1\" Copyright (c) 1993 Martin Birgmeier
2.\" All rights reserved.
3.\"
4.\" You may redistribute unmodified or modified versions of this source
5.\" code provided that the above copyright notice and this and the
6.\" following conditions are retained.
7.\"
8.\" This software is provided ``as is'', and comes with no warranties
9.\" of any kind. I shall in no event be liable for anything that happens
10.\" to anyone/anything when using this software.
11.\"
12.\" @(#)rand48.3 V1.0 MB 8 Oct 1993
| 1\" Copyright (c) 1993 Martin Birgmeier
2.\" All rights reserved.
3.\"
4.\" You may redistribute unmodified or modified versions of this source
5.\" code provided that the above copyright notice and this and the
6.\" following conditions are retained.
7.\"
8.\" This software is provided ``as is'', and comes with no warranties
9.\" of any kind. I shall in no event be liable for anything that happens
10.\" to anyone/anything when using this software.
11.\"
12.\" @(#)rand48.3 V1.0 MB 8 Oct 1993
|
13.\" $FreeBSD: head/lib/libc/gen/rand48.3 50476 1999-08-28 00:22:10Z peter $
| 13.\" $FreeBSD: head/lib/libc/gen/rand48.3 57686 2000-03-02 09:14:21Z sheldonh $
|
14.\"
15.Dd October 8, 1993
16.Dt RAND48 3
17.Os FreeBSD
18.Sh NAME
19.Nm drand48 ,
20.Nm erand48 ,
21.Nm lrand48 ,
22.Nm nrand48 ,
23.Nm mrand48 ,
24.Nm jrand48 ,
25.Nm srand48 ,
26.Nm seed48 ,
27.Nm lcong48
28.Nd pseudo random number generators and initialization routines
29.Sh SYNOPSIS
30.Fd #include <stdlib.h>
31.Ft double
32.Fn drand48 void
33.Ft double
34.Fn erand48 "unsigned short xseed[3]"
35.Ft long
36.Fn lrand48 void
37.Ft long
38.Fn nrand48 "unsigned short xseed[3]"
39.Ft long
40.Fn mrand48 void
41.Ft long
42.Fn jrand48 "unsigned short xseed[3]"
43.Ft void
44.Fn srand48 "long seed"
45.Ft "unsigned short *"
46.Fn seed48 "unsigned short xseed[3]"
47.Ft void
48.Fn lcong48 "unsigned short p[7]"
49.Sh DESCRIPTION
50The
51.Fn rand48
52family of functions generates pseudo-random numbers using a linear
| 14.\"
15.Dd October 8, 1993
16.Dt RAND48 3
17.Os FreeBSD
18.Sh NAME
19.Nm drand48 ,
20.Nm erand48 ,
21.Nm lrand48 ,
22.Nm nrand48 ,
23.Nm mrand48 ,
24.Nm jrand48 ,
25.Nm srand48 ,
26.Nm seed48 ,
27.Nm lcong48
28.Nd pseudo random number generators and initialization routines
29.Sh SYNOPSIS
30.Fd #include <stdlib.h>
31.Ft double
32.Fn drand48 void
33.Ft double
34.Fn erand48 "unsigned short xseed[3]"
35.Ft long
36.Fn lrand48 void
37.Ft long
38.Fn nrand48 "unsigned short xseed[3]"
39.Ft long
40.Fn mrand48 void
41.Ft long
42.Fn jrand48 "unsigned short xseed[3]"
43.Ft void
44.Fn srand48 "long seed"
45.Ft "unsigned short *"
46.Fn seed48 "unsigned short xseed[3]"
47.Ft void
48.Fn lcong48 "unsigned short p[7]"
49.Sh DESCRIPTION
50The
51.Fn rand48
52family of functions generates pseudo-random numbers using a linear
|
53congruential algorithm working on integers 48 bits in size. The
| 53congruential algorithm working on integers 48 bits in size.
54The
|
54particular formula employed is
55r(n+1) = (a * r(n) + c) mod m
56where the default values are
57for the multiplicand a = 0xfdeece66d = 25214903917 and
58the addend c = 0xb = 11. The modulo is always fixed at m = 2 ** 48.
59r(n) is called the seed of the random number generator.
60.Pp
61For all the six generator routines described next, the first
62computational step is to perform a single iteration of the algorithm.
63.Pp
64.Fn drand48
65and
66.Fn erand48
| 55particular formula employed is
56r(n+1) = (a * r(n) + c) mod m
57where the default values are
58for the multiplicand a = 0xfdeece66d = 25214903917 and
59the addend c = 0xb = 11. The modulo is always fixed at m = 2 ** 48.
60r(n) is called the seed of the random number generator.
61.Pp
62For all the six generator routines described next, the first
63computational step is to perform a single iteration of the algorithm.
64.Pp
65.Fn drand48
66and
67.Fn erand48
|
67return values of type double. The full 48 bits of r(n+1) are
| 68return values of type double.
69The full 48 bits of r(n+1) are
|
68loaded into the mantissa of the returned value, with the exponent set
69such that the values produced lie in the interval [0.0, 1.0).
70.Pp
71.Fn lrand48
72and
73.Fn nrand48
74return values of type long in the range
75[0, 2**31-1]. The high-order (31) bits of
76r(n+1) are loaded into the lower bits of the returned value, with
77the topmost (sign) bit set to zero.
78.Pp
79.Fn mrand48
80and
81.Fn jrand48
82return values of type long in the range
83[-2**31, 2**31-1]. The high-order (32) bits of
84r(n+1) are loaded into the returned value.
85.Pp
86.Fn drand48 ,
87.Fn lrand48 ,
88and
89.Fn mrand48
90use an internal buffer to store r(n). For these functions
91the initial value of r(0) = 0x1234abcd330e = 20017429951246.
92.Pp
93On the other hand,
94.Fn erand48 ,
95.Fn nrand48 ,
96and
97.Fn jrand48
98use a user-supplied buffer to store the seed r(n),
99which consists of an array of 3 shorts, where the zeroth member
100holds the least significant bits.
101.Pp
102All functions share the same multiplicand and addend.
103.Pp
104.Fn srand48
105is used to initialize the internal buffer r(n) of
106.Fn drand48 ,
107.Fn lrand48 ,
108and
109.Fn mrand48
110such that the 32 bits of the seed value are copied into the upper 32 bits
111of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e.
112Additionally, the constant multiplicand and addend of the algorithm are
113reset to the default values given above.
114.Pp
115.Fn seed48
116also initializes the internal buffer r(n) of
117.Fn drand48 ,
118.Fn lrand48 ,
119and
120.Fn mrand48 ,
121but here all 48 bits of the seed can be specified in an array of 3 shorts,
| 70loaded into the mantissa of the returned value, with the exponent set
71such that the values produced lie in the interval [0.0, 1.0).
72.Pp
73.Fn lrand48
74and
75.Fn nrand48
76return values of type long in the range
77[0, 2**31-1]. The high-order (31) bits of
78r(n+1) are loaded into the lower bits of the returned value, with
79the topmost (sign) bit set to zero.
80.Pp
81.Fn mrand48
82and
83.Fn jrand48
84return values of type long in the range
85[-2**31, 2**31-1]. The high-order (32) bits of
86r(n+1) are loaded into the returned value.
87.Pp
88.Fn drand48 ,
89.Fn lrand48 ,
90and
91.Fn mrand48
92use an internal buffer to store r(n). For these functions
93the initial value of r(0) = 0x1234abcd330e = 20017429951246.
94.Pp
95On the other hand,
96.Fn erand48 ,
97.Fn nrand48 ,
98and
99.Fn jrand48
100use a user-supplied buffer to store the seed r(n),
101which consists of an array of 3 shorts, where the zeroth member
102holds the least significant bits.
103.Pp
104All functions share the same multiplicand and addend.
105.Pp
106.Fn srand48
107is used to initialize the internal buffer r(n) of
108.Fn drand48 ,
109.Fn lrand48 ,
110and
111.Fn mrand48
112such that the 32 bits of the seed value are copied into the upper 32 bits
113of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e.
114Additionally, the constant multiplicand and addend of the algorithm are
115reset to the default values given above.
116.Pp
117.Fn seed48
118also initializes the internal buffer r(n) of
119.Fn drand48 ,
120.Fn lrand48 ,
121and
122.Fn mrand48 ,
123but here all 48 bits of the seed can be specified in an array of 3 shorts,
|
122where the zeroth member specifies the lowest bits. Again,
| 124where the zeroth member specifies the lowest bits.
125Again,
|
123the constant multiplicand and addend of the algorithm are
124reset to the default values given above.
125.Fn seed48
126returns a pointer to an array of 3 shorts which contains the old seed.
127This array is statically allocated, thus its contents are lost after
128each new call to
129.Fn seed48 .
130.Pp
131Finally,
132.Fn lcong48
133allows full control over the multiplicand and addend used in
134.Fn drand48 ,
135.Fn erand48 ,
136.Fn lrand48 ,
137.Fn nrand48 ,
138.Fn mrand48 ,
139and
140.Fn jrand48 ,
141and the seed used in
142.Fn drand48 ,
143.Fn lrand48 ,
144and
145.Fn mrand48 .
146An array of 7 shorts is passed as parameter; the first three shorts are
147used to initialize the seed; the second three are used to initialize the
148multiplicand; and the last short is used to initialize the addend.
149It is thus not possible to use values greater than 0xffff as the addend.
150.Pp
151Note that all three methods of seeding the random number generator
152always also set the multiplicand and addend for any of the six
153generator calls.
154.Pp
155For a more powerful random number generator, see
156.Xr random 3 .
157.Sh AUTHORS
158.An Martin Birgmeier
159.Sh SEE ALSO
160.Xr rand 3 ,
161.Xr random 3
| 126the constant multiplicand and addend of the algorithm are
127reset to the default values given above.
128.Fn seed48
129returns a pointer to an array of 3 shorts which contains the old seed.
130This array is statically allocated, thus its contents are lost after
131each new call to
132.Fn seed48 .
133.Pp
134Finally,
135.Fn lcong48
136allows full control over the multiplicand and addend used in
137.Fn drand48 ,
138.Fn erand48 ,
139.Fn lrand48 ,
140.Fn nrand48 ,
141.Fn mrand48 ,
142and
143.Fn jrand48 ,
144and the seed used in
145.Fn drand48 ,
146.Fn lrand48 ,
147and
148.Fn mrand48 .
149An array of 7 shorts is passed as parameter; the first three shorts are
150used to initialize the seed; the second three are used to initialize the
151multiplicand; and the last short is used to initialize the addend.
152It is thus not possible to use values greater than 0xffff as the addend.
153.Pp
154Note that all three methods of seeding the random number generator
155always also set the multiplicand and addend for any of the six
156generator calls.
157.Pp
158For a more powerful random number generator, see
159.Xr random 3 .
160.Sh AUTHORS
161.An Martin Birgmeier
162.Sh SEE ALSO
163.Xr rand 3 ,
164.Xr random 3
|