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Implmement BCD floating point and update number parsing and printing Implements a BCD floating point system with 10 decimal digits of precistion and an exponent range of -63 to +63. Also include parsing integer and floating point values and printing them out.
author William Astle <lost@l-w.ca>
date Sun, 15 Oct 2023 22:15:36 -0600
parents fbb8f369ce76
children 1c1a0150fdda
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1 This is the LWBasic project. Its goal is to create a replacement Basic for
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2 the TRS80 Color Computer. This Basic will not be binary compatible with the
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3 stock ROM. In particular, any various peeks, pokes, executes, and the like
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4 intended to mess with the interpreter internals are unlikely to work, and,
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5 in fact, may be completely detrimental.
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6
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7 There are two versions of LWBasic. One is for the Coco 1 and 2. The other
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8 is for the Coco 3. The primary differences between the two are in the
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9 startup code and features that rely on the existence of Coco 3 hardware. The
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10 main differences for the Coco 3 version are:
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11
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12 * 32/40/64/80 column text modes with attributes
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13 * 256/320/512/640 column bitmap graphics with up to 16 colours (256/320)
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14 or 4 colours (512/640)
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15 * palette register setting
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16 * graphics and text screen located outside main program memory
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17 * disk I/O buffers located outside main program memory
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18 * separate heaps for strings, scalars, arrays, and program text not limited
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19 to the 64K address space of the CPU
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20 * ROM/RAM copy at startup and initialization of Coco 3 specific hardware;
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21 defaulting to the 80 column text screen
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22
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23 Both versions can either be installed in ROM or loaded from disk or tape.
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24 In the case of loading from disk or tape, the machine must have at least
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25 64K of RAM. The loadable versions do not include certain initalization
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26 routines that are only relevant to cold starting the hardware.
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27
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28 For the Coco 3 version, the ROM is a single 32K chunk intended to replace
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29 the 32K internal ROM. For the Coco 1/2 version, there are three chunks: an
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30 "Extended Color Basic" chunk (8K for the ECB socket), a "Color Basic" chunk
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31 (8K for the CB socket), and "Disk Extended Color Basic", a 16K chunk
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32 intended to be installed in a cartridge ROM, probably a disk controller. On
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33 machines with a single 16K internal ROM, the "Extended Color Basic" and
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34 "Color Basic" chunks should arranged with "Extended Color Basic" at the
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35 lowest address and "Color Basic" immediately above.
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36
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37 An important note about the hardware interrupt vectors in the ROMs: the Coco
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38 1/2 get the FFFx vectors from the top 16 bytes of the "Color Basic" chunk.
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39 The Coco 3 gets the FFFx vectors from the top 16 bytes of the 32K internal
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40 ROM.
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41
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42 Note that LWBasic does not look for the DK signature of a Disk Basic ROM
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43 and, thus, will not autostart whatever Disk Basic you happen to have
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44 installed. This is most relevant on a Coco 3 where the upper 16K of the
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45 LWBasic ROM is internal instead of in a cartrige.
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47
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48 Numbers
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49 =======
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50
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51 LWBasic has three numeric types: a 32 bit signed integer, stored as two's
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52 complement, a decimal floating point type stored in packed BCD with
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53 10 digits of precision and a base 10 exponent range of -63 to +63, and a
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54 double precision decimal floating point type with 20 decimal digits of
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55 precision and a base 10 exponent range from -2047 to +2047.
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56
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57 The BCD format using 48 bits is stored as follows:
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58
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59 Offset Size Content
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60 0 1 Sign bit - 1 for negative
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61 1 7 Decimal exponent with a bias of 64; 0 indicates a value of 0
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62 8 40 10 BCD digits of the significand
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63
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64 *** Planned but not implememted
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65 The BCD double format using 96 bits is stored as follows:
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66
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67 Offset Size Content
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68 0 1 sign bit - 1 for negative
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69 1 3 <reserved>
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70 4 12 Decimal exponent with a bias of 2048; 0 indicates value of 0
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71 16 80 20 BCD digits of the significand
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72
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73 It is worth noting the reason for using the BCD format instead of binary
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74 floating point. Because interactions with the computer are typically in base
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75 10, it makes sense to avoid the horrendous complications of attempting to
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76 maximize the accuracy of converting binary floating point to decimal and
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77 back again. While this is trivial for integers, it is non-trivial for
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78 floating point where the variations in accuracy and the need for rounding is
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79 unavoidable.
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80
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81 At the expense of some extra CPU cycles for doing the calculations, base 10
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82 accuracy is preserved, at least to the precision limit of the data type.
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83 This also allows pre-parsing numbers and being able to display them again
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84 accurately when generating a program listing, even if extra nonsignificant
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85 digits like trailing decimal zeroes are not reproduced.
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86
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87 It is, however, critical to note that despite the BCD representation, these
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88 values are still floating point and have the inherent inaccuracies of all
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89 limited precision data types. The simple difference is that it makes the
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90 numbers in the computer behave exactly like scientific notiation with no
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91 unexpected surprises.