In our series about C64 ROM commentaries (English version by Lee Davison, German version by Data Becker), I’m now presenting a most unusual C64 ROM commentary – based on a commented disassembly of the Apple II ROM.
“S-C DocuMentor for Applesoft” is a commented disassembly of the BASIC ROM of the Apple II computer. Like Commodore BASIC, “Applesoft” BASIC is based on Microsoft BASIC for 6502, but on an older revision. Since the two BASIC interpreters are almost the same instruction for instruction (modulo some command extensions on both sides), the commentary translated over very nicely.
The cross-referenced HTML version of the “S-C C64 BASIC Disassembly” is available here at pagetable.com/c64rom.
The raw txt files of all commentaries are maintained at github.com/mist64/c64disasm. Fixes and additions happily accepted!
VERY NICE
I’ve been working on adding a “float” pseudo opcode to my assembler:
https://github.com/AntonTreuenfels/HXA_Cross_Assembler
I’ve been checking its performance against your C64 BASIC ROM disassembly, to see if it produced the same hex values as appear in the ROM. My work does, but sometimes the decimal polynomial coefficients had to be adjusted slightly from what appears in the disassembly to make that happen. I’m pretty sure my decimal values are correct, as I can produce correct results for any floating point value that is not part of a polynomial.
The coefficients that appear differ from Taylor’s series values, in general drifting further away the higher the order of the coefficient. I trace this to their being derived from a minimax formula, designed to minimize the maximum error over a given range. So the results of using them are accurate within the limits of C64 floating point math.
In my test program, I put the expected result next to the decimal value being tested. I also put what I assume is the Taylor’s series value that the decimal value was first derived from. Again, that Taylor’s series value differs from the one actually used. So except as a hint as to where the actual value first came from, it’s not otherwise terribly useful.
If you have the time and the interest, you may wish to update the commentary of the C64 disassembly.
Also I haven’t decided on my “float” pseudo op is finally going to work. Mostly because the five-byte EXCESS-128 format appears to be more widely used than just by Commodore. But for now:
; Hobby Cross-Assembler Test 603
; Miscellaneous\FLOAT
; ok: FLOAT pseudo op
; by Anton Treuenfels
; first created: 09/18/24
; last revised: 09/19/24
; no errors to detect
.listfile ; optional psop
.errfile ; optional psop
; ——————————-
.cpu “T_16_L” ; required psop
.org $1000 ; required psop
; ——————————-
.assume float:cbm
.float 0, 0.0, 00.000 # 00 00 00 00 00
# these are from the C64 BASIC ROM
# https://www.pagetable.com/c64ref/c64disasm/
# polynomial coefficients are minimax, not Taylor’s series
# – they are designed to minimize the maximum error over a given range
# https://www.c64-wiki.com/wiki/POLY1
# https://www.lemon64.com/forum/viewtopic.php?t=56351
.float 3.141592653 # $AEA8 82 49 0F DA A1 PI
.float -32768.0 # $B1A5 90 80 00 00 00
.float 1.0 # $B9BC 81 00 00 00 00
# 4th degree polynomial used by LOG()
.float 0.43425594189 # $B9C2 7F 5E 56 CB 79 (2*(1/LN(2)))/7
.float 0.57658454134 # $B9C7 80 13 9B 0B 64 (2*(1/LN(2)))/5
.float 0.96180075921 # $B9CC 80 76 38 93 16 (2*(1/LN(2)))/3
.float 2.88539007307 # $B9D1 82 38 AA 3B 20 (2*(1/LN(2)))/1
.float 0.70710678120 # $B9D6 80 35 04 F3 34 1/SQR(2)
.float 1.41421356239 # $B9DB 81 35 04 F3 34 SQR(2)
.float -0.5 # $B9E0 80 80 00 00 00
.float 0.69314718061 # $B9E5 80 31 72 17 F8 LN(2)
.float 10.0 # $BAF9 84 20 00 00 00
# used by binary -> ASCII conversion
.float 99999999.90625 # $BDB3 9B 3E BC 1F FD
.float 999999999.25 # $BDB8 9E 6E 6B 27 FD
.float 1e9 # $BDBD 9E 6E 6B 28 00
.float 0.5 # $BF11 80 00 00 00 00
.float 1.44269504089 # $BFBF 81 38 AA 3B 29 1/LN(2)
# 8th degree polynomial used by EXP()
.float 0.21498763701e-4 # $BFC5 71 34 58 3E 56 (LN(2)**7)/7!
.float 0.14352314037e-3 # $BFCA 74 16 7E B3 1B (LN(2)**6)/7!
.float 0.0013422634825 # $BFCF 77 2F EE E3 85 (LN(2)**5)/5!
.float 0.0096140170136 # $BFD4 7A 1D 84 1C 2A (LN(2)**4)/4!
.float 0.055505126870 # $BFD9 7C 63 59 58 0A (LN(2)**3)/3!
.float 0.24022638462 # $BFDE 7E 75 FD E7 C6 (LN(2)**2)/2!
.float 0.69314718619 # $BFE3 80 31 72 18 10 (LN(2)**1)/1!
.float 1.0 # $BFE8 81 00 00 00 00
# used by RND()
.float 11879546 # $E08D 98 35 44 7A 00 multiplier
.float 3.927677739E-8 # $E092 68 28 B1 46 00 offset
.float 1.57079632679 # $E2E0 81 49 0F DA A2 PI/2
.float 6.283185307 # $E2E5 83 49 0F DA A2 PI*2
.float 0.25 # $E2EA 7F 00 00 00 00
# 6th degree polynomial used by SIN()
.float -14.381390673 # $E2F0 84 E6 1A 2D 1B ((PI*2)**11)/11!
.float 42.007797125 # $E2F5 86 28 07 FB F8 ((PI*2)**9)/9!
.float -76.704170260 # $E2FA 87 99 68 89 01 ((PI*2)**7)/7!
.float 81.605223690 # $E2FF 87 23 35 DF E1 ((PI*2)**5)/5!
.float -41.34170211 # $E304 86 A5 5D E7 28 ((PI*2)**3)/3!
.float 6.283185307 # $E309 83 49 0F DA A2 ((PI*2)**1)/1!
# 12th degree polynomial used by ATN()
.float -0.68479391193E-3 # $E33F 76 B3 83 BD D3 -1/23
.float 0.4850942156E-2 # $E344 79 1E F4 A6 F5 1/21
.float -0.016111701845 # $E349 7B 83 FC B0 10 -1/19
.float 0.03420963805 # $E34E 7C 0C 1F 67 CA 1/17
.float -0.05427913276 # $E353 7C DE 53 CB C1 -1/15
.float 0.07245719655 # $E358 7D 14 64 70 4C 1/13
.float -0.0898023954 # $E35D 7D B7 EA 51 7A -1/11
.float 0.11093241345 # $E362 7D 63 30 88 7E 1/9
.float -0.1428398077 # $E367 7E 92 44 99 3A -1/7
.float 0.1999991205 # $E36C 7E 4C CC 91 C7 1/5
.float -0.3333333157 # $E371 7F AA AA AA 13 -1/3
.float 1.0 # $E376 81 00 00 00 00
; ——————————-
.end ; optional psop