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 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 68.Fn drand48 69and 70.Fn erand48 71return values of type double. 72The full 48 bits of r(n+1) are 73loaded into the mantissa of the returned value, with the exponent set 74such that the values produced lie in the interval [0.0, 1.0). 75.Pp 76.Fn lrand48 77and 78.Fn nrand48 79return values of type long in the range 80[0, 2**31-1]. The high-order (31) bits of 81r(n+1) are loaded into the lower bits of the returned value, with 82the topmost (sign) bit set to zero. 83.Pp 84.Fn mrand48 85and 86.Fn jrand48 87return values of type long in the range 88[-2**31, 2**31-1]. The high-order (32) bits of 89r(n+1) are loaded into the returned value. 90.Pp 91.Fn drand48 , 92.Fn lrand48 , 93and 94.Fn mrand48 95use an internal buffer to store r(n). For these functions 96the initial value of r(0) = 0x1234abcd330e = 20017429951246. 97.Pp 98On the other hand, 99.Fn erand48 , 100.Fn nrand48 , 101and 102.Fn jrand48 103use a user-supplied buffer to store the seed r(n), 104which consists of an array of 3 shorts, where the zeroth member 105holds the least significant bits. 106.Pp 107All functions share the same multiplicand and addend. 108.Pp 109.Fn srand48 110is used to initialize the internal buffer r(n) of 111.Fn drand48 , 112.Fn lrand48 , 113and 114.Fn mrand48 115such that the 32 bits of the seed value are copied into the upper 32 bits 116of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e. 117Additionally, the constant multiplicand and addend of the algorithm are 118reset to the default values given above. 119.Pp 120.Fn seed48 121also initializes the internal buffer r(n) of 122.Fn drand48 , 123.Fn lrand48 , 124and 125.Fn mrand48 , 126but here all 48 bits of the seed can be specified in an array of 3 shorts, 127where the zeroth member specifies the lowest bits. 128Again, 129the constant multiplicand and addend of the algorithm are 130reset to the default values given above. 131.Fn seed48 132returns a pointer to an array of 3 shorts which contains the old seed. 133This array is statically allocated, thus its contents are lost after 134each new call to 135.Fn seed48 . 136.Pp 137Finally, 138.Fn lcong48 139allows full control over the multiplicand and addend used in 140.Fn drand48 , 141.Fn erand48 , 142.Fn lrand48 , 143.Fn nrand48 , 144.Fn mrand48 , 145and 146.Fn jrand48 , 147and the seed used in 148.Fn drand48 , 149.Fn lrand48 , 150and 151.Fn mrand48 . 152An array of 7 shorts is passed as parameter; the first three shorts are 153used to initialize the seed; the second three are used to initialize the 154multiplicand; and the last short is used to initialize the addend. 155It is thus not possible to use values greater than 0xffff as the addend. 156.Pp 157Note that all three methods of seeding the random number generator 158always also set the multiplicand and addend for any of the six 159generator calls. 160.Pp 161For a more powerful random number generator, see 162.Xr random 3 . 163.Sh AUTHORS 164.An Martin Birgmeier 165.Sh SEE ALSO 166.Xr rand 3 , 167.Xr random 3 168