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.\" 14.Dd October 8, 1993 15.Dt RAND48 3 16.Os FreeBSD 17.Sh NAME 18.Nm drand48 , 19.Nm erand48 , 20.Nm lrand48 , 21.Nm nrand48 , 22.Nm mrand48 , 23.Nm jrand48 , 24.Nm srand48 , 25.Nm seed48 , 26.Nm lcong48 27.Nd pseudo random number generators and initialization routines 28.Sh SYNOPSIS 29.Fd #include <stdlib.h> 30.Ft double 31.Fn drand48 void 32.Ft double 33.Fn erand48 "unsigned short xseed[3]" 34.Ft long 35.Fn lrand48 void 36.Ft long 37.Fn nrand48 "unsigned short xseed[3]" 38.Ft long 39.Fn mrand48 void 40.Ft long 41.Fn jrand48 "unsigned short xseed[3]" 42.Ft void 43.Fn srand48 "long seed" 44.Ft "unsigned short *" 45.Fn seed48 "unsigned short xseed[3]" 46.Ft void 47.Fn lcong48 "unsigned short p[7]" 48.Sh DESCRIPTION 49The 50.Fn rand48 51family of functions generates pseudo-random numbers using a linear 52congruential algorithm working on integers 48 bits in size. The 53particular formula employed is 54r(n+1) = (a * r(n) + c) mod m 55where the default values are 56for the multiplicand a = 0xfdeece66d = 25214903917 and 57the addend c = 0xb = 11. The modulo is always fixed at m = 2 ** 48. 58r(n) is called the seed of the random number generator. 59.Pp 60For all the six generator routines described next, the first 61computational step is to perform a single iteration of the algorithm. 62.Pp 63.Fn drand48 64and 65.Fn erand48 66return values of type double. The full 48 bits of r(n+1) are 67loaded into the mantissa of the returned value, with the exponent set 68such that the values produced lie in the interval [0.0, 1.0). 69.Pp 70.Fn lrand48 71and 72.Fn nrand48 73return values of type long in the range 74[0, 2**31-1]. The high-order (31) bits of 75r(n+1) are loaded into the lower bits of the returned value, with 76the topmost (sign) bit set to zero. 77.Pp 78.Fn mrand48 79and 80.Fn jrand48 81return values of type long in the range 82[-2**31, 2**31-1]. The high-order (32) bits of 83r(n+1) are loaded into the returned value. 84.Pp 85.Fn drand48 , 86.Fn lrand48 , 87and 88.Fn mrand48 89use an internal buffer to store r(n). For these functions 90the initial value of r(0) = 0x1234abcd330e = 20017429951246. 91.Pp 92On the other hand, 93.Fn erand48 , 94.Fn nrand48 , 95and 96.Fn jrand48 97use a user-supplied buffer to store the seed r(n), 98which consists of an array of 3 shorts, where the zeroth member 99holds the least significant bits. 100.Pp 101All functions share the same multiplicand and addend. 102.Pp 103.Fn srand48 104is used to initialize the internal buffer r(n) of 105.Fn drand48 , 106.Fn lrand48 , 107and 108.Fn mrand48 109such that the 32 bits of the seed value are copied into the upper 32 bits 110of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e. 111Additionally, the constant multiplicand and addend of the algorithm are 112reset to the default values given above. 113.Pp 114.Fn seed48 115also initializes the internal buffer r(n) of 116.Fn drand48 , 117.Fn lrand48 , 118and 119.Fn mrand48 , 120but here all 48 bits of the seed can be specified in an array of 3 shorts, 121where the zeroth member specifies the lowest bits. Again, 122the constant multiplicand and addend of the algorithm are 123reset to the default values given above. 124.Fn seed48 125returns a pointer to an array of 3 shorts which contains the old seed. 126This array is statically allocated, thus its contents are lost after 127each new call to 128.Fn seed48 . 129.Pp 130Finally, 131.Fn lcong48 132allows full control over the multiplicand and addend used in 133.Fn drand48 , 134.Fn erand48 , 135.Fn lrand48 , 136.Fn nrand48 , 137.Fn mrand48 , 138and 139.Fn jrand48 , 140and the seed used in 141.Fn drand48 , 142.Fn lrand48 , 143and 144.Fn mrand48 . 145An array of 7 shorts is passed as parameter; the first three shorts are 146used to initialize the seed; the second three are used to initialize the 147multiplicand; and the last short is used to initialize the addend. 148It is thus not possible to use values greater than 0xffff as the addend. 149.Pp 150Note that all three methods of seeding the random number generator 151always also set the multiplicand and addend for any of the six 152generator calls. 153.Pp 154For a more powerful random number generator, see 155.Xr random 3 156.Sh AUTHOR 157Martin Birgmeier 158.Sh SEE ALSO 159.Xr rand 3 , 160.Xr random 3 . 161