scale-float float integer    scaled-float

float-radix float    float-radix

float-sign float-1 &optional float-2    signed-float

float-digits float    digits1

float-precision float    digits2

integer-decode-float float    significand, exponent, integer-sign

digits2 - a non-negative integer.

exponent - an integer.

float - a float.

float-1 - a float.

float-2 - a float.

float-radix - an integer.

integer - a non-negative integer.

integer-sign - the integer -1, or the integer 1.

scaled-float - a float.

sign - A float of the same type as float but numerically equal to 1.0 or -1.0.

signed-float - a float.

significand - a float.

decode-float divides float by an integral power of b so as to bring its value between 1/b (inclusive) and 1 (exclusive), and returns the quotient as the first value. If float is zero, however, the result equals the absolute value of float (that is, if there is a negative zero, its significand is considered to be a positive zero).

scale-float returns (* float (expt (float b float) integer)) , where b is the radix of the floating-point representation. float is not necessarily between 1/b and 1.

float-radix returns the radix of float.

float-sign returns a number z such that z and float-1 have the same sign and also such that z and float-2 have the same absolute value. If float-2 is not supplied, its value is (float 1 float-1). If an implementation has distinct representations for negative zero and positive zero, then (float-sign -0.0)  -1.0.

float-digits returns the number of radix b digits used in the representation of float (including any implicit digits, such as a "hidden bit").

float-precision returns the number of significant radix b digits present in float; if float is a float zero, then the result is an integer zero.

For normalized floats, the results of float-digits and float-precision are the same, but the precision is less than the number of representation digits for a denormalized or zero number.

integer-decode-float computes three values that characterize float - the significand scaled so as to be an integer, and the same last two values that are returned by decode-float. If float is zero, integer-decode-float returns zero as the first value. The second value bears the same relationship to the first value as for decode-float:

 (multiple-value-bind (signif expon sign)
                      (integer-decode-float f)
   (scale-float (float signif f) expon)) ==(abs f)

 ;; Note that since the purpose of this functionality is to expose
 ;; details of the implementation, all of these examples are necessarily
 ;; very implementation-dependent.  Results may vary widely.

 ;; Values shown here are chosen consistently from one particular implementation.
 (decode-float .5)  0.5, 0, 1.0
 (decode-float 1.0)  0.5, 1, 1.0
 (scale-float 1.0 1)  2.0
 (scale-float 10.01 -2)  2.5025
 (scale-float 23.0 0)  23.0
 (float-radix 1.0)  2
 (float-sign 5.0)  1.0
 (float-sign -5.0)  -1.0
 (float-sign 0.0)  1.0
 (float-sign 1.0 0.0)  0.0
 (float-sign 1.0 -10.0)  10.0
 (float-sign -1.0 10.0)  -10.0
 (float-digits 1.0)  24
 (float-precision 1.0)  24
 (float-precision least-positive-single-float)  1
 (integer-decode-float 1.0)  8388608, -23, 1

The function scale-float should signal an error if its first argument is not a float or if its second argument is not an integer.

The function float-sign should signal an error if its first argument is not a float or if its second argument is supplied but is not a float.

 (multiple-value-bind (signif expon sign)
                      (decode-float f)
   (scale-float signif expon))
==(abs f)

 (multiple-value-bind (signif expon sign)
                      (decode-float f)
   (* (scale-float signif expon) sign))
== f