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working version of Q extensions

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Florian Stecker
2022-04-25 14:09:45 -05:00
parent 1f92d1af9c
commit 51f7b98ccb
7 changed files with 111 additions and 193 deletions
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128
mat.h
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@@ -8,119 +8,25 @@
// library for matrix computations in variable rings (based on GMP types)
#ifdef QEXT_SQRT5
#ifdef QEXT
typedef mpq_t NUMBER [2];
#define INIT(x) do { mpq_init((x)[0]); mpq_init((x)[1]); } while(0)
#define CLEAR(x) do { mpq_clear((x)[0]); mpq_clear((x)[1]); } while(0)
#define SET(x,y) do { mpq_set((x)[0],(y)[0]); mpq_set((x)[1],(y)[1]); } while(0)
#define SET_INT(x,y) do { mpq_set_si((x)[0],(y),1); mpq_set_si((x)[1],0,1); } while(0)
#define SET_ZERO(x) SET_INT(x,0)
#define SET_ONE(x) SET_INT(x,1)
#define ADD(x,y,z) do { mpq_add((x)[0],(y)[0],(z)[0]); mpq_add((x)[1],(y)[1],(z)[1]); } while(0)
#define SUB(x,y,z) do { mpq_sub((x)[0],(y)[0],(z)[0]); mpq_sub((x)[1],(y)[1],(z)[1]); } while(0)
#define MUL multiply_sqrt5
#define DIV divide_sqrt5
#define CMP compare_sqrt5
#define PRINT(x) gmp_printf("%Qd + %Qd*sqrt(5)", (x)[0], (x)[1])
#define SPRINT(buf, x) gmp_sprintf(buf, "%Qd+%Qd*sqrt(5)", (x)[0], (x)[1])
#include "qext.h"
static void multiply_sqrt5(NUMBER out, NUMBER a, NUMBER b)
{
// could be in place!!!
mpq_t tmp, result[2];
mpq_inits(tmp, result[0], result[1], 0);
mpq_mul(result[0], a[1], b[1]);
mpq_set_si(tmp, 5, 1);
mpq_mul(result[0], result[0], tmp);
mpq_mul(tmp, a[0], b[0]);
mpq_add(result[0], result[0], tmp);
mpq_mul(result[1], a[1], b[0]);
mpq_mul(tmp, a[0], b[1]);
mpq_add(result[1], result[1], tmp);
mpq_set(out[0], result[0]);
mpq_set(out[1], result[1]);
mpq_clears(tmp, result[0], result[1], 0);
}
static void divide_sqrt5(NUMBER out, NUMBER a, NUMBER b)
{
mpq_t denom, num, tmp, neg5, result[2];
mpq_inits(denom, num, tmp, neg5, result[0], result[1], 0);
mpq_set_si(neg5, -5, 1);
mpq_mul(denom, b[1], b[1]);
mpq_mul(denom, denom, neg5);
mpq_mul(tmp, b[0], b[0]);
mpq_add(denom, denom, tmp);
mpq_mul(num, a[1], b[1]);
mpq_mul(num, num, neg5);
mpq_mul(tmp, a[0], b[0]);
mpq_add(num, num, tmp);
mpq_div(result[0], num, denom);
mpq_mul(num, a[1], b[0]);
mpq_mul(tmp, a[0], b[1]);
mpq_sub(num, num, tmp);
mpq_div(result[1], num, denom);
mpq_set(out[0], result[0]);
mpq_set(out[1], result[1]);
mpq_clears(denom, num, tmp, neg5, result[0], result[1], 0);
}
static int compare_sqrt5(NUMBER x, NUMBER y)
{
int result;
mpq_t p, q, p2, q2, c5;
mpq_inits(p, q, p2, q2, c5, 0);
mpq_sub(p, x[0], y[0]);
mpq_sub(q, x[1], y[1]);
/*
want to know if p + sqrt(5) q > 0
if p>0 and q>0: always true
if p>0 and q<0: equivalent to |p|^2 > 5 |q|^2
if p<0 and q>0: equivalent to |p|^2 < 5 |q|^2
if p<0 and q<0: always false
*/
if(mpq_sgn(p) > 0 && mpq_sgn(q) > 0) {
result = 1;
goto done;
}
if(mpq_sgn(p) < 0 && mpq_sgn(q) < 0) {
result = -1;
goto done;
}
mpq_mul(p2, p, p);
mpq_mul(q2, q, q);
mpq_set_si(c5, 5, 1);
mpq_mul(q2, q2, c5);
if(mpq_sgn(p) > 0)
result = mpq_cmp(p2, q2); // this can't be zero, or else |p/q| = sqrt(5), but it's irrational
else if(mpq_sgn(p) < 0)
result = -mpq_cmp(p2, q2); // this can be zero if p = 0 and q = 0
else // p = 0
return mpq_sgn(q);
done:
mpq_clears(p, q, p2, q2, c5, 0);
return result;
}
#define NUMBER qext_number
#define INIT qext_init
#define CLEAR qext_clear
#define SET qext_set
#define SET_INT qext_set_int
#define SET_Q qext_set_q
#define SET_ZERO(x) qext_set_int((x),0)
#define SET_ONE(x) qext_set_int((x),1)
#define ADD qext_add
#define SUB qext_sub
#define MUL qext_mul
// #define DIV qext_div
#define CMP qext_cmp
#define PRINT qext_print
#define SNPRINT qext_snprint
#endif