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.\" $DragonFly: src/lib/libc/gen/rand48.3,v 1.4 2008/04/20 19:21:42 swildner Exp $ 15.\" 16.Dd October 8, 1993 17.Dt RAND48 3 18.Os 19.Sh NAME 20.Nm drand48 , 21.Nm erand48 , 22.Nm lrand48 , 23.Nm nrand48 , 24.Nm mrand48 , 25.Nm jrand48 , 26.Nm srand48 , 27.Nm seed48 , 28.Nm lcong48 29.Nd pseudo random number generators and initialization routines 30.Sh LIBRARY 31.Lb libc 32.Sh SYNOPSIS 33.In stdlib.h 34.Ft double 35.Fn drand48 void 36.Ft double 37.Fn erand48 "unsigned short xseed[3]" 38.Ft long 39.Fn lrand48 void 40.Ft long 41.Fn nrand48 "unsigned short xseed[3]" 42.Ft long 43.Fn mrand48 void 44.Ft long 45.Fn jrand48 "unsigned short xseed[3]" 46.Ft void 47.Fn srand48 "long seed" 48.Ft "unsigned short *" 49.Fn seed48 "unsigned short xseed[3]" 50.Ft void 51.Fn lcong48 "unsigned short p[7]" 52.Sh DESCRIPTION 53The 54.Nm rand48 55family of functions generates pseudo-random numbers using a linear 56congruential algorithm working on integers 48 bits in size. 57The 58particular formula employed is 59r(n+1) = (a * r(n) + c) mod m 60where the default values are 61for the multiplicand a = 0xfdeece66d = 25214903917 and 62the addend c = 0xb = 11. 63The modulo is always fixed at m = 2 ** 48. 64r(n) is called the seed of the random number generator. 65.Pp 66For all the six generator routines described next, the first 67computational step is to perform a single iteration of the algorithm. 68.Pp 69The 70.Fn drand48 71and 72.Fn erand48 73functions 74return values of type double. 75The full 48 bits of r(n+1) are 76loaded into the mantissa of the returned value, with the exponent set 77such that the values produced lie in the interval [0.0, 1.0). 78.Pp 79The 80.Fn lrand48 81and 82.Fn nrand48 83functions 84return values of type long in the range 85[0, 2**31-1]. The 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]. The high-order (32) bits of 96r(n+1) are loaded into the returned value. 97.Pp 98The 99.Fn drand48 , 100.Fn lrand48 , 101and 102.Fn mrand48 103functions 104use an internal buffer to store r(n). For these functions 105the initial value of r(0) = 0x1234abcd330e = 20017429951246. 106.Pp 107On the other hand, 108.Fn erand48 , 109.Fn nrand48 , 110and 111.Fn jrand48 112use a user-supplied buffer to store the seed r(n), 113which consists of an array of 3 shorts, where the zeroth member 114holds the least significant bits. 115.Pp 116All functions share the same multiplicand and addend. 117.Pp 118The 119.Fn srand48 120function 121is used to initialize the internal buffer r(n) of 122.Fn drand48 , 123.Fn lrand48 , 124and 125.Fn mrand48 126such that the 32 bits of the seed value are copied into the upper 32 bits 127of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e. 128Additionally, the constant multiplicand and addend of the algorithm are 129reset to the default values given above. 130.Pp 131The 132.Fn seed48 133function 134also initializes the internal buffer r(n) of 135.Fn drand48 , 136.Fn lrand48 , 137and 138.Fn mrand48 , 139but here all 48 bits of the seed can be specified in an array of 3 shorts, 140where the zeroth member specifies the lowest bits. 141Again, 142the constant multiplicand and addend of the algorithm are 143reset to the default values given above. 144The 145.Fn seed48 146function 147returns a pointer to an array of 3 shorts which contains the old seed. 148This array is statically allocated, thus its contents are lost after 149each new call to 150.Fn seed48 . 151.Pp 152Finally, 153.Fn lcong48 154allows full control over the multiplicand and addend used in 155.Fn drand48 , 156.Fn erand48 , 157.Fn lrand48 , 158.Fn nrand48 , 159.Fn mrand48 , 160and 161.Fn jrand48 , 162and the seed used in 163.Fn drand48 , 164.Fn lrand48 , 165and 166.Fn mrand48 . 167An array of 7 shorts is passed as argument; the first three shorts are 168used to initialize the seed; the second three are used to initialize the 169multiplicand; and the last short is used to initialize the addend. 170It is thus not possible to use values greater than 0xffff as the addend. 171.Pp 172Note that all three methods of seeding the random number generator 173always also set the multiplicand and addend for any of the six 174generator calls. 175.Pp 176For a more powerful random number generator, see 177.Xr random 3 . 178.Sh SEE ALSO 179.Xr rand 3 , 180.Xr random 3 181.Sh AUTHORS 182.An Martin Birgmeier 183