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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.