This header provides functions for performing fixed-precision arithmetic on integer or rational numbers. More...

#include <stdio.h>
#include <stdlib.h>
#include "assert.h"
#include "arithmetique.h"

Include dependency graph for arith_fixprec.h:

This graph shows which files directly or indirectly include this file:

Data Structures
struct	qval_s

Macros
#define	LINEAR_ARITH_FIXPREC_H

#define	NOWUNUSED __attribute__((unused))

Integers Functions
This section describes the functions for performing integer arithmetic. These functions start with the prefix `zval_`. Integers are stored in objects of type `zval_t`.
#define	zval_init(z) ((z) = 0)
	Initialize z and set its value to 0. More...

#define	zval_clear(z)
	Free the space occupied by z. More...

#define	zval_set(z1, z2) ((z1) = (z2))
	Set the value of z1 from z2. More...

#define	zval_set_i(z, n) ((z) = (n))
	Set the value of z from the `signed long` n. More...

#define	zval_init_set(z1, z2) ((z1) = (z2))
	Initialize z1 and set its value from z2. More...

#define	zval_init_set_i(z, n) ((z) = (n))
	Initialize z and set its value from the `signed long` n. More...

#define	zval_get_i(z) (z)
	Return the value of z as a `signed long`. More...

#define	zval_add(z1, z2, z3) ((z1) = (z2) + (z3))
	Set z1 to z2 + z3. More...

#define	zval_sub(z1, z2, z3) ((z1) = (z2) - (z3))
	Set z1 to z2 - z3. More...

#define	zval_mul(z1, z2, z3) ((z1) = value_protected_mult(z2, z3))
	Set z1 to z2 times z3. More...

#define	zval_div(z1, z2, z3) ((z1) = (z2) / (z3))
	Set z1 to z2/z3. More...

#define	zval_addmul(z1, z2, z3) ((z1) += value_protected_mult(z2, z3))
	Set z1 to z1 + z2 times z3. More...

#define	zval_submul(z1, z2, z3) ((z1) -= value_protected_mult(z2, z3))
	Set z1 to z1 - z2 times z3. More...

#define	zval_neg(z1, z2) ((z1) = -(z2))
	Set z1 to -z2. More...

#define	zval_abs(z1, z2) ((z1) = ABS(z2))
	Set z1 to the absolute value of z2. More...

#define	zval_mod(z1, z2, z3) ((z1) = (z2) % (z3))
	Set z1 to z2 `mod` z3. More...

#define	zval_gcd(z1, z2, z3) ((z1) = pgcd(z2, z3))
	Set z1 to the greatest common divisor of z2 and z3. More...

#define	zval_lcm(z1, z2, z3) ((z1) = ppcm(z2, z3))
	Set z1 to the least common multiple of z2 and z3. More...

#define	zval_cmp(z1, z2) ((z1) - (z2))
	Compare z1 and z2. More...

#define	zval_cmp_i(z, n) ((z) - (n))
	Compare z with a `signed long` n. More...

#define	zval_sgn(z) (value_sign(z))
	Return +1 if z > 0, 0 if z = 0, and -1 if z < 0. More...

#define	zval_equal(z1, z2) ((z1) == (z2))
	Return non-zero if z1 and z2 are equal, zero if they are non-equal. More...

#define	zval_equal_i(z, n) ((z) == (n))
	Return non-zero if z and the `unsigned long` n are equal, zero if they are non-equal. More...

#define	zval_fprint(stream, z) (fprintf(stream, "%li", z))
	Output z on stdio stream stream. More...

#define	zval_print(z) (printf("%li", z))
	Output z on `stdout`. More...

typedef long int	zval_t
	Type of integer numbers. More...

Rational Number Functions
This section describes the functions for performing arithmetic on rational numbers. These functions start with the prefix `qval_`. Rational numbers are stored in objects of type `qval_t`.
#define	qval_clear(q)
	Free the space occupied by q. More...

#define	qval_equal_i(q1, q2num, q2den) (qval_cmp_i(q1, q2num, q2den) == 0)
	Return non-zero if q and q2num/q2den* are* equal, zero if they are non-equal. More...

#define	qval_print(q) (qval_fprint(stdout, q))
	Output q on `stdout`. More...

typedef struct qval_s *	qval_p

typedef qval_s	qval_t[1]
	Type of rational numbers. More...

static void	qval_canonicalize_unsafe (qval_t q)

static void NOWUNUSED	qval_canonicalize (qval_t q)
	Remove any factors that are common to the numerator and denominator of q, and make the denominator positive. More...

static void NOWUNUSED	qval_init (qval_t q)
	Initialize q and set its value to 0/1. More...

static void NOWUNUSED	qval_set (qval_t q1, qval_t q2)
	Set the value of q1 from q2. More...

static void NOWUNUSED	qval_set_i (qval_t q1, Value q2num, Value q2den)
	Set the value of q to q2num/q2den. More...

static void NOWUNUSED	qval_add (qval_t q1, qval_t q2, qval_t q3)
	Set q1 to q2 + q3. More...

static void NOWUNUSED	qval_sub (qval_t q1, qval_t q2, qval_t q3)
	Set q1 to q2 - q3. More...

static void NOWUNUSED	qval_mul (qval_t q1, qval_t q2, qval_t q3)
	Set q1 to q2 times q3. More...

static void NOWUNUSED	qval_div (qval_t q1, qval_t q2, qval_t q3)
	Set q1 to q2/q3. More...

static void NOWUNUSED	qval_neg (qval_t q1, qval_t q2)
	Set q1 to -q2. More...

static void NOWUNUSED	qval_abs (qval_t q1, qval_t q2)
	Set q1 to the absolute value of q2. More...

static void NOWUNUSED	qval_inv (qval_t q1, qval_t q2)
	Set q1 to 1/q2. More...

static int NOWUNUSED	qval_cmp (qval_t q1, qval_t q2)
	Compare q1 and q2. More...

static int NOWUNUSED	qval_cmp_i (qval_t q1, Value q2num, Value q2den)
	Compare q1 and q2num/q2den. More...

static int NOWUNUSED	qval_sgn (qval_t q)
	Return +1 if q > 0, 0 if q = 0, and -1 if q < 0. More...

static int NOWUNUSED	qval_equal (qval_t q1, qval_t q2)
	Return non-zero if q1 and q2 are equal, zero if they are non-equal. More...

static int NOWUNUSED	qval_fprint (FILE *stream, qval_t q)
	Output q on stdio stream stream. More...

Detailed Description

This header provides functions for performing fixed-precision arithmetic on integer or rational numbers.

Definition in file arith_fixprec.h.

Macro Definition Documentation

◆ LINEAR_ARITH_FIXPREC_H

#define LINEAR_ARITH_FIXPREC_H

Definition at line 40 of file arith_fixprec.h.

◆ NOWUNUSED

#define NOWUNUSED __attribute__((unused))

Definition at line 48 of file arith_fixprec.h.

◆ qval_clear

#define qval_clear ( q )

Free the space occupied by q.

Definition at line 258 of file arith_fixprec.h.

◆ qval_equal_i

#define qval_equal_i	(	q1,
		q2num,
		q2den
	)	(qval_cmp_i(q1, q2num, q2den) == 0)

Return non-zero if q and q2num/q2den are equal, zero if they are non-equal.

Definition at line 433 of file arith_fixprec.h.

◆ qval_print

#define qval_print ( q ) (qval_fprint(stdout, q))

Output q on stdout.

Definition at line 452 of file arith_fixprec.h.

◆ zval_abs

#define zval_abs	(	z1,
		z2
	)	((z1) = ABS(z2))

Set z1 to the absolute value of z2.

Definition at line 136 of file arith_fixprec.h.

◆ zval_add

#define zval_add	(	z1,
		z2,
		z3
	)	((z1) = (z2) + (z3))

Set z1 to z2 + z3.

Definition at line 101 of file arith_fixprec.h.

◆ zval_addmul

#define zval_addmul	(	z1,
		z2,
		z3
	)	((z1) += value_protected_mult(z2, z3))

Set z1 to z1 + z2 times z3.

Definition at line 121 of file arith_fixprec.h.

◆ zval_clear

#define zval_clear ( z )

Free the space occupied by z.

Definition at line 71 of file arith_fixprec.h.

◆ zval_cmp

#define zval_cmp	(	z1,
		z2
	)	((z1) - (z2))

Compare z1 and z2.

Return a positive value if z1 > z2, zero if z1 = z2, or a negative value if z1 < z2.

Definition at line 162 of file arith_fixprec.h.

◆ zval_cmp_i

#define zval_cmp_i	(	z,
		n
	)	((z) - (n))

Compare z with a signed long n.

Return a positive value if z > n, zero if z = n, or a negative value if z < n.

Definition at line 169 of file arith_fixprec.h.

◆ zval_div

#define zval_div	(	z1,
		z2,
		z3
	)	((z1) = (z2) / (z3))

Set z1 to z2/z3.

Definition at line 116 of file arith_fixprec.h.

◆ zval_equal

#define zval_equal	(	z1,
		z2
	)	((z1) == (z2))

Return non-zero if z1 and z2 are equal, zero if they are non-equal.

Definition at line 179 of file arith_fixprec.h.

◆ zval_equal_i

#define zval_equal_i	(	z,
		n
	)	((z) == (n))

Return non-zero if z and the unsigned long n are equal, zero if they are non-equal.

Definition at line 185 of file arith_fixprec.h.

◆ zval_fprint

#define zval_fprint	(	stream,
		z
	)	(fprintf(stream, "%li", z))

Output z on stdio stream stream.

Definition at line 190 of file arith_fixprec.h.

◆ zval_gcd

#define zval_gcd	(	z1,
		z2,
		z3
	)	((z1) = pgcd(z2, z3))

Set z1 to the greatest common divisor of z2 and z3.

The result is always positive, irrespective of the signs of z2 and z3. Except if both inputs are zero; then it is undefined.

Definition at line 148 of file arith_fixprec.h.

◆ zval_get_i

#define zval_get_i ( z ) (z)

Return the value of z as a signed long.

Definition at line 96 of file arith_fixprec.h.

◆ zval_init

#define zval_init ( z ) ((z) = 0)

Initialize z and set its value to 0.

Definition at line 66 of file arith_fixprec.h.

◆ zval_init_set

#define zval_init_set	(	z1,
		z2
	)	((z1) = (z2))

Initialize z1 and set its value from z2.

Definition at line 86 of file arith_fixprec.h.

◆ zval_init_set_i

#define zval_init_set_i	(	z,
		n
	)	((z) = (n))

Initialize z and set its value from the signed long n.

Definition at line 91 of file arith_fixprec.h.

◆ zval_lcm

#define zval_lcm	(	z1,
		z2,
		z3
	)	((z1) = ppcm(z2, z3))

Set z1 to the least common multiple of z2 and z3.

The result is always positive, irrespective of the signs of z2 and z3. z1 will be zero if either z2 or z3 is zero.

Definition at line 155 of file arith_fixprec.h.

◆ zval_mod

#define zval_mod	(	z1,
		z2,
		z3
	)	((z1) = (z2) % (z3))

Set z1 to z2 mod z3.

Definition at line 141 of file arith_fixprec.h.

◆ zval_mul

#define zval_mul	(	z1,
		z2,
		z3
	)	((z1) = value_protected_mult(z2, z3))

Set z1 to z2 times z3.

Definition at line 111 of file arith_fixprec.h.

◆ zval_neg

#define zval_neg	(	z1,
		z2
	)	((z1) = -(z2))

Set z1 to -z2.

Definition at line 131 of file arith_fixprec.h.

◆ zval_print

#define zval_print ( z ) (printf("%li", z))

Output z on stdout.

Definition at line 195 of file arith_fixprec.h.

◆ zval_set

#define zval_set	(	z1,
		z2
	)	((z1) = (z2))

Set the value of z1 from z2.

Definition at line 76 of file arith_fixprec.h.

◆ zval_set_i

#define zval_set_i	(	z,
		n
	)	((z) = (n))

Set the value of z from the signed long n.

Definition at line 81 of file arith_fixprec.h.

◆ zval_sgn

#define zval_sgn ( z ) (value_sign(z))

Return +1 if z > 0, 0 if z = 0, and -1 if z < 0.

Definition at line 174 of file arith_fixprec.h.

◆ zval_sub

#define zval_sub	(	z1,
		z2,
		z3
	)	((z1) = (z2) - (z3))

Set z1 to z2 - z3.

Definition at line 106 of file arith_fixprec.h.

◆ zval_submul

#define zval_submul	(	z1,
		z2,
		z3
	)	((z1) -= value_protected_mult(z2, z3))

Set z1 to z1 - z2 times z3.

Definition at line 126 of file arith_fixprec.h.

Typedef Documentation

◆ qval_p

typedef struct qval_s * qval_p

◆ qval_t

typedef qval_s qval_t[1]

Type of rational numbers.

Definition at line 216 of file arith_fixprec.h.

◆ zval_t

typedef long int zval_t

Type of integer numbers.

Definition at line 61 of file arith_fixprec.h.

Function Documentation

◆ qval_abs()

static void NOWUNUSED qval_abs	(	qval_t	q1,
		qval_t	q2
	)

static

Set q1 to the absolute value of q2.

Definition at line 349 of file arith_fixprec.h.

 {
         zval_abs(q1->num, q2->num);
         zval_set(q1->den, q2->den);
 }

References zval_abs, and zval_set.

◆ qval_add()

static void NOWUNUSED qval_add	(	qval_t	q1,
		qval_t	q2,
		qval_t	q3
	)

static

Set q1 to q2 + q3.

Definition at line 283 of file arith_fixprec.h.

 {
         zval_t q3num; zval_init(q3num); zval_set(q3num, q3->num);
         zval_t lcm; zval_init(lcm); zval_lcm(lcm, q2->den, q3->den);
         zval_t tmp; zval_init(tmp);
         zval_div(tmp, lcm, q2->den);
         zval_mul(q1->num, q2->num, tmp);
         zval_div(tmp, lcm, q3->den);
         zval_addmul(q1->num, q3num, tmp);
         zval_set(q1->den, lcm);
         zval_clear(q3num); zval_clear(lcm); zval_clear(tmp);
         qval_canonicalize_unsafe(q1);
 }

References qval_canonicalize_unsafe(), zval_addmul, zval_clear, zval_div, zval_init, zval_lcm, zval_mul, and zval_set.

Here is the call graph for this function:

◆ qval_canonicalize()

static void NOWUNUSED qval_canonicalize ( qval_t q )

static

Remove any factors that are common to the numerator and denominator of q, and make the denominator positive.

Definition at line 238 of file arith_fixprec.h.

 {
         if (zval_cmp_i(q->den, 0) < 0) {
                 zval_neg(q->num, q->num);
                 zval_neg(q->den, q->den);
         }
         qval_canonicalize_unsafe(q);
 }

References qval_canonicalize_unsafe(), zval_cmp_i, and zval_neg.

Referenced by qval_div(), qval_inv(), and qval_set_i().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ qval_canonicalize_unsafe()

static void qval_canonicalize_unsafe ( qval_t q )

static

Definition at line 218 of file arith_fixprec.h.

 {
         if (zval_cmp_i(q->num, 0) == 0) {
                 zval_set_i(q->den, 1);
                 return;
         }
         else {
                 zval_t gcd; zval_init(gcd);
                 zval_abs(gcd, q->num);
                 zval_gcd(gcd, gcd, q->den);
                 zval_div(q->num, q->num, gcd);
                 zval_div(q->den, q->den, gcd);
                 zval_clear(gcd);
         }
 }

References zval_abs, zval_clear, zval_cmp_i, zval_div, zval_gcd, zval_init, and zval_set_i.

Referenced by qval_add(), qval_canonicalize(), qval_mul(), and qval_sub().

Here is the caller graph for this function:

◆ qval_cmp()

static int NOWUNUSED qval_cmp	(	qval_t	q1,
		qval_t	q2
	)

static

Compare q1 and q2.

Return a positive value if q1 > q2, qero if q1 = q2, or a negative value if q1 < q2. To determine if two rationals are equal, qval_equal is faster than qval_cmp.

Definition at line 375 of file arith_fixprec.h.

 {
         zval_t lcm; zval_init(lcm); zval_lcm(lcm, q1->den, q2->den);
         zval_t z1; zval_init(z1);
         zval_t z2; zval_init(z2);
         zval_t tmp; zval_init(tmp);
         zval_div(tmp, lcm, q1->den);
         zval_mul(z1, q1->num, tmp);
         zval_div(tmp, lcm, q2->den);
         zval_mul(z2, q2->num, tmp);
         int res = zval_cmp(z1, z2);
         zval_clear(lcm); zval_clear(z1); zval_clear(z2); zval_clear(tmp);
         return res;
 }

References zval_clear, zval_cmp, zval_div, zval_init, zval_lcm, and zval_mul.

◆ qval_cmp_i()

static int NOWUNUSED qval_cmp_i	(	qval_t	q1,
		Value	q2num,
		Value	q2den
	)

static

Compare q1 and q2num/q2den.

Return a positive value if q1 > q2num/q2den, zero if q1 = q2num/q2den, or a negative value if q1 < q2num/q2den.

Definition at line 396 of file arith_fixprec.h.

 {
         zval_t lcm; zval_init(lcm); zval_lcm(lcm, q1->den, q2den);
         zval_t z1; zval_init(z1);
         zval_t z2; zval_init(z2);
         zval_t tmp; zval_init(tmp);
         zval_div(tmp, lcm, q1->den);
         zval_mul(z1, q1->num, tmp);
         zval_div(tmp, lcm, q2den);
         zval_mul(z2, q2num, tmp);
         int res = zval_cmp(z1, z2);
         zval_clear(lcm); zval_clear(z1); zval_clear(z2); zval_clear(tmp);
         return res;
 }

References zval_clear, zval_cmp, zval_div, zval_init, zval_lcm, and zval_mul.

◆ qval_div()

static void NOWUNUSED qval_div	(	qval_t	q1,
		qval_t	q2,
		qval_t	q3
	)

static

Set q1 to q2/q3.

Definition at line 327 of file arith_fixprec.h.

 {
         zval_t q3num; zval_init(q3num); zval_set(q3num, q3->num);
         assert(zval_cmp_i(q3num, 0) != 0);
         zval_mul(q1->num, q2->num, q3->den);
         zval_mul(q1->den, q2->den, q3num);
         zval_clear(q3num);
         qval_canonicalize(q1);
 }

References assert, qval_canonicalize(), zval_clear, zval_cmp_i, zval_init, zval_mul, and zval_set.

Here is the call graph for this function:

◆ qval_equal()

static int NOWUNUSED qval_equal	(	qval_t	q1,
		qval_t	q2
	)

static

Return non-zero if q1 and q2 are equal, zero if they are non-equal.

Although qval_cmp can be used for the same purpose, this function is faster.

Definition at line 424 of file arith_fixprec.h.

 {
         return zval_cmp(q1->den, q2->den) == 0 && zval_cmp(q1->num, q2->num) == 0;
 }

References zval_cmp.

◆ qval_fprint()

static int NOWUNUSED qval_fprint	(	FILE *	stream,
		qval_t	q
	)

static

Output q on stdio stream stream.

Definition at line 438 of file arith_fixprec.h.

 {
         int c;
         c = zval_fprint(stream, q->num);
         if (zval_cmp_i(q->den, 1)) {
                 c += fprintf(stream, "/");
                 c += zval_fprint(stream, q->den);
         }
         return c;
 }

References fprintf(), zval_cmp_i, and zval_fprint.

Here is the call graph for this function:

◆ qval_init()

static void NOWUNUSED qval_init ( qval_t q )

static

Initialize q and set its value to 0/1.

Definition at line 250 of file arith_fixprec.h.

                                           {
         q->num = 0;
         q->den = 1;
 }

◆ qval_inv()

static void NOWUNUSED qval_inv	(	qval_t	q1,
		qval_t	q2
	)

static

Set q1 to 1/q2.

Definition at line 358 of file arith_fixprec.h.

 {
         zval_t q2num; zval_init(q2num); zval_set(q2num, q2->num);
         assert(zval_cmp_i(q2num, 0) != 0);
         zval_set(q1->num, q2->den);
         zval_set(q1->den, q2num);
         zval_clear(q2num);
         qval_canonicalize(q1);
 }

References assert, qval_canonicalize(), zval_clear, zval_cmp_i, zval_init, and zval_set.

Here is the call graph for this function:

◆ qval_mul()

static void NOWUNUSED qval_mul	(	qval_t	q1,
		qval_t	q2,
		qval_t	q3
	)

static

Set q1 to q2 times q3.

Definition at line 317 of file arith_fixprec.h.

 {
         zval_mul(q1->num, q2->num, q3->num);
         zval_mul(q1->den, q2->den, q3->den);
         qval_canonicalize_unsafe(q1);
 }

References qval_canonicalize_unsafe(), and zval_mul.

Here is the call graph for this function:

◆ qval_neg()

static void NOWUNUSED qval_neg	(	qval_t	q1,
		qval_t	q2
	)

static

Set q1 to -q2.

Definition at line 340 of file arith_fixprec.h.

 {
         zval_neg(q1->num, q2->num);
         zval_set(q1->den, q2->den);
 }

References zval_neg, and zval_set.

◆ qval_set()

static void NOWUNUSED qval_set	(	qval_t	q1,
		qval_t	q2
	)

static

Set the value of q1 from q2.

Definition at line 263 of file arith_fixprec.h.

 {
         zval_set(q1->num, q2->num);
         zval_set(q1->den, q2->den);
 }

References zval_set.

◆ qval_set_i()

static void NOWUNUSED qval_set_i	(	qval_t	q1,
		Value	q2num,
		Value	q2den
	)

static

Set the value of q to q2num/q2den.

Definition at line 272 of file arith_fixprec.h.

 {
         assert(zval_cmp_i(q2den, 0) != 0);
         zval_set_i(q1->num, q2num);
         zval_set_i(q1->den, q2den);
         qval_canonicalize(q1);
 }

References assert, qval_canonicalize(), zval_cmp_i, and zval_set_i.

Here is the call graph for this function:

◆ qval_sgn()

static int NOWUNUSED qval_sgn ( qval_t q )

static

Return +1 if q > 0, 0 if q = 0, and -1 if q < 0.

Definition at line 414 of file arith_fixprec.h.

 {
         return zval_sgn(q->num);
 }

References zval_sgn.

◆ qval_sub()

static void NOWUNUSED qval_sub	(	qval_t	q1,
		qval_t	q2,
		qval_t	q3
	)

static

Set q1 to q2 - q3.

Definition at line 300 of file arith_fixprec.h.

 {
         zval_t q3num; zval_init(q3num); zval_set(q3num, q3->num);
         zval_t lcm; zval_init(lcm); zval_lcm(lcm, q2->den, q3->den);
         zval_t tmp; zval_init(tmp);
         zval_div(tmp, lcm, q2->den);
         zval_mul(q1->num, q2->num, tmp);
         zval_div(tmp, lcm, q3->den);
         zval_submul(q1->num, q3num, tmp);
         zval_set(q1->den, lcm);
         zval_clear(q3num); zval_clear(lcm); zval_clear(tmp);
         qval_canonicalize_unsafe(q1);
 }

References qval_canonicalize_unsafe(), zval_clear, zval_div, zval_init, zval_lcm, zval_mul, zval_set, and zval_submul.

Here is the call graph for this function:

Data Structures

Macros

Integers Functions

Rational Number Functions

Detailed Description

Macro Definition Documentation

◆ LINEAR_ARITH_FIXPREC_H

◆ NOWUNUSED

◆ qval_clear

◆ qval_equal_i

◆ qval_print

◆ zval_abs

◆ zval_add

◆ zval_addmul

◆ zval_clear

◆ zval_cmp

◆ zval_cmp_i

◆ zval_div

◆ zval_equal

◆ zval_equal_i

◆ zval_fprint

◆ zval_gcd

◆ zval_get_i

◆ zval_init

◆ zval_init_set

◆ zval_init_set_i

◆ zval_lcm

◆ zval_mod

◆ zval_mul

◆ zval_neg

◆ zval_print

◆ zval_set

◆ zval_set_i

◆ zval_sgn

◆ zval_sub

◆ zval_submul

Typedef Documentation

◆ qval_p

◆ qval_t

◆ zval_t

Function Documentation

◆ qval_abs()

◆ qval_add()

◆ qval_canonicalize()

◆ qval_canonicalize_unsafe()

◆ qval_cmp()

◆ qval_cmp_i()

◆ qval_div()

◆ qval_equal()

◆ qval_fprint()

◆ qval_init()

◆ qval_inv()

◆ qval_mul()

◆ qval_neg()

◆ qval_set()

◆ qval_set_i()

◆ qval_sgn()

◆ qval_sub()