diff --git a/cpp/src/exp2.cc b/cpp/src/exp2.cc index 7f3a93d..ac0ae43 100644 --- a/cpp/src/exp2.cc +++ b/cpp/src/exp2.cc @@ -19,6 +19,8 @@ #include "synth.h" #include "exp2.h" +#include + int32_t exp2tab[EXP2_N_SAMPLES << 1]; void Exp2::init() { @@ -34,3 +36,30 @@ void Exp2::init() { exp2tab[(EXP2_N_SAMPLES << 1) - 2] = (1U << 31) - exp2tab[(EXP2_N_SAMPLES << 1) - 1]; } +int32_t tanhtab[TANH_N_SAMPLES << 1]; + +static double dtanh(double y) { + return 1 - y * y; +} + +void Tanh::init() { + double step = 4.0 / TANH_N_SAMPLES; + double y = 0; + for (int i = 0; i < TANH_N_SAMPLES; i++) { + tanhtab[(i << 1) + 1] = (1 << 24) * y + 0.5; + //printf("%d\n", tanhtab[(i << 1) + 1]); + // Use a basic 4th order Runge-Kutte to compute tanh from its + // differential equation. + double k1 = dtanh(y); + double k2 = dtanh(y + 0.5 * step * k1); + double k3 = dtanh(y + 0.5 * step * k2); + double k4 = dtanh(y + step * k3); + double dy = (step / 6) * (k1 + k4 + 2 * (k2 + k3)); + y += dy; + } + for (int i = 0; i < TANH_N_SAMPLES - 1; i++) { + tanhtab[i << 1] = tanhtab[(i << 1) + 3] - tanhtab[(i << 1) + 1]; + } + int32_t lasty = (1 << 24) * y + 0.5; + tanhtab[(TANH_N_SAMPLES << 1) - 2] = lasty - tanhtab[(TANH_N_SAMPLES << 1) - 1]; +} diff --git a/cpp/src/exp2.h b/cpp/src/exp2.h index 2c08fb1..016ca33 100644 --- a/cpp/src/exp2.h +++ b/cpp/src/exp2.h @@ -44,3 +44,37 @@ int32_t Exp2::lookup(int32_t x) { return y >> (6 - (x >> 24)); } #endif + +class Tanh { + public: + static void init(); + + // Q24 in, Q24 out + static int32_t lookup(int32_t x); +}; + +#define TANH_LG_N_SAMPLES 10 +#define TANH_N_SAMPLES (1 << TANH_LG_N_SAMPLES) + +extern int32_t tanhtab[TANH_N_SAMPLES << 1]; + +inline +int32_t Tanh::lookup(int32_t x) { + int32_t signum = x >> 31; + x ^= signum; + if (x >= (4 << 24)) { + if (x >= (17 << 23)) { + return signum ^ (1 << 24); + } + int32_t sx = ((int64_t)-48408812 * (int64_t)x) >> 24; + return signum ^ ((1 << 24) - 2 * Exp2::lookup(sx)); + } else { + const int SHIFT = 26 - TANH_LG_N_SAMPLES; + int lowbits = x & ((1 << SHIFT) - 1); + int x_int = (x >> (SHIFT - 1)) & ((TANH_N_SAMPLES - 1) << 1); + int dy = tanhtab[x_int]; + int y0 = tanhtab[x_int + 1]; + int y = y0 + (((int64_t)dy * (int64_t)lowbits) >> SHIFT); + return y ^ signum; + } +} diff --git a/cpp/src/main.cc b/cpp/src/main.cc index e20ca8a..ee45d59 100644 --- a/cpp/src/main.cc +++ b/cpp/src/main.cc @@ -81,6 +81,22 @@ void test_log_accuracy() { cout << "Max error: " << maxerr << endl; } +void test_tanh_accuracy() { + Tanh::init(); + double maxerr = 0; + for (int i = 0; i < 1000000; i++) { + int32_t x = (rand() & ((1 << 29) - 1)) - (1 << 28); + int32_t y = Tanh::lookup(x); + double yd = (1 << 24) * tanh(x * (1.0 / (1 << 24))); + double err = fabs(y - yd); + if (err > maxerr) { + cout << "x = " << x << ", y = " << y << ", yd = " << (int)yd << endl; + maxerr = err; + } + } + cout << "Max error: " << maxerr << endl; +} + void test_pure_accuracy() { int32_t worstfreq; int32_t worstphase; @@ -264,6 +280,7 @@ int main(int argc, char **argv) { //FmCore::dump(); //test_sin_accuracy(); test_log_accuracy(); + test_tanh_accuracy(); //benchmark_fm_op(); //test_pure_accuracy(); //benchmark_sin(); diff --git a/cpp/src/pitchenv.cc b/cpp/src/pitchenv.cc index ee91b03..7cb564c 100644 --- a/cpp/src/pitchenv.cc +++ b/cpp/src/pitchenv.cc @@ -17,8 +17,6 @@ #include "synth.h" #include "pitchenv.h" -using namespace std; - int PitchEnv::unit_; void PitchEnv::init(double sample_rate) {