of X.
 
  -- Scheme Procedure: $cosh x
      Return the hyperbolic cosine of X.
 
  -- Scheme Procedure: $tanh x
      Return the hyperbolic tangent of X.
 
  -- Scheme Procedure: $asinh x
      Return the hyperbolic arcsine of X.
 
  -- Scheme Procedure: $acosh x
      Return the hyperbolic arccosine of X.
 
  -- Scheme Procedure: $atanh x
      Return the hyperbolic arctangent of X.
 
    For the hyperbolic arc-functions, the Guile library exports C
 functions corresponding to these Scheme procedures, but taking and
 returning arguments of type `double' rather than the usual `SCM'.
 
  -- C Function: double scm_asinh (double x)
  -- C Function: double scm_acosh (double x)
  -- C Function: double scm_atanh (double x)
      Return the hyperbolic arcsine, arccosine or arctangent of X
      respectively.
 
    For all the other Scheme procedures above, except `expt' and `atan2'
 (whose entries specifically mention an equivalent C function), the
 equivalent C functions are those provided by the standard mathematics
 library.  The mapping is as follows.
 
      Scheme Procedure   C Function
      `$abs'             `fabs'
      `$sqrt'            `sqrt'
      `$sin'             `sin'
      `$cos'             `cos'
      `$tan'             `tan'
      `$asin'            `asin'
      `$acos'            `acos'
      `$atan'            `atan'
      `$exp'             `exp'
      `$log'             `log'
      `$sinh'            `sinh'
      `$cosh'            `cosh'
      `$tanh'            `tanh'
 
 Naturally, these C functions expect and return `double' arguments.
 

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