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: src/lib/libc/gen/rand48.3,v 1.8.2.6 2003/03/15 15:11:05 trhodes Exp $ 14.\" 15.Dd October 8, 1993 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 = 0xfdeece66d = 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]. The high-order (31) bits of 85r(n+1) are loaded into the lower bits of the returned value, with 86the topmost (sign) bit set to zero. 87.Pp 88The 89.Fn mrand48 90and 91.Fn jrand48 92functions 93return values of type long in the range 94[-2**31, 2**31-1]. The high-order (32) bits of 95r(n+1) are loaded into the returned value. 96.Pp 97The 98.Fn drand48 , 99.Fn lrand48 , 100and 101.Fn mrand48 102functions 103use an internal buffer to store r(n). For these functions 104the initial value of r(0) = 0x1234abcd330e = 20017429951246. 105.Pp 106On the other hand, 107.Fn erand48 , 108.Fn nrand48 , 109and 110.Fn jrand48 111use a user-supplied buffer to store the seed r(n), 112which consists of an array of 3 shorts, where the zeroth member 113holds the least significant bits. 114.Pp 115All functions share the same multiplicand and addend. 116.Pp 117The 118.Fn srand48 119function 120is used to initialize the internal buffer r(n) of 121.Fn drand48 , 122.Fn lrand48 , 123and 124.Fn mrand48 125such that the 32 bits of the seed value are copied into the upper 32 bits 126of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e. 127Additionally, the constant multiplicand and addend of the algorithm are 128reset to the default values given above. 129.Pp 130The 131.Fn seed48 132function 133also initializes the internal buffer r(n) of 134.Fn drand48 , 135.Fn lrand48 , 136and 137.Fn mrand48 , 138but here all 48 bits of the seed can be specified in an array of 3 shorts, 139where the zeroth member specifies the lowest bits. 140Again, 141the constant multiplicand and addend of the algorithm are 142reset to the default values given above. 143The 144.Fn seed48 145function 146returns a pointer to an array of 3 shorts which contains the old seed. 147This array is statically allocated, thus its contents are lost after 148each new call to 149.Fn seed48 . 150.Pp 151Finally, 152.Fn lcong48 153allows full control over the multiplicand and addend used in 154.Fn drand48 , 155.Fn erand48 , 156.Fn lrand48 , 157.Fn nrand48 , 158.Fn mrand48 , 159and 160.Fn jrand48 , 161and the seed used in 162.Fn drand48 , 163.Fn lrand48 , 164and 165.Fn mrand48 . 166An array of 7 shorts is passed as argument; the first three shorts are 167used to initialize the seed; the second three are used to initialize the 168multiplicand; and the last short is used to initialize the addend. 169It is thus not possible to use values greater than 0xffff as the addend. 170.Pp 171Note that all three methods of seeding the random number generator 172always also set the multiplicand and addend for any of the six 173generator calls. 174.Pp 175For a more powerful random number generator, see 176.Xr random 3 . 177.Sh AUTHORS 178.An Martin Birgmeier 179.Sh SEE ALSO 180.Xr rand 3 , 181.Xr random 3 182