compute sine using very simple floating arithmetic
/*
Practical C Programming, Third Edition
By Steve Oualline
Third Edition August 1997
ISBN: 1-56592-306-5
Publisher: O'Reilly
*/
/* Usage: *
* sine <value> *
* *
* <value> is an angle in radians *
* *
* Format used in f.fffe+X *
* *
* f.fff is a 4 digit fraction *
* + is a sign (+ or -) *
* X is a single digit exponent *
* *
* sine(x) = x - x**3 + x**5 - x**7 *
* ----- ---- ---- . . . . *
* 3! 5! 7! *
* *
* Warning: This program is intended to show some of *
* problems with floating point. It not intended *
* to be used to produce exact values for the *
* sin function. *
* *
* Note: Even though we specify only one-digit for the *
* exponent, two are used for some calculations. *
* This is due to the fact that printf has no *
* format for a single digit exponent. *
*/
#include <stdlib.h>
#include <math.h>
#include <stdio.h>
/*
* float_2_ascii -- turn a floating-point string *
* into ascii. *
* *
* Parameters *
* number -- number to turn into ascii *
* *
* Returns *
* Pointer to the string containing the number *
* *
* Warning: Uses static storage, so later calls *
* overwrite earlier entries *
*/
static char *float_2_ascii(float number)
{
static char result[10]; /*place to put the number */
sprintf(result,"%8.3E", number);
return (result);
}
/*
* fix_float -- turn high precision numbers into *
* low precision numbers to simulate a *
* very dumb floating-point structure. *
* *
* Parameters *
* number -- number to take care of *
* *
* Returns *
* number accurate to 5 places only *
* *
* Note: This works by changing a number into ascii and *
* back. Very slow, but it works. *
*/
float fix_float(float number)
{
float result; /* result of the conversion */
char ascii[10]; /* ascii version of number */
sprintf(ascii,"%8.4e", number);
sscanf(ascii, "%e", &result);
return (result);
}
/*
* factorial -- compute the factorial of a number. *
* *
* Parameters *
* number -- number to use for factorial *
* *
* Returns *
* factorial(number) or number! *
* *
* Note: Even though this is a floating-point routine, *
* using numbers that are not whole numbers *
* does not make sense. *
*/
float factorial(float number)
{
if (number <= 1.0)
return (number);
else
return (number *factorial(number - 1.0));
}
int main(int argc, char *argv[])
{
float total; /* total of series so far */
float new_total;/* newer version of total */
float term_top;/* top part of term */
float term_bottom;/* bottom of current term */
float term; /* current term */
float exp; /* exponent of current term */
float sign; /* +1 or -1 (changes on each term) */
float value; /* value of the argument to sin */
int index; /* index for counting terms */
if (argc != 2) {
fprintf(stderr,"Usage is:\n");
fprintf(stderr," sine <value>\n");
exit (8);
}
value = fix_float(atof(&argv[1][0]));
total = 0.0;
exp = 1.0;
sign = 1.0;
for (index = 0; /* take care of below */ ; ++index) {
term_top = fix_float(pow(value, exp));
term_bottom = fix_float(factorial(exp));
term = fix_float(term_top / term_bottom);
printf("x**%d %s\n", (int)exp,
float_2_ascii(term_top));
printf("%d! %s\n", (int)exp,
float_2_ascii(term_bottom));
printf("x**%d/%d! %s\n", (int)exp, (int)exp,
float_2_ascii(term));
printf("\n");
new_total = fix_float(total + sign * term);
if (new_total == total)
break;
total = new_total;
sign = -sign;
exp = exp + 2.0;
printf(" total %s\n", float_2_ascii(total));
printf("\n");
}
printf("%d term computed\n", index+1);
printf("sin(%s)=\n", float_2_ascii(value));
printf(" %s\n", float_2_ascii(total));
printf("Actual sin(%G)=%G\n",
atof(&argv[1][0]), sin(atof(&argv[1][0])));
return (0);
}
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