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--- base:kernal_floating_point_mathematics [2016-02-06 01:17] – malcontent
+++ base:kernal_floating_point_mathematics [2017-10-22 15:22] – [7.3 Integer to FP] shrydar
@@ Line 3: / Line 3: @@
 [[http://en.wikipedia.org/wiki/Floating_point|Floating point]] numbers are handled by the C64's BASIC and Kernal ROMs. Called directly from machine language programs, they execute faster than when burdened by the BASIC interpreter. The difficulty lies in the variety of ways you must prepare the registers and zero-page before calling certain routines. Macros are recommended when dealing with FP in assembly.\\
-Floating point numbers are stored with 5 bytes. The first byte is the exponent, stored in excess $80 format (E = E - $80). Second byte holds the sign of the mantissa in its uppermost bit. The normalised mantissa (1 =< M < 2) is assumed to have a leading 1, and the following bits hold the fraction. If the exponent is 0, the number is interpreted as 0 regardless of the contents of the mantissa.
+Floating point numbers are stored with 5 bytes. The first byte is the exponent, stored in excess $80 format (E = E - $80). Second byte holds the sign of the mantissa in its uppermost bit. The normalized mantissa (0 =< M < 1) is assumed to have a leading 1, and the following bits hold the fraction. If the exponent is 0, the number is interpreted as 0 regardless of the contents of the mantissa.
 00 00 00 00 =   1 =  2<sup>1</sup> x %1.000...\\
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 The first routine is the actual code. The other entries simply set up $62/$63 for you. This routine wrecks FAC2, so if it is needed, it should be loaded after the conversion. It also uselessly (from our ML standpoint) sets the data type flag at $0d. Skipping these routines and jumping straight to the normalization routine at **$b8d2** gives greater control, i.e. 24-bit and 32-bit integer inputs are possible, as are signed 8-bit inputs. For example, to convert a 24-bit number, load FAC1 with the number from the most-significant byte to the least. Store zero in the last mantissa byte, and also in the sign and rounding bytes ($66 and $70). Then set the exponent to 24 (24 + $80 = $98). Jump to $b8d2 with the carry indicating whether the result should be positive (set) or negative (clear).
+The above process is basically what the KERNAL authors did to implement the 24 bit TI variable in BASIC (though they zero the high byte instead of the low, and hence use a mantissa of $a0).
+You can take advantage of their work with the following pair of calls to convert a 24 bit unsigned integer held in YXA:
+    sec
+    jsr $af87  ; sets mantissa to 00yyxxaa
+    jsr $af7e  ; set rest of FAC1 and JMP to $b8d2
 ==== 7.4 String to FP ====