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

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

. If arguments`x`and`y`are 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

`x`the result will be its positive square root; otherwise an error will be signaled.

- Function:
**real-expt***x1 x2*¶ -
Returns

`x1`raised to the power`x2`if that result is a real number; otherwise signals an error.`(real-expt 0.0`

`x2`)- returns 1.0 for
`x2`equal to 0.0; - returns 0.0 for positive real
`x2`; - signals an error otherwise.

- returns 1.0 for

- Function:
**quo***x1 x2*¶ - Function:
**rem***x1 x2*¶ - Function:
**mod***x1 x2*¶ -
`x2`should be non-zero.(quo

`x1``x2`) ==>`n_q`(rem`x1``x2`) ==>`x_r`(mod`x1``x2`) ==>`x_m`where

`n_q`is`x1`/`x2`rounded towards zero, 0 < |`x_r`| < |`x2`|, 0 < |`x_m`| < |`x2`|,`x_r`and`x_m`differ from`x1`by a multiple of`x2`,`x_r`has the same sign as`x1`, and`x_m`has the same sign as`x2`.From this we can conclude that for

`x2`not equal to 0,(=

`x1`(+ (*`x2`(quo`x1``x2`)) (rem`x1``x2`))) ==> #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 of`z`In general, the mathematical function ln is multiply defined. The value of ln

`z`is 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 of`x`’ otherwise it signals an error.`(abs -7) ==> 7`

- Function:
**make-rectangular***x1 x2*¶ - Function:
**make-polar***x3 x4*¶ -
These procedures are part of every implementation that supports general complex numbers. Suppose

`x1`,`x2`,`x3`, and`x4`are real numbers and`z`is a complex number such that`z`=`x1`+`x2`i =`x3`. e^i`x4`Then

`(make-rectangular``x1``x2`) ==>`z`(make-polar`x3``x4`) ==>`z`where -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.