random.c revision 300965
11573Srgrimes/* 21573Srgrimes * Copyright (c) 1983, 1993 31573Srgrimes * The Regents of the University of California. All rights reserved. 41573Srgrimes * 51573Srgrimes * Redistribution and use in source and binary forms, with or without 61573Srgrimes * modification, are permitted provided that the following conditions 71573Srgrimes * are met: 81573Srgrimes * 1. Redistributions of source code must retain the above copyright 91573Srgrimes * notice, this list of conditions and the following disclaimer. 101573Srgrimes * 2. Redistributions in binary form must reproduce the above copyright 111573Srgrimes * notice, this list of conditions and the following disclaimer in the 121573Srgrimes * documentation and/or other materials provided with the distribution. 13251672Semaste * 3. Neither the name of the University nor the names of its contributors 141573Srgrimes * may be used to endorse or promote products derived from this software 151573Srgrimes * without specific prior written permission. 161573Srgrimes * 171573Srgrimes * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 181573Srgrimes * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 191573Srgrimes * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 201573Srgrimes * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 211573Srgrimes * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 221573Srgrimes * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 231573Srgrimes * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 241573Srgrimes * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 251573Srgrimes * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 261573Srgrimes * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 271573Srgrimes * SUCH DAMAGE. 281573Srgrimes */ 291573Srgrimes 301573Srgrimes#if defined(LIBC_SCCS) && !defined(lint) 3123662Speterstatic char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95"; 321573Srgrimes#endif /* LIBC_SCCS and not lint */ 3392986Sobrien#include <sys/cdefs.h> 3492986Sobrien__FBSDID("$FreeBSD: head/lib/libc/stdlib/random.c 300965 2016-05-29 16:39:28Z ache $"); 351573Srgrimes 3671579Sdeischen#include "namespace.h" 37249035Sdelphij#include <sys/param.h> 38249035Sdelphij#include <sys/sysctl.h> 39124738Sdas#include <stdint.h> 401573Srgrimes#include <stdlib.h> 4171579Sdeischen#include "un-namespace.h" 421573Srgrimes 431573Srgrimes/* 441573Srgrimes * random.c: 451573Srgrimes * 461573Srgrimes * An improved random number generation package. In addition to the standard 471573Srgrimes * rand()/srand() like interface, this package also has a special state info 481573Srgrimes * interface. The initstate() routine is called with a seed, an array of 491573Srgrimes * bytes, and a count of how many bytes are being passed in; this array is 501573Srgrimes * then initialized to contain information for random number generation with 511573Srgrimes * that much state information. Good sizes for the amount of state 521573Srgrimes * information are 32, 64, 128, and 256 bytes. The state can be switched by 531573Srgrimes * calling the setstate() routine with the same array as was initiallized 541573Srgrimes * with initstate(). By default, the package runs with 128 bytes of state 551573Srgrimes * information and generates far better random numbers than a linear 561573Srgrimes * congruential generator. If the amount of state information is less than 571573Srgrimes * 32 bytes, a simple linear congruential R.N.G. is used. 581573Srgrimes * 59124738Sdas * Internally, the state information is treated as an array of uint32_t's; the 601573Srgrimes * zeroeth element of the array is the type of R.N.G. being used (small 611573Srgrimes * integer); the remainder of the array is the state information for the 62124738Sdas * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of 631573Srgrimes * state information, which will allow a degree seven polynomial. (Note: 641573Srgrimes * the zeroeth word of state information also has some other information 651573Srgrimes * stored in it -- see setstate() for details). 668870Srgrimes * 671573Srgrimes * The random number generation technique is a linear feedback shift register 681573Srgrimes * approach, employing trinomials (since there are fewer terms to sum up that 691573Srgrimes * way). In this approach, the least significant bit of all the numbers in 701573Srgrimes * the state table will act as a linear feedback shift register, and will 711573Srgrimes * have period 2^deg - 1 (where deg is the degree of the polynomial being 721573Srgrimes * used, assuming that the polynomial is irreducible and primitive). The 731573Srgrimes * higher order bits will have longer periods, since their values are also 741573Srgrimes * influenced by pseudo-random carries out of the lower bits. The total 751573Srgrimes * period of the generator is approximately deg*(2**deg - 1); thus doubling 761573Srgrimes * the amount of state information has a vast influence on the period of the 771573Srgrimes * generator. Note: the deg*(2**deg - 1) is an approximation only good for 7892889Sobrien * large deg, when the period of the shift is the dominant factor. 791573Srgrimes * With deg equal to seven, the period is actually much longer than the 801573Srgrimes * 7*(2**7 - 1) predicted by this formula. 8123662Speter * 8223662Speter * Modified 28 December 1994 by Jacob S. Rosenberg. 8323662Speter * The following changes have been made: 8423662Speter * All references to the type u_int have been changed to unsigned long. 8523662Speter * All references to type int have been changed to type long. Other 8623662Speter * cleanups have been made as well. A warning for both initstate and 8723662Speter * setstate has been inserted to the effect that on Sparc platforms 8823662Speter * the 'arg_state' variable must be forced to begin on word boundaries. 8923662Speter * This can be easily done by casting a long integer array to char *. 9023662Speter * The overall logic has been left STRICTLY alone. This software was 9123662Speter * tested on both a VAX and Sun SpacsStation with exactly the same 9223662Speter * results. The new version and the original give IDENTICAL results. 9323662Speter * The new version is somewhat faster than the original. As the 9423662Speter * documentation says: "By default, the package runs with 128 bytes of 9523662Speter * state information and generates far better random numbers than a linear 9623662Speter * congruential generator. If the amount of state information is less than 9723662Speter * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of 9823662Speter * 128 bytes, this new version runs about 19 percent faster and for a 16 9923662Speter * byte buffer it is about 5 percent faster. 1001573Srgrimes */ 1011573Srgrimes 1021573Srgrimes/* 1031573Srgrimes * For each of the currently supported random number generators, we have a 1041573Srgrimes * break value on the amount of state information (you need at least this 1051573Srgrimes * many bytes of state info to support this random number generator), a degree 1061573Srgrimes * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 1071573Srgrimes * the separation between the two lower order coefficients of the trinomial. 1081573Srgrimes */ 1091573Srgrimes#define TYPE_0 0 /* linear congruential */ 1101573Srgrimes#define BREAK_0 8 1111573Srgrimes#define DEG_0 0 1121573Srgrimes#define SEP_0 0 1131573Srgrimes 1141573Srgrimes#define TYPE_1 1 /* x**7 + x**3 + 1 */ 1151573Srgrimes#define BREAK_1 32 1161573Srgrimes#define DEG_1 7 1171573Srgrimes#define SEP_1 3 1181573Srgrimes 1191573Srgrimes#define TYPE_2 2 /* x**15 + x + 1 */ 1201573Srgrimes#define BREAK_2 64 1211573Srgrimes#define DEG_2 15 1221573Srgrimes#define SEP_2 1 1231573Srgrimes 1241573Srgrimes#define TYPE_3 3 /* x**31 + x**3 + 1 */ 1251573Srgrimes#define BREAK_3 128 1261573Srgrimes#define DEG_3 31 1271573Srgrimes#define SEP_3 3 1281573Srgrimes 1291573Srgrimes#define TYPE_4 4 /* x**63 + x + 1 */ 1301573Srgrimes#define BREAK_4 256 1311573Srgrimes#define DEG_4 63 1321573Srgrimes#define SEP_4 1 1331573Srgrimes 1341573Srgrimes/* 1351573Srgrimes * Array versions of the above information to make code run faster -- 1361573Srgrimes * relies on fact that TYPE_i == i. 1371573Srgrimes */ 1381573Srgrimes#define MAX_TYPES 5 /* max number of types above */ 1391573Srgrimes 140118731Sache#define NSHUFF 50 /* to drop some "seed -> 1st value" linearity */ 141110321Sache 142124738Sdasstatic const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 143124738Sdasstatic const int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 1441573Srgrimes 1451573Srgrimes/* 1461573Srgrimes * Initially, everything is set up as if from: 1471573Srgrimes * 14818832Sache * initstate(1, randtbl, 128); 1491573Srgrimes * 1501573Srgrimes * Note that this initialization takes advantage of the fact that srandom() 1511573Srgrimes * advances the front and rear pointers 10*rand_deg times, and hence the 1521573Srgrimes * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 1531573Srgrimes * element of the state information, which contains info about the current 1541573Srgrimes * position of the rear pointer is just 1551573Srgrimes * 1561573Srgrimes * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 1571573Srgrimes */ 1581573Srgrimes 159124738Sdasstatic uint32_t randtbl[DEG_3 + 1] = { 1601573Srgrimes TYPE_3, 161300953Sache 0x2cf41758, 0x27bb3711, 0x4916d4d1, 0x7b02f59f, 0x9b8e28eb, 0xc0e80269, 162300953Sache 0x696f5c16, 0x878f1ff5, 0x52d9c07f, 0x916a06cd, 0xb50b3a20, 0x2776970a, 163300953Sache 0xee4eb2a6, 0xe94640ec, 0xb1d65612, 0x9d1ed968, 0x1043f6b7, 0xa3432a76, 164300953Sache 0x17eacbb9, 0x3c09e2eb, 0x4f8c2b3, 0x708a1f57, 0xee341814, 0x95d0e4d2, 165300953Sache 0xb06f216c, 0x8bd2e72e, 0x8f7c38d7, 0xcfc6a8fc, 0x2a59495, 0xa20d2a69, 166300953Sache 0xe29d12d1 1671573Srgrimes}; 1681573Srgrimes 1691573Srgrimes/* 1701573Srgrimes * fptr and rptr are two pointers into the state info, a front and a rear 1711573Srgrimes * pointer. These two pointers are always rand_sep places aparts, as they 1721573Srgrimes * cycle cyclically through the state information. (Yes, this does mean we 1731573Srgrimes * could get away with just one pointer, but the code for random() is more 1741573Srgrimes * efficient this way). The pointers are left positioned as they would be 1751573Srgrimes * from the call 1761573Srgrimes * 1771573Srgrimes * initstate(1, randtbl, 128); 1781573Srgrimes * 1791573Srgrimes * (The position of the rear pointer, rptr, is really 0 (as explained above 1801573Srgrimes * in the initialization of randtbl) because the state table pointer is set 1811573Srgrimes * to point to randtbl[1] (as explained below). 1821573Srgrimes */ 183124738Sdasstatic uint32_t *fptr = &randtbl[SEP_3 + 1]; 184124738Sdasstatic uint32_t *rptr = &randtbl[1]; 1851573Srgrimes 1861573Srgrimes/* 1871573Srgrimes * The following things are the pointer to the state information table, the 1881573Srgrimes * type of the current generator, the degree of the current polynomial being 1891573Srgrimes * used, and the separation between the two pointers. Note that for efficiency 1901573Srgrimes * of random(), we remember the first location of the state information, not 1911573Srgrimes * the zeroeth. Hence it is valid to access state[-1], which is used to 1921573Srgrimes * store the type of the R.N.G. Also, we remember the last location, since 1931573Srgrimes * this is more efficient than indexing every time to find the address of 1941573Srgrimes * the last element to see if the front and rear pointers have wrapped. 1951573Srgrimes */ 196124738Sdasstatic uint32_t *state = &randtbl[1]; 197124738Sdasstatic int rand_type = TYPE_3; 198124738Sdasstatic int rand_deg = DEG_3; 199124738Sdasstatic int rand_sep = SEP_3; 200124738Sdasstatic uint32_t *end_ptr = &randtbl[DEG_3 + 1]; 2011573Srgrimes 202241031Sdesstatic inline uint32_t 203300953Sachegood_rand(uint32_t ctx) 20418832Sache{ 2051573Srgrimes/* 20618832Sache * Compute x = (7^5 * x) mod (2^31 - 1) 20718832Sache * wihout overflowing 31 bits: 20818832Sache * (2^31 - 1) = 127773 * (7^5) + 2836 20918832Sache * From "Random number generators: good ones are hard to find", 21018832Sache * Park and Miller, Communications of the ACM, vol. 31, no. 10, 21118832Sache * October 1988, p. 1195. 21218832Sache */ 213300953Sache int32_t hi, lo, x; 21418832Sache 215300953Sache /* Transform to [1, 0x7ffffffe] range. */ 216300953Sache x = (ctx % 0x7ffffffe) + 1; 21718832Sache hi = x / 127773; 21818832Sache lo = x % 127773; 21918832Sache x = 16807 * lo - 2836 * hi; 220110280Sache if (x < 0) 22118832Sache x += 0x7fffffff; 222300953Sache /* Transform to [0, 0x7ffffffd] range. */ 223300953Sache return (x - 1); 22418832Sache} 22518832Sache 22618832Sache/* 2271573Srgrimes * srandom: 2281573Srgrimes * 2291573Srgrimes * Initialize the random number generator based on the given seed. If the 2301573Srgrimes * type is the trivial no-state-information type, just remember the seed. 2311573Srgrimes * Otherwise, initializes state[] based on the given "seed" via a linear 2321573Srgrimes * congruential generator. Then, the pointers are set to known locations 2331573Srgrimes * that are exactly rand_sep places apart. Lastly, it cycles the state 2341573Srgrimes * information a given number of times to get rid of any initial dependencies 2351573Srgrimes * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 2361573Srgrimes * for default usage relies on values produced by this routine. 2371573Srgrimes */ 2381573Srgrimesvoid 239241031Sdessrandom(unsigned long x) 2401573Srgrimes{ 241124738Sdas int i, lim; 2421573Srgrimes 243124738Sdas state[0] = (uint32_t)x; 2441573Srgrimes if (rand_type == TYPE_0) 245110321Sache lim = NSHUFF; 2461573Srgrimes else { 2471573Srgrimes for (i = 1; i < rand_deg; i++) 24818832Sache state[i] = good_rand(state[i - 1]); 2491573Srgrimes fptr = &state[rand_sep]; 2501573Srgrimes rptr = &state[0]; 251110321Sache lim = 10 * rand_deg; 2521573Srgrimes } 253110321Sache for (i = 0; i < lim; i++) 254110321Sache (void)random(); 2551573Srgrimes} 2561573Srgrimes 2571573Srgrimes/* 25824151Sache * srandomdev: 25924151Sache * 26024151Sache * Many programs choose the seed value in a totally predictable manner. 261249035Sdelphij * This often causes problems. We seed the generator using pseudo-random 262249035Sdelphij * data from the kernel. 263249035Sdelphij * 264249035Sdelphij * Note that this particular seeding procedure can generate states 265249035Sdelphij * which are impossible to reproduce by calling srandom() with any 266249035Sdelphij * value, since the succeeding terms in the state buffer are no longer 267249035Sdelphij * derived from the LC algorithm applied to a fixed seed. 26824151Sache */ 26926624Sachevoid 270241031Sdessrandomdev(void) 27124151Sache{ 272249035Sdelphij int mib[2]; 27324151Sache size_t len; 27424151Sache 27524151Sache if (rand_type == TYPE_0) 276249035Sdelphij len = sizeof(state[0]); 27724151Sache else 278249035Sdelphij len = rand_deg * sizeof(state[0]); 27924151Sache 280249035Sdelphij mib[0] = CTL_KERN; 281249035Sdelphij mib[1] = KERN_ARND; 282249035Sdelphij sysctl(mib, 2, state, &len, NULL, 0); 28324151Sache 28424151Sache if (rand_type != TYPE_0) { 28524151Sache fptr = &state[rand_sep]; 28624151Sache rptr = &state[0]; 28724151Sache } 28824151Sache} 28924151Sache 29024151Sache/* 2911573Srgrimes * initstate: 2921573Srgrimes * 2931573Srgrimes * Initialize the state information in the given array of n bytes for future 2941573Srgrimes * random number generation. Based on the number of bytes we are given, and 2951573Srgrimes * the break values for the different R.N.G.'s, we choose the best (largest) 2961573Srgrimes * one we can and set things up for it. srandom() is then called to 2971573Srgrimes * initialize the state information. 2988870Srgrimes * 2991573Srgrimes * Note that on return from srandom(), we set state[-1] to be the type 3001573Srgrimes * multiplexed with the current value of the rear pointer; this is so 3011573Srgrimes * successive calls to initstate() won't lose this information and will be 3021573Srgrimes * able to restart with setstate(). 3038870Srgrimes * 3041573Srgrimes * Note: the first thing we do is save the current state, if any, just like 3051573Srgrimes * setstate() so that it doesn't matter when initstate is called. 3061573Srgrimes * 3071573Srgrimes * Returns a pointer to the old state. 30823662Speter * 309124738Sdas * Note: The Sparc platform requires that arg_state begin on an int 31023662Speter * word boundary; otherwise a bus error will occur. Even so, lint will 31123662Speter * complain about mis-alignment, but you should disregard these messages. 3121573Srgrimes */ 3131573Srgrimeschar * 314241031Sdesinitstate(unsigned long seed, char *arg_state, long n) 3151573Srgrimes{ 31692889Sobrien char *ostate = (char *)(&state[-1]); 317124738Sdas uint32_t *int_arg_state = (uint32_t *)arg_state; 3181573Srgrimes 319300397Sache if (n < BREAK_0) 320300397Sache return (NULL); 3211573Srgrimes if (rand_type == TYPE_0) 3221573Srgrimes state[-1] = rand_type; 3231573Srgrimes else 3241573Srgrimes state[-1] = MAX_TYPES * (rptr - state) + rand_type; 3251573Srgrimes if (n < BREAK_1) { 3261573Srgrimes rand_type = TYPE_0; 3271573Srgrimes rand_deg = DEG_0; 3281573Srgrimes rand_sep = SEP_0; 3291573Srgrimes } else if (n < BREAK_2) { 3301573Srgrimes rand_type = TYPE_1; 3311573Srgrimes rand_deg = DEG_1; 3321573Srgrimes rand_sep = SEP_1; 3331573Srgrimes } else if (n < BREAK_3) { 3341573Srgrimes rand_type = TYPE_2; 3351573Srgrimes rand_deg = DEG_2; 3361573Srgrimes rand_sep = SEP_2; 3371573Srgrimes } else if (n < BREAK_4) { 3381573Srgrimes rand_type = TYPE_3; 3391573Srgrimes rand_deg = DEG_3; 3401573Srgrimes rand_sep = SEP_3; 3411573Srgrimes } else { 3421573Srgrimes rand_type = TYPE_4; 3431573Srgrimes rand_deg = DEG_4; 3441573Srgrimes rand_sep = SEP_4; 3451573Srgrimes } 346124738Sdas state = int_arg_state + 1; /* first location */ 3471573Srgrimes end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 3481573Srgrimes srandom(seed); 3491573Srgrimes if (rand_type == TYPE_0) 350124738Sdas int_arg_state[0] = rand_type; 3511573Srgrimes else 352124738Sdas int_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type; 353241031Sdes return (ostate); 3541573Srgrimes} 3551573Srgrimes 3561573Srgrimes/* 3571573Srgrimes * setstate: 3581573Srgrimes * 3591573Srgrimes * Restore the state from the given state array. 3601573Srgrimes * 3611573Srgrimes * Note: it is important that we also remember the locations of the pointers 3621573Srgrimes * in the current state information, and restore the locations of the pointers 3631573Srgrimes * from the old state information. This is done by multiplexing the pointer 3641573Srgrimes * location into the zeroeth word of the state information. 3651573Srgrimes * 3661573Srgrimes * Note that due to the order in which things are done, it is OK to call 3671573Srgrimes * setstate() with the same state as the current state. 3681573Srgrimes * 3691573Srgrimes * Returns a pointer to the old state information. 37023662Speter * 371124738Sdas * Note: The Sparc platform requires that arg_state begin on an int 37223662Speter * word boundary; otherwise a bus error will occur. Even so, lint will 37323662Speter * complain about mis-alignment, but you should disregard these messages. 3741573Srgrimes */ 3751573Srgrimeschar * 376241031Sdessetstate(char *arg_state) 3771573Srgrimes{ 378124738Sdas uint32_t *new_state = (uint32_t *)arg_state; 379124738Sdas uint32_t type = new_state[0] % MAX_TYPES; 380124738Sdas uint32_t rear = new_state[0] / MAX_TYPES; 3811573Srgrimes char *ostate = (char *)(&state[-1]); 3821573Srgrimes 383300953Sache if (type != TYPE_0 && rear >= degrees[type]) 384300397Sache return (NULL); 385300397Sache if (rand_type == TYPE_0) 386300397Sache state[-1] = rand_type; 387300397Sache else 388300397Sache state[-1] = MAX_TYPES * (rptr - state) + rand_type; 389300397Sache rand_type = type; 390300397Sache rand_deg = degrees[type]; 391300397Sache rand_sep = seps[type]; 392124738Sdas state = new_state + 1; 3931573Srgrimes if (rand_type != TYPE_0) { 3941573Srgrimes rptr = &state[rear]; 3951573Srgrimes fptr = &state[(rear + rand_sep) % rand_deg]; 3961573Srgrimes } 3971573Srgrimes end_ptr = &state[rand_deg]; /* set end_ptr too */ 398241031Sdes return (ostate); 3991573Srgrimes} 4001573Srgrimes 4011573Srgrimes/* 4021573Srgrimes * random: 4031573Srgrimes * 4041573Srgrimes * If we are using the trivial TYPE_0 R.N.G., just do the old linear 4051573Srgrimes * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 4061573Srgrimes * the same in all the other cases due to all the global variables that have 4071573Srgrimes * been set up. The basic operation is to add the number at the rear pointer 4081573Srgrimes * into the one at the front pointer. Then both pointers are advanced to 4091573Srgrimes * the next location cyclically in the table. The value returned is the sum 4101573Srgrimes * generated, reduced to 31 bits by throwing away the "least random" low bit. 4111573Srgrimes * 4121573Srgrimes * Note: the code takes advantage of the fact that both the front and 4131573Srgrimes * rear pointers can't wrap on the same call by not testing the rear 4141573Srgrimes * pointer if the front one has wrapped. 4151573Srgrimes * 4161573Srgrimes * Returns a 31-bit random number. 4171573Srgrimes */ 4181573Srgrimeslong 419241031Sdesrandom(void) 4201573Srgrimes{ 421124738Sdas uint32_t i; 422124738Sdas uint32_t *f, *r; 4231573Srgrimes 42423662Speter if (rand_type == TYPE_0) { 42523662Speter i = state[0]; 426300953Sache state[0] = i = good_rand(i); 42723662Speter } else { 42823662Speter /* 42923662Speter * Use local variables rather than static variables for speed. 43023662Speter */ 43123662Speter f = fptr; r = rptr; 43223662Speter *f += *r; 433300965Sache i = *f >> 1; /* chucking least random bit */ 43423662Speter if (++f >= end_ptr) { 43523662Speter f = state; 43623662Speter ++r; 43723662Speter } 43823662Speter else if (++r >= end_ptr) { 43923662Speter r = state; 44023662Speter } 44123662Speter 44223662Speter fptr = f; rptr = r; 4431573Srgrimes } 444241031Sdes return ((long)i); 4451573Srgrimes} 446