Fast SIN approximation for usage in e.g. additive synthesizers

  • Author or source: neotec
  • Created: 2008-12-09 11:56:33
notes
This code presents 2 'fastsin' functions. fastsin2 is less accurate than fastsin. In fact
it's a simple taylor series, but optimized for integer phase.

phase is in 0 -> (2^32)-1 range and maps to 0 -> ~2PI

I get about 55000000 fastsin's per second on my P4,3.2GHz which would give a nice Kawai K5
emulation using 64 harmonics and 8->16 voices.
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float fastsin(UINT32 phase)
{
    const float frf3 = -1.0f / 6.0f;
    const float frf5 = 1.0f / 120.0f;
    const float frf7 = -1.0f / 5040.0f;
    const float frf9 = 1.0f / 362880.0f;
    const float f0pi5 = 1.570796327f;
    float x, x2, asin;
    UINT32 tmp = 0x3f800000 | (phase >> 7);
    if (phase & 0x40000000)
            tmp ^= 0x007fffff;
    x = (*((float*)&tmp) - 1.0f) * f0pi5;
    x2 = x * x;
    asin = ((((frf9 * x2 + frf7) * x2 + frf5) * x2 + frf3) * x2 + 1.0f) * x;
    return (phase & 0x80000000) ? -asin : asin;
}

float fastsin2(UINT32 phase)
{
    const float frf3 = -1.0f / 6.0f;
    const float frf5 = 1.0f / 120.0f;
    const float frf7 = -1.0f / 5040.0f;
    const float f0pi5 = 1.570796327f;
    float x, x2, asin;
    UINT32 tmp = 0x3f800000 | (phase >> 7);
    if (phase & 0x40000000)
            tmp ^= 0x007fffff;
    x = (*((float*)&tmp) - 1.0f) * f0pi5;
    x2 = x * x;
    asin = (((frf7 * x2 + frf5) * x2 + frf3) * x2 + 1.0f) * x;
    return (phase & 0x80000000) ? -asin : asin;
}

Comments

  • Date: 2008-12-09 12:11:11
  • By: neotec
PS: To use this as an OSC you'll need the following vars/equ's:

UINT32 phase = 0;
UINT32 step = frequency * powf(2.0f, 32.0f) / samplerate;

Then it's just:
...
out = fastsin(phase);
phase += step;
...

Woah! Seven multiplies, on top of those adds and memory lookup. Is this really all that fast?