1.\" $NetBSD: rand48.3,v 1.4 1998/02/05 18:50:15 perry Exp $ 2.\" 3.\" Copyright (c) 1993 Martin Birgmeier 4.\" All rights reserved. 5.\" 6.\" You may redistribute unmodified or modified versions of this source 7.\" code provided that the above copyright notice and this and the 8.\" following conditions are retained. 9.\" 10.\" This software is provided ``as is'', and comes with no warranties 11.\" of any kind. I shall in no event be liable for anything that happens 12.\" to anyone/anything when using this software. 13.\" 14.Dd October 8, 1993 15.Dt RAND48 3 16.Os 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 LIBRARY 29.Lb libc 30.Sh SYNOPSIS 31.Fd #include <stdlib.h> 32.Ft double 33.Fn drand48 void 34.Ft double 35.Fn erand48 "unsigned short xseed[3]" 36.Ft long 37.Fn lrand48 void 38.Ft long 39.Fn nrand48 "unsigned short xseed[3]" 40.Ft long 41.Fn mrand48 void 42.Ft long 43.Fn jrand48 "unsigned short xseed[3]" 44.Ft void 45.Fn srand48 "long seed" 46.Ft "unsigned short *" 47.Fn seed48 "unsigned short xseed[3]" 48.Ft void 49.Fn lcong48 "unsigned short p[7]" 50.Sh DESCRIPTION 51The 52.Fn rand48 53family of functions generates pseudo-random numbers using a linear 54congruential algorithm working on integers 48 bits in size. The 55particular formula employed is 56r(n+1) = (a * r(n) + c) mod m 57where the default values are 58for the multiplicand a = 0xfdeece66d = 25214903917 and 59the addend c = 0xb = 11. The modulus is always fixed at m = 2 ** 48. 60r(n) is called the seed of the random number generator. 61.Pp 62For all the six generator routines described next, the first 63computational step is to perform a single iteration of the algorithm. 64.Pp 65.Fn drand48 66and 67.Fn erand48 68return values of type double. The full 48 bits of r(n+1) are 69loaded into the mantissa of the returned value, with the exponent set 70such that the values produced lie in the interval [0.0, 1.0). 71.Pp 72.Fn lrand48 73and 74.Fn nrand48 75return values of type long in the range 76[0, 2**31-1]. The high-order (31) bits of 77r(n+1) are loaded into the lower bits of the returned value, with 78the topmost (sign) bit set to zero. 79.Pp 80.Fn mrand48 81and 82.Fn jrand48 83return values of type long in the range 84[-2**31, 2**31-1]. The high-order (32) bits of 85r(n+1) are loaded into the returned value. 86.Pp 87.Fn drand48 , 88.Fn lrand48 , 89and 90.Fn mrand48 91use an internal buffer to store r(n). For these functions 92the initial value of r(0) = 0x1234abcd330e = 20017429951246. 93.Pp 94On the other hand, 95.Fn erand48 , 96.Fn nrand48 , 97and 98.Fn jrand48 99use a user-supplied buffer to store the seed r(n), 100which consists of an array of 3 shorts, where the zeroth member 101holds the least significant bits. 102.Pp 103All functions share the same multiplicand and addend. 104.Pp 105.Fn srand48 106is used to initialize the internal buffer r(n) of 107.Fn drand48 , 108.Fn lrand48 , 109and 110.Fn mrand48 111such that the 32 bits of the seed value are copied into the upper 32 bits 112of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e. 113Additionally, the constant multiplicand and addend of the algorithm are 114reset to the default values given above. 115.Pp 116.Fn seed48 117also initializes the internal buffer r(n) of 118.Fn drand48 , 119.Fn lrand48 , 120and 121.Fn mrand48 , 122but here all 48 bits of the seed can be specified in an array of 3 shorts, 123where the zeroth member specifies the lowest bits. Again, 124the constant multiplicand and addend of the algorithm are 125reset to the default values given above. 126.Fn seed48 127returns a pointer to an array of 3 shorts which contains the old seed. 128This array is statically allocated, thus its contents are lost after 129each new call to 130.Fn seed48 . 131.Pp 132Finally, 133.Fn lcong48 134allows full control over the multiplicand and addend used in 135.Fn drand48 , 136.Fn erand48 , 137.Fn lrand48 , 138.Fn nrand48 , 139.Fn mrand48 , 140and 141.Fn jrand48 , 142and the seed used in 143.Fn drand48 , 144.Fn lrand48 , 145and 146.Fn mrand48 . 147An array of 7 shorts is passed as parameter; the first three shorts are 148used to initialize the seed; the second three are used to initialize the 149multiplicand; and the last short is used to initialize the addend. 150It is thus not possible to use values greater than 0xffff as the addend. 151.Pp 152Note that all three methods of seeding the random number generator 153always also set the multiplicand and addend for any of the six 154generator calls. 155.Pp 156For a more powerful random number generator, see 157.Xr random 3 158.Sh AUTHOR 159Martin Birgmeier 160.Sh SEE ALSO 161.Xr rand 3 , 162.Xr random 3 . 163