Solver for the HP-15C
Message #1 Posted by Thomas Klemm on 4 Mar 2012, 9:58 p.m.
There was a recent discussion comparing the HP-35s and the HP-15c:
33s, 35s or 15cLE--which to buy?
Then we were reminded of Valentin's 48-step routine for the HP-35s to find real and/or complex roots:
35s - find roots of 3rd and higher order equations
Only when I asked myself how would I do that for the HP-15C I realized its biggest drawback:
there's no easy way to store complex numbers.
My first idea was to use matrices but it turned out that it was easier to use plain registers.
The step-size h is stored in register 0,
while the name/number of the program is specified in the variable I.
So let's assume we want to solve program B with step-size h = 10-4 and starting guess 2:
EEX 4 CHS
STO 0
RCL MATRIX B
STO I
2 A
Intermediate values of |dz| are displayed:
(( running ))
0.148589460
(( running ))
0.002695411
(( running ))
0.000000017
(( running ))
0.000000000
(( running ))
1.854105968
Should that annoy you just remove the PSE-command in line 058.
Kind regards
Thomas
Some definitions:
- z = x + i y
- F+ = F(z + h) = F+x + i F+y
- F-- = F(z - h) = F--x + i F--y
- F = F(z) = Fx + i Fy
Intermedidate results are kept in these registers:
0: h
1: x
2: y
3: F-x
4: F-y
5: Fx
6: Fy
001 - 42,21,11 LBL A 026 - 43 36 LASTx 051 - 10 ÷
002 - 44 1 STO 1 027 - 30 - 052 - 45 0 RCL 0
003 - 42 30 Re<>Im 028 - 2 2 053 - 20 ×
004 - 44 2 STO 2 029 - 10 ÷ 054 - 44,30, 1 STO - 1
005 - 42,21, 0 LBL 0 030 - 34 x<>y 055 - 42 30 Re<>Im
006 - 45 0 RCL 0 031 - 45 5 RCL 5 056 - 44,30, 2 STO - 2
007 - 16 CHS 032 - 45 6 RCL 6 057 - 43 16 ABS
008 - 32 1 GSB 1 033 - 42 25 I 058 - 42 31 PSE
009 - 44 3 STO 3 034 - 36 ENTER 059 - 45 0 RCL 0
010 - 42 30 Re<>Im 035 - 40 + 060 - 43 11 x^2
011 - 44 4 STO 4 036 - 30 - 061 - 43,30, 8 TEST 8
012 - 0 0 037 - 1 1 062 - 22 0 GTO 0
013 - 32 1 GSB 1 038 - 43 36 LASTx 063 - 45 1 RCL 1
014 - 44 5 STO 5 039 - 43 33 R-^ 064 - 45 2 RCL 2
015 - 42 30 Re<>Im 040 - 10 ÷ 065 - 42 25 I
016 - 44 6 STO 6 041 - 43 33 R-^ 066 - 43 32 RTN
017 - 45 0 RCL 0 042 - 43 36 LASTx 067 - 42,21, 1 LBL 1
018 - 32 1 GSB 1 043 - 10 ÷ 068 - 45 1 RCL 1
019 - 36 ENTER 044 - 34 x<>y 069 - 45 2 RCL 2
020 - 36 ENTER 045 - 20 × 070 - 42 25 I
021 - 45 3 RCL 3 046 - 43 36 LASTx 071 - 40 +
022 - 45 4 RCL 4 047 - 33 R-v 072 - 36 ENTER
023 - 42 25 I 048 - 30 - 073 - 36 ENTER
024 - 40 + 049 - 11 SQRT x 074 - 36 ENTER
025 - 34 x<>y 050 - 40 + 075 - 22 25 GTO I
These are examples from Valentin's paper "Boldly Going ... Going Back to the Roots":
076 - 42,21,12 LBL B 081 - 42,21,13 LBL C 105 - 42,21,14 LBL D 113 - 42,21,15 LBL E
077 - 14 y^x 082 - 2 2 106 - 43 11 x^2 114 - 2 2
078 - 43 26 PI 083 - 36 ENTER 107 - 6 6 115 - 40 +
079 - 30 - 084 - 3 3 108 - 30 - 116 - 20 ×
080 - 43 32 RTN 085 - 42 25 I 109 - 20 × 117 - 1 1
086 - 20 × 110 - 2 2 118 - 0 0
087 - 1 1 111 - 30 - 119 - 40 +
088 - 36 ENTER 112 - 43 32 RTN 120 - 20 ×
089 - 2 2 121 - 2 2
090 - 42 25 I 122 - 0 0
091 - 30 - 123 - 30 -
092 - 20 × 124 - 43 32 RTN
093 - 3 3
094 - 36 ENTER
095 - 4 4
096 - 42 25 I
097 - 30 -
098 - 20 ×
099 - 6 6
100 - 36 ENTER
101 - 8 8
102 - 42 25 I
103 - 30 -
104 - 43 32 RTN
For those using nonpareil:
<?xml version="1.0" encoding="ISO-8859-1"?>
<!DOCTYPE state SYSTEM "nonpareil.dtd">
<state version="1.00" model="15C" platform="voyager" arch="nut">
<ui/>
<chip name="Nut">
<registers>
<reg name="a" data="000000fffff000"/>
<reg name="b" data="000000fffff000"/>
<reg name="c" data="00000000000eae"/>
<reg name="m" data="00000000000000"/>
<reg name="n" data="00000000000000"/>
<reg name="g" data="04"/>
<reg name="p" data="c"/>
<reg name="q" data="4"/>
<reg name="q_sel" data="0"/>
<reg name="fo" data="00"/>
<reg name="s" data="0800"/>
<reg name="pc" data="0000"/>
<reg name="stack" index="0" data="006d"/>
<reg name="stack" index="1" data="0042"/>
<reg name="stack" index="2" data="0000"/>
<reg name="stack" index="3" data="0000"/>
<reg name="decimal" data="0"/>
<reg name="carry" data="0"/>
<reg name="awake" data="0"/>
<reg name="pf_addr" data="00"/>
<reg name="ram_addr" data="007"/>
<reg name="active_bank" index="0" data="0"/>
<reg name="active_bank" index="1" data="0"/>
<reg name="active_bank" index="2" data="0"/>
<reg name="active_bank" index="3" data="0"/>
<reg name="active_bank" index="4" data="0"/>
<reg name="active_bank" index="5" data="0"/>
<reg name="active_bank" index="6" data="0"/>
<reg name="active_bank" index="7" data="0"/>
<reg name="active_bank" index="8" data="0"/>
<reg name="active_bank" index="9" data="0"/>
<reg name="active_bank" index="a" data="0"/>
<reg name="active_bank" index="b" data="0"/>
<reg name="active_bank" index="c" data="0"/>
<reg name="active_bank" index="d" data="0"/>
<reg name="active_bank" index="e" data="0"/>
<reg name="active_bank" index="f" data="0"/>
</registers>
</chip>
<chip name="Voyager LCD">
<registers>
<reg name="enable" data="1"/>
<reg name="blink" data="0"/>
</registers>
</chip>
<memory as="ram">
<loc addr="000" data="00000000000000"/>
<loc addr="001" data="00000000000000"/>
<loc addr="002" data="00000000000000"/>
<loc addr="003" data="00000000000000"/>
<loc addr="004" data="000000fffff000"/>
<loc addr="005" data="00000000000008"/>
<loc addr="006" data="0000000000000c"/>
<loc addr="007" data="00000000000eae"/>
<loc addr="008" data="00000000000000"/>
<loc addr="009" data="2faf8befbe2280"/>
<loc addr="00a" data="00000000000000"/>
<loc addr="010" data="00000000000000"/>
<loc addr="011" data="00000000000000"/>
<loc addr="012" data="00000000000000"/>
<loc addr="013" data="00000000000000"/>
<loc addr="014" data="00000000000000"/>
<loc addr="015" data="c0d2d2d2d2d2d2"/>
<loc addr="016" data="000000000007ee"/>
<loc addr="017" data="00000000000000"/>
<loc addr="018" data="00000000000000"/>
<loc addr="019" data="00000000000000"/>
<loc addr="01a" data="00000000a00000"/>
<loc addr="0c0" data="00000000000000"/>
<loc addr="0c1" data="00000000000000"/>
<loc addr="0c2" data="00000000000000"/>
<loc addr="0c3" data="00000000000000"/>
<loc addr="0c4" data="00000000000000"/>
<loc addr="0c5" data="00000000000000"/>
<loc addr="0c6" data="00000000000000"/>
<loc addr="0c7" data="00000000000000"/>
<loc addr="0c8" data="00000000000000"/>
<loc addr="0c9" data="00000000000000"/>
<loc addr="0ca" data="00000000000000"/>
<loc addr="0cb" data="00000000000000"/>
<loc addr="0cc" data="00000000000000"/>
<loc addr="0cd" data="00000000000000"/>
<loc addr="0ce" data="00000000000000"/>
<loc addr="0cf" data="00000000000000"/>
<loc addr="0d0" data="00000000000000"/>
<loc addr="0d1" data="00000000000000"/>
<loc addr="0d2" data="00000000000000"/>
<loc addr="0d3" data="00000000000000"/>
<loc addr="0d4" data="00000000000000"/>
<loc addr="0d5" data="00000000000000"/>
<loc addr="0d6" data="00000000000000"/>
<loc addr="0d7" data="00000000000000"/>
<loc addr="0d8" data="00000000000000"/>
<loc addr="0d9" data="00000000000000"/>
<loc addr="0da" data="00000000000000"/>
<loc addr="0db" data="00000000000000"/>
<loc addr="0dc" data="00000000000000"/>
<loc addr="0dd" data="00000000000000"/>
<loc addr="0de" data="00000000000000"/>
<loc addr="0df" data="00000000000000"/>
<loc addr="0e0" data="00000000000000"/>
<loc addr="0e1" data="00000000000000"/>
<loc addr="0e2" data="00000000000000"/>
<loc addr="0e3" data="00000000000000"/>
<loc addr="0e4" data="00000000000000"/>
<loc addr="0e5" data="00000000000000"/>
<loc addr="0e6" data="00000000000000"/>
<loc addr="0e7" data="00000000000000"/>
<loc addr="0e8" data="00000000000000"/>
<loc addr="0e9" data="00000000000000"/>
<loc addr="0ea" data="00000000000000"/>
<loc addr="0eb" data="00000000000000"/>
<loc addr="0ec" data="00000000000000"/>
<loc addr="0ed" data="00000000000000"/>
<loc addr="0ee" data="b2fbf0f2fcfaf0"/>
<loc addr="0ef" data="f1fcfaf20eb2fb"/>
<loc addr="0f0" data="f2fcfbf6ba0db2"/>
<loc addr="0f1" data="fba4f8c1f6fcfb"/>
<loc addr="0f2" data="a4f4c1f3fcfba4"/>
<loc addr="0f3" data="f2c1f1fca4f3c1"/>
<loc addr="0f4" data="f20cb2fbb6cd0b"/>
<loc addr="0f5" data="88c1c1c1faa432"/>
<loc addr="0f6" data="3101b2a4323110"/>
<loc addr="0f7" data="78ba30dcb3a2df"/>
<loc addr="0f8" data="dba1dffc30fdfa"/>
<loc addr="0f9" data="cafbc4b1fcc5fd"/>
<loc addr="0fa" data="b1b4fdb4b1f1fb"/>
<loc addr="0fb" data="fac1a43433c5fd"/>
<loc addr="0fc" data="f2fbb1c5faa434"/>
<loc addr="0fd" data="33c1c1213046db"/>
<loc addr="0fe" data="4521f044db4321"/>
<loc addr="0ff" data="c3300042db410a"/>
</memory>
</state>
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