CHAPTER 11 THE FLOATING POINT ARITHMETIC PACKAGE The routines which do floating point arithmetic are a part of the operating system ROM. The Atari computer uses the 6502's decimal math mode. This mode uses numbers represented in packed Binary Coded Decimal (BCD). This means that each byte of a floating point number holds two decimal digits. The actual method of representing a full number is complicated and probably not very important to a programmer. However, for those with the knowledge to use it, the format is given below. Floating point number representation byte 0 xx excess 64 exponent + sign xx \ xx \ xx > 10 BCD digits xx / byte 7 xx / The decimal point is shifted to left of the MSD and the exponent is adjusted accordingly. Therefore, the decimal point doesn't need to be represented. For programming purposes, floating point numbers can be in ASCII code. It takes up to 14 bytes to store a floating point number in this manner. The floating point package has a routine to convert numbers between ASCII and floating point. USE OF THE FLOATING POINT PACKAGE The floating point package has several routines to convert between ASCII and FP and to do the arithmetic functions. These are the important data base variables. Floating point data base variables FR0 $00D4,6 (212): 6 byte buffer for floating point number FR1 $00E0,6 (224): 6 byte buffer for floating point number CIX $00F2 (242): index for INBUFF address INBUFF $00F3,2 (243): 2 byte pointer to ASCII floating point number FLPTR $00FC,2 (252): 2 byte pointer to user buffer for floating point number LBUFF $0580,? (1408): result buffer for FASC routine MAKING THE CALL To do a floating point function, first set the proper pointers and JSR to the operation entry point. Below is a list of the entry points and parameters. ASCII to floating point Converts ASCII representation pointed to by INBUFF to FP in FR0. AFP = $D800 INBUFF = address of ASCII number CIX = buffer offset if any JSR AFP FLOATING POINT TO ASCII Converts floating Point number in FR0 to ASCII. The result will be in LBUFF. INBUFF will point to the ASCII number which will have the bit 7 of the last byte set to 1. FASC = $D8E6 JSR FASC INTEGER TO FLOATING POINT CONVERSION. Converts a 2 byte unsigned integer (0 to 65535) in FR0 to floating point in FR0. IFP = $D9AA JSR IFP FLOATING POINT TO INTEGER CONVERSION. Converts floating point number in FR0 to 2 byte integer in FR0. FPI = $D9D2 JSR FPI BCS overflow ADDITION Adds floating point numbers in FR0 and FR1 with result in FR0. FADD = $DA66 JSR FADD BCS out of range SUBTRACTION subtracts FR1 from FR0 with the result in FR0. FSUB = $DA60 JSR FSUB BCS out of range MULTIPLICATION Multiplies FR0 by FR1 with the result in FR0. FMUL = $DADB JSR FMUL BCS out of range DIVISION Divides FR0 by FR1 with result in FR0. FDIV = $DB28 JSR FDIV BCS out of range or divisor is 0 LOGARITHMS Puts logarithm of FR0 in FR0 LOG = $DECD LOG10 = $DED1 JSR LOG ;for natural log. or JSR LOG10 ;for base 10 log. BCS negative number or overflow EXPONENTIATION Put exponentiation of FR0 in FR0 EXP = $DDC0 EXP10 = $DDCC JSR EXP ;for e ** Z or JSR EXP10 ;for 10 ** Z POLYNOMIAL EVALUATION Puts the result of an n degree polynomial evaluation of FR0 in FR0. PLYEVL = $DD40 LDX LSB of pointer to list of floating point coefficients, ordered high to low. LDY MSB of above LDA number of coefficients in list JSR PLYEVL BCS overflow CLEAR FR0 Sets FR0 to all zeroes ZFR0 = $DA44 JSR ZFR0 CLEAR ZERO PAGE FLOATING POINT NUMBER Clears user floating point number in page zero. ZF1 = $DA46 LDX address of zero page FP buffer JSR ZF1 LOAD FR0 WITH FLOATING POINT NUMBER Loads FR0 with user FP number in buffer pointed to by 6502 X and Y registers or by FLPTR. After either operation below, FLPTR will point to the user FP buffer. FLD0R = $DD89 LDX lsb of pointer LDY msb JSR FLD0R or FLD0P = $DD8D FLPTR = address of FP number JSR FLD0P LOAD FR1 WITH FLOATING POINT NUMBER Loads FR1 with user FP number in buffer pointed to by 6502 X and Y registers or by FLPTR. After either operation below, FLPTR will point to the user FP buffer. FLD1R = $DD98 LDX lsb of pointer LDY msb JSR FLD1R or FLD1P = $DD9C FLPTR = address of FP number JSR FLD1P STORE FR0 IN USER BUFFER stores the contents of FR0 in user FP buffer pointed to by 6502 X and Y registers or by FLPTR. After either operation below, FLPTR will point to the user FP buffer. FST0R = $DDA7 LDX lsb of pointer LDY msb JSR FST0R or FST0P = $DDAB FLPTR = address of FP number JSR FST0P MOVE FR0 TO FR1 Moves the contents of FR0 to FR1 FMOVE = $DDB6 JSR FMOVE The usual use sequence of the floating point package might be to: load FR0 and FR1 with FP numbes from user specified buffers do the math then store FR0 in a user buffer. An alternative might be to: convert an ASCII representation to FP (the result is automatically in FR0). move FR0 to FR1. Convert the second ASCII number. Do the math. Convert FR0 back to ASCII. Store the number back into a user buffer. The floating point package uses the following blocks of RAM. RAM used by floating point package $00D4 - $00FF $057E - $05FF If the floating point package is not used the above ram is free. Useful data base variables and OS equates FR0 $00D4,6 (212): system FP buffer FR1 $00E0,6 (224): system FP buffer CIX $00F2 (242): INBUFF index INBUFF $00F3,2 (243): pointer to ASCII FP buffer FLPTR $00FC,2 (252): pointer to user FP buffer LBUFF $0580 (1408): result buffer for FP to ASCII AFP $D800 (55296): ASCII to FP FASC $D8E6 (55526): FP to ASCII IFP $D9AA (55722): integer to FP FPI $D9D2 (55762): FP to integer ZFR0 $DA44 (55876): clear FR0 ZF1 $DA46 (55878): clear zero page FP buffer FSUB $DA60 (55904): FR0 - FR1 FADD $DA66 (55910): FR0 + FR1 FMUL $DADB (56027): FR0 * FR1 FDIV $DB28 (56104): FR0 / FR1 FLD0R $DD89 (56713): load FR0 by X,Y pointer FLD0P $DD8D (56717): load FR0 by FLPTR pointer FLD1R $DD98 (56728): load FR1 by X,Y pointer FLD1P $DD9C (56732): load FR1 by FLPTR pointer FST0R $DDA7 (56743): store FR0 at buffer by X,Y pointer FST1P $DDAB (56747): store FR0 at buffer by FLPTR pointer FMOVE $DDB6 (56758): move FR0 to FR1 EXP $DDC0 (56768): e exponentiation EXP10 $DDCC (56780): base 10 exponentiation PLYEVL $DD40 (56640): polynomial evaluation LOG $DECD (57037): natural log of FR0 LOG10 $DED1 (57041): base 10 log of FR0