Texas Instruments TI89 Developer Guide - Page 224

182 Chapter 16: Working with Numbers 16.3. EXACT/APPROX/AUTO Modes The EXACT/APPROX mode setting controls the way numbers are treated by the computer algebra system. In simplest terms EXACT mode causes the simplifier to convert float numbers to integers or fractions. APPROX mode causes the simplifier to convert integers and fractions to float numbers. In AUTO mode the simplifier does not alter the number types unless an operation must combine a float number with a nonfloat number. When this combination occurs, the nonfloat number is converted to a float number before they are combined. Number conversions due to mode are performed by push_internal_simplify when it encounters each number. Lower level routines in the computer algebra assume that the enforcement of the mode setting has occurred before they are called. Thus, if an application calls push_internal_simplify, push_simplify, or push_simplify_statements to evaluate an expression, the numbers in the expression will be handled according to the mode setting. However, if an application directly calls lower level computer algebra routines with numeric arguments, the mode setting will not be enforced. For example, if the mode setting is EXACT, and an application passes the expression 1.5 + 2 to push_internal_simplify, the result will be 7/2. The float value 1.5 is automatically converted to 3/2. However, if the application passes 1.5 and 2 to the push_sum routine, the result will be 3.5. push_sum does not enforce the mode setting, and the default action for combining floats and nonfloats is to convert the nonfloat into a float. To duplicate the computer algebra's numeric behavior, an application has two choices. • Always enter the computer algebra simplifier through one of the three main entry points (push_internal_simplify, push_simplify, push_simplify_statements). Thus, the mode setting will be enforced by push_internal_simplify. • Take responsibility for checking the mode setting and when necessary, applying the appropriate conversions to its numeric arguments before calling lower level routines. Finally, an application may decide to ignore the current mode setting and enforce one of its own choosing. An example is the built-in graphing application. The grapher saves the current mode setting, changes the mode setting to APPROX while it is active, and restores the current mode setting when it finishes. The current status of the EXACT/APPROX mode setting is maintained in the global variable NG_control. The macros IS_ARITH_EXACT, IS_ARITH_APPROX, and IS_ARITH_AUTO are used to test the status of the mode. The macros SET_ARITH_EXACT, SET_ARITH_APPROX, and SET_ARITH_AUTO are used to alter the mode setting. TI-89 / TI-92 Plus Developer Guide Not for Distribution Beta Version January 26, 2001