[rational] implements the algebraic operations for rationals. A rational number is represented by its numerator and denominator. NF: gcd(Z,N)=1 /\ N>0
| Rational | Abstract rational type |
In the following functions the integer and rational operands won't be consumed and the resulting integer or rational have to be released.
Rational Rat_cons(Integer Z, Integer N) | constructs a rational from numerator 'Z' and denominator 'N' |
Rational Rat_copy(Rational a) | copies rational 'a' |
void Rat_free(Rational a) | frees rational 'a' |
Rational Rat_Int_to(Integer a) | constructs a rational from numerator 'a' ( a/1 ) |
Rational Rat_Int_div(Integer a, Integer b) | divides integer 'a' thru integer 'b' giving a rational |
void Rat_des(Rational r, Integer* z, Integer* n) | destructs rational 'r' to numerator 'z' and denominator 'n' |
Integer Rat_nom(Rational r) | copies numerator of rational 'r' |
Integer Rat_den(Rational r) | copies denominator of rational 'r' |
void showRat(Rational r) | prints rational 'r' to stdout; for debugging |
c_bool Rat_is0(Rational r) | r == 0 ? |
int Rat_cmp(Rational a, Rational b) | a < b ? -1 : a == b ? 0 : 1 |
c_bool Rat_eq(Rational a, Rational b) | a == b ? |
c_bool Rat_ne(Rational a, Rational b) | a != b ? |
c_bool Rat_lt(Rational a, Rational b) | a < b ? |
c_bool Rat_le(Rational a, Rational b) | a <= b ? |
c_bool Rat_gt(Rational a, Rational b) | a > b ? |
c_bool Rat_ge(Rational a, Rational b) | a >= b ? |
int Rat_sgn(Rational r) | signum of rational 'r' (0,-1,1) |
Rational Rat_abs(Rational r) | absolute value |r| |
Rational Rat_neg(Rational r) | negation -r |
Rational Rat_inv(Rational r) | inverse 1 / r ( r != 0 ) |
Rational Rat_add(Rational a, Rational b) | addition a + b |
Rational Rat_sub(Rational a, Rational b) | substraction a - b |
Rational Rat_mlt(Rational a, Rational b) | multiplication a * b |
Rational Rat_quo(Rational a, Rational b) | division a / b |
Q --> Z
Integer Rat_floor(Rational r) | greatest Integer z with z <= r |
Integer Rat_ceiling(Rational r) | smallest Integer z with z >= r |
Integer Rat_round(Rational r) | rounding |
Q --> Q
Rational Rat_fix_floor(Rational r, int b, long n) | Rational(floor(r * b ^ n), b ^n) |
Rational Rat_fix_ceiling(Rational r, int b, long n) | Rational(ceiling(r * b ^ n), b ^n) |
Rational Rat_fix_round(Rational r, int b, long n) | Rational(round(r * b ^ n), b ^n) |
Q <--> String
c_string Rat_to_Str(Rational r, int Base, int Digits) | converts rational 'r' into a string; allocs memory |
Rational Rat_Str_to(c_string s, int Base) | converts string 's' into a rational; not consuming 's' assuming 'Rat_Str_ok(s,Base)' |
c_bool Rat_s_ok(c_string s, int Base) | whether string 's' represents a fix point numeral |
void Rat_references(Rational x, StdCPtr (*act)(StdCPtr r)) | performs 'act' on all pointer references in rational 'x' ( garbage collection service for xaron ) |