char filter(){
fp_t abs = fp_add(fp_add(fp_mul(acc[0], acc[0]),
fp_mul(acc[1], acc[1])),
fp_mul(acc[2], acc[2]));
////////////////////////////////////////////////////////////////////////////////
//idle state filter
if (!(fp_cmp(abs, 10486)==1 /*0.32*/ ||
fp_cmp(abs, 8847)==2 /*0.27*/)) { // if between 0.01 - 0.09
return false;
}
////////////////////////////////////////////////////////////////////////////////
// def = directional equivalence filter
const fp_t def_sensitivity = 2621; //0.08
if (fp_cmp(acc[0], fp_sub(dir_filter_ref[0], def_sensitivity))==2 ||
fp_cmp(acc[0], fp_add(dir_filter_ref[0], def_sensitivity))== 1 ||
fp_cmp(acc[1], fp_sub(dir_filter_ref[1], def_sensitivity))==2 ||
fp_cmp(acc[1], fp_add(dir_filter_ref[1], def_sensitivity))== 1 ||
fp_cmp(acc[2], fp_sub(dir_filter_ref[2], def_sensitivity))==2 ||
fp_cmp(acc[2], fp_add(dir_filter_ref[2], def_sensitivity))==1) {
dir_filter_ref[0] = acc[0];
dir_filter_ref[1] = acc[1];
dir_filter_ref[2] = acc[2];
return true;
}
return false;
}
char filter(){
fp_t abs = fp_add(fp_add(fp_mul(acc[0], acc[0]),
fp_mul(acc[1], acc[1])),
fp_mul(acc[2], acc[2]));
////////////////////////////////////////////////////////////////////////////////
//idle state filter
if (!(fp_cmp(abs, d2fp(0.32))==1 ||
fp_cmp(abs, d2fp(0.27))==-1)) { // if between 0.01 - 0.09
return false;
}
////////////////////////////////////////////////////////////////////////////////
// def = directional equivalence filter
fp_t def_sensitivity = d2fp(0.08);
if (fp_cmp(acc[0], fp_sub(dir_filter_ref[0], def_sensitivity))==-1 ||
fp_cmp(acc[0], fp_add(dir_filter_ref[0], def_sensitivity))== 1 ||
fp_cmp(acc[1], fp_sub(dir_filter_ref[1], def_sensitivity))==-1 ||
fp_cmp(acc[1], fp_add(dir_filter_ref[1], def_sensitivity))== 1 ||
fp_cmp(acc[2], fp_sub(dir_filter_ref[2], def_sensitivity))==-1 ||
fp_cmp(acc[2], fp_add(dir_filter_ref[2], def_sensitivity))==1) {
dir_filter_ref[0] = acc[0];
dir_filter_ref[1] = acc[1];
dir_filter_ref[2] = acc[2];
return true;
}
return false;
}
int fp2_srt(fp2_t c, fp2_t a) {
int r = 0;
fp_t t1;
fp_t t2;
fp_t t3;
fp_null(t1);
fp_null(t2);
fp_null(t3);
TRY {
fp_new(t1);
fp_new(t2);
fp_new(t3);
/* t1 = a[0]^2 - u^2 * a[1]^2 */
fp_sqr(t1, a[0]);
fp_sqr(t2, a[1]);
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_add(t1, t1, t2);
}
for (int i = 0; i <= fp_prime_get_qnr(); i++) {
fp_sub(t1, t1, t2);
}
fp_add(t1, t1, t2);
if (fp_srt(t2, t1)) {
/* t1 = (a_0 + sqrt(t1)) / 2 */
fp_add(t1, a[0], t2);
fp_set_dig(t3, 2);
fp_inv(t3, t3);
fp_mul(t1, t1, t3);
if (!fp_srt(t3, t1)) {
/* t1 = (a_0 - sqrt(t1)) / 2 */
fp_sub(t1, a[0], t2);
fp_set_dig(t3, 2);
fp_inv(t3, t3);
fp_mul(t1, t1, t3);
fp_srt(t3, t1);
}
/* c_0 = sqrt(t1) */
fp_copy(c[0], t3);
/* c_1 = a_1 / (2 * sqrt(t1)) */
fp_dbl(t3, t3);
fp_inv(t3, t3);
fp_mul(c[1], a[1], t3);
r = 1;
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t1);
fp_free(t2);
fp_free(t3);
}
return r;
}
void fp2_sqr_basic(fp2_t c, fp2_t a) {
fp_t t0, t1, t2;
fp_null(t0);
fp_null(t1);
fp_null(t2);
TRY {
fp_new(t0);
fp_new(t1);
fp_new(t2);
/* t0 = (a_0 + a_1). */
fp_add(t0, a[0], a[1]);
/* t1 = (a_0 - a_1). */
fp_sub(t1, a[0], a[1]);
/* t1 = a_0 + u^2 * a_1. */
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_sub(t1, t1, a[1]);
}
for (int i = 0; i <= fp_prime_get_qnr(); i++) {
fp_add(t1, t1, a[1]);
}
if (fp_prime_get_qnr() == -1) {
/* t2 = 2 * a_0. */
fp_dbl(t2, a[0]);
/* c_1 = 2 * a_0 * a_1. */
fp_mul(c[1], t2, a[1]);
/* c_0 = a_0^2 + a_1^2 * u^2. */
fp_mul(c[0], t0, t1);
} else {
/* c_1 = a_0 * a_1. */
fp_mul(c[1], a[0], a[1]);
/* c_0 = a_0^2 + a_1^2 * u^2. */
fp_mul(c[0], t0, t1);
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_add(c[0], c[0], c[1]);
}
for (int i = 0; i <= fp_prime_get_qnr(); i++) {
fp_sub(c[0], c[0], c[1]);
}
/* c_1 = 2 * a_0 * a_1. */
fp_dbl(c[1], c[1]);
}
/* c = c_0 + c_1 * u. */
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
fp_free(t2);
}
}
void SynthController::updateCutoff()
{
fixed envValue = envelope_.GetValue();
fixed envContrib = fp_sub(FP_ONE, envValue);
envContrib = fp_mul(envContrib, cutoffEnvMod_);
envContrib = fp_sub(FP_ONE, envContrib);
fixed current = fp_mul(cutoff_, envContrib);
hwParameters_.cutoff_ = int(fp2fl(current)*255);
}
/* sub */
static int sub(void *a, void *b, void *c) {
LTC_ARGCHK(a != NULL);
LTC_ARGCHK(b != NULL);
LTC_ARGCHK(c != NULL);
fp_sub(a, b, c);
return CRYPT_OK;
}
void fp2_mul_art(fp2_t c, fp2_t a) {
fp_t t;
fp_null(t);
TRY {
fp_new(t);
#ifdef FP_QNRES
/* (a_0 + a_1 * i) * i = -a_1 + a_0 * i. */
fp_copy(t, a[0]);
fp_neg(c[0], a[1]);
fp_copy(c[1], t);
#else
/* (a_0 + a_1 * u) * u = (a_1 * u^2) + a_0 * u. */
fp_copy(t, a[0]);
fp_neg(c[0], a[1]);
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_sub(c[0], c[0], a[1]);
}
fp_copy(c[1], t);
#endif
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t);
}
}
void fp2_norm_low(fp2_t c, fp2_t a) {
fp2_t t;
bn_t b;
fp2_null(t);
bn_null(b);
TRY {
fp2_new(t);
bn_new(b);
#if FP_PRIME == 158
fp_dbl(t[0], a[0]);
fp_dbl(t[0], t[0]);
fp_sub(t[0], t[0], a[1]);
fp_dbl(t[1], a[1]);
fp_dbl(t[1], t[1]);
fp_add(c[1], a[0], t[1]);
fp_copy(c[0], t[0]);
#elif defined(FP_QNRES)
/* If p = 3 mod 8, (1 + i) is a QNR/CNR. */
fp_neg(t[0], a[1]);
fp_add(c[1], a[0], a[1]);
fp_add(c[0], t[0], a[0]);
#else
switch (fp_prime_get_mod8()) {
case 3:
/* If p = 3 mod 8, (1 + u) is a QNR/CNR. */
fp_neg(t[0], a[1]);
fp_add(c[1], a[0], a[1]);
fp_add(c[0], t[0], a[0]);
break;
case 5:
/* If p = 5 mod 8, (u) is a QNR/CNR. */
fp2_mul_art(c, a);
break;
case 7:
/* If p = 7 mod 8, we choose (2^(lg_4(b-1)) + u) as QNR/CNR. */
fp2_mul_art(t, a);
fp2_dbl(c, a);
fp_prime_back(b, ep_curve_get_b());
for (int i = 1; i < bn_bits(b) / 2; i++) {
fp2_dbl(c, c);
}
fp2_add(c, c, t);
break;
default:
THROW(ERR_NO_VALID);
break;
}
#endif
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp2_free(t);
bn_free(b);
}
}
/* d = a - b (mod c) */
int fp_submod(fp_int *a, fp_int *b, fp_int *c, fp_int *d)
{
fp_int tmp;
fp_zero(&tmp);
fp_sub(a, b, &tmp);
return fp_mod(&tmp, c, d);
}
static int
tfm_rsa_private_calculate(fp_int * in, fp_int * p, fp_int * q,
fp_int * dmp1, fp_int * dmq1, fp_int * iqmp,
fp_int * out)
{
fp_int vp, vq, u;
fp_init_multi(&vp, &vq, &u, NULL);
/* vq = c ^ (d mod (q - 1)) mod q */
/* vp = c ^ (d mod (p - 1)) mod p */
fp_mod(in, p, &u);
fp_exptmod(&u, dmp1, p, &vp);
fp_mod(in, q, &u);
fp_exptmod(&u, dmq1, q, &vq);
/* C2 = 1/q mod p (iqmp) */
/* u = (vp - vq)C2 mod p. */
fp_sub(&vp, &vq, &u);
if (fp_isneg(&u))
fp_add(&u, p, &u);
fp_mul(&u, iqmp, &u);
fp_mod(&u, p, &u);
/* c ^ d mod n = vq + u q */
fp_mul(&u, q, &u);
fp_add(&u, &vq, out);
fp_zero_multi(&vp, &vq, &u, NULL);
return 0;
}
void fp2_inv(fp2_t c, fp2_t a) {
fp_t t0, t1;
fp_null(t0);
fp_null(t1);
TRY {
fp_new(t0);
fp_new(t1);
/* t0 = a_0^2, t1 = a_1^2. */
fp_sqr(t0, a[0]);
fp_sqr(t1, a[1]);
/* t1 = 1/(a_0^2 + a_1^2). */
#ifndef FP_QNRES
if (fp_prime_get_qnr() != -1) {
if (fp_prime_get_qnr() == -2) {
fp_dbl(t1, t1);
fp_add(t0, t0, t1);
} else {
if (fp_prime_get_qnr() < 0) {
fp_mul_dig(t1, t1, -fp_prime_get_qnr());
fp_add(t0, t0, t1);
} else {
fp_mul_dig(t1, t1, fp_prime_get_qnr());
fp_sub(t0, t0, t1);
}
}
} else {
fp_add(t0, t0, t1);
}
#else
fp_add(t0, t0, t1);
#endif
fp_inv(t1, t0);
/* c_0 = a_0/(a_0^2 + a_1^2). */
fp_mul(c[0], a[0], t1);
/* c_1 = - a_1/(a_0^2 + a_1^2). */
fp_mul(c[1], a[1], t1);
fp_neg(c[1], c[1]);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
}
}
unsigned char derive_group2(){
fp_t a, b, c, d;
fp_t minDist = 0x7fff; //0x7fff;
char minGroup=0;
fp_t *ref;
char i;
for (i = 0; i < 14; i++){
ref = quantizerMap2[i];
a = fp_sub(ref[0], acc[0]);
b = fp_sub(ref[1], acc[1]);
c = fp_sub(ref[2], acc[2]);
d = fp_add(fp_add(fp_mul(a,a), fp_mul(b,b)), fp_mul(c,c));
if (fp_cmp(d, minDist) == 2){
minDist = d;
minGroup = i;
}
}
/* UARTSendArray("group=", 6); */
/* UARTSendInt(minGroup); */
return minGroup;
}
void set_filter(int channel, filterType_t type, fixed param1,fixed param2,int mix,bool bassyMapping)
{
filter_t* flt=&filter[channel];
if(flt->type!=type) //reset only on filter type change (maybe no reset would make interresting bugs)
{
flt->height[0]=0; //idle state
flt->height[1]=0; //idle state
flt->speed[0]=0; //paused (to avoid having it goind crazy)
flt->speed[1]=0; //paused (to avoid having it goind crazy)
flt->hipdelay[0]=0 ;
flt->hipdelay[1]=0 ;
flt->type=type;
}
flt->dirt=fp_mul(i2fp(100),i2fp(1)-param1)+fp_mul(i2fp(5000),param1) ;
flt->mix =fp_mul(i2fp(mix),fp_inv_255) ;
if (param1 != flt->parm1)
{
flt->parm1=param1;
//adjust parm to get the most of the parameters, as the fx are more useful with near-limit parameters.
if (bassyMapping)
{
static const fixed fpFreqDivider = fl2fp(1/22050.0f);
static const fixed fpZeroSix = fl2fp(0.6f);
static const fixed fpThreeOne = fl2fp(3.1f);
fixed power = fp_add(fpZeroSix,fp_mul(param1,fpThreeOne));
fixed frequency = fl2fp(pow(10.0f,fp2fl(power))) ;
frequency=fp_mul(frequency,fpFreqDivider);
flt->freq=frequency;
}
else
{
flt->freq=fp_mul(param1,param1); //0 - .5 - 1 => 0 - .25 - 1
}
}
if (param2 != flt->parm2)
{
flt->parm2=param2;
flt->reso=i2fp(1)-param2 ;
flt->reso=fp_sub(fl2fp(1.f),fp_mul(flt->reso,fp_mul(flt->reso,flt->reso))); //0 - .5 - 1 => 0 - .93 - 1
}
}
int
main()
{
if (fp_add (1, 1) != 2) fail ("fp_add 1+1");
if (fp_sub (3, 2) != 1) fail ("fp_sub 3-2");
if (fp_mul (2, 3) != 6) fail ("fp_mul 2*3");
if (fp_div (3, 2) != 1.5) fail ("fp_div 3/2");
if (fp_neg (1) != -1) fail ("fp_neg 1");
if (dp_add (1, 1) != 2) fail ("dp_add 1+1");
if (dp_sub (3, 2) != 1) fail ("dp_sub 3-2");
if (dp_mul (2, 3) != 6) fail ("dp_mul 2*3");
if (dp_div (3, 2) != 1.5) fail ("dp_div 3/2");
if (dp_neg (1) != -1) fail ("dp_neg 1");
if (fp_to_dp (1.5) != 1.5) fail ("fp_to_dp 1.5");
if (dp_to_fp (1.5) != 1.5) fail ("dp_to_fp 1.5");
if (floatsisf (1) != 1) fail ("floatsisf 1");
if (floatsidf (1) != 1) fail ("floatsidf 1");
if (fixsfsi (1.42) != 1) fail ("fixsfsi 1.42");
if (fixunssfsi (1.42) != 1) fail ("fixunssfsi 1.42");
if (fixdfsi (1.42) != 1) fail ("fixdfsi 1.42");
if (fixunsdfsi (1.42) != 1) fail ("fixunsdfsi 1.42");
if (eqsf2 (1, 1) == 0) fail ("eqsf2 1==1");
if (eqsf2 (1, 2) != 0) fail ("eqsf2 1==2");
if (nesf2 (1, 2) == 0) fail ("nesf2 1!=1");
if (nesf2 (1, 1) != 0) fail ("nesf2 1!=1");
if (gtsf2 (2, 1) == 0) fail ("gtsf2 2>1");
if (gtsf2 (1, 1) != 0) fail ("gtsf2 1>1");
if (gtsf2 (0, 1) != 0) fail ("gtsf2 0>1");
if (gesf2 (2, 1) == 0) fail ("gesf2 2>=1");
if (gesf2 (1, 1) == 0) fail ("gesf2 1>=1");
if (gesf2 (0, 1) != 0) fail ("gesf2 0>=1");
if (ltsf2 (1, 2) == 0) fail ("ltsf2 1<2");
if (ltsf2 (1, 1) != 0) fail ("ltsf2 1<1");
if (ltsf2 (1, 0) != 0) fail ("ltsf2 1<0");
if (lesf2 (1, 2) == 0) fail ("lesf2 1<=2");
if (lesf2 (1, 1) == 0) fail ("lesf2 1<=1");
if (lesf2 (1, 0) != 0) fail ("lesf2 1<=0");
if (fail_count != 0)
abort ();
exit (0);
}
int ed_affine_is_valid(const fp_t x, const fp_t y) {
fp_t tmpFP0;
fp_t tmpFP1;
fp_t tmpFP2;
fp_null(tmpFP0);
fp_null(tmpFP1);
fp_null(tmpFP2);
int r = 0;
TRY {
fp_new(tmpFP0);
fp_new(tmpFP1);
fp_new(tmpFP2);
// a * X^2 + Y^2 - 1 - d * X^2 * Y^2 =?= 0
fp_sqr(tmpFP0, x);
fp_mul(tmpFP0, core_get()->ed_a, tmpFP0);
fp_sqr(tmpFP1, y);
fp_add(tmpFP1, tmpFP0, tmpFP1);
fp_sub_dig(tmpFP1, tmpFP1, 1);
fp_sqr(tmpFP0, x);
fp_mul(tmpFP0, core_get()->ed_d, tmpFP0);
fp_sqr(tmpFP2, y);
fp_mul(tmpFP2, tmpFP0, tmpFP2);
fp_sub(tmpFP0, tmpFP1, tmpFP2);
r = fp_is_zero(tmpFP0);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp_free(tmpFP0);
fp_free(tmpFP1);
fp_free(tmpFP2);
}
return r;
}
void pp_dbl_k2_basic(fp2_t l, ep_t r, ep_t p, ep_t q) {
fp_t s;
ep_t t;
fp_null(s);
ep_null(t);
TRY {
fp_new(s);
ep_new(t);
ep_copy(t, p);
ep_dbl_slp_basic(r, s, p);
fp_add(l[0], t->x, q->x);
fp_mul(l[0], l[0], s);
fp_sub(l[0], t->y, l[0]);
fp_copy(l[1], q->y);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp_free(s);
ep_free(t);
}
}
/* a/b => cb + d == a */
int fp_div(fp_int *a, fp_int *b, fp_int *c, fp_int *d)
{
fp_int q, x, y, t1, t2;
int n, t, i, norm, neg;
/* is divisor zero ? */
if (fp_iszero (b) == 1) {
return FP_VAL;
}
/* if a < b then q=0, r = a */
if (fp_cmp_mag (a, b) == FP_LT) {
if (d != NULL) {
fp_copy (a, d);
}
if (c != NULL) {
fp_zero (c);
}
return FP_OKAY;
}
fp_init(&q);
q.used = a->used + 2;
fp_init(&t1);
fp_init(&t2);
fp_init_copy(&x, a);
fp_init_copy(&y, b);
/* fix the sign */
neg = (a->sign == b->sign) ? FP_ZPOS : FP_NEG;
x.sign = y.sign = FP_ZPOS;
/* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
norm = fp_count_bits(&y) % DIGIT_BIT;
if (norm < (int)(DIGIT_BIT-1)) {
norm = (DIGIT_BIT-1) - norm;
fp_mul_2d (&x, norm, &x);
fp_mul_2d (&y, norm, &y);
} else {
norm = 0;
}
/* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
n = x.used - 1;
t = y.used - 1;
/* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
fp_lshd (&y, n - t); /* y = y*b**{n-t} */
while (fp_cmp (&x, &y) != FP_LT) {
++(q.dp[n - t]);
fp_sub (&x, &y, &x);
}
/* reset y by shifting it back down */
fp_rshd (&y, n - t);
/* step 3. for i from n down to (t + 1) */
for (i = n; i >= (t + 1); i--) {
if (i > x.used) {
continue;
}
/* step 3.1 if xi == yt then set q{i-t-1} to b-1,
* otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
if (x.dp[i] == y.dp[t]) {
q.dp[i - t - 1] = ((((fp_word)1) << DIGIT_BIT) - 1);
} else {
fp_word tmp;
tmp = ((fp_word) x.dp[i]) << ((fp_word) DIGIT_BIT);
tmp |= ((fp_word) x.dp[i - 1]);
tmp /= ((fp_word) y.dp[t]);
q.dp[i - t - 1] = (fp_digit) (tmp);
}
/* while (q{i-t-1} * (yt * b + y{t-1})) >
xi * b**2 + xi-1 * b + xi-2
do q{i-t-1} -= 1;
*/
q.dp[i - t - 1] = (q.dp[i - t - 1] + 1);
do {
q.dp[i - t - 1] = (q.dp[i - t - 1] - 1);
/* find left hand */
fp_zero (&t1);
t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
t1.dp[1] = y.dp[t];
t1.used = 2;
fp_mul_d (&t1, q.dp[i - t - 1], &t1);
/* find right hand */
t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
t2.dp[2] = x.dp[i];
t2.used = 3;
} while (fp_cmp_mag(&t1, &t2) == FP_GT);
/* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
fp_mul_d (&y, q.dp[i - t - 1], &t1);
fp_lshd (&t1, i - t - 1);
fp_sub (&x, &t1, &x);
/* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
if (x.sign == FP_NEG) {
fp_copy (&y, &t1);
fp_lshd (&t1, i - t - 1);
fp_add (&x, &t1, &x);
q.dp[i - t - 1] = q.dp[i - t - 1] - 1;
}
}
/* now q is the quotient and x is the remainder
* [which we have to normalize]
*/
/* get sign before writing to c */
x.sign = x.used == 0 ? FP_ZPOS : a->sign;
if (c != NULL) {
fp_clamp (&q);
fp_copy (&q, c);
c->sign = neg;
}
if (d != NULL) {
fp_div_2d (&x, norm, &x, NULL);
/* the following is a kludge, essentially we were seeing the right remainder but
with excess digits that should have been zero
*/
for (i = b->used; i < x.used; i++) {
x.dp[i] = 0;
}
fp_clamp(&x);
fp_copy (&x, d);
}
return FP_OKAY;
}
void SynthController::SetParameterValue(const SynthController::Parameter& parameter, const fixed& value)
{
bool envSetup = false;
switch(parameter)
{
case WAVE_SELECT:
oscillator_.SetShape(value);
break;
case WAVE_LOOP_START:
oscillator_.SetLoopStart(value);
break;
case WAVE_LOOP_END:
oscillator_.SetLoopWidth(value);
break;
case WAVE_OCTAVE:
{
int32_t octave = 0;
if (value < fl2fp(0.33f))
{
octave = -1;
}
if (value > fl2fp(0.66f))
{
octave = 1;
}
oscillator_.SetOctave(octave);
break;
}
case ANALOG_OSC_ON:
enableAnalog_ = value > fl2fp(0.5f);
break;
case ANALOG_PITCH_FINE_TUNE:
analogPitchFineTune_ = fp2fl(value)*256 - 128 ;
break;
case PITCH_GLIDE:
{
const fixed GLIDE_MULTIPLIER = fl2fp(0.4f);
fixed glideFactor = (value != 0 )
? fp_sub(GLIDE_MULTIPLIER, fp_mul(value, GLIDE_MULTIPLIER))
: SET_GLIDE_OFF;
anaPitchControl_.SetGlide(glideFactor);
digiPitchControl_.SetGlide(glideFactor);
break;
}
case NOISE_MIX:
noiseMix_ = value;
updateLevels();
break;
case KEYBOARD_MODE:
{
NoteControl::Mode mode = (NoteControl::Mode)int(fp2fl(value)*NoteControl::LAST*0.999f);
noteControl_.SetMode(mode);
break;
}
case ENV_ATTACK:
attack_ = MAX_ENVELOPE_TICK*fp2fl(value);
envSetup = true;
break;
case ENV_DECAY:
{
fixed scaledDecay = fp_add(value, ENVELOPE_SCALE);
decay_ = MAX_ENVELOPE_TICK*fp2fl(scaledDecay);
envSetup = true;
}
break;
case ENV_SUSTAIN:
{
fixed scaledSustain = fp_add(value, ENVELOPE_SCALE);
if (scaledSustain > FP_ONE)
{
scaledSustain = FP_ONE;
}
sustain_ = scaledSustain;
envSetup = true;
}
break;
case ENV_RELEASE:
release_ = MAX_ENVELOPE_TICK*fp2fl(value);
envSetup = true;
break;
case VCA_ENV_GATER:
envelope_.SetScaler(value);
break;
case VCF_ENV_MOD:
cutoffEnvMod_ = value;
break;
case AMP_GAIN:
gain_ = value;
updateLevels();
break;
}
if (envSetup)
{
envelope_.Setup(attack_, decay_, sustain_, release_);
}
}
void SynthController::updateLevels()
{
noiseGenerator_.SetLevel(fp_mul(gain_,noiseMix_));
oscillator_.SetGain(fp_mul(gain_,fp_sub(FP_ONE,noiseMix_)));
}
void pp_dbl_k12_projc_lazyr(fp12_t l, ep2_t r, ep2_t q, ep_t p) {
fp2_t t0, t1, t2, t3, t4, t5, t6;
dv2_t u0, u1;
int one = 1, zero = 0;
fp2_null(t0);
fp2_null(t1);
fp2_null(t2);
fp2_null(t3);
fp2_null(t4);
fp2_null(t5);
fp2_null(t6);
dv2_null(u0);
dv2_null(u1);
TRY {
fp2_new(t0);
fp2_new(t1);
fp2_new(t2);
fp2_new(t3);
fp2_new(t4);
fp2_new(t5);
fp2_new(t6);
dv2_new(u0);
dv2_new(u1);
if (ep2_curve_is_twist() == EP_MTYPE) {
one ^= 1;
zero ^= 1;
}
if (ep_curve_opt_b() == RLC_TWO) {
/* C = z1^2. */
fp2_sqr(t0, q->z);
/* B = y1^2. */
fp2_sqr(t1, q->y);
/* t5 = B + C. */
fp2_add(t5, t0, t1);
/* t3 = E = 3b'C = 3C * (1 - i). */
fp2_dbl(t3, t0);
fp2_add(t0, t0, t3);
fp_add(t2[0], t0[0], t0[1]);
fp_sub(t2[1], t0[1], t0[0]);
/* t0 = x1^2. */
fp2_sqr(t0, q->x);
/* t4 = A = (x1 * y1)/2. */
fp2_mul(t4, q->x, q->y);
fp_hlv(t4[0], t4[0]);
fp_hlv(t4[1], t4[1]);
/* t3 = F = 3E. */
fp2_dbl(t3, t2);
fp2_add(t3, t3, t2);
/* x3 = A * (B - F). */
fp2_sub(r->x, t1, t3);
fp2_mul(r->x, r->x, t4);
/* G = (B + F)/2. */
fp2_add(t3, t1, t3);
fp_hlv(t3[0], t3[0]);
fp_hlv(t3[1], t3[1]);
/* y3 = G^2 - 3E^2. */
fp2_sqrn_low(u0, t2);
fp2_addd_low(u1, u0, u0);
fp2_addd_low(u1, u1, u0);
fp2_sqrn_low(u0, t3);
fp2_subc_low(u0, u0, u1);
/* H = (Y + Z)^2 - B - C. */
fp2_add(t3, q->y, q->z);
fp2_sqr(t3, t3);
fp2_sub(t3, t3, t5);
fp2_rdcn_low(r->y, u0);
/* z3 = B * H. */
fp2_mul(r->z, t1, t3);
/* l11 = E - B. */
fp2_sub(l[1][1], t2, t1);
/* l10 = (3 * xp) * t0. */
fp_mul(l[one][zero][0], p->x, t0[0]);
fp_mul(l[one][zero][1], p->x, t0[1]);
/* l01 = F * (-yp). */
fp_mul(l[zero][zero][0], t3[0], p->y);
fp_mul(l[zero][zero][1], t3[1], p->y);
} else {
/* A = x1^2. */
fp2_sqr(t0, q->x);
/* B = y1^2. */
fp2_sqr(t1, q->y);
/* C = z1^2. */
fp2_sqr(t2, q->z);
/* D = 3bC, for general b. */
fp2_dbl(t3, t2);
fp2_add(t3, t3, t2);
ep2_curve_get_b(t4);
fp2_mul(t3, t3, t4);
/* E = (x1 + y1)^2 - A - B. */
fp2_add(t4, q->x, q->y);
fp2_sqr(t4, t4);
fp2_sub(t4, t4, t0);
fp2_sub(t4, t4, t1);
/* F = (y1 + z1)^2 - B - C. */
fp2_add(t5, q->y, q->z);
fp2_sqr(t5, t5);
fp2_sub(t5, t5, t1);
fp2_sub(t5, t5, t2);
/* G = 3D. */
fp2_dbl(t6, t3);
fp2_add(t6, t6, t3);
/* x3 = E * (B - G). */
fp2_sub(r->x, t1, t6);
fp2_mul(r->x, r->x, t4);
/* y3 = (B + G)^2 -12D^2. */
fp2_add(t6, t6, t1);
fp2_sqr(t6, t6);
fp2_sqr(t2, t3);
fp2_dbl(r->y, t2);
fp2_dbl(t2, r->y);
fp2_dbl(r->y, t2);
fp2_add(r->y, r->y, t2);
fp2_sub(r->y, t6, r->y);
/* z3 = 4B * F. */
fp2_dbl(r->z, t1);
fp2_dbl(r->z, r->z);
fp2_mul(r->z, r->z, t5);
/* l00 = D - B. */
fp2_sub(l[one][one], t3, t1);
/* l10 = (3 * xp) * A. */
fp_mul(l[one][zero][0], p->x, t0[0]);
fp_mul(l[one][zero][1], p->x, t0[1]);
/* l01 = F * (-yp). */
fp_mul(l[zero][zero][0], t5[0], p->y);
fp_mul(l[zero][zero][1], t5[1], p->y);
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp2_free(t0);
fp2_free(t1);
fp2_free(t2);
fp2_free(t3);
fp2_free(t4);
fp2_free(t5);
fp2_free(t6);
dv2_free(u0);
dv2_free(u1);
}
}
void fp2_subm_low(fp2_t c, fp2_t a, fp2_t b) {
fp_sub(c[0], a[0], b[0]);
fp_sub(c[1], a[1], b[1]);
}
void fp3_sqr_basic(fp3_t c, fp3_t a) {
dv_t t0, t1, t2, t3, t4, t5;
dv_null(t0);
dv_null(t1);
dv_null(t2);
dv_null(t3);
dv_null(t4);
dv_null(t5);
TRY {
dv_new(t0);
dv_new(t1);
dv_new(t2);
dv_new(t3);
dv_new(t4);
dv_new(t5);
/* t0 = a_0^2. */
fp_sqrn_low(t0, a[0]);
/* t1 = 2 * a_1 * a_2. */
fp_dbl(t2, a[1]);
fp_muln_low(t1, t2, a[2]);
/* t2 = a_2^2. */
fp_sqrn_low(t2, a[2]);
/* t3 = (a_0 + a_2 + a_1)^2, t4 = (a_0 + a_2 - a_1)^2. */
fp_add(t3, a[0], a[2]);
fp_add(t4, t3, a[1]);
fp_sub(t5, t3, a[1]);
fp_sqrn_low(t3, t4);
fp_sqrn_low(t4, t5);
/* t4 = (t4 + t3)/2. */
fp_addd_low(t4, t4, t3);
fp_hlvd_low(t4, t4);
/* t3 = t3 - t4 - t1. */
fp_addc_low(t5, t1, t4);
fp_subc_low(t3, t3, t5);
/* c_2 = t4 - t0 - t2. */
fp_addc_low(t5, t0, t2);
fp_subc_low(t4, t4, t5);
fp_rdc(c[2], t4);
/* c_0 = t0 + t1 * B. */
fp_subc_low(t0, t0, t1);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_subc_low(t0, t0, t1);
}
fp_rdc(c[0], t0);
/* c_1 = t3 + t2 * B. */
fp_subc_low(t3, t3, t2);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_subc_low(t3, t3, t2);
}
fp_rdc(c[1], t3);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
dv_free(t0);
dv_free(t1);
dv_free(t2);
dv_free(t3);
dv_free(t4);
dv_free(t5);
}
}
void pp_dbl_k2_projc_lazyr(fp2_t l, ep_t r, ep_t p, ep_t q) {
fp_t t0, t1, t2, t3, t4, t5;
dv_t u0, u1;
fp_null(t0);
fp_null(t1);
fp_null(t2);
fp_null(t3);
fp_null(t4);
fp_null(t5);
dv_null(u0);
dv_null(u1);
TRY {
fp_new(t0);
fp_new(t1);
fp_new(t2);
fp_new(t3);
fp_new(t4);
fp_new(t5);
dv_new(u0);
dv_new(u1);
/* For these curves, we always can choose a = -3. */
/* dbl-2001-b formulas: 3M + 5S + 8add + 1*4 + 2*8 + 1*3 */
/* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b */
/* t0 = delta = z1^2. */
fp_sqr(t0, p->z);
/* t1 = gamma = y1^2. */
fp_sqr(t1, p->y);
/* t2 = beta = x1 * y1^2. */
fp_mul(t2, p->x, t1);
/* t3 = alpha = 3 * (x1 - z1^2) * (x1 + z1^2). */
fp_sub(t3, p->x, t0);
fp_add(t4, p->x, t0);
fp_mul(t4, t3, t4);
fp_dbl(t3, t4);
fp_add(t3, t3, t4);
/* t2 = 4 * beta. */
fp_dbl(t2, t2);
fp_dbl(t2, t2);
/* z3 = (y1 + z1)^2 - gamma - delta. */
fp_add(r->z, p->y, p->z);
fp_sqr(r->z, r->z);
fp_sub(r->z, r->z, t1);
fp_sub(r->z, r->z, t0);
/* l0 = 2 * gamma - alpha * (delta * xq + x1). */
fp_dbl(t1, t1);
fp_mul(t5, t0, q->x);
fp_add(t5, t5, p->x);
fp_mul(t5, t5, t3);
fp_sub(l[0], t1, t5);
/* x3 = alpha^2 - 8 * beta. */
fp_dbl(t5, t2);
fp_sqr(r->x, t3);
fp_sub(r->x, r->x, t5);
/* y3 = alpha * (4 * beta - x3) - 8 * gamma^2. */
fp_sqrn_low(u0, t1);
fp_addc_low(u0, u0, u0);
fp_subm_low(r->y, t2, r->x);
fp_muln_low(u1, r->y, t3);
fp_subc_low(u1, u1, u0);
fp_rdcn_low(r->y, u1);
/* l1 = - z3 * delta * yq. */
fp_mul(l[1], r->z, t0);
fp_mul(l[1], l[1], q->y);
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
fp_free(t2);
fp_free(t3);
fp_free(t4);
fp_free(t5);
dv_free(u0);
dv_free(u1);
}
}
static int tfm_ecc_projective_dbl_point(ecc_point *P, ecc_point *R, void *modulus, void *Mp)
{
fp_int t1, t2;
fp_digit mp;
LTC_ARGCHK(P != NULL);
LTC_ARGCHK(R != NULL);
LTC_ARGCHK(modulus != NULL);
LTC_ARGCHK(Mp != NULL);
mp = *((fp_digit*)Mp);
fp_init(&t1);
fp_init(&t2);
if (P != R) {
fp_copy(P->x, R->x);
fp_copy(P->y, R->y);
fp_copy(P->z, R->z);
}
/* t1 = Z * Z */
fp_sqr(R->z, &t1);
fp_montgomery_reduce(&t1, modulus, mp);
/* Z = Y * Z */
fp_mul(R->z, R->y, R->z);
fp_montgomery_reduce(R->z, modulus, mp);
/* Z = 2Z */
fp_add(R->z, R->z, R->z);
if (fp_cmp(R->z, modulus) != FP_LT) {
fp_sub(R->z, modulus, R->z);
}
/* &t2 = X - T1 */
fp_sub(R->x, &t1, &t2);
if (fp_cmp_d(&t2, 0) == FP_LT) {
fp_add(&t2, modulus, &t2);
}
/* T1 = X + T1 */
fp_add(&t1, R->x, &t1);
if (fp_cmp(&t1, modulus) != FP_LT) {
fp_sub(&t1, modulus, &t1);
}
/* T2 = T1 * T2 */
fp_mul(&t1, &t2, &t2);
fp_montgomery_reduce(&t2, modulus, mp);
/* T1 = 2T2 */
fp_add(&t2, &t2, &t1);
if (fp_cmp(&t1, modulus) != FP_LT) {
fp_sub(&t1, modulus, &t1);
}
/* T1 = T1 + T2 */
fp_add(&t1, &t2, &t1);
if (fp_cmp(&t1, modulus) != FP_LT) {
fp_sub(&t1, modulus, &t1);
}
/* Y = 2Y */
fp_add(R->y, R->y, R->y);
if (fp_cmp(R->y, modulus) != FP_LT) {
fp_sub(R->y, modulus, R->y);
}
/* Y = Y * Y */
fp_sqr(R->y, R->y);
fp_montgomery_reduce(R->y, modulus, mp);
/* T2 = Y * Y */
fp_sqr(R->y, &t2);
fp_montgomery_reduce(&t2, modulus, mp);
/* T2 = T2/2 */
if (fp_isodd(&t2)) {
fp_add(&t2, modulus, &t2);
}
fp_div_2(&t2, &t2);
/* Y = Y * X */
fp_mul(R->y, R->x, R->y);
fp_montgomery_reduce(R->y, modulus, mp);
/* X = T1 * T1 */
fp_sqr(&t1, R->x);
fp_montgomery_reduce(R->x, modulus, mp);
/* X = X - Y */
fp_sub(R->x, R->y, R->x);
if (fp_cmp_d(R->x, 0) == FP_LT) {
fp_add(R->x, modulus, R->x);
}
/* X = X - Y */
fp_sub(R->x, R->y, R->x);
if (fp_cmp_d(R->x, 0) == FP_LT) {
fp_add(R->x, modulus, R->x);
}
/* Y = Y - X */
fp_sub(R->y, R->x, R->y);
if (fp_cmp_d(R->y, 0) == FP_LT) {
fp_add(R->y, modulus, R->y);
}
/* Y = Y * T1 */
fp_mul(R->y, &t1, R->y);
fp_montgomery_reduce(R->y, modulus, mp);
/* Y = Y - T2 */
fp_sub(R->y, &t2, R->y);
if (fp_cmp_d(R->y, 0) == FP_LT) {
fp_add(R->y, modulus, R->y);
}
return CRYPT_OK;
}
/**
Add two ECC points
@param P The point to add
@param Q The point to add
@param R [out] The destination of the double
@param modulus The modulus of the field the ECC curve is in
@param mp The "b" value from montgomery_setup()
@return CRYPT_OK on success
*/
static int tfm_ecc_projective_add_point(ecc_point *P, ecc_point *Q, ecc_point *R, void *modulus, void *Mp)
{
fp_int t1, t2, x, y, z;
fp_digit mp;
LTC_ARGCHK(P != NULL);
LTC_ARGCHK(Q != NULL);
LTC_ARGCHK(R != NULL);
LTC_ARGCHK(modulus != NULL);
LTC_ARGCHK(Mp != NULL);
mp = *((fp_digit*)Mp);
fp_init(&t1);
fp_init(&t2);
fp_init(&x);
fp_init(&y);
fp_init(&z);
/* should we dbl instead? */
fp_sub(modulus, Q->y, &t1);
if ( (fp_cmp(P->x, Q->x) == FP_EQ) &&
(Q->z != NULL && fp_cmp(P->z, Q->z) == FP_EQ) &&
(fp_cmp(P->y, Q->y) == FP_EQ || fp_cmp(P->y, &t1) == FP_EQ)) {
return tfm_ecc_projective_dbl_point(P, R, modulus, Mp);
}
fp_copy(P->x, &x);
fp_copy(P->y, &y);
fp_copy(P->z, &z);
/* if Z is one then these are no-operations */
if (Q->z != NULL) {
/* T1 = Z' * Z' */
fp_sqr(Q->z, &t1);
fp_montgomery_reduce(&t1, modulus, mp);
/* X = X * T1 */
fp_mul(&t1, &x, &x);
fp_montgomery_reduce(&x, modulus, mp);
/* T1 = Z' * T1 */
fp_mul(Q->z, &t1, &t1);
fp_montgomery_reduce(&t1, modulus, mp);
/* Y = Y * T1 */
fp_mul(&t1, &y, &y);
fp_montgomery_reduce(&y, modulus, mp);
}
/* T1 = Z*Z */
fp_sqr(&z, &t1);
fp_montgomery_reduce(&t1, modulus, mp);
/* T2 = X' * T1 */
fp_mul(Q->x, &t1, &t2);
fp_montgomery_reduce(&t2, modulus, mp);
/* T1 = Z * T1 */
fp_mul(&z, &t1, &t1);
fp_montgomery_reduce(&t1, modulus, mp);
/* T1 = Y' * T1 */
fp_mul(Q->y, &t1, &t1);
fp_montgomery_reduce(&t1, modulus, mp);
/* Y = Y - T1 */
fp_sub(&y, &t1, &y);
if (fp_cmp_d(&y, 0) == FP_LT) {
fp_add(&y, modulus, &y);
}
/* T1 = 2T1 */
fp_add(&t1, &t1, &t1);
if (fp_cmp(&t1, modulus) != FP_LT) {
fp_sub(&t1, modulus, &t1);
}
/* T1 = Y + T1 */
fp_add(&t1, &y, &t1);
if (fp_cmp(&t1, modulus) != FP_LT) {
fp_sub(&t1, modulus, &t1);
}
/* X = X - T2 */
fp_sub(&x, &t2, &x);
if (fp_cmp_d(&x, 0) == FP_LT) {
fp_add(&x, modulus, &x);
}
/* T2 = 2T2 */
fp_add(&t2, &t2, &t2);
if (fp_cmp(&t2, modulus) != FP_LT) {
fp_sub(&t2, modulus, &t2);
}
/* T2 = X + T2 */
fp_add(&t2, &x, &t2);
if (fp_cmp(&t2, modulus) != FP_LT) {
fp_sub(&t2, modulus, &t2);
}
/* if Z' != 1 */
if (Q->z != NULL) {
/* Z = Z * Z' */
fp_mul(&z, Q->z, &z);
fp_montgomery_reduce(&z, modulus, mp);
}
/* Z = Z * X */
fp_mul(&z, &x, &z);
fp_montgomery_reduce(&z, modulus, mp);
/* T1 = T1 * X */
fp_mul(&t1, &x, &t1);
fp_montgomery_reduce(&t1, modulus, mp);
/* X = X * X */
fp_sqr(&x, &x);
fp_montgomery_reduce(&x, modulus, mp);
/* T2 = T2 * x */
fp_mul(&t2, &x, &t2);
fp_montgomery_reduce(&t2, modulus, mp);
/* T1 = T1 * X */
fp_mul(&t1, &x, &t1);
fp_montgomery_reduce(&t1, modulus, mp);
/* X = Y*Y */
fp_sqr(&y, &x);
fp_montgomery_reduce(&x, modulus, mp);
/* X = X - T2 */
fp_sub(&x, &t2, &x);
if (fp_cmp_d(&x, 0) == FP_LT) {
fp_add(&x, modulus, &x);
}
/* T2 = T2 - X */
fp_sub(&t2, &x, &t2);
if (fp_cmp_d(&t2, 0) == FP_LT) {
fp_add(&t2, modulus, &t2);
}
/* T2 = T2 - X */
fp_sub(&t2, &x, &t2);
if (fp_cmp_d(&t2, 0) == FP_LT) {
fp_add(&t2, modulus, &t2);
}
/* T2 = T2 * Y */
fp_mul(&t2, &y, &t2);
fp_montgomery_reduce(&t2, modulus, mp);
/* Y = T2 - T1 */
fp_sub(&t2, &t1, &y);
if (fp_cmp_d(&y, 0) == FP_LT) {
fp_add(&y, modulus, &y);
}
/* Y = Y/2 */
if (fp_isodd(&y)) {
fp_add(&y, modulus, &y);
}
fp_div_2(&y, &y);
fp_copy(&x, R->x);
fp_copy(&y, R->y);
fp_copy(&z, R->z);
return CRYPT_OK;
}
/**
* Doubles a point represented in projective coordinates on an ordinary prime
* elliptic curve.
*
* @param r - the result.
* @param p - the point to double.
*/
static void ep_dbl_projc_imp(ep_t r, const ep_t p) {
fp_t t0, t1, t2, t3, t4, t5;
fp_null(t1);
fp_null(t2);
fp_null(t3);
fp_null(t4);
fp_null(t5);
TRY {
fp_new(t0);
fp_new(t1);
fp_new(t2);
fp_new(t3);
fp_new(t4);
fp_new(t5);
if (!p->norm && ep_curve_opt_a() == OPT_MINUS3) {
/* dbl-2001-b formulas: 3M + 5S + 8add + 1*4 + 2*8 + 1*3 */
/* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b */
/* t0 = delta = z1^2. */
fp_sqr(t0, p->z);
/* t1 = gamma = y1^2. */
fp_sqr(t1, p->y);
/* t2 = beta = x1 * y1^2. */
fp_mul(t2, p->x, t1);
/* t3 = alpha = 3 * (x1 - z1^2) * (x1 + z1^2). */
fp_sub(t3, p->x, t0);
fp_add(t4, p->x, t0);
fp_mul(t4, t3, t4);
fp_dbl(t3, t4);
fp_add(t3, t3, t4);
/* x3 = alpha^2 - 8 * beta. */
fp_dbl(t2, t2);
fp_dbl(t2, t2);
fp_dbl(t5, t2);
fp_sqr(r->x, t3);
fp_sub(r->x, r->x, t5);
/* z3 = (y1 + z1)^2 - gamma - delta. */
fp_add(r->z, p->y, p->z);
fp_sqr(r->z, r->z);
fp_sub(r->z, r->z, t1);
fp_sub(r->z, r->z, t0);
/* y3 = alpha * (4 * beta - x3) - 8 * gamma^2. */
fp_dbl(t1, t1);
fp_sqr(t1, t1);
fp_dbl(t1, t1);
fp_sub(r->y, t2, r->x);
fp_mul(r->y, r->y, t3);
fp_sub(r->y, r->y, t1);
} else if (ep_curve_opt_a() == OPT_ZERO) {
/* dbl-2009-l formulas: 2M + 5S + 6add + 1*8 + 3*2 + 1*3. */
/* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l */
/* A = X1^2 */
fp_sqr(t0, p->x);
/* B = Y1^2 */
fp_sqr(t1, p->y);
/* C = B^2 */
fp_sqr(t2, t1);
/* D = 2*((X1+B)^2-A-C) */
fp_add(t1, t1, p->x);
fp_sqr(t1, t1);
fp_sub(t1, t1, t0);
fp_sub(t1, t1, t2);
fp_dbl(t1, t1);
/* E = 3*A */
fp_dbl(t3, t0);
fp_add(t0, t3, t0);
/* F = E^2 */
fp_sqr(t3, t0);
/* Z3 = 2*Y1*Z1 */
fp_mul(r->z, p->y, p->z);
fp_dbl(r->z, r->z);
/* X3 = F-2*D */
fp_sub(r->x, t3, t1);
fp_sub(r->x, r->x, t1);
/* Y3 = E*(D-X3)-8*C */
fp_sub(r->y, t1, r->x);
fp_mul(r->y, r->y, t0);
fp_dbl(t2, t2);
fp_dbl(t2, t2);
fp_dbl(t2, t2);
fp_sub(r->y, r->y, t2);
} else {
/* dbl-2007-bl formulas: 1M + 8S + 1*a + 10add + 1*8 + 2*2 + 1*3 */
/* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-2007-bl */
/* t0 = x1^2, t1 = y1^2, t2 = y1^4. */
fp_sqr(t0, p->x);
fp_sqr(t1, p->y);
fp_sqr(t2, t1);
if (!p->norm) {
/* t3 = z1^2. */
fp_sqr(t3, p->z);
if (ep_curve_get_a() == OPT_ZERO) {
/* z3 = 2 * y1 * z1. */
fp_mul(r->z, p->y, p->z);
fp_dbl(r->z, r->z);
} else {
/* z3 = (y1 + z1)^2 - y1^2 - z1^2. */
fp_add(r->z, p->y, p->z);
fp_sqr(r->z, r->z);
fp_sub(r->z, r->z, t1);
fp_sub(r->z, r->z, t3);
}
} else {
/* z3 = 2 * y1. */
fp_dbl(r->z, p->y);
}
/* t4 = S = 2*((x1 + y1^2)^2 - x1^2 - y1^4). */
fp_add(t4, p->x, t1);
fp_sqr(t4, t4);
fp_sub(t4, t4, t0);
fp_sub(t4, t4, t2);
fp_dbl(t4, t4);
/* t5 = M = 3 * x1^2 + a * z1^4. */
fp_dbl(t5, t0);
fp_add(t5, t5, t0);
if (!p->norm) {
fp_sqr(t3, t3);
switch (ep_curve_opt_a()) {
case OPT_ZERO:
break;
case OPT_ONE:
fp_add(t5, t5, ep_curve_get_a());
break;
case OPT_DIGIT:
fp_mul_dig(t1, t3, ep_curve_get_a()[0]);
fp_add(t5, t5, t1);
break;
default:
fp_mul(t1, ep_curve_get_a(), t3);
fp_add(t5, t5, t1);
break;
}
} else {
switch (ep_curve_opt_a()) {
case OPT_ZERO:
break;
case OPT_ONE:
fp_add_dig(t5, t5, (dig_t)1);
break;
case OPT_DIGIT:
fp_add_dig(t5, t5, ep_curve_get_a()[0]);
break;
default:
fp_add(t5, t5, ep_curve_get_a());
break;
}
}
/* x3 = T = M^2 - 2 * S. */
fp_sqr(r->x, t5);
fp_dbl(t1, t4);
fp_sub(r->x, r->x, t1);
/* y3 = M * (S - T) - 8 * y1^4. */
fp_dbl(t2, t2);
fp_dbl(t2, t2);
fp_dbl(t2, t2);
fp_sub(t4, t4, r->x);
fp_mul(t5, t5, t4);
fp_sub(r->y, t5, t2);
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
fp_free(t2);
fp_free(t3);
fp_free(t4);
fp_free(t5);
}
}
void pp_dbl_lit_k12(fp12_t l, ep_t r, ep_t p, ep2_t q) {
fp_t t0, t1, t2, t3, t4, t5, t6;
int one = 1, zero = 0;
fp_null(t0);
fp_null(t1);
fp_null(t2);
fp_null(t3);
fp_null(t4);
fp_null(t5);
fp_null(t6);
TRY {
fp_new(t0);
fp_new(t1);
fp_new(t2);
fp_new(t3);
fp_new(t4);
fp_new(t5);
fp_new(t6);
fp_sqr(t0, p->x);
fp_sqr(t1, p->y);
fp_sqr(t2, p->z);
fp_mul(t4, ep_curve_get_b(), t2);
fp_dbl(t3, t4);
fp_add(t3, t3, t4);
fp_add(t4, p->x, p->y);
fp_sqr(t4, t4);
fp_sub(t4, t4, t0);
fp_sub(t4, t4, t1);
fp_add(t5, p->y, p->z);
fp_sqr(t5, t5);
fp_sub(t5, t5, t1);
fp_sub(t5, t5, t2);
fp_dbl(t6, t3);
fp_add(t6, t6, t3);
fp_sub(r->x, t1, t6);
fp_mul(r->x, r->x, t4);
fp_add(r->y, t1, t6);
fp_sqr(r->y, r->y);
fp_sqr(t4, t3);
fp_dbl(t6, t4);
fp_add(t6, t6, t4);
fp_dbl(t6, t6);
fp_dbl(t6, t6);
fp_sub(r->y, r->y, t6);
fp_mul(r->z, t1, t5);
fp_dbl(r->z, r->z);
fp_dbl(r->z, r->z);
r->norm = 0;
if (ep2_curve_is_twist() == EP_MTYPE) {
one ^= 1;
zero ^= 1;
}
fp2_dbl(l[zero][one], q->x);
fp2_add(l[zero][one], l[zero][one], q->x);
fp_mul(l[zero][one][0], l[zero][one][0], t0);
fp_mul(l[zero][one][1], l[zero][one][1], t0);
fp_sub(l[zero][zero][0], t3, t1);
fp_zero(l[zero][zero][1]);
fp_mul(l[one][one][0], q->y[0], t5);
fp_mul(l[one][one][1], q->y[1], t5);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
fp_free(t2);
fp_free(t3);
fp_free(t4);
fp_free(t5);
fp_free(t6);
}
}
/**
* Computes the constants required for evaluating Frobenius maps.
*/
static void fp3_calc() {
bn_t e;
fp3_t t0, t1, t2;
ctx_t *ctx = core_get();
bn_null(e);
fp3_null(t0);
fp3_null(t1);
fp3_null(t2);
TRY {
bn_new(e);
fp3_new(t0);
fp3_new(t1);
fp3_new(t2);
fp_set_dig(ctx->fp3_base[0], -fp_prime_get_cnr());
fp_neg(ctx->fp3_base[0], ctx->fp3_base[0]);
e->used = FP_DIGS;
dv_copy(e->dp, fp_prime_get(), FP_DIGS);
bn_sub_dig(e, e, 1);
bn_div_dig(e, e, 3);
fp_exp(ctx->fp3_base[0], ctx->fp3_base[0], e);
fp_sqr(ctx->fp3_base[1], ctx->fp3_base[0]);
fp3_zero(t0);
fp_set_dig(t0[1], 1);
dv_copy(e->dp, fp_prime_get(), FP_DIGS);
bn_sub_dig(e, e, 1);
bn_div_dig(e, e, 6);
/* t0 = u^((p-1)/6). */
fp3_exp(t0, t0, e);
fp_copy(ctx->fp3_p[0], t0[2]);
fp3_sqr(t1, t0);
fp_copy(ctx->fp3_p[1], t1[1]);
fp3_mul(t2, t1, t0);
fp_copy(ctx->fp3_p[2], t2[0]);
fp3_sqr(t2, t1);
fp_copy(ctx->fp3_p[3], t2[2]);
fp3_mul(t2, t2, t0);
fp_copy(ctx->fp3_p[4], t2[1]);
fp_mul(ctx->fp3_p2[0], ctx->fp3_p[0], ctx->fp3_base[1]);
fp_mul(t0[0], ctx->fp3_p2[0], ctx->fp3_p[0]);
fp_neg(ctx->fp3_p2[0], t0[0]);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_sub(ctx->fp3_p2[0], ctx->fp3_p2[0], t0[0]);
}
fp_mul(ctx->fp3_p2[1], ctx->fp3_p[1], ctx->fp3_base[0]);
fp_mul(ctx->fp3_p2[1], ctx->fp3_p2[1], ctx->fp3_p[1]);
fp_sqr(ctx->fp3_p2[2], ctx->fp3_p[2]);
fp_mul(ctx->fp3_p2[3], ctx->fp3_p[3], ctx->fp3_base[1]);
fp_mul(t0[0], ctx->fp3_p2[3], ctx->fp3_p[3]);
fp_neg(ctx->fp3_p2[3], t0[0]);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_sub(ctx->fp3_p2[3], ctx->fp3_p2[3], t0[0]);
}
fp_mul(ctx->fp3_p2[4], ctx->fp3_p[4], ctx->fp3_base[0]);
fp_mul(ctx->fp3_p2[4], ctx->fp3_p2[4], ctx->fp3_p[4]);
fp_mul(ctx->fp3_p3[0], ctx->fp3_p[0], ctx->fp3_base[0]);
fp_mul(t0[0], ctx->fp3_p3[0], ctx->fp3_p2[0]);
fp_neg(ctx->fp3_p3[0], t0[0]);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_sub(ctx->fp3_p3[0], ctx->fp3_p3[0], t0[0]);
}
fp_mul(ctx->fp3_p3[1], ctx->fp3_p[1], ctx->fp3_base[1]);
fp_mul(t0[0], ctx->fp3_p3[1], ctx->fp3_p2[1]);
fp_neg(ctx->fp3_p3[1], t0[0]);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_sub(ctx->fp3_p3[1], ctx->fp3_p3[1], t0[0]);
}
fp_mul(ctx->fp3_p3[2], ctx->fp3_p[2], ctx->fp3_p2[2]);
fp_mul(ctx->fp3_p3[3], ctx->fp3_p[3], ctx->fp3_base[0]);
fp_mul(t0[0], ctx->fp3_p3[3], ctx->fp3_p2[3]);
fp_neg(ctx->fp3_p3[3], t0[0]);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_sub(ctx->fp3_p3[3], ctx->fp3_p3[3], t0[0]);
}
fp_mul(ctx->fp3_p3[4], ctx->fp3_p[4], ctx->fp3_base[1]);
fp_mul(t0[0], ctx->fp3_p3[4], ctx->fp3_p2[4]);
fp_neg(ctx->fp3_p3[4], t0[0]);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_sub(ctx->fp3_p3[4], ctx->fp3_p3[4], t0[0]);
}
for (int i = 0; i < 5; i++) {
fp_mul(ctx->fp3_p4[i], ctx->fp3_p[i], ctx->fp3_p3[i]);
fp_mul(ctx->fp3_p5[i], ctx->fp3_p2[i], ctx->fp3_p3[i]);
}
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
bn_free(e);
fp3_free(t0);
fp3_free(t1);
fp3_free(t2);
}
}
void fp3_sub_basic(fp2_t c, fp2_t a, fp2_t b) {
fp_sub(c[0], a[0], b[0]);
fp_sub(c[1], a[1], b[1]);
fp_sub(c[2], a[2], b[2]);
}
/**
* Doubles a point represented in affine coordinates on an ordinary prime
* elliptic curve.
*
* @param[out] r - the result.
* @param[out] s - the slope.
* @param[in] p - the point to double.
*/
static void ep_dbl_basic_imp(ep_t r, fp_t s, const ep_t p) {
fp_t t0, t1, t2;
fp_null(t0);
fp_null(t1);
fp_null(t2);
TRY {
fp_new(t0);
fp_new(t1);
fp_new(t2);
/* t0 = 1/2 * y1. */
fp_dbl(t0, p->y);
fp_inv(t0, t0);
/* t1 = 3 * x1^2 + a. */
fp_sqr(t1, p->x);
fp_copy(t2, t1);
fp_dbl(t1, t1);
fp_add(t1, t1, t2);
switch (ep_curve_opt_a()) {
case OPT_ZERO:
break;
case OPT_ONE:
fp_add_dig(t1, t1, (dig_t)1);
break;
#if FP_RDC != MONTY
case OPT_DIGIT:
fp_add_dig(t1, t1, ep_curve_get_a()[0]);
break;
#endif
default:
fp_add(t1, t1, ep_curve_get_a());
break;
}
/* t1 = (3 * x1^2 + a)/(2 * y1). */
fp_mul(t1, t1, t0);
if (s != NULL) {
fp_copy(s, t1);
}
/* t2 = t1^2. */
fp_sqr(t2, t1);
/* x3 = t1^2 - 2 * x1. */
fp_dbl(t0, p->x);
fp_sub(t0, t2, t0);
/* y3 = t1 * (x1 - x3) - y1. */
fp_sub(t2, p->x, t0);
fp_mul(t1, t1, t2);
fp_sub(r->y, t1, p->y);
fp_copy(r->x, t0);
fp_copy(r->z, p->z);
r->norm = 1;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
fp_free(t2);
}
}