Mathematics

Last modified Monday, 06-Mar-2023 15:04:35 UTC.

Mathematics is relatively straightforward library to use. You must #include <math.h> and must link in the math library at compilation:
```
gcc mathprog.c -o mathprog -lm
     
```
Some things are defined in stdlib.h instead of math.h.
Math constants
- The math.h library defines many (often neglected) constants. It is always advisable to use these definitions.
- M_E - The base of natural logarithms (e).
- M_LOG2E - The base-2 logarithm of e.
- M_LOG10E - The base-10 logarithm of e.
- M_LN2 - The natural logarithm of 2.
- M_LN10 - The natural logarithm of 10.
- M_PI - Pi
- M_PI_2 - Pi/2
- M_PI_4 - Pi/4
- M_1_PI - 1/Pi
- M_2_PI - 2/Pi
- M_2_SQRTPI - 2/sqrt(Pi)
- M_SQRT2 - The positive square root of 2.
- M_SQRT1_2 - The positive square root of 1/2.
- HUGE or MAXFLOAT - The maximum value of a float
- HUGE_VAL - positive infinity.
Common maths functions
- Absolutes, fractions, remainders
  - int abs(int x); - Compute absolute value of x
  - long labs(long x); - Compute absolute value of x
  - double fabs(double x); - Compute absolute value of x
  - double rint(double x); - Get integral value nearest to x
  - double ceil(double x); - Get smallest integral value that exceeds x
  - double floor(double x); - Get largest integral value less than x
  - div_t div(int number,int denom) - Divide one integer by another and get quotient and remainder
  - ldiv_t ldiv(long number,long denom) - Divide one integer by another and get quotient and remainder
  - double fmod(double x,double y) - Divide x by y with integral quotient and return remainder
  - double frexp(double x,int *expptr) - Breaks down x into mantissa and exponent (base 2)
  - double ldexp(double x,int exp) - Computes x * 2^exp
  - double modf(double x,double *intptr) - Breaks x into fractional and integer parts.
- Trigonometric functions
  - double acos(double x) - Compute arc cosine of x.
  - double asin(double x) - Compute arc sine of x.
  - double atan(double x) - Compute arc tangent of x.
  - double atan2(double y, double x) - Compute arc tangent of y/x.
  - double cos(double x) - Compute cosine of angle in radians.
  - double cosh(double x) - Compute the hyperbolic cosine of x.
  - double sin(double x) - Compute sine of angle in radians.
  - double sinh(double x) - Compute the hyperbolic sine of x.
  - double tan(double x) - Compute tangent of angle in radians.
  - double tanh(double x) - Compute the hyperbolic tangent of x.
  - SinCurve.c - Program using some maths functions
- Exponents
  - double exp(double x) - Compute exponential of x
  - double log(double x) - Compute log(x).
  - double log10(double x ) - Compute log to the base 10 of x.
  - double pow(double x, double y) - Compute x raised to the power y.
  - double sqrt(double x) - Compute the square root of x.
- Random numbers
  - int rand(void) - Returns a random number in the range 0 to RAND_MAX, which is at least 32767.
  - void srand(unsigned int seed) - Uses seed for a new sequence of random numbers. The initial seed is 1.
  - RandomX.c - Program that uses random numbers
There are a number a machine dependent values defined in values.h
- BITSPERBYTE - Number of bits in a byte
- MAXSHORT - Largest possible short
- MAXINT - Largest possible int
- MAXLONG - Largest possible long
- MINFLOAT - The smallest float
- MAXFLOAT - The largest float
- FMINEXP - The minimum exponent of a float
- FMAXEXP - The maximum exponent of a float
- MINDOUBLE - The smallest double
- MAXDOUBLE - The largest double
- DMINEXP - The minimum exponent of a double
- DMAXEXP - The maximum exponent of a double
and more defined in limits.h
- CHAR_BIT - Max # of bits in a "char"
- SCHAR_MIN - Min value of a "signed char"
- SCHAR_MAX - Max value of a "signed char"
- UCHAR_MAX - Max value of an "unsigned char"
- SHRT_MIN - Min value of a "short int"
- SHRT_MAX - Max value of a "short int"
- USHRT_MAX - Max value of "unsigned short int"
- INT_MIN - Min value of an "int"
- INT_MAX - Max value of an "int"
- UINT_MAX - Max value of an "unsigned int"
- LONG_MIN - Min value of a "long int"
- LONG_MAX - Max value of a "long int"
- ULONG_MAX - Max value of "unsigned long int"
- DBL_DIG - Digits of precision of a "double"
- DBL_MAX - Max decimal value of a "double"
- DBL_MIN - Min decimal value of a "double"
- FLT_DIG - Digits of precision of a "float"
- FLT_MAX - Max decimal value of a "float"
- FLT_MIN - Min decimal value of a "float"
NumericLimits.c

Exercises

Exam Style Questions

What compiler flag need to be given to use mathematics functions in C?

How could the following program be improved?

#include <stdio.h>

#define PI 3.14159265

int main(int argc,char *argv[]) {

    double Radius,Area;

    Radius = 27;
    Area = PI * Radius * Radius;
    printf("%f\n",Area);

    return(0);
}

How can you find out the number of digits of precision a double variable supports?