calc: Conversions
8.4 Conversions
===============
The commands described in this section convert numbers from one form to
another; they are two-key sequences beginning with the letter ‘c’.
The ‘c f’ (‘calc-float’) [‘pfloat’] command converts the number on
the top of the stack to floating-point form. For example, ‘23’ is
converted to ‘23.0’, ‘3:2’ is converted to ‘1.5’, and ‘2.3’ is left the
same. If the value is a composite object such as a complex number or
vector, each of the components is converted to floating-point. If the
value is a formula, all numbers in the formula are converted to
floating-point. Note that depending on the current floating-point
precision, conversion to floating-point format may lose information.
As a special exception, integers which appear as powers or subscripts
are not floated by ‘c f’. If you really want to float a power, you can
use a ‘j s’ command to select the power followed by ‘c f’. Because ‘c
f’ cannot examine the formula outside of the selection, it does not
notice that the thing being floated is a power. 
Selecting
Subformulas.
The normal ‘c f’ command is “pervasive” in the sense that it applies
to all numbers throughout the formula. The ‘pfloat’ algebraic function
never stays around in a formula; ‘pfloat(a + 1)’ changes to ‘a + 1.0’ as
soon as it is evaluated.
With the Hyperbolic flag, ‘H c f’ [‘float’] operates only on the
number or vector of numbers at the top level of its argument. Thus,
‘float(1)’ is 1.0, but ‘float(a + 1)’ is left unevaluated because its
argument is not a number.
You should use ‘H c f’ if you wish to guarantee that the final value,
once all the variables have been assigned, is a float; you would use ‘c
f’ if you wish to do the conversion on the numbers that appear right
now.
The ‘c F’ (‘calc-fraction’) [‘pfrac’] command converts a
floating-point number into a fractional approximation. By default, it
produces a fraction whose decimal representation is the same as the
input number, to within the current precision. You can also give a
numeric prefix argument to specify a tolerance, either directly, or, if
the prefix argument is zero, by using the number on top of the stack as
the tolerance. If the tolerance is a positive integer, the fraction is
correct to within that many significant figures. If the tolerance is a
non-positive integer, it specifies how many digits fewer than the
current precision to use. If the tolerance is a floating-point number,
the fraction is correct to within that absolute amount.
The ‘pfrac’ function is pervasive, like ‘pfloat’. There is also a
non-pervasive version, ‘H c F’ [‘frac’], which is analogous to ‘H c f’
discussed above.
The ‘c d’ (‘calc-to-degrees’) [‘deg’] command converts a number into
degrees form. The value on the top of the stack may be an HMS form
(interpreted as degrees-minutes-seconds), or a real number which will be
interpreted in radians regardless of the current angular mode.
The ‘c r’ (‘calc-to-radians’) [‘rad’] command converts an HMS form or
angle in degrees into an angle in radians.
The ‘c h’ (‘calc-to-hms’) [‘hms’] command converts a real number,
interpreted according to the current angular mode, to an HMS form
describing the same angle. In algebraic notation, the ‘hms’ function
also accepts three arguments: ‘hms(H, M, S)’. (The three-argument
version is independent of the current angular mode.)
The ‘calc-from-hms’ command converts the HMS form on the top of the
stack into a real number according to the current angular mode.
The ‘c p’ (‘calc-polar’) command converts the complex number on the
top of the stack from polar to rectangular form, or from rectangular to
polar form, whichever is appropriate. Real numbers are left the same.
This command is equivalent to the ‘rect’ or ‘polar’ functions in
algebraic formulas, depending on the direction of conversion. (It uses
‘polar’, except that if the argument is already a polar complex number,
it uses ‘rect’ instead. The ‘I c p’ command always uses ‘rect’.)
The ‘c c’ (‘calc-clean’) [‘pclean’] command “cleans” the number on
the top of the stack. Floating point numbers are re-rounded according
to the current precision. Polar numbers whose angular components have
strayed from the -180 to +180 degree range are normalized. (Note that
results will be undesirable if the current angular mode is different
from the one under which the number was produced!) Integers and
fractions are generally unaffected by this operation. Vectors and
formulas are cleaned by cleaning each component number (i.e.,
pervasively).
If the simplification mode is set below basic simplification, it is
raised for the purposes of this command. Thus, ‘c c’ applies the basic
simplifications even if their automatic application is disabled.
Simplification Modes.
A numeric prefix argument to ‘c c’ sets the floating-point precision
to that value for the duration of the command. A positive prefix (of at
least 3) sets the precision to the specified value; a negative or zero
prefix decreases the precision by the specified amount.
The keystroke sequences ‘c 0’ through ‘c 9’ are equivalent to ‘c c’
with the corresponding negative prefix argument. If roundoff errors
have changed 2.0 into 1.999999, typing ‘c 1’ to clip off one decimal
place often conveniently does the trick.
The ‘c c’ command with a numeric prefix argument, and the ‘c 0’
through ‘c 9’ commands, also “clip” very small floating-point numbers to
zero. If the exponent is less than or equal to the negative of the
specified precision, the number is changed to 0.0. For example, if the
current precision is 12, then ‘c 2’ changes the vector ‘[1e-8, 1e-9,
1e-10, 1e-11]’ to ‘[1e-8, 1e-9, 0, 0]’. Numbers this small generally
arise from roundoff noise.
If the numbers you are using really are legitimately this small, you
should avoid using the ‘c 0’ through ‘c 9’ commands. (The plain ‘c c’
command rounds to the current precision but does not clip small
numbers.)
One more property of ‘c 0’ through ‘c 9’, and of ‘c c’ with a prefix
argument, is that integer-valued floats are converted to plain integers,
so that ‘c 1’ on ‘[1., 1.5, 2., 2.5, 3.]’ produces ‘[1, 1.5, 2, 2.5,
3]’. This is not done for huge numbers (‘1e100’ is technically an
integer-valued float, but you wouldn’t want it automatically converted
to a 100-digit integer).
With the Hyperbolic flag, ‘H c c’ and ‘H c 0’ through ‘H c 9’ operate
non-pervasively [‘clean’].
Info Catalog
calc: Complex Number Functions
calc: Arithmetic
calc: Date Arithmetic