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  1. /*
  2.  * Copyright (c) 1993 Martin Birgmeier
  3.  * All rights reserved.
  4.  *
  5.  * You may redistribute unmodified or modified versions of this source
  6.  * code provided that the above copyright notice and this and the
  7.  * following conditions are retained.
  8.  *
  9.  * This software is provided ``as is'', and comes with no warranties
  10.  * of any kind. I shall in no event be liable for anything that happens
  11.  * to anyone/anything when using this software.
  12.  */
  13.  
  14. /*
  15. FUNCTION
  16.    <<rand48>>, <<drand48>>, <<erand48>>, <<lrand48>>, <<nrand48>>, <<mrand48>>, <<jrand48>>, <<srand48>>, <<seed48>>, <<lcong48>>---pseudo-random number generators and initialization routines
  17.  
  18. INDEX
  19.        rand48
  20. INDEX
  21.        drand48
  22. INDEX
  23.        erand48
  24. INDEX
  25.        lrand48
  26. INDEX
  27.        nrand48
  28. INDEX
  29.        mrand48
  30. INDEX
  31.        jrand48
  32. INDEX
  33.        srand48
  34. INDEX
  35.        seed48
  36. INDEX
  37.        lcong48
  38.  
  39. ANSI_SYNOPSIS
  40.        #include <stdlib.h>
  41.        double drand48(void);
  42.        double erand48(unsigned short <[xseed]>[3]);
  43.        long lrand48(void);
  44.        long nrand48(unsigned short <[xseed]>[3]);
  45.        long mrand48(void);
  46.        long jrand48(unsigned short <[xseed]>[3]);
  47.        void srand48(long <[seed]>);
  48.        unsigned short *seed48(unsigned short <[xseed]>[3]);
  49.        void lcong48(unsigned short <[p]>[7]);
  50.  
  51. TRAD_SYNOPSIS
  52.        #include <stdlib.h>
  53.        double drand48();
  54.  
  55.        double erand48(<[xseed]>)
  56.        unsigned short <[xseed]>[3];
  57.  
  58.        long lrand48();
  59.  
  60.        long nrand48(<[xseed]>)
  61.        unsigned short <[xseed]>[3];
  62.  
  63.        long mrand48();
  64.  
  65.        long jrand48(<[xseed]>)
  66.        unsigned short <[xseed]>[3];
  67.  
  68.        void srand48(<[seed]>)
  69.        long <[seed]>;
  70.  
  71.        unsigned short *seed48(<[xseed]>)
  72.        unsigned short <[xseed]>[3];
  73.  
  74.        void lcong48(<[p]>)
  75.        unsigned short <[p]>[7];
  76.  
  77. DESCRIPTION
  78. The <<rand48>> family of functions generates pseudo-random numbers
  79. using a linear congruential algorithm working on integers 48 bits in size.
  80. The particular formula employed is
  81. r(n+1) = (a * r(n) + c) mod m
  82. where the default values are
  83. for the multiplicand a = 0xfdeece66d = 25214903917 and
  84. the addend c = 0xb = 11. The modulo is always fixed at m = 2 ** 48.
  85. r(n) is called the seed of the random number generator.
  86.  
  87. For all the six generator routines described next, the first
  88. computational step is to perform a single iteration of the algorithm.
  89.  
  90. <<drand48>> and <<erand48>>
  91. return values of type double. The full 48 bits of r(n+1) are
  92. loaded into the mantissa of the returned value, with the exponent set
  93. such that the values produced lie in the interval [0.0, 1.0].
  94.  
  95. <<lrand48>> and <<nrand48>>
  96. return values of type long in the range
  97. [0, 2**31-1]. The high-order (31) bits of
  98. r(n+1) are loaded into the lower bits of the returned value, with
  99. the topmost (sign) bit set to zero.
  100.  
  101. <<mrand48>> and <<jrand48>>
  102. return values of type long in the range
  103. [-2**31, 2**31-1]. The high-order (32) bits of
  104. r(n+1) are loaded into the returned value.
  105.  
  106. <<drand48>>, <<lrand48>>, and <<mrand48>>
  107. use an internal buffer to store r(n). For these functions
  108. the initial value of r(0) = 0x1234abcd330e = 20017429951246.
  109.  
  110. On the other hand, <<erand48>>, <<nrand48>>, and <<jrand48>>
  111. use a user-supplied buffer to store the seed r(n),
  112. which consists of an array of 3 shorts, where the zeroth member
  113. holds the least significant bits.
  114.  
  115. All functions share the same multiplicand and addend.
  116.  
  117. <<srand48>> is used to initialize the internal buffer r(n) of
  118. <<drand48>>, <<lrand48>>, and <<mrand48>>
  119. such that the 32 bits of the seed value are copied into the upper 32 bits
  120. of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e.
  121. Additionally, the constant multiplicand and addend of the algorithm are
  122. reset to the default values given above.
  123.  
  124. <<seed48>> also initializes the internal buffer r(n) of
  125. <<drand48>>, <<lrand48>>, and <<mrand48>>,
  126. but here all 48 bits of the seed can be specified in an array of 3 shorts,
  127. where the zeroth member specifies the lowest bits. Again,
  128. the constant multiplicand and addend of the algorithm are
  129. reset to the default values given above.
  130. <<seed48>> returns a pointer to an array of 3 shorts which contains
  131. the old seed.
  132. This array is statically allocated, thus its contents are lost after
  133. each new call to <<seed48>>.
  134.  
  135. Finally, <<lcong48>> allows full control over the multiplicand and
  136. addend used in <<drand48>>, <<erand48>>, <<lrand48>>, <<nrand48>>,
  137. <<mrand48>>, and <<jrand48>>,
  138. and the seed used in <<drand48>>, <<lrand48>>, and <<mrand48>>.
  139. An array of 7 shorts is passed as parameter; the first three shorts are
  140. used to initialize the seed; the second three are used to initialize the
  141. multiplicand; and the last short is used to initialize the addend.
  142. It is thus not possible to use values greater than 0xffff as the addend.
  143.  
  144. Note that all three methods of seeding the random number generator
  145. always also set the multiplicand and addend for any of the six
  146. generator calls.
  147.  
  148. For a more powerful random number generator, see <<random>>.
  149.  
  150. PORTABILITY
  151. SUS requires these functions.
  152.  
  153. No supporting OS subroutines are required.
  154. */
  155.  
  156. #include "rand48.h"
  157.  
  158. void
  159. _DEFUN (__dorand48, (r, xseed),
  160.        struct _reent *r _AND
  161.        unsigned short xseed[3])
  162. {
  163.   unsigned long accu;
  164.   unsigned short temp[2];
  165.  
  166.   _REENT_CHECK_RAND48(r);
  167.   accu = (unsigned long) __rand48_mult[0] * (unsigned long) xseed[0] +
  168.     (unsigned long) __rand48_add;
  169.   temp[0] = (unsigned short) accu;     /* lower 16 bits */
  170.   accu >>= sizeof(unsigned short) * 8;
  171.   accu += (unsigned long) __rand48_mult[0] * (unsigned long) xseed[1] +
  172.     (unsigned long) __rand48_mult[1] * (unsigned long) xseed[0];
  173.   temp[1] = (unsigned short) accu;     /* middle 16 bits */
  174.   accu >>= sizeof(unsigned short) * 8;
  175.   accu += __rand48_mult[0] * xseed[2] + __rand48_mult[1] * xseed[1] + __rand48_mult[2] * xseed[0];
  176.   xseed[0] = temp[0];
  177.   xseed[1] = temp[1];
  178.   xseed[2] = (unsigned short) accu;
  179. }
  180.