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.\" $FreeBSD$ 14.\" 15.Dd February 2, 2010 16.Dt RAND48 3 17.Os 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 LIBRARY 30.Lb libc 31.Sh SYNOPSIS 32.In stdlib.h 33.Ft double 34.Fn drand48 void 35.Ft double 36.Fn erand48 "unsigned short xseed[3]" 37.Ft long 38.Fn lrand48 void 39.Ft long 40.Fn nrand48 "unsigned short xseed[3]" 41.Ft long 42.Fn mrand48 void 43.Ft long 44.Fn jrand48 "unsigned short xseed[3]" 45.Ft void 46.Fn srand48 "long seed" 47.Ft "unsigned short *" 48.Fn seed48 "unsigned short xseed[3]" 49.Ft void 50.Fn lcong48 "unsigned short p[7]" 51.Sh DESCRIPTION 52The 53.Fn rand48 54family of functions generates pseudo-random numbers using a linear 55congruential algorithm working on integers 48 bits in size. 56The 57particular formula employed is 58r(n+1) = (a * r(n) + c) mod m 59where the default values are 60for the multiplicand a = 0x5deece66d = 25214903917 and 61the addend c = 0xb = 11. 62The modulo is always fixed at m = 2 ** 48. 63r(n) is called the seed of the random number generator. 64.Pp 65For all the six generator routines described next, the first 66computational step is to perform a single iteration of the algorithm. 67.Pp 68The 69.Fn drand48 70and 71.Fn erand48 72functions 73return values of type double. 74The full 48 bits of r(n+1) are 75loaded into the mantissa of the returned value, with the exponent set 76such that the values produced lie in the interval [0.0, 1.0). 77.Pp 78The 79.Fn lrand48 80and 81.Fn nrand48 82functions 83return values of type long in the range 84[0, 2**31-1]. 85The high-order (31) bits of 86r(n+1) are loaded into the lower bits of the returned value, with 87the topmost (sign) bit set to zero. 88.Pp 89The 90.Fn mrand48 91and 92.Fn jrand48 93functions 94return values of type long in the range 95[-2**31, 2**31-1]. 96The high-order (32) bits of 97r(n+1) are loaded into the returned value. 98.Pp 99The 100.Fn drand48 , 101.Fn lrand48 , 102and 103.Fn mrand48 104functions 105use an internal buffer to store r(n). 106For these functions 107the initial value of r(0) = 0x1234abcd330e = 20017429951246. 108.Pp 109On the other hand, 110.Fn erand48 , 111.Fn nrand48 , 112and 113.Fn jrand48 114use a user-supplied buffer to store the seed r(n), 115which consists of an array of 3 shorts, where the zeroth member 116holds the least significant bits. 117.Pp 118All functions share the same multiplicand and addend. 119.Pp 120The 121.Fn srand48 122function 123is used to initialize the internal buffer r(n) of 124.Fn drand48 , 125.Fn lrand48 , 126and 127.Fn mrand48 128such that the 32 bits of the seed value are copied into the upper 32 bits 129of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e. 130Additionally, the constant multiplicand and addend of the algorithm are 131reset to the default values given above. 132.Pp 133The 134.Fn seed48 135function 136also initializes the internal buffer r(n) of 137.Fn drand48 , 138.Fn lrand48 , 139and 140.Fn mrand48 , 141but here all 48 bits of the seed can be specified in an array of 3 shorts, 142where the zeroth member specifies the lowest bits. 143Again, 144the constant multiplicand and addend of the algorithm are 145reset to the default values given above. 146The 147.Fn seed48 148function 149returns a pointer to an array of 3 shorts which contains the old seed. 150This array is statically allocated, thus its contents are lost after 151each new call to 152.Fn seed48 . 153.Pp 154Finally, 155.Fn lcong48 156allows full control over the multiplicand and addend used in 157.Fn drand48 , 158.Fn erand48 , 159.Fn lrand48 , 160.Fn nrand48 , 161.Fn mrand48 , 162and 163.Fn jrand48 , 164and the seed used in 165.Fn drand48 , 166.Fn lrand48 , 167and 168.Fn mrand48 . 169An array of 7 shorts is passed as argument; the first three shorts are 170used to initialize the seed; the second three are used to initialize the 171multiplicand; and the last short is used to initialize the addend. 172It is thus not possible to use values greater than 0xffff as the addend. 173.Pp 174Note that all three methods of seeding the random number generator 175always also set the multiplicand and addend for any of the six 176generator calls. 177.Pp 178For a more powerful random number generator, see 179.Xr random 3 . 180.Sh SEE ALSO 181.Xr rand 3 , 182.Xr random 3 183.Sh AUTHORS 184.An Martin Birgmeier 185