digits1—a non-negative integer.
digits2—a non-negative integer.
integer—a non-negative integer.
or the integer
sign—A float of the same type as float
but numerically equal to
decode-float computes three values that characterize
The first value is of the same type
as float and
represents the significand.
The second value represents the exponent
to which the radix (notated in this description by b) must
be raised to obtain the value that, when multiplied with the first
result, produces the absolute value of float.
If float is zero, any integer value may be returned,
provided that the identity shown for
The third value
is of the same type as float
and is 1.0 if float is greater
than or equal to zero or -1.0 otherwise.
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).
(expt (float b float
)), where b is the radix of the floating-point
representation. float is not necessarily between 1/b and 1.
the radix of float.
float-sign returns a number
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,
(float-sign -0.0) →
the number of radix b digits
used in the representation of float (including any implicit
digits, such as a “hidden bit”).
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-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
the significand scaled so as to be an integer,
and the same last two
values that are returned by
If float is zero,
zero as the first value.
The second value bears the same relationship to the first value
(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 implementation's representation for floats.
integer-decode-float should signal an error
if their only argument is not a float.
scale-float should signal an error if its first argument
is not a float or if its second argument is not an integer.
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.
The product of the first result of
of the radix raised to the power of the second result, and of the third result
is exactly equal to the value of 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