`(require 'math-real)`

Although this package defines real and complex functions, it is safe
to load into an integer-only implementation; those functions will be
defined to #f.

— Function: **real-exp**` x`

— Function:**real-ln**` x`

— Function:**real-log**` y x`

— Function:**real-sin**` x`

— Function:**real-cos**` x`

— Function:**real-tan**` x`

— Function:**real-asin**` x`

— Function:**real-acos**` x`

— Function:**real-atan**` x`

— Function:**atan**` y x`

— Function:

— Function:

— Function:

— Function:

— Function:

— Function:

— Function:

— Function:

— Function:

These procedures are part of every implementation that supports general real numbers; they compute the usual transcendental functions. ‘

real-ln’ computes the natural logarithm ofx; ‘real-log’ computes the logarithm ofxbasey, which is`(/ (real-ln x) (real-ln y))`

. If argumentsxandyare not both real; or if the correct result would not be real, then these procedures signal an error.

— Function: **real-sqrt**` x`

For non-negative real

xthe result will be its positive square root; otherwise an error will be signaled.

— Function: **real-expt**` x1 x2`

Returns

x1raised to the powerx2if that result is a real number; otherwise signals an error.

`(real-expt 0.0`

x2`)`

- returns 1.0 for
x2equal to 0.0;- returns 0.0 for positive real
x2;- signals an error otherwise.

— Function: **quo**` x1 x2`

— Function:**rem**` x1 x2`

— Function:**mod**` x1 x2`

— Function:

— Function:

x2should be non-zero.(quox1x2) ==>n_q(remx1x2) ==>x_r(modx1x2) ==>x_mwhere

n_qisx1/x2rounded towards zero, 0 < |x_r| < |x2|, 0 < |x_m| < |x2|,x_randx_mdiffer fromx1by a multiple ofx2,x_rhas the same sign asx1, andx_mhas the same sign asx2.From this we can conclude that for

x2not equal to 0,(=x1(+ (*x2(quox1x2)) (remx1x2))) ==> #tprovided all numbers involved in that computation are exact.

(quo 2/3 1/5) ==> 3 (mod 2/3 1/5) ==> 1/15 (quo .666 1/5) ==> 3.0 (mod .666 1/5) ==> 65.99999999999995e-3

— Function: **ln**` z`

These procedures are part of every implementation that supports general real numbers. ‘

Ln’ computes the natural logarithm ofzIn general, the mathematical function ln is multiply defined. The value of ln

zis defined to be the one whose imaginary part lies in the range from -pi (exclusive) to pi (inclusive).

— Function: **abs**` x`

For real argument

x, ‘Abs’ returns the absolute value ofx' otherwise it signals an error.(abs -7) ==> 7

— Function: **make-rectangular**` x1 x2`

— Function:**make-polar**` x3 x4`

— Function:

These procedures are part of every implementation that supports general complex numbers. Suppose

x1,x2,x3, andx4are real numbers andzis a complex number such thatz=x1+x2i =x3. e^ix4Then

(make-rectangularx1x2) ==>z(make-polarx3x4) ==>zwhere -pi < x_angle <= pi with x_angle =

x4+ 2pi n for some integer n.If an argument is not real, then these procedures signal an error.