How to resolve the algorithm Pathological floating point problems step by step in the 360 Assembly programming language
How to resolve the algorithm Pathological floating point problems step by step in the 360 Assembly programming language
Table of Contents
Problem Statement
Most programmers are familiar with the inexactness of floating point calculations in a binary processor. The classic example being: In many situations the amount of error in such calculations is very small and can be overlooked or eliminated with rounding. There are pathological problems however, where seemingly simple, straight-forward calculations are extremely sensitive to even tiny amounts of imprecision. This task's purpose is to show how your language deals with such classes of problems.
A sequence that seems to converge to a wrong limit. Consider the sequence:
As n grows larger, the series should converge to 6 but small amounts of error will cause it to approach 100.
Display the values of the sequence where n = 3, 4, 5, 6, 7, 8, 20, 30, 50 & 100 to at least 16 decimal places.
The Chaotic Bank Society is offering a new investment account to their customers. You first deposit $e - 1 where e is 2.7182818... the base of natural logarithms. After each year, your account balance will be multiplied by the number of years that have passed, and $1 in service charges will be removed. So ...
What will your balance be after 25 years?
Siegfried Rump's example. Consider the following function, designed by Siegfried Rump in 1988.
Demonstrate how to solve at least one of the first two problems, or both, and the third if you're feeling particularly jaunty.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Pathological floating point problems step by step in the 360 Assembly programming language
Source code in the 360 programming language
* Pathological floating point problems 03/05/2016
PATHOFP CSECT
USING PATHOFP,R13
SAVEAR B STM-SAVEAR(R15)
DC 17F'0'
STM STM R14,R12,12(R13)
ST R13,4(R15)
ST R15,8(R13)
LR R13,R15
LE F0,=E'2'
STE F0,U u(1)=2
LE F0,=E'-4'
STE F0,U+4 u(2)=-4
LA R6,3 n=3
LA R7,U+4 @u(n-1)
LA R8,U @u(n-2)
LA R9,U+8 @u(n)
LOOPN CH R6,=H'100' do n=3 to 100
BH ELOOPN
LE F4,0(R7) u(n-1)
LE F2,=E'1130' 1130
DER F2,F4 1130/u(n-1)
LE F0,=E'111' 111
SER F0,F2 111-1130/u(n-1)
LE F2,0(R7) u(n-1)
LE F4,0(R8) u(n-2)
MER F2,F4 u(n-1)*u(n-2)
LE F6,=E'3000' 3000
DER F6,F2 3000/(u(n-1)*u(n-2))
AER F0,F6 111-1130/u(n-1)+3000/(u(n-1)*u(n-2))
STE F0,0(R9) store into u(n)
XDECO R6,PG+0 n
LE F0,0(R9) u(n)
LA R0,3 number of decimals
BAL R14,FORMATF format(u(n),'F13.3')
MVC PG+12(13),0(R1) put into buffer
XPRNT PG,80 print buffer
LA R6,1(R6) n=n+1
LA R7,4(R7) @u(n-1)
LA R8,4(R8) @u(n-2)
LA R9,4(R9) @u(n)
B LOOPN
ELOOPN L R13,4(0,R13)
LM R14,R12,12(R13)
XR R15,R15
BR R14
COPY FORMATF
LTORG
PG DC CL80' ' buffer
U DS 100E
YREGS
YFPREGS
END PATHOFP
You may also check:How to resolve the algorithm Globally replace text in several files step by step in the D programming language
You may also check:How to resolve the algorithm Abundant, deficient and perfect number classifications step by step in the Go programming language
You may also check:How to resolve the algorithm URL decoding step by step in the Racket programming language
You may also check:How to resolve the algorithm Statistics/Basic step by step in the Julia programming language
You may also check:How to resolve the algorithm Elementary cellular automaton step by step in the Ada programming language