/*
  This file is for functions for field arithmetic
*/
// 20221231 djb: const for GF_mul
// 20221230 djb: add linker line

// linker define gf_iszero gf_add gf_mul gf_inv gf_frac GF_mul

#include "gf.h"

#include "params.h"

gf gf_iszero(gf a)
{
	uint32_t t = a;

	t -= 1;
	t >>= 20;

	return (gf) t;
}

gf gf_add(gf in0, gf in1)
{
	return in0 ^ in1;
}

gf gf_mul(gf in0, gf in1)
{
	int i;

	uint32_t tmp;
	uint32_t t0;
	uint32_t t1;
	uint32_t t;

	t0 = in0;
	t1 = in1;

	tmp = t0 * (t1 & 1);

	for (i = 1; i < GFBITS; i++)
		tmp ^= (t0 * (t1 & (1 << i)));

	t = tmp & 0x7FC000;
	tmp ^= t >> 9;
	tmp ^= t >> 12;

	t = tmp & 0x3000;
	tmp ^= t >> 9;
	tmp ^= t >> 12;

	return tmp & ((1 << GFBITS)-1);
}

/* input: field element in */
/* return: in^2 */
static inline gf gf_sq(gf in)
{
	const uint32_t B[] = {0x55555555, 0x33333333, 0x0F0F0F0F, 0x00FF00FF};

	uint32_t x = in; 
	uint32_t t;

	x = (x | (x << 8)) & B[3];
	x = (x | (x << 4)) & B[2];
	x = (x | (x << 2)) & B[1];
	x = (x | (x << 1)) & B[0];

	t = x & 0x7FC000;
	x ^= t >> 9;
	x ^= t >> 12;

	t = x & 0x3000;
	x ^= t >> 9;
	x ^= t >> 12;

	return x & ((1 << GFBITS)-1);
}

gf gf_inv(gf in)
{
	gf tmp_11;
	gf tmp_1111;

	gf out = in;

	out = gf_sq(out);
	tmp_11 = gf_mul(out, in); // 11

	out = gf_sq(tmp_11);
	out = gf_sq(out);
	tmp_1111 = gf_mul(out, tmp_11); // 1111

	out = gf_sq(tmp_1111);
	out = gf_sq(out);
	out = gf_sq(out);
	out = gf_sq(out);
	out = gf_mul(out, tmp_1111); // 11111111

	out = gf_sq(out);
	out = gf_sq(out);
	out = gf_mul(out, tmp_11); // 1111111111

	out = gf_sq(out);
	out = gf_mul(out, in); // 11111111111

	return gf_sq(out); // 111111111110
}

/* input: field element den, num */
/* return: (num/den) */
gf gf_frac(gf den, gf num)
{
	return gf_mul(gf_inv(den), num);
}

/* input: in0, in1 in GF((2^m)^t)*/
/* output: out = in0*in1 */
void GF_mul(gf *out, const gf *in0, const gf *in1)
{
	int i, j;

	gf prod[ SYS_T*2-1 ];

	for (i = 0; i < SYS_T*2-1; i++)
		prod[i] = 0;

	for (i = 0; i < SYS_T; i++)
		for (j = 0; j < SYS_T; j++)
			prod[i+j] ^= gf_mul(in0[i], in1[j]);

	//
 
	for (i = (SYS_T-1)*2; i >= SYS_T; i--)
	{
		prod[i - SYS_T +  9] ^= gf_mul(prod[i], (gf)  877);
		prod[i - SYS_T +  7] ^= gf_mul(prod[i], (gf) 2888);
		prod[i - SYS_T +  5] ^= gf_mul(prod[i], (gf) 1781);
		prod[i - SYS_T +  0] ^= gf_mul(prod[i], (gf)  373);
	}

	for (i = 0; i < SYS_T; i++)
		out[i] = prod[i];
}

