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1.1 ! root 1: .TH DRAND48 3L "630 MTG" ! 2: .SH NAME ! 3: drand48, erand48, lrand48, nrand48, mrand48, jrand48, srand48, seed48, lcong48 \- generate uniformly distributed pseudo-random numbers ! 4: .SH SYNOPSIS ! 5: .EQ ! 6: delim $$ ! 7: .EN ! 8: .B double drand48 ( ) ! 9: .sp ! 10: \f3double erand48 ( xsubi )\f1 ! 11: .br ! 12: \f3unsigned short xsubi [3];\f1 ! 13: .sp ! 14: .B long lrand48 ( ) ! 15: .sp ! 16: \f3long nrand48 ( xsubi )\f1 ! 17: .br ! 18: \f3unsigned short xsubi [3];\f1 ! 19: .sp ! 20: .B long mrand48 ( ) ! 21: .sp ! 22: \f3long jrand48 ( xsubi )\f1 ! 23: .br ! 24: \f3unsigned short xsubi [3];\f1 ! 25: .sp ! 26: .B void srand48 (seedval) ! 27: .br ! 28: .B long seedval; ! 29: .sp ! 30: .B unsigned short \(**seed48 (seed16v) ! 31: .br ! 32: .B unsigned short seed16v[3]; ! 33: .sp ! 34: .B void lcong48 (param) ! 35: .br ! 36: .B unsigned short param[7]; ! 37: .SH DESCRIPTION ! 38: .EQ ! 39: delim $$ ! 40: .EN ! 41: This family of functions generates pseudo-random numbers using the ! 42: well-known linear congruential algorithm and 48-bit integer arithmetic. ! 43: .PP ! 44: Functions ! 45: .I drand48\^ ! 46: and ! 47: .I erand48\^ ! 48: return non-negative double-precision floating-point values ! 49: uniformly distributed over the interval $[0.0,~1.0).$ ! 50: .PP ! 51: Functions ! 52: .I lrand48\^ ! 53: and ! 54: .I nrand48\^ ! 55: return non-negative long integers uniformly distributed over the ! 56: interval $[0,~2 sup 31 ).$ ! 57: .PP ! 58: Functions ! 59: .I mrand48\^ ! 60: and ! 61: .I jrand48\^ ! 62: return signed long integers uniformly distributed over the interval ! 63: $[-2 sup 31 ,~2 sup 31 ).$ ! 64: .PP ! 65: Functions ! 66: .I srand48, seed48\^ ! 67: and ! 68: .I lcong48\^ ! 69: are initialization entry points, one of which should be invoked before ! 70: either ! 71: .I drand48, lrand48\^ ! 72: or ! 73: .I mrand48\^ ! 74: is called. ! 75: (Although it is not recommended practice, ! 76: constant default initializer values will be supplied automatically if ! 77: .I drand48, lrand48\^ ! 78: or ! 79: .I mrand48\^ ! 80: is called without a prior call to an initialization entry point.) ! 81: Functions ! 82: .I erand48, nrand48\^ ! 83: and ! 84: .I jrand48\^ ! 85: do not require an initialization entry point to be called first. ! 86: .PP ! 87: All the routines work by generating a sequence of 48-bit integer values, ! 88: $X sub i ,$ according to the linear congruential formula ! 89: .PP ! 90: .ce ! 91: .EQ I ! 92: X sub{n+1}~=~(aX sub n^+^c) sub{roman mod~m}~~~~~~~~n>=0. ! 93: .EN ! 94: .PP ! 95: The parameter $m^=^2 sup 48$; hence 48-bit integer arithmetic is ! 96: performed. ! 97: Unless ! 98: .I lcong48\^ ! 99: has been invoked, the multiplier value $a$ and the addend value $c$ ! 100: are given by ! 101: .PP ! 102: .RS 6 ! 103: .EQ I ! 104: a~mark =~roman 5DEECE66D^sub 16~=~roman 273673163155^sub 8 ! 105: .EN ! 106: .br ! 107: .EQ I ! 108: c~lineup =~roman B^sub 16~=~roman 13^sub 8 . ! 109: .EN ! 110: .RE ! 111: .PP ! 112: The value returned by any of the functions ! 113: .I drand48, erand48, lrand48, nrand48, mrand48\^ ! 114: or ! 115: .I jrand48\^ ! 116: is computed by first generating the next 48-bit $X sub i$ in the sequence. ! 117: Then the appropriate number of bits, according to the type of data item ! 118: to be returned, are copied from the high-order (leftmost) bits of $X sub i$ ! 119: and transformed into the returned value. ! 120: .PP ! 121: The functions ! 122: .I drand48, lrand48\^ ! 123: and ! 124: .I mrand48\^ ! 125: store the last 48-bit $X sub i$ generated in an internal buffer, ! 126: and must be initialized prior to being invoked. ! 127: The functions ! 128: .I erand48, nrand48\^ ! 129: and ! 130: .I jrand48\^ ! 131: require the calling program to provide storage for the ! 132: successive $X sub i$ values in the array ! 133: specified as an argument when the functions are invoked. ! 134: These routines do not have to be initialized; the calling ! 135: program must place the desired initial value of $X sub i$ into the ! 136: array and pass it as an argument. ! 137: By using different ! 138: arguments, functions ! 139: .I erand48, nrand48\^ ! 140: and ! 141: .I jrand48\^ ! 142: allow separate modules of a large program to generate several ! 143: .I independent\^ ! 144: streams of pseudo-random numbers, i.e., the sequence of numbers ! 145: in each stream will ! 146: .I not\^ ! 147: depend upon how many times the routines have been called to generate ! 148: numbers for the other streams. ! 149: .PP ! 150: The initializer function ! 151: .I srand48\^ ! 152: sets the high-order 32 bits of $X sub i$ to the 32 bits contained in ! 153: its argument. ! 154: The low-order 16 bits of $X sub i$ are set to the arbitrary value ! 155: $roman 330E sub 16 .$ ! 156: .PP ! 157: The initializer function ! 158: .I seed48\^ ! 159: sets the value of $X sub i$ to the 48-bit value specified in the ! 160: argument array. ! 161: In addition, the previous value of $X sub i$ is copied into a 48-bit ! 162: internal buffer, used only by ! 163: .I seed48,\^ ! 164: and a pointer to this buffer is the value returned by ! 165: .I seed48.\^ ! 166: This returned pointer, which can just be ignored if not needed, is useful ! 167: if a program is to be restarted from a given point at some future time ! 168: \(em use the pointer to get at and store the last $X sub i$ value, and ! 169: then use this value to reinitialize via ! 170: .I seed48\^ ! 171: when the program is restarted. ! 172: .PP ! 173: The initialization function ! 174: .I lcong48\^ ! 175: allows the user to specify the initial $X sub i ,$ the multiplier value ! 176: $a,$ and the addend value $c.$ ! 177: Argument array elements ! 178: .I param[0-2]\^ ! 179: specify $X sub i ,$ ! 180: .I param[3-5]\^ ! 181: specify the multiplier $a,$ and ! 182: .I param[6]\^ ! 183: specifies the 16-bit addend $c.$ ! 184: After ! 185: .I lcong48\^ ! 186: has been called, a subsequent call to either ! 187: .I srand48\^ ! 188: or ! 189: .I seed48\^ ! 190: will restore the ``standard'' multiplier and addend values, $a$ and $c,$ ! 191: specified on the previous page. ! 192: .SH "SEE ALSO" ! 193: rand(3L). ! 194: .Ee
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