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 $
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
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
67return values of type double. The 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,
122where the zeroth member specifies the lowest bits. Again,
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
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 $
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
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
67return values of type double. The 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,
122where the zeroth member specifies the lowest bits. Again,
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