/*
|
/*
|
* Copyright (c) 1993 Martin Birgmeier
|
* Copyright (c) 1993 Martin Birgmeier
|
* All rights reserved.
|
* All rights reserved.
|
*
|
*
|
* You may redistribute unmodified or modified versions of this source
|
* You may redistribute unmodified or modified versions of this source
|
* code provided that the above copyright notice and this and the
|
* code provided that the above copyright notice and this and the
|
* following conditions are retained.
|
* following conditions are retained.
|
*
|
*
|
* This software is provided ``as is'', and comes with no warranties
|
* This software is provided ``as is'', and comes with no warranties
|
* of any kind. I shall in no event be liable for anything that happens
|
* of any kind. I shall in no event be liable for anything that happens
|
* to anyone/anything when using this software.
|
* to anyone/anything when using this software.
|
*/
|
*/
|
|
|
/*
|
/*
|
FUNCTION
|
FUNCTION
|
<<rand48>>, <<drand48>>, <<erand48>>, <<lrand48>>, <<nrand48>>, <<mrand48>>, <<jrand48>>, <<srand48>>, <<seed48>>, <<lcong48>> ---pseudo random number generators and initialization routines
|
<<rand48>>, <<drand48>>, <<erand48>>, <<lrand48>>, <<nrand48>>, <<mrand48>>, <<jrand48>>, <<srand48>>, <<seed48>>, <<lcong48>> ---pseudo random number generators and initialization routines
|
|
|
INDEX
|
INDEX
|
rand48
|
rand48
|
INDEX
|
INDEX
|
drand48
|
drand48
|
INDEX
|
INDEX
|
erand48
|
erand48
|
INDEX
|
INDEX
|
lrand48
|
lrand48
|
INDEX
|
INDEX
|
nrand48
|
nrand48
|
INDEX
|
INDEX
|
mrand48
|
mrand48
|
INDEX
|
INDEX
|
jrand48
|
jrand48
|
INDEX
|
INDEX
|
srand48
|
srand48
|
INDEX
|
INDEX
|
seed48
|
seed48
|
INDEX
|
INDEX
|
lcong48
|
lcong48
|
|
|
ANSI_SYNOPSIS
|
ANSI_SYNOPSIS
|
#include <stdlib.h>
|
#include <stdlib.h>
|
double drand48(void);
|
double drand48(void);
|
double erand48(unsigned short <[xseed]>[3]);
|
double erand48(unsigned short <[xseed]>[3]);
|
long lrand48(void);
|
long lrand48(void);
|
long nrand48(unsigned short <[xseed]>[3]);
|
long nrand48(unsigned short <[xseed]>[3]);
|
long mrand48(void);
|
long mrand48(void);
|
long jrand48(unsigned short <[xseed]>[3]);
|
long jrand48(unsigned short <[xseed]>[3]);
|
void srand48(long <[seed]>);
|
void srand48(long <[seed]>);
|
unsigned short *seed48(unsigned short <[xseed]>[3]);
|
unsigned short *seed48(unsigned short <[xseed]>[3]);
|
void lcong48(unsigned short <[p]>[7]);
|
void lcong48(unsigned short <[p]>[7]);
|
|
|
TRAD_SYNOPSIS
|
TRAD_SYNOPSIS
|
#include <stdlib.h>
|
#include <stdlib.h>
|
double drand48();
|
double drand48();
|
|
|
double erand48(<[xseed]>)
|
double erand48(<[xseed]>)
|
unsigned short <[xseed]>[3];
|
unsigned short <[xseed]>[3];
|
|
|
long lrand48();
|
long lrand48();
|
|
|
long nrand48(<[xseed]>)
|
long nrand48(<[xseed]>)
|
unsigned short <[xseed]>[3];
|
unsigned short <[xseed]>[3];
|
|
|
long mrand48();
|
long mrand48();
|
|
|
long jrand48(<[xseed]>)
|
long jrand48(<[xseed]>)
|
unsigned short <[xseed]>[3];
|
unsigned short <[xseed]>[3];
|
|
|
void srand48(<[seed]>)
|
void srand48(<[seed]>)
|
long <[seed]>;
|
long <[seed]>;
|
|
|
unsigned short *seed48(<[xseed]>)
|
unsigned short *seed48(<[xseed]>)
|
unsigned short <[xseed]>[3];
|
unsigned short <[xseed]>[3];
|
|
|
void lcong48(<[p]>)
|
void lcong48(<[p]>)
|
unsigned short <[p]>[7];
|
unsigned short <[p]>[7];
|
|
|
DESCRIPTION
|
DESCRIPTION
|
The <<rand48>> family of functions generates pseudo-random numbers
|
The <<rand48>> family of functions generates pseudo-random numbers
|
using a linear congruential algorithm working on integers 48 bits in size.
|
using a linear congruential algorithm working on integers 48 bits in size.
|
The particular formula employed is
|
The particular formula employed is
|
r(n+1) = (a * r(n) + c) mod m
|
r(n+1) = (a * r(n) + c) mod m
|
where the default values are
|
where the default values are
|
for the multiplicand a = 0xfdeece66d = 25214903917 and
|
for the multiplicand a = 0xfdeece66d = 25214903917 and
|
the addend c = 0xb = 11. The modulo is always fixed at m = 2 ** 48.
|
the addend c = 0xb = 11. The modulo is always fixed at m = 2 ** 48.
|
r(n) is called the seed of the random number generator.
|
r(n) is called the seed of the random number generator.
|
|
|
For all the six generator routines described next, the first
|
For all the six generator routines described next, the first
|
computational step is to perform a single iteration of the algorithm.
|
computational step is to perform a single iteration of the algorithm.
|
|
|
<<drand48>> and <<erand48>>
|
<<drand48>> and <<erand48>>
|
return values of type double. The full 48 bits of r(n+1) are
|
return values of type double. The full 48 bits of r(n+1) are
|
loaded into the mantissa of the returned value, with the exponent set
|
loaded into the mantissa of the returned value, with the exponent set
|
such that the values produced lie in the interval [0.0, 1.0].
|
such that the values produced lie in the interval [0.0, 1.0].
|
|
|
<<lrand48>> and <<nrand48>>
|
<<lrand48>> and <<nrand48>>
|
return values of type long in the range
|
return values of type long in the range
|
[0, 2**31-1]. The high-order (31) bits of
|
[0, 2**31-1]. The high-order (31) bits of
|
r(n+1) are loaded into the lower bits of the returned value, with
|
r(n+1) are loaded into the lower bits of the returned value, with
|
the topmost (sign) bit set to zero.
|
the topmost (sign) bit set to zero.
|
|
|
<<mrand48>> and <<jrand48>>
|
<<mrand48>> and <<jrand48>>
|
return values of type long in the range
|
return values of type long in the range
|
[-2**31, 2**31-1]. The high-order (32) bits of
|
[-2**31, 2**31-1]. The high-order (32) bits of
|
r(n+1) are loaded into the returned value.
|
r(n+1) are loaded into the returned value.
|
|
|
<<drand48>>, <<lrand48>>, and <<mrand48>>
|
<<drand48>>, <<lrand48>>, and <<mrand48>>
|
use an internal buffer to store r(n). For these functions
|
use an internal buffer to store r(n). For these functions
|
the initial value of r(0) = 0x1234abcd330e = 20017429951246.
|
the initial value of r(0) = 0x1234abcd330e = 20017429951246.
|
|
|
On the other hand, <<erand48>>, <<nrand48>>, and <<jrand48>>
|
On the other hand, <<erand48>>, <<nrand48>>, and <<jrand48>>
|
use a user-supplied buffer to store the seed r(n),
|
use a user-supplied buffer to store the seed r(n),
|
which consists of an array of 3 shorts, where the zeroth member
|
which consists of an array of 3 shorts, where the zeroth member
|
holds the least significant bits.
|
holds the least significant bits.
|
|
|
All functions share the same multiplicand and addend.
|
All functions share the same multiplicand and addend.
|
|
|
<<srand48>> is used to initialize the internal buffer r(n) of
|
<<srand48>> is used to initialize the internal buffer r(n) of
|
<<drand48>>, <<lrand48>>, and <<mrand48>>
|
<<drand48>>, <<lrand48>>, and <<mrand48>>
|
such that the 32 bits of the seed value are copied into the upper 32 bits
|
such that the 32 bits of the seed value are copied into the upper 32 bits
|
of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e.
|
of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e.
|
Additionally, the constant multiplicand and addend of the algorithm are
|
Additionally, the constant multiplicand and addend of the algorithm are
|
reset to the default values given above.
|
reset to the default values given above.
|
|
|
<<seed48>> also initializes the internal buffer r(n) of
|
<<seed48>> also initializes the internal buffer r(n) of
|
<<drand48>>, <<lrand48>>, and <<mrand48>>,
|
<<drand48>>, <<lrand48>>, and <<mrand48>>,
|
but here all 48 bits of the seed can be specified in an array of 3 shorts,
|
but here all 48 bits of the seed can be specified in an array of 3 shorts,
|
where the zeroth member specifies the lowest bits. Again,
|
where the zeroth member specifies the lowest bits. Again,
|
the constant multiplicand and addend of the algorithm are
|
the constant multiplicand and addend of the algorithm are
|
reset to the default values given above.
|
reset to the default values given above.
|
<<seed48>> returns a pointer to an array of 3 shorts which contains
|
<<seed48>> returns a pointer to an array of 3 shorts which contains
|
the old seed.
|
the old seed.
|
This array is statically allocated, thus its contents are lost after
|
This array is statically allocated, thus its contents are lost after
|
each new call to <<seed48>>.
|
each new call to <<seed48>>.
|
|
|
Finally, <<lcong48>> allows full control over the multiplicand and
|
Finally, <<lcong48>> allows full control over the multiplicand and
|
addend used in <<drand48>>, <<erand48>>, <<lrand48>>, <<nrand48>>,
|
addend used in <<drand48>>, <<erand48>>, <<lrand48>>, <<nrand48>>,
|
<<mrand48>>, and <<jrand48>>,
|
<<mrand48>>, and <<jrand48>>,
|
and the seed used in <<drand48>>, <<lrand48>>, and <<mrand48>>.
|
and the seed used in <<drand48>>, <<lrand48>>, and <<mrand48>>.
|
An array of 7 shorts is passed as parameter; the first three shorts are
|
An array of 7 shorts is passed as parameter; the first three shorts are
|
used to initialize the seed; the second three are used to initialize the
|
used to initialize the seed; the second three are used to initialize the
|
multiplicand; and the last short is used to initialize the addend.
|
multiplicand; and the last short is used to initialize the addend.
|
It is thus not possible to use values greater than 0xffff as the addend.
|
It is thus not possible to use values greater than 0xffff as the addend.
|
|
|
Note that all three methods of seeding the random number generator
|
Note that all three methods of seeding the random number generator
|
always also set the multiplicand and addend for any of the six
|
always also set the multiplicand and addend for any of the six
|
generator calls.
|
generator calls.
|
|
|
For a more powerful random number generator, see <<random>>.
|
For a more powerful random number generator, see <<random>>.
|
|
|
PORTABILITY
|
PORTABILITY
|
SUS requires these functions.
|
SUS requires these functions.
|
|
|
No supporting OS subroutines are required.
|
No supporting OS subroutines are required.
|
*/
|
*/
|
|
|
#include "rand48.h"
|
#include "rand48.h"
|
|
|
void
|
void
|
_DEFUN (__dorand48, (r, xseed),
|
_DEFUN (__dorand48, (r, xseed),
|
struct _reent *r _AND
|
struct _reent *r _AND
|
unsigned short xseed[3])
|
unsigned short xseed[3])
|
{
|
{
|
unsigned long accu;
|
unsigned long accu;
|
unsigned short temp[2];
|
unsigned short temp[2];
|
|
|
accu = (unsigned long) __rand48_mult[0] * (unsigned long) xseed[0] +
|
accu = (unsigned long) __rand48_mult[0] * (unsigned long) xseed[0] +
|
(unsigned long) __rand48_add;
|
(unsigned long) __rand48_add;
|
temp[0] = (unsigned short) accu; /* lower 16 bits */
|
temp[0] = (unsigned short) accu; /* lower 16 bits */
|
accu >>= sizeof(unsigned short) * 8;
|
accu >>= sizeof(unsigned short) * 8;
|
accu += (unsigned long) __rand48_mult[0] * (unsigned long) xseed[1] +
|
accu += (unsigned long) __rand48_mult[0] * (unsigned long) xseed[1] +
|
(unsigned long) __rand48_mult[1] * (unsigned long) xseed[0];
|
(unsigned long) __rand48_mult[1] * (unsigned long) xseed[0];
|
temp[1] = (unsigned short) accu; /* middle 16 bits */
|
temp[1] = (unsigned short) accu; /* middle 16 bits */
|
accu >>= sizeof(unsigned short) * 8;
|
accu >>= sizeof(unsigned short) * 8;
|
accu += __rand48_mult[0] * xseed[2] + __rand48_mult[1] * xseed[1] + __rand48_mult[2] * xseed[0];
|
accu += __rand48_mult[0] * xseed[2] + __rand48_mult[1] * xseed[1] + __rand48_mult[2] * xseed[0];
|
xseed[0] = temp[0];
|
xseed[0] = temp[0];
|
xseed[1] = temp[1];
|
xseed[1] = temp[1];
|
xseed[2] = (unsigned short) accu;
|
xseed[2] = (unsigned short) accu;
|
}
|
}
|
|
|
