Practical C Programming, Third Edition

By Steve Oualline

Third Edition August 1997

ISBN: 1-56592-306-5

Publisher: O'Reilly

/* Usage: *

* sine *

* *

* 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

* 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(floatnumber)

{

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 \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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