December 2002
Beginner to intermediate
576 pages
14h 6m
English
This program is designed to compute the sine function using a power series. A very limited floating-point format is used to demonstrate some of the problems that can occur when using floating point.
The program computes each term in the power series and displays
the result. It continues computing terms until the last term is so small
that it doesn’t contribute to the final result. For comparison purposes,
the result of the library function sin is displayed as well as the computed
sine.
The program is invoked by:
sine valuewhere value is an angle in radians. For example, to compute sin(0) we use the command:
% sine 0
x**1 0.000E+00
1! 1.000E+00
x**1/1! 0.000E+00
1 term computed
sin(0.000E+00)=
0.000E+00
Actual sin(0)=0And to compute sin(π) we use the command:
% sine 3.141 x**1 3.141E+00 1! 1.000E+00 x**1/1! 3.141E+00 total 3.141E+00 x**3 3.099E+01 3! 6.000E+00 x**3/3! 5.165E+00 total -2.024E+00 x**5 3.057E+02 5! 1.200E+02 x**5/5! 2.548E+00 total 5.239E-01 x**7 3.016E+03 7! 5.040E+03 x**7/7! 5.985E-01 total -7.457E-02 x**9 2.976E+04 9! 3.629E+05 x**9/9! 8.201E-02 total 7.438E-03 x**11 2.936E+05 11! 3.992E+07 x**11/11! 7.355E-03 total 8.300E-05 x**13 2.897E+06 13! 6.227E+09 x**13/13! 4.652E-04 total 5.482E-04 x**15 2.858E+07 15! 1.308E+12 x**15/15! 2.185E-05 total 5.263E-04 x**17 2.819E+08 17! 3.557E+14 x**17/17! 7.927E-07 total 5.271E-04 x**19 2.782E+09 19! 1.217E+17 x**19/19! 2.287E-08 total 5.271E-04 x**21 2.744E+10 21! 5.109E+19 x**21/21! ...