diff options
Diffstat (limited to 'Build/source/texk/web2c/mplibdir/mpmathdouble.w')
-rw-r--r-- | Build/source/texk/web2c/mplibdir/mpmathdouble.w | 132 |
1 files changed, 131 insertions, 1 deletions
diff --git a/Build/source/texk/web2c/mplibdir/mpmathdouble.w b/Build/source/texk/web2c/mplibdir/mpmathdouble.w index 7a6d99a4aa7..d5663b2df97 100644 --- a/Build/source/texk/web2c/mplibdir/mpmathdouble.w +++ b/Build/source/texk/web2c/mplibdir/mpmathdouble.w @@ -1,4 +1,4 @@ -% $Id: mpmathdouble.w 2057 2015-03-20 01:33:59Z luigi $ +% $Id: mpmathdouble.w 2070 2015-10-06 10:35:23Z luigi $ % % This file is part of MetaPost; % the MetaPost program is in the public domain. @@ -64,6 +64,7 @@ static void mp_number_angle_to_scaled (mp_number *A); static void mp_number_fraction_to_scaled (mp_number *A); static void mp_number_scaled_to_fraction (mp_number *A); static void mp_number_scaled_to_angle (mp_number *A); +static void mp_double_m_unif_rand (MP mp, mp_number *ret, mp_number x_orig); static void mp_double_m_norm_rand (MP mp, mp_number *ret); static void mp_double_m_exp (MP mp, mp_number *ret, mp_number x_orig); static void mp_double_m_log (MP mp, mp_number *ret, mp_number x_orig); @@ -262,6 +263,7 @@ void * mp_initialize_double_math (MP mp) { math->n_arg = mp_double_n_arg; math->m_log = mp_double_m_log; math->m_exp = mp_double_m_exp; + math->m_unif_rand = mp_double_m_unif_rand; math->m_norm_rand = mp_double_m_norm_rand; math->pyth_add = mp_double_pyth_add; math->pyth_sub = mp_double_pyth_sub; @@ -1215,6 +1217,81 @@ mp_number_to_double(*n_cos), mp_number_to_double(*n_sin)); #endif } +@ This is the http://www-cs-faculty.stanford.edu/~uno/programs/rng.c +with small cosmetic modifications. + +@c +#define KK 100 /* the long lag */ +#define LL 37 /* the short lag */ +#define MM (1L<<30) /* the modulus */ +#define mod_diff(x,y) (((x)-(y))&(MM-1)) /* subtraction mod MM */ +/* */ +static long ran_x[KK]; /* the generator state */ +/* */ +static void ran_array(long aa[],int n) /* put n new random numbers in aa */ + /* long aa[] destination */ + /* int n array length (must be at least KK) */ +{ + register int i,j; + for (j=0;j<KK;j++) aa[j]=ran_x[j]; + for (;j<n;j++) aa[j]=mod_diff(aa[j-KK],aa[j-LL]); + for (i=0;i<LL;i++,j++) ran_x[i]=mod_diff(aa[j-KK],aa[j-LL]); + for (;i<KK;i++,j++) ran_x[i]=mod_diff(aa[j-KK],ran_x[i-LL]); +} +/* */ +/* the following routines are from exercise 3.6--15 */ +/* after calling ran_start, get new randoms by, e.g., "x=ran_arr_next()" */ +/* */ +#define QUALITY 1009 /* recommended quality level for high-res use */ +static long ran_arr_buf[QUALITY]; +static long ran_arr_dummy=-1, ran_arr_started=-1; +static long *ran_arr_ptr=&ran_arr_dummy; /* the next random number, or -1 */ +/* */ +#define TT 70 /* guaranteed separation between streams */ +#define is_odd(x) ((x)&1) /* units bit of x */ +/* */ +static void ran_start(long seed) /* do this before using ran_array */ + /* long seed selector for different streams */ +{ + register int t,j; + long x[KK+KK-1]; /* the preparation buffer */ + register long ss=(seed+2)&(MM-2); + for (j=0;j<KK;j++) { + x[j]=ss; /* bootstrap the buffer */ + ss<<=1; if (ss>=MM) ss-=MM-2; /* cyclic shift 29 bits */ + } + x[1]++; /* make x[1] (and only x[1]) odd */ + for (ss=seed&(MM-1),t=TT-1; t; ) { + for (j=KK-1;j>0;j--) x[j+j]=x[j], x[j+j-1]=0; /* "square" */ + for (j=KK+KK-2;j>=KK;j--) + x[j-(KK-LL)]=mod_diff(x[j-(KK-LL)],x[j]), + x[j-KK]=mod_diff(x[j-KK],x[j]); + if (is_odd(ss)) { /* "multiply by z" */ + for (j=KK;j>0;j--) x[j]=x[j-1]; + x[0]=x[KK]; /* shift the buffer cyclically */ + x[LL]=mod_diff(x[LL],x[KK]); + } + if (ss) ss>>=1; else t--; + } + for (j=0;j<LL;j++) ran_x[j+KK-LL]=x[j]; + for (;j<KK;j++) ran_x[j-LL]=x[j]; + for (j=0;j<10;j++) ran_array(x,KK+KK-1); /* warm things up */ + ran_arr_ptr=&ran_arr_started; +} +/* */ +#define ran_arr_next() (*ran_arr_ptr>=0? *ran_arr_ptr++: ran_arr_cycle()) +static long ran_arr_cycle(void) +{ + if (ran_arr_ptr==&ran_arr_dummy) + ran_start(314159L); /* the user forgot to initialize */ + ran_array(ran_arr_buf,QUALITY); + ran_arr_buf[KK]=-1; + ran_arr_ptr=ran_arr_buf+1; + return ran_arr_buf[0]; +} + + + @ To initialize the |randoms| table, we call the following routine. @c @@ -1237,6 +1314,10 @@ void mp_init_randoms (MP mp, int seed) { mp_new_randoms (mp); mp_new_randoms (mp); mp_new_randoms (mp); /* ``warm up'' the array */ + + ran_start((unsigned long) seed); + + } @ @c @@ -1255,6 +1336,18 @@ void mp_number_modulo (mp_number *a, mp_number b) { +@ To consume a random integer for the uniform generator, the program below will say `|next_unif_random|'. + +@c +static void mp_next_unif_random (MP mp, mp_number *ret) { + double a; + unsigned long int op; + (void)mp; + op = (unsigned)ran_arr_next(); + a = op/(MM*1.0); + ret->data.dval = a; +} + @ To consume a random fraction, the program below will say `|next_random|'. @@ -1269,6 +1362,43 @@ static void mp_next_random (MP mp, mp_number *ret) { } +@ To produce a uniform random number in the range |0<=u<x| or |0>=u>x| +or |0=u=x|, given a |scaled| value~|x|, we proceed as shown here. + +Note that the call of |take_fraction| will produce the values 0 and~|x| +with about half the probability that it will produce any other particular +values between 0 and~|x|, because it rounds its answers. + +@c +static void mp_double_m_unif_rand (MP mp, mp_number *ret, mp_number x_orig) { + mp_number y; /* trial value */ + mp_number x, abs_x; + mp_number u; + new_fraction (y); + new_number (x); + new_number (abs_x); + new_number (u); + mp_number_clone (&x, x_orig); + mp_number_clone (&abs_x, x); + mp_double_abs (&abs_x); + mp_next_unif_random(mp, &u); + y.data.dval = abs_x.data.dval * u.data.dval; + free_number (u); + if (mp_number_equal(y, abs_x)) { + mp_number_clone (ret, ((math_data *)mp->math)->zero_t); + } else if (mp_number_greater(x, ((math_data *)mp->math)->zero_t)) { + mp_number_clone (ret, y); + } else { + mp_number_clone (ret, y); + mp_number_negate (ret); + } + free_number (abs_x); + free_number (x); + free_number (y); +} + + + @ Finally, a normal deviate with mean zero and unit standard deviation can readily be obtained with the ratio method (Algorithm 3.4.1R in {\sl The Art of Computer Programming\/}). |