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fft11.cl
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184 lines (151 loc) · 5.57 KB
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// Copyright (C) Mihai Preda & George Woltman
#if FFT_FP64
#if 0
// Adapted from https://web.archive.org/web/20101126231320/http://cnx.org/content/col10569/1.7/pdf
// 40 FMA + 150 ADD
void fft11(T2 *u) {
double
C1 = 0.1, C2 = 0.33166247903553997,
C3 = 0.51541501300188641, C4 = 0.94125353283118118,
C5 = 1.4143537075597825, C6 = 0.85949297361449739,
C7 = 0.042314838273285138, C8 = 0.38639279888589612,
C9 = 0.51254589567199993, C10 = 1.0702757469471715,
C11 = 0.55486073394528501, C12 = 1.2412944743900585,
C13 = 0.20897833842005759, C14 = 0.374157173124608,
C15 = 0.049929922194110285, C16 = 0.65815896284539277,
C17 = 0.63306543373877588, C18 = 1.0822460581641111,
C19 = 0.81720737907134011, C20 = 0.4240870953187183;
X2(u[1], u[10]);
X2(u[2], u[9]);
X2(u[3], u[8]);
X2(u[4], u[7]);
X2(u[5], u[6]);
T2 t1 = u[1];
T2 t6 = u[10];
T2 t2 = u[2];
T2 t7 = u[9];
T2 t3 = u[3];
T2 t8 = u[8];
T2 t4 = u[4];
T2 t9 = u[7];
T2 t5 = u[5];
T2 t10 = u[6];
T2 t11 = t1 + t2;
T2 t12 = t3 + t5;
T2 t13 = t4 + t11 + t12;
T2 s0 = u[0] - C1 * t13;
u[0] = u[0] + t13;
T2 t14 = t7 - t8;
T2 t15 = t6 + t10;
T2 am2 = (t14 - t15 - t9) * C2;
T2 am3 = (t2 - t4) * C3;
T2 am4 = (t1 - t4) * C4;
T2 am5 = (t2 - t1) * C5;
T2 am6 = (t5 - t4) * C6;
T2 am7 = (t3 - t4) * C7;
T2 am8 = (t5 - t3) * C8;
T2 am11 = (t12 - t11) * C11;
T2 am14 = (t6 + t7) * C14;
T2 am17 = (t8 - t10) * C17;
T2 am20 = (t14 + t15) * C20;
T2 s7 = am11 + C10 * (t1 - t3);
T2 s8 = am11 + (t2 - t5) * C9;
T2 s9 = am14 + (t6 - t9) * C13;
T2 s10 = -am14 + (t7 + t9) * C12;
T2 s11 = am17 + (t8 - t9) * C16;
T2 s12 = -am17 + (t9 - t10) * C15;
T2 s13 = am20 + (t6 - t8) * C19;
T2 s14 = -am20 + (t7 + t10) * C18;
u[1] = s0 + am3 + am4 - am6 - am7;
u[10] = mul_t4(s9 + s10 + s11 + s12 - am2);
X2(u[1], u[10]);
u[2] = s0 + s7 + am7 + am8;
u[9] = mul_t4(s13 + am2 + s11);
X2(u[2], u[9]);
u[3] = s0 - s7 - am4 - am5;
u[8] = mul_t4(s13 - am2 - s9);
X2(u[3], u[8]);
u[4] = s0 + s8 + am6 - am8;
u[7] = -mul_t4(s14 + am2 + s12);
X2(u[4], u[7]);
u[5] = s0 - s8 - am3 + am5;
u[6] = mul_t4(s14 - am2 - s10);
X2(u[5], u[6]);
}
#else
// 110 FMA + 30 ADD (or 100 FMA + 50 ADD)
// See prime95's gwnum/zr11.mac file for more detailed explanation
void fft11(T2 *u) {
const double COS1 = 0.8412535328311811688; // cos(tau/11)
const double COS2 = 0.4154150130018864255; // cos(2*tau/11)
const double COS3 = -0.1423148382732851404; // cos(3*tau/11)
const double COS4 = -0.6548607339452850640; // cos(4*tau/11)
const double COS5 = -0.9594929736144973898; // cos(5*tau/11)
const double SIN1 = 0.5406408174555975821; // sin(tau/11)
const double SIN2_SIN1 = 1.682507065662362337; // sin(2*tau/11) / sin(tau/11) = .910/.541
const double SIN3_SIN1 = 1.830830026003772851; // sin(3*tau/11) / sin(tau/11) = .990/.541
const double SIN4_SIN1 = 1.397877389115792056; // sin(4*tau/11) / sin(tau/11) = .756/.541
const double SIN5_SIN1 = 0.521108558113202723; // sin(5*tau/11) / sin(tau/11) = .282/.541
X2_mul_t4(u[1], u[10]); // (r2+ i2+), (i2- -r2-)
X2_mul_t4(u[2], u[9]); // (r3+ i3+), (i3- -r3-)
X2_mul_t4(u[3], u[8]); // (r4+ i4+), (i4- -r4-)
X2_mul_t4(u[4], u[7]); // (r5+ i5+), (i5- -r5-)
X2_mul_t4(u[5], u[6]); // (r6+ i6+), (i6- -r6-)
T2 tmp211a = fmaT2(COS1, u[1], u[0]);
T2 tmp310a = fmaT2(COS2, u[1], u[0]);
T2 tmp49a = fmaT2(COS3, u[1], u[0]);
T2 tmp58a = fmaT2(COS4, u[1], u[0]);
T2 tmp67a = fmaT2(COS5, u[1], u[0]);
u[0] = u[0] + u[1];
tmp211a = fmaT2(COS2, u[2], tmp211a);
tmp310a = fmaT2(COS4, u[2], tmp310a);
tmp49a = fmaT2(COS5, u[2], tmp49a);
tmp58a = fmaT2(COS3, u[2], tmp58a);
tmp67a = fmaT2(COS1, u[2], tmp67a);
u[0] = u[0] + u[2];
tmp211a = fmaT2(COS3, u[3], tmp211a);
tmp310a = fmaT2(COS5, u[3], tmp310a);
tmp49a = fmaT2(COS2, u[3], tmp49a);
tmp58a = fmaT2(COS1, u[3], tmp58a);
tmp67a = fmaT2(COS4, u[3], tmp67a);
u[0] = u[0] + u[3];
tmp211a = fmaT2(COS4, u[4], tmp211a);
tmp310a = fmaT2(COS3, u[4], tmp310a);
tmp49a = fmaT2(COS1, u[4], tmp49a);
tmp58a = fmaT2(COS5, u[4], tmp58a);
tmp67a = fmaT2(COS2, u[4], tmp67a);
u[0] = u[0] + u[4];
tmp211a = fmaT2(COS5, u[5], tmp211a);
tmp310a = fmaT2(COS1, u[5], tmp310a);
tmp49a = fmaT2(COS4, u[5], tmp49a);
tmp58a = fmaT2(COS2, u[5], tmp58a);
tmp67a = fmaT2(COS3, u[5], tmp67a);
u[0] = u[0] + u[5];
T2 tmp211b = fmaT2(SIN2_SIN1, u[9], u[10]); // .910/.541
T2 tmp310b = fmaT2(SIN2_SIN1, u[10], -u[6]);
T2 tmp49b = fmaT2(SIN2_SIN1, -u[8], u[7]);
T2 tmp58b = fmaT2(SIN2_SIN1, -u[6], u[8]);
T2 tmp67b = fmaT2(SIN2_SIN1, -u[7], -u[9]);
tmp211b = fmaT2(SIN3_SIN1, u[8], tmp211b); // .990/.541
tmp310b = fmaT2(SIN3_SIN1, -u[7], tmp310b);
tmp49b = fmaT2(SIN3_SIN1, u[10], tmp49b);
tmp58b = fmaT2(SIN3_SIN1, -u[9], tmp58b);
tmp67b = fmaT2(SIN3_SIN1, u[6], tmp67b);
tmp211b = fmaT2(SIN4_SIN1, u[7], tmp211b); // .756/.541
tmp310b = fmaT2(SIN4_SIN1, u[9], tmp310b);
tmp49b = fmaT2(SIN4_SIN1, u[6], tmp49b);
tmp58b = fmaT2(SIN4_SIN1, u[10], tmp58b);
tmp67b = fmaT2(SIN4_SIN1, u[8], tmp67b);
tmp211b = fmaT2(SIN5_SIN1, u[6], tmp211b); // .282/.541
tmp310b = fmaT2(SIN5_SIN1, -u[8], tmp310b);
tmp49b = fmaT2(SIN5_SIN1, -u[9], tmp49b);
tmp58b = fmaT2(SIN5_SIN1, u[7], tmp58b);
tmp67b = fmaT2(SIN5_SIN1, u[10], tmp67b);
fma_addsub(u[1], u[10], SIN1, tmp211a, tmp211b);
fma_addsub(u[2], u[9], SIN1, tmp310a, tmp310b);
fma_addsub(u[3], u[8], SIN1, tmp49a, tmp49b);
fma_addsub(u[4], u[7], SIN1, tmp58a, tmp58b);
fma_addsub(u[5], u[6], SIN1, tmp67a, tmp67b);
}
#endif
#endif