186
Chapter 16: Working with Numbers
TI
-
89 / TI
-
92 Plus Developer Guide
Not for Distribution
Beta Version January 26, 2001
types that can be added. The primary system routines for estack arithmetic are
push_sum
,
push_difference
,
push_product
,
push_ratio
, and
push_exponentiate
.
Rational values combine to form rational values unless the operation overflows or
underflows. Since the float range is larger than the rational range, rational
operations quietly overflow and underflow into float values.
Float values combine to form float values. Float operations overflow to the
correctly signed symbolic infinity.
Rational values combine with float values to form float values. The rational
values are converted to float values to facilitate these combinations.
In addition to the primary routines, the system provides some specialized
routines.
replace_top2_with_sum
,
replace_top2_with_difference
,
replace_top2_with_prod
,
replace_top2_with_ratio
, and
replace_top2_with_pow
perform the corresponding operation on the top two
entries on the expression stack.
add_to_top
,
subtract_from_top
,
times_top
,
divide_top
, and
raise_to_top
perform the corresponding operation with the top
entry on the estack and a specified input argument.
See
Appendix A: System Routines — EStack Arithmetic
for descriptions of
these and other routines for performing arithmetic operations on the expression
stack.
16.7. Complex Numbers
The representation of complex values is different in the external and internal
tokenized forms. The external tokenized form uses the I_TAG which represents
the imaginary number. So, 1 + 2
i
tokenizes into an expression involving tagged
integers, addition, multiplication, and the I_TAG. Since the I_TAG might appear
anywhere in a general expression, this representation makes it difficult to
recognize and operate on complex values.
The simplifier, via
push_internal_simplify
, converts complex values to internal
tokenized form which uses an IM_RE_TAG on top of the imaginary part on top of
the real part of the complex value. This form places the knowledge that the value
is complex at the top of the representation in the form of the IM_RE_TAG. This
change greatly facilitates recognizing and operating on complex values.
External tokenized values are only handled by
push_internal_simplify
, which
converts them to internal form, and by
push_simplify_statements
and
push_simplify
, which use
push_internal_simplify
. Do not pass external
tokenized form to other evaluation/simplification routines. External tokenized
values are also handled by the display routines; for example,
display_statements
,
Parse1DExpr
, etc.
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