ImathRandom.cpp

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//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
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//-----------------------------------------------------------------------------
//
//	Routines that generate pseudo-random numbers compatible
//	with the standard erand48(), nrand48(), etc. functions.
//
//-----------------------------------------------------------------------------

#include "ImathRandom.h"
#include "ImathInt64.h"

namespace Imath {
namespace {

//
// Static state used by Imath::drand48(), Imath::lrand48() and Imath::srand48()
//

unsigned short staticState[3] = {0, 0, 0};


void
rand48Next (unsigned short state[3])
{
    //
    // drand48() and friends are all based on a linear congruential
    // sequence,
    //
    //   x[n+1] = (a * x[n] + c) % m,
    //
    // where a and c are as specified below, and m == (1 << 48)
    //

    static const Int64 a = Int64 (0x5deece66dLL);
    static const Int64 c = Int64 (0xbLL);

    //
    // Assemble the 48-bit value x[n] from the
    // three 16-bit values stored in state.
    //

    Int64 x = (Int64 (state[2]) << 32) |
          (Int64 (state[1]) << 16) |
           Int64 (state[0]);

    //
    // Compute x[n+1], except for the "modulo m" part.
    //

    x = a * x + c;

    //
    // Disassemble the 48 least significant bits of x[n+1] into
    // three 16-bit values.  Discard the 16 most significant bits;
    // this takes care of the "modulo m" operation.
    //
    // We assume that sizeof (unsigned short) == 2.
    //

    state[2] = (unsigned short)(x >> 32);
    state[1] = (unsigned short)(x >> 16);
    state[0] = (unsigned short)(x);
}

} // namespace


double
erand48 (unsigned short state[3])
{
    //
    // Generate double-precision floating-point values between 0.0 and 1.0:
    //
    // The exponent is set to 0x3ff, which indicates a value greater
    // than or equal to 1.0, and less than 2.0.  The 48 most significant
    // bits of the significand (mantissa) are filled with pseudo-random
    // bits generated by rand48Next().  The remaining 4 bits are a copy
    // of the 4 most significant bits of the significand.  This results
    // in bit patterns between 0x3ff0000000000000 and 0x3fffffffffffffff,
    // which correspond to uniformly distributed floating-point values
    // between 1.0 and 1.99999999999999978.  Subtracting 1.0 from those
    // values produces numbers between 0.0 and 0.99999999999999978, that
    // is, between 0.0 and 1.0-DBL_EPSILON.
    //

    rand48Next (state);

    union {double d; Int64 i;} u;

    u.i = (Int64 (0x3ff)    << 52) |	// sign and exponent
      (Int64 (state[2]) << 36) |	// significand
      (Int64 (state[1]) << 20) |
      (Int64 (state[0]) <<  4) |
      (Int64 (state[2]) >> 12);

    return u.d - 1;
}


double
drand48 ()
{
    return Imath::erand48 (staticState);
}


long int
nrand48 (unsigned short state[3])
{
    //
    // Generate uniformly distributed integers between 0 and 0x7fffffff.
    //

    rand48Next (state);

    return ((long int) (state[2]) << 15) |
       ((long int) (state[1]) >>  1);
}


long int
lrand48 ()
{
    return Imath::nrand48 (staticState);
}


void
srand48 (long int seed)
{
    staticState[2] = (unsigned short)(seed >> 16);
    staticState[1] = (unsigned short)(seed);
    staticState[0] = 0x330e;
}


float
Rand32::nextf ()
{
    //
    // Generate single-precision floating-point values between 0.0 and 1.0:
    //
    // The exponent is set to 0x7f, which indicates a value greater than
    // or equal to 1.0, and less than 2.0.  The 23 bits of the significand
    // (mantissa) are filled with pseudo-random bits generated by
    // Rand32::next().  This results in in bit patterns between 0x3f800000
    // and 0x3fffffff, which correspond to uniformly distributed floating-
    // point values between 1.0 and 1.99999988.  Subtracting 1.0 from
    // those values produces numbers between 0.0 and 0.99999988, that is,
    // between 0.0 and 1.0-FLT_EPSILON.
    //

    next ();

    union {float f; unsigned int i;} u;

    u.i = 0x3f800000 | (_state & 0x7fffff);
    return u.f - 1;
}

} // namespace Imath