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authorAkira Kakuto <kakuto@fuk.kindai.ac.jp>2015-10-07 01:43:37 +0000
committerAkira Kakuto <kakuto@fuk.kindai.ac.jp>2015-10-07 01:43:37 +0000
commit4ca2692153042a0c2f7db8d681e190b867ae2faf (patch)
tree5ce3f1b1d2b21911766b40bb856a8279cec96fed /Build
parent357d78ed0c02ea3e4c41bac6c13f2cdb7c50784c (diff)
web2c/mplibdir: Sync with the upstream.
git-svn-id: svn://tug.org/texlive/trunk@38574 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Build')
-rw-r--r--Build/source/texk/web2c/mplibdir/ChangeLog5
-rw-r--r--Build/source/texk/web2c/mplibdir/mp.w24
-rw-r--r--Build/source/texk/web2c/mplibdir/mpmath.w43
-rw-r--r--Build/source/texk/web2c/mplibdir/mpmathbinary.w176
-rw-r--r--Build/source/texk/web2c/mplibdir/mpmathdecimal.w143
-rw-r--r--Build/source/texk/web2c/mplibdir/mpmathdouble.w132
6 files changed, 500 insertions, 23 deletions
diff --git a/Build/source/texk/web2c/mplibdir/ChangeLog b/Build/source/texk/web2c/mplibdir/ChangeLog
index db853ec24eb..c3db5d08ce2 100644
--- a/Build/source/texk/web2c/mplibdir/ChangeLog
+++ b/Build/source/texk/web2c/mplibdir/ChangeLog
@@ -1,3 +1,8 @@
+2015-10-07 Akira Kakuto <kakuto@fuk.kindai.ac.jp>
+
+ *mpmath.w, mpmathbinary.w, mpmathdecimal.w, mp.w, mpmathdouble.w:
+ Sync with the upstream trunk.
+
2015-09-21 Akira Kakuto <kakuto@fuk.kindai.ac.jp>
* mpmathdecimal.w: Sync with the upstream trunk.
diff --git a/Build/source/texk/web2c/mplibdir/mp.w b/Build/source/texk/web2c/mplibdir/mp.w
index d40a45fda8c..a5b6a619cc4 100644
--- a/Build/source/texk/web2c/mplibdir/mp.w
+++ b/Build/source/texk/web2c/mplibdir/mp.w
@@ -1,4 +1,4 @@
-% $Id: mp.w 2060 2015-05-07 11:01:39Z luigi $
+% $Id: mp.w 2070 2015-10-06 10:35:23Z luigi $
%
% This file is part of MetaPost;
% the MetaPost program is in the public domain.
@@ -331,6 +331,7 @@ typedef struct mp_number_data mp_number;
typedef void (*convert_func) (mp_number *r);
typedef void (*m_log_func) (MP mp, mp_number *r, mp_number a);
typedef void (*m_exp_func) (MP mp, mp_number *r, mp_number a);
+typedef void (*m_unif_rand_func) (MP mp, mp_number *ret, mp_number x_orig);
typedef void (*m_norm_rand_func) (MP mp, mp_number *ret);
typedef void (*pyth_add_func) (MP mp, mp_number *r, mp_number a, mp_number b);
typedef void (*pyth_sub_func) (MP mp, mp_number *r, mp_number a, mp_number b);
@@ -475,6 +476,7 @@ typedef struct math_data {
n_arg_func n_arg;
m_log_func m_log;
m_exp_func m_exp;
+ m_unif_rand_func m_unif_rand;
m_norm_rand_func m_norm_rand;
pyth_add_func pyth_add;
pyth_sub_func pyth_sub;
@@ -2566,9 +2568,12 @@ void mp_new_randoms (MP mp) {
mp->j_random = 54;
}
-@ To consume a random fraction, the program below will say `|next_random|'.
+@ To consume a random fraction, the program below will say `|next_random|'.
+Now each number system has its own implementation,
+true to the original as much as possibile.
@c
+/* Unused.
static void mp_next_random (MP mp, mp_number *ret) {
if ( mp->j_random==0 )
mp_new_randoms(mp);
@@ -2576,7 +2581,7 @@ static void mp_next_random (MP mp, mp_number *ret) {
decr(mp->j_random);
number_clone (*ret, mp->randoms[mp->j_random]);
}
-
+*/
@ 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.
@@ -2584,10 +2589,15 @@ 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.
+This is the original one,
+that stays as reference:
+As said before, now each number system has its own implementation.
+
@c
+/*Unused.
static void mp_unif_rand (MP mp, mp_number *ret, mp_number x_orig) {
- mp_number y; /* trial value */
+ mp_number y; // trial value
mp_number x, abs_x;
mp_number u;
new_fraction (y);
@@ -2612,7 +2622,7 @@ static void mp_unif_rand (MP mp, mp_number *ret, mp_number x_orig) {
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
@@ -10965,6 +10975,7 @@ This first set goes into the header
@d n_arg(R,A,B) (((math_data *)(mp->math))->n_arg)(mp,&(R),A,B)
@d m_log(R,A) (((math_data *)(mp->math))->m_log)(mp,&(R),A)
@d m_exp(R,A) (((math_data *)(mp->math))->m_exp)(mp,&(R),A)
+@d m_unif_rand(R,A) (((math_data *)(mp->math))->m_unif_rand)(mp,&(R),A)
@d m_norm_rand(R) (((math_data *)(mp->math))->m_norm_rand)(mp,&(R))
@d velocity(R,A,B,C,D,E) (((math_data *)(mp->math))->velocity)(mp,&(R),A,B,C,D,E)
@d ab_vs_cd(R,A,B,C,D) (((math_data *)(mp->math))->ab_vs_cd)(mp,&(R),A,B,C,D)
@@ -24861,7 +24872,8 @@ static void mp_do_unary (MP mp, quarterword c) {
{
mp_number vvx;
new_number (vvx);
- mp_unif_rand (mp, &vvx, cur_exp_value_number ());
+ /*mp_unif_rand (mp, &vvx, cur_exp_value_number ());*/
+ m_unif_rand (vvx, cur_exp_value_number ());
set_cur_exp_value_number (vvx);
free_number (vvx);
}
diff --git a/Build/source/texk/web2c/mplibdir/mpmath.w b/Build/source/texk/web2c/mplibdir/mpmath.w
index b7d1948ec3e..b713dc14151 100644
--- a/Build/source/texk/web2c/mplibdir/mpmath.w
+++ b/Build/source/texk/web2c/mplibdir/mpmath.w
@@ -1,4 +1,4 @@
-% $Id: mpmath.w 2057 2015-03-20 01:33:59Z luigi $
+% $Id: mpmath.w 2070 2015-10-06 10:35:23Z luigi $
%
% This file is part of MetaPost;
% the MetaPost program is in the public domain.
@@ -56,6 +56,7 @@ 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_m_unif_rand (MP mp, mp_number *ret, mp_number x_orig);
static void mp_m_norm_rand (MP mp, mp_number *ret);
static void mp_m_exp (MP mp, mp_number *ret, mp_number x_orig);
static void mp_m_log (MP mp, mp_number *ret, mp_number x_orig);
@@ -254,6 +255,7 @@ void * mp_initialize_scaled_math (MP mp) {
math->n_arg = mp_n_arg;
math->m_log = mp_m_log;
math->m_exp = mp_m_exp;
+ math->m_unif_rand = mp_m_unif_rand;
math->m_norm_rand = mp_m_norm_rand;
math->pyth_add = mp_pyth_add;
math->pyth_sub = mp_pyth_sub;
@@ -1836,6 +1838,45 @@ 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_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_number_abs (&abs_x);
+ mp_next_random(mp, &u);
+ /*take_fraction (y, abs_x, u);*/
+ mp_number_take_fraction (mp,&y, abs_x,u);
+ free_number (u);
+ if (mp_number_equal(y, abs_x)) {
+ /*set_number_to_zero(*ret);*/
+ 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
diff --git a/Build/source/texk/web2c/mplibdir/mpmathbinary.w b/Build/source/texk/web2c/mplibdir/mpmathbinary.w
index 38cd823499a..43edabab86c 100644
--- a/Build/source/texk/web2c/mplibdir/mpmathbinary.w
+++ b/Build/source/texk/web2c/mplibdir/mpmathbinary.w
@@ -27,6 +27,7 @@
#define MPMATHBINARY_H 1
#include "mplib.h"
#include "mpmp.h" /* internal header */
+#include <gmp.h>
#include <mpfr.h>
@<Internal library declarations@>;
#endif
@@ -61,6 +62,7 @@ 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_binary_m_unif_rand (MP mp, mp_number *ret, mp_number x_orig);
static void mp_binary_m_norm_rand (MP mp, mp_number *ret);
static void mp_binary_m_exp (MP mp, mp_number *ret, mp_number x_orig);
static void mp_binary_m_log (MP mp, mp_number *ret, mp_number x_orig);
@@ -396,6 +398,7 @@ void * mp_initialize_binary_math (MP mp) {
math->n_arg = mp_binary_n_arg;
math->m_log = mp_binary_m_log;
math->m_exp = mp_binary_m_exp;
+ math->m_unif_rand = mp_binary_m_unif_rand;
math->m_norm_rand = mp_binary_m_norm_rand;
math->pyth_add = mp_binary_pyth_add;
math->pyth_sub = mp_binary_pyth_sub;
@@ -870,32 +873,54 @@ The definitions below are temporarily here
@<Declarations...@>=
static void mp_wrapup_numeric_token(MP mp, unsigned char *start, unsigned char *stop);
-@ Precision check is TODO
-@d too_precise(a) 0
+@ The check of the precision is based on the article "27 Bits are not enough for 8-Digit accuracy"
+@ by Bennet Goldberg which roughly says that
+@ given $p$ digits in base 10 and $q$ digits in base 2,
+@ conversion from base 10 round-trip through base 2 if and only if $10^p < $2^{q-1}$.
+@ In our case $p/\log_{10}2 + 1 < q$, or $q\geq a$
+@ where $q$ is the current precision in bits and $a=\left\lceil p/\log_{10}2 + 1\right\rceil$.
+@ Therefore if $a>q$ the number could be too precise and we emit a warning.
+@d too_precise(a) (a>precision_bits)
@c
void mp_wrapup_numeric_token(MP mp, unsigned char *start, unsigned char *stop) {
int invalid = 0;
mpfr_t result;
size_t l = stop-start+1;
+ unsigned long lp, lpbit;
+ /*size_t lp = l; */
char *buf = mp_xmalloc(mp, l+1, 1);
+ char *bufp = buf;
buf[l] = '\0';
mpfr_init2(result, precision_bits);
(void)strncpy(buf,(const char *)start, l);
invalid = mpfr_set_str(result,buf, 10, ROUNDING);
//fprintf(stdout,"scan of [%s] produced %s, ", buf, mp_binnumber_tostring(result));
+ lp = (unsigned long) l;
+
+ /* strip leading - or + or 0 or .*/
+ if ( (*bufp=='-') || (*bufp=='+') || (*bufp=='0') || (*bufp=='.') ) { lp--; bufp++;}
+ /* strip also . */
+ lp = strchr(bufp,'.') ? lp-1: lp;
+ /* strip also trailing 0s */
+ bufp = buf+l-1;
+ while(*bufp == '0') {bufp--; lp--;}
+ lp = lp>0? lp: 1;
+ /* bits needed for buf */
+ lpbit = (unsigned long)ceil(lp/log10(2)+1);
free(buf);
+ bufp = NULL;
if (invalid == 0) {
set_cur_mod(result);
// fprintf(stdout,"mod=%s\n", mp_binary_number_tostring(mp,mp->cur_mod_->data.n));
- if (too_precise(l)) {
+ if (too_precise(lpbit)) {
if (mpfr_positive_p((mpfr_ptr)(internal_value (mp_warning_check).data.num)) &&
(mp->scanner_status != tex_flushing)) {
char msg[256];
const char *hlp[] = {"Continue and I'll try to cope",
- "with that big value; but it might be dangerous.",
+ "with that value; but it might be dangerous.",
"(Set warningcheck:=0 to suppress this message.)",
NULL };
- mp_snprintf (msg, 256, "Number is too large (%s)", mp_binary_number_tostring(mp,mp->cur_mod_->data.n));
+ mp_snprintf (msg, 256, "Number is too precise (%d vs. numberprecision = %f)", (unsigned int)lp,mpfr_get_d(internal_value (mp_number_precision).data.num, ROUNDING));
@.Number is too large@>;
mp_error (mp, msg, hlp, true);
}
@@ -1500,6 +1525,82 @@ void mp_binary_sin_cos (MP mp, mp_number z_orig, mp_number *n_cos, mp_number *n_
mpfr_clear (one_eighty);
}
+@ 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
@@ -1522,6 +1623,9 @@ 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
@@ -1529,6 +1633,22 @@ void mp_binary_number_modulo (mp_number *a, mp_number b) {
mpfr_remainder (a->data.num, a->data.num, b.data.num, ROUNDING);
}
+@ 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) {
+ mp_number rop;
+ unsigned long int op;
+ float flt_op ;
+ (void)mp;
+ mp_new_number (mp, &rop, mp_scaled_type);
+ op = (unsigned)ran_arr_next();
+ flt_op = op/(MM*1.0);
+ mpfr_set_d ((mpfr_ptr)(rop.data.num), flt_op,ROUNDING);
+ mp_number_clone (ret, rop);
+ free_number (rop);
+}
+
@ To consume a random fraction, the program below will say `|next_random|'.
@@ -1542,6 +1662,52 @@ static void mp_next_random (MP mp, mp_number *ret) {
mp_number_clone (ret, mp->randoms[mp->j_random]);
}
+@ 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_binary_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;
+ char *r ;mpfr_exp_t e;
+ 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_binary_abs (&abs_x);
+ mp_next_unif_random(mp, &u);
+ mpfr_mul (y.data.num, abs_x.data.num, u.data.num, ROUNDING);
+ 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);
+ }
+ r = mpfr_get_str(NULL, // char *str,
+ &e, // mpfr_exp_t *expptr,
+ 10, // int b,
+ 0, // size_t n,
+ ret->data.num, // mpfr_t op,
+ ROUNDING // mpfr_rnd_t rnd
+ );
+ printf("\nret=%s e=%ld\n",r,e);
+ mpfr_free_str(r);
+ 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
diff --git a/Build/source/texk/web2c/mplibdir/mpmathdecimal.w b/Build/source/texk/web2c/mplibdir/mpmathdecimal.w
index 2d5a7e3d0a0..d0550c51a80 100644
--- a/Build/source/texk/web2c/mplibdir/mpmathdecimal.w
+++ b/Build/source/texk/web2c/mplibdir/mpmathdecimal.w
@@ -68,6 +68,7 @@ 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_decimal_m_unif_rand (MP mp, mp_number *ret, mp_number x_orig);
static void mp_decimal_m_norm_rand (MP mp, mp_number *ret);
static void mp_decimal_m_exp (MP mp, mp_number *ret, mp_number x_orig);
static void mp_decimal_m_log (MP mp, mp_number *ret, mp_number x_orig);
@@ -542,6 +543,7 @@ void * mp_initialize_decimal_math (MP mp) {
math->n_arg = mp_decimal_n_arg;
math->m_log = mp_decimal_m_log;
math->m_exp = mp_decimal_m_exp;
+ math->m_unif_rand = mp_decimal_m_unif_rand;
math->m_norm_rand = mp_decimal_m_norm_rand;
math->pyth_add = mp_decimal_pyth_add;
math->pyth_sub = mp_decimal_pyth_sub;
@@ -1424,8 +1426,8 @@ int mp_round_unscaled(mp_number x_orig) {
@c
void mp_number_floor (mp_number *i) {
- int round = set.round;
- set.round = DEC_ROUND_FLOOR;
+ int round = set.round;
+ set.round = DEC_ROUND_FLOOR;
decNumberToIntegralValue(i->data.num, i->data.num, &set);
set.round = round;
}
@@ -1724,6 +1726,81 @@ mp_number_to_double(*n_cos), mp_number_to_double(*n_sin));
mp_check_decNumber(mp, n_sin->data.num, &set);
}
+@ 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
@@ -1746,6 +1823,9 @@ 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
@@ -1754,14 +1834,21 @@ void mp_decimal_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) {
+ decNumber a;
+ decNumber b;
+ unsigned long int op;
+ (void)mp;
+ op = (unsigned)ran_arr_next();
+ decNumberFromInt32(&a, op);
+ decNumberFromInt32(&b, MM);
+ decNumberDivide (&a, &a, &b, &set); /* a = a/b */
+ decNumberCopy(ret->data.num, &a);
+ mp_check_decNumber(mp, ret->data.num, &set);
+}
@ To consume a random fraction, the program below will say `|next_random|'.
@@ -1776,6 +1863,43 @@ 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_decimal_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_decimal_abs (&abs_x);
+ mp_next_unif_random(mp, &u);
+ decNumberMultiply (y.data.num, abs_x.data.num, u.data.num, &set);
+ 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\/}).
@@ -1810,7 +1934,6 @@ static void mp_decimal_m_norm_rand (MP mp, mp_number *ret) {
mp_number_clone (&xa, r);
mp_decimal_m_log (mp,&la, u);
mp_set_decimal_from_substraction(&la, ((math_data *)mp->math)->twelve_ln_2_k, la);
- /*mp_decimal_ab_vs_cd (mp,&ab_vs_cd, ((math_data *)mp->math)->one_k, la, xa, xa);*/
mp_ab_vs_cd (mp,&ab_vs_cd, ((math_data *)mp->math)->one_k, la, xa, xa);
} while (mp_number_less(ab_vs_cd,((math_data *)mp->math)->zero_t));
mp_number_clone (ret, xa);
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\/}).