diff options
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/ChangeLog | 8 | ||||
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/lmplib.c | 3 | ||||
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/mp.w | 25 | ||||
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/mpmath.w | 67 | ||||
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/mpmathbinary.w | 104 | ||||
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/mpmathdecimal.w | 110 | ||||
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/mpmathdouble.w | 96 | ||||
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/mpost.w | 2 | ||||
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/mpstrings.w | 2 | ||||
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/mpxout.w | 1 | ||||
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/pngout.w | 2 | ||||
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/psout.w | 1 | ||||
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/svgout.w | 2 | ||||
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/tfmin.w | 2 |
14 files changed, 390 insertions, 35 deletions
diff --git a/Build/source/texk/web2c/mplibdir/ChangeLog b/Build/source/texk/web2c/mplibdir/ChangeLog index 17480cb9de1..4cba35f7910 100644 --- a/Build/source/texk/web2c/mplibdir/ChangeLog +++ b/Build/source/texk/web2c/mplibdir/ChangeLog @@ -1,12 +1,18 @@ +2015-03-19 Luigi Scarso <luigi.scarso@gmail.com> + Fixed normal rand. generator for double/decimal/binary + systems. + 2015-01-20 Luigi Scarso <luigi.scarso@gmail.com> Added cur_sym_mod() == mp_normal_sym to the cur_sym==0 condition mp_cur_tok + 2015-01-19 Luigi Scarso <luigi.scarso@gmail.com> fixed a bug in mp_recycle_value with NULL node + 2015-01-15 Luigi Scarso <luigi.scarso@gmail.com> - * mpmathdecimal.w: better management for static data in mpmathdecimal.w + mpmathdecimal.w: better management for static data in mpmathdecimal.w (thanks to Philipp Gesang <phg@phi-gamma.net>) 2014-12-04 Luigi Scarso <luigi.scarso@gmail.com> diff --git a/Build/source/texk/web2c/mplibdir/lmplib.c b/Build/source/texk/web2c/mplibdir/lmplib.c index 6a3f83e8775..ab1b707b237 100644 --- a/Build/source/texk/web2c/mplibdir/lmplib.c +++ b/Build/source/texk/web2c/mplibdir/lmplib.c @@ -52,9 +52,6 @@ #include "mplibsvg.h" #include "mplibpng.h" - /*@unused@*/ static const char _svn_version[] = - "$Id: lmplib.c 2036 2014-06-26 18:44:57Z luigi $"; - int luaopen_mplib(lua_State * L); /* forward */ /* metatable identifiers and tests */ diff --git a/Build/source/texk/web2c/mplibdir/mp.w b/Build/source/texk/web2c/mplibdir/mp.w index 4ba9f3586a9..9735f6f33b2 100644 --- a/Build/source/texk/web2c/mplibdir/mp.w +++ b/Build/source/texk/web2c/mplibdir/mp.w @@ -1,4 +1,4 @@ -% $Id: mp.w 2055 2015-01-22 15:39:12Z luigi $ +% $Id: mp.w 2057 2015-03-20 01:33:59Z 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_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); typedef void (*n_arg_func) (MP mp, mp_number *r, mp_number a, mp_number b); @@ -471,9 +472,10 @@ typedef struct math_data { velocity_func velocity; ab_vs_cd_func ab_vs_cd; crossing_point_func crossing_point; - n_arg_func n_arg; - m_log_func m_log; - m_exp_func m_exp; + n_arg_func n_arg; + m_log_func m_log; + m_exp_func m_exp; + m_norm_rand_func m_norm_rand; pyth_add_func pyth_add; pyth_sub_func pyth_sub; fraction_to_round_scaled_func fraction_to_round_scaled; @@ -2603,9 +2605,14 @@ static void mp_unif_rand (MP mp, mp_number *ret, mp_number x_orig) { @ 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\/}). +{\sl The Art of Computer Programming\/}). This is the original one, +that stays as reference: +Now each number system has its own implementation, +true to the original as much as possibile. +. @c +/* Unused. static void mp_norm_rand (MP mp, mp_number *ret) { mp_number ab_vs_cd; mp_number abs_x; @@ -2623,7 +2630,7 @@ static void mp_norm_rand (MP mp, mp_number *ret) { mp_number v; new_number (v); mp_next_random(mp, &v); - number_substract (v, fraction_half_t); + number_substract (v, fraction_half_t); take_fraction (xa, sqrt_8_e_k, v); free_number (v); mp_next_random(mp, &u); @@ -2644,6 +2651,7 @@ static void mp_norm_rand (MP mp, mp_number *ret) { free_number (xa); free_number (u); } +*/ @* Packed data. @@ -10940,6 +10948,7 @@ 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_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) @d crossing_point(R,A,B,C) (((math_data *)(mp->math))->crossing_point)(mp,&(R),A,B,C) @@ -24536,7 +24545,8 @@ static void mp_do_nullary (MP mp, quarterword c) { { mp_number r; new_number (r); - mp_norm_rand (mp, &r); + /*mp_norm_rand (mp, &r);*/ + m_norm_rand (r); mp->cur_exp.type = mp_known; set_cur_exp_value_number (r); free_number (r); @@ -30002,7 +30012,6 @@ Here's one of the simplest: @ @<Declare action procedures for use by |do_statement|@>= static void mp_do_random_seed (MP mp); - @ @c void mp_do_random_seed (MP mp) { mp_value new_expr; diff --git a/Build/source/texk/web2c/mplibdir/mpmath.w b/Build/source/texk/web2c/mplibdir/mpmath.w index 82d41746c72..b7d1948ec3e 100644 --- a/Build/source/texk/web2c/mplibdir/mpmath.w +++ b/Build/source/texk/web2c/mplibdir/mpmath.w @@ -1,4 +1,4 @@ -% $Id: mpmath.w 2037 2014-09-02 14:59:07Z luigi $ +% $Id: mpmath.w 2057 2015-03-20 01:33:59Z 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_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); static void mp_pyth_sub (MP mp, mp_number *r, mp_number a, mp_number b); @@ -253,6 +254,7 @@ 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_norm_rand = mp_m_norm_rand; math->pyth_add = mp_pyth_add; math->pyth_sub = mp_pyth_sub; math->fraction_to_scaled = mp_number_fraction_to_scaled; @@ -1816,4 +1818,65 @@ char * mp_number_tostring (MP mp, mp_number n) { @ @c void mp_number_modulo (mp_number *a, mp_number b) { a->data.val = a->data.val % b.data.val; -}
\ No newline at end of file +} + + + + + +@ To consume a random fraction, the program below will say `|next_random|'. + +@c +static void mp_next_random (MP mp, mp_number *ret) { + if ( mp->j_random==0 ) + mp_new_randoms(mp); + else + mp->j_random = mp->j_random-1; + mp_number_clone (ret, mp->randoms[mp->j_random]); +} + + + +@ 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\/}). + +@c +static void mp_m_norm_rand (MP mp, mp_number *ret) { + mp_number ab_vs_cd; + mp_number abs_x; + mp_number u; + mp_number r; + mp_number la, xa; + new_number (ab_vs_cd); + new_number (la); + new_number (xa); + new_number (abs_x); + new_number (u); + new_number (r); + do { + do { + mp_number v; + new_number (v); + mp_next_random(mp, &v); + mp_number_substract (&v, ((math_data *)mp->math)->fraction_half_t); + mp_number_take_fraction (mp,&xa, ((math_data *)mp->math)->sqrt_8_e_k, v); + free_number (v); + mp_next_random(mp, &u); + mp_number_clone (&abs_x, xa); + mp_number_abs (&abs_x); + } while (!mp_number_less(abs_x, u)); + mp_number_make_fraction (mp, &r, xa, u); + mp_number_clone (&xa, r); + mp_m_log (mp,&la, u); + mp_set_number_from_substraction(&la, ((math_data *)mp->math)->twelve_ln_2_k, la); + 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); + free_number (ab_vs_cd); + free_number (r); + free_number (abs_x); + free_number (la); + free_number (xa); + free_number (u); +} diff --git a/Build/source/texk/web2c/mplibdir/mpmathbinary.w b/Build/source/texk/web2c/mplibdir/mpmathbinary.w index ca223c6e353..b8b8508d8aa 100644 --- a/Build/source/texk/web2c/mplibdir/mpmathbinary.w +++ b/Build/source/texk/web2c/mplibdir/mpmathbinary.w @@ -47,6 +47,7 @@ First, here are some very important constants. #define DEBUG 0 static void mp_binary_scan_fractional_token (MP mp, int n); static void mp_binary_scan_numeric_token (MP mp, int n); +static void mp_binary_ab_vs_cd (MP mp, mp_number *ret, mp_number a, mp_number b, mp_number c, mp_number d); static void mp_ab_vs_cd (MP mp, mp_number *ret, mp_number a, mp_number b, mp_number c, mp_number d); static void mp_binary_crossing_point (MP mp, mp_number *ret, mp_number a, mp_number b, mp_number c); static void mp_binary_number_modulo (mp_number *a, mp_number b); @@ -60,6 +61,7 @@ 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_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); static void mp_binary_pyth_sub (MP mp, mp_number *r, mp_number a, mp_number b); @@ -298,7 +300,7 @@ void * mp_initialize_binary_math (MP mp) { mpfr_set_si(math->one_eighty_deg_t.data.num, 180 * angle_multiplier, ROUNDING); /* various approximations */ mp_new_number (mp, &math->one_k, mp_scaled_type); - mpfr_set_si(math->one_k.data.num, 1024, ROUNDING); + mpfr_set_d(math->one_k.data.num, 1.0/64, ROUNDING); mp_new_number (mp, &math->sqrt_8_e_k, mp_scaled_type); { mpfr_set_d(math->sqrt_8_e_k.data.num, 112428.82793 / 65536.0, ROUNDING); @@ -394,6 +396,7 @@ 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_norm_rand = mp_binary_m_norm_rand; math->pyth_add = mp_binary_pyth_add; math->pyth_sub = mp_binary_pyth_sub; math->fraction_to_scaled = mp_number_fraction_to_scaled; @@ -1524,4 +1527,101 @@ void mp_init_randoms (MP mp, int seed) { @ @c void mp_binary_number_modulo (mp_number *a, mp_number b) { mpfr_remainder (a->data.num, a->data.num, b.data.num, ROUNDING); -}
\ No newline at end of file +} + + + +@ To consume a random fraction, the program below will say `|next_random|'. + +@c +static void mp_next_random (MP mp, mp_number *ret) { + if ( mp->j_random==0 ) + mp_new_randoms(mp); + else + mp->j_random = mp->j_random-1; + mp_number_clone (ret, mp->randoms[mp->j_random]); +} + + +@ 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\/}). + +@c +static void mp_binary_m_norm_rand (MP mp, mp_number *ret) { + mp_number ab_vs_cd; + mp_number abs_x; + mp_number u; + mp_number r; + mp_number la, xa; + new_number (ab_vs_cd); + new_number (la); + new_number (xa); + new_number (abs_x); + new_number (u); + new_number (r); + + do { + do { + mp_number v; + new_number (v); + mp_next_random(mp, &v); + mp_number_substract (&v, ((math_data *)mp->math)->fraction_half_t); + mp_binary_number_take_fraction (mp,&xa, ((math_data *)mp->math)->sqrt_8_e_k, v); + free_number (v); + mp_next_random(mp, &u); + mp_number_clone (&abs_x, xa); + mp_binary_abs (&abs_x); + } while (!mp_number_less(abs_x, u)); + mp_binary_number_make_fraction (mp, &r, xa, u); + mp_number_clone (&xa, r); + mp_binary_m_log (mp,&la, u); + mp_set_binary_from_substraction(&la, ((math_data *)mp->math)->twelve_ln_2_k, la); + mp_binary_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); + free_number (ab_vs_cd); + free_number (r); + free_number (abs_x); + free_number (la); + free_number (xa); + free_number (u); +} + + + +@ The following subroutine is used only in norm_rand and tests if $ab$ is +greater than, equal to, or less than~$cd$. +The result is $+1$, 0, or~$-1$ in the three respective cases. + +@c +static void mp_binary_ab_vs_cd (MP mp, mp_number *ret, mp_number a_orig, mp_number b_orig, mp_number c_orig, mp_number d_orig) { + mpfr_t a, b, c, d; + mpfr_t ab, cd; + + int cmp = 0; + (void)mp; + mpfr_inits2(precision_bits, a,b,c,d,ab,cd,(mpfr_ptr)0); + mpfr_set(a, (mpfr_ptr )a_orig.data.num, ROUNDING); + mpfr_set(b, (mpfr_ptr )b_orig.data.num, ROUNDING); + mpfr_set(c, (mpfr_ptr )c_orig.data.num, ROUNDING); + mpfr_set(d, (mpfr_ptr )d_orig.data.num, ROUNDING); + + mpfr_mul(ab,a,b, ROUNDING); + mpfr_mul(cd,c,d, ROUNDING); + + mpfr_set(ret->data.num, zero, ROUNDING); + cmp = mpfr_cmp(ab,cd); + if (cmp) { + if (cmp>0) + mpfr_set(ret->data.num, one, ROUNDING); + else + mpfr_set(ret->data.num, minusone, ROUNDING); + } + mp_check_mpfr_t(mp, ret->data.num); + mpfr_clears(a,b,c,d,ab,cd,(mpfr_ptr)0); + return; +} + + diff --git a/Build/source/texk/web2c/mplibdir/mpmathdecimal.w b/Build/source/texk/web2c/mplibdir/mpmathdecimal.w index c65e2a5a420..3ae1cce3042 100644 --- a/Build/source/texk/web2c/mplibdir/mpmathdecimal.w +++ b/Build/source/texk/web2c/mplibdir/mpmathdecimal.w @@ -55,6 +55,7 @@ First, here are some very important constants. static void mp_decimal_scan_fractional_token (MP mp, int n); static void mp_decimal_scan_numeric_token (MP mp, int n); static void mp_ab_vs_cd (MP mp, mp_number *ret, mp_number a, mp_number b, mp_number c, mp_number d); +/*static void mp_decimal_ab_vs_cd (MP mp, mp_number *ret, mp_number a, mp_number b, mp_number c, mp_number d);*/ static void mp_decimal_crossing_point (MP mp, mp_number *ret, mp_number a, mp_number b, mp_number c); static void mp_decimal_number_modulo (mp_number *a, mp_number b); static void mp_decimal_print_number (MP mp, mp_number n); @@ -67,6 +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_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); static void mp_decimal_pyth_sub (MP mp, mp_number *r, mp_number a, mp_number b); @@ -444,7 +446,7 @@ void * mp_initialize_decimal_math (MP mp) { decNumberFromInt32(math->one_eighty_deg_t.data.num, 180 * angle_multiplier); /* various approximations */ mp_new_number (mp, &math->one_k, mp_scaled_type); - decNumberFromInt32(math->one_k.data.num, 1024); + decNumberFromDouble(math->one_k.data.num, 1.0/64); mp_new_number (mp, &math->sqrt_8_e_k, mp_scaled_type); { decNumberFromDouble(math->sqrt_8_e_k.data.num, 112428.82793 / 65536.0); @@ -540,6 +542,7 @@ 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_norm_rand = mp_decimal_m_norm_rand; math->pyth_add = mp_decimal_pyth_add; math->pyth_sub = mp_decimal_pyth_sub; math->fraction_to_scaled = mp_number_fraction_to_scaled; @@ -1748,4 +1751,107 @@ void mp_init_randoms (MP mp, int seed) { @ @c void mp_decimal_number_modulo (mp_number *a, mp_number b) { decNumberRemainder(a->data.num, a->data.num, b.data.num, &set); -}
\ No newline at end of file +} + + + + + + + + + + + + +@ To consume a random fraction, the program below will say `|next_random|'. + +@c +static void mp_next_random (MP mp, mp_number *ret) { + if ( mp->j_random==0 ) + mp_new_randoms(mp); + else + mp->j_random = mp->j_random-1; + mp_number_clone (ret, mp->randoms[mp->j_random]); +} + + +@ 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\/}). + +@c +static void mp_decimal_m_norm_rand (MP mp, mp_number *ret) { + mp_number ab_vs_cd; + mp_number abs_x; + mp_number u; + mp_number r; + mp_number la, xa; + new_number (ab_vs_cd); + new_number (la); + new_number (xa); + new_number (abs_x); + new_number (u); + new_number (r); + + do { + do { + mp_number v; + new_number (v); + mp_next_random(mp, &v); + mp_number_substract (&v, ((math_data *)mp->math)->fraction_half_t); + mp_decimal_number_take_fraction (mp,&xa, ((math_data *)mp->math)->sqrt_8_e_k, v); + free_number (v); + mp_next_random(mp, &u); + mp_number_clone (&abs_x, xa); + mp_decimal_abs (&abs_x); + } while (!mp_number_less(abs_x, u)); + mp_decimal_number_make_fraction (mp, &r, xa, u); + 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); + free_number (ab_vs_cd); + free_number (r); + free_number (abs_x); + free_number (la); + free_number (xa); + free_number (u); +} + + + + +@ The following subroutine could be used in norm_rand and tests if $ab$ is +greater than, equal to, or less than~$cd$. +The result is $+1$, 0, or~$-1$ in the three respective cases. +This is not necessary, even if it's shorter than the current ab_vs_cd +and looks as a native implememtation. + +@c +/* +void mp_decimal_ab_vs_cd (MP mp, mp_number *ret, mp_number a_orig, mp_number b_orig, mp_number c_orig, mp_number d_orig) { + decNumber a, b, c, d; + decNumber ab, cd; + (void)mp; + + decNumberCopy(&a, (decNumber *)a_orig.data.num); + decNumberCopy(&b, (decNumber *)b_orig.data.num); + decNumberCopy(&c, (decNumber *)c_orig.data.num); + decNumberCopy(&d, (decNumber *)d_orig.data.num); + + + decNumberMultiply (&ab, (decNumber *)a_orig.data.num, (decNumber *)b_orig.data.num, &set); + decNumberMultiply (&cd, (decNumber *)c_orig.data.num, (decNumber *)d_orig.data.num, &set); + decNumberCompare(ret->data.num, &ab, &cd, &set); + mp_check_decNumber(mp, ret->data.num, &set); + return; + +} +*/ + + + diff --git a/Build/source/texk/web2c/mplibdir/mpmathdouble.w b/Build/source/texk/web2c/mplibdir/mpmathdouble.w index a6203d0e601..7a6d99a4aa7 100644 --- a/Build/source/texk/web2c/mplibdir/mpmathdouble.w +++ b/Build/source/texk/web2c/mplibdir/mpmathdouble.w @@ -1,4 +1,4 @@ -% $Id: mpmathdouble.w 2037 2014-09-02 14:59:07Z luigi $ +% $Id: mpmathdouble.w 2057 2015-03-20 01:33:59Z luigi $ % % This file is part of MetaPost; % the MetaPost program is in the public domain. @@ -51,6 +51,7 @@ First, here are some very important constants. static void mp_double_scan_fractional_token (MP mp, int n); static void mp_double_scan_numeric_token (MP mp, int n); static void mp_ab_vs_cd (MP mp, mp_number *ret, mp_number a, mp_number b, mp_number c, mp_number d); +static void mp_double_ab_vs_cd (MP mp, mp_number *ret, mp_number a, mp_number b, mp_number c, mp_number d); static void mp_double_crossing_point (MP mp, mp_number *ret, mp_number a, mp_number b, mp_number c); static void mp_number_modulo (mp_number *a, mp_number b); static void mp_double_print_number (MP mp, mp_number n); @@ -63,6 +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_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); static void mp_double_pyth_sub (MP mp, mp_number *r, mp_number a, mp_number b); @@ -182,11 +184,11 @@ void * mp_initialize_double_math (MP mp) { math->one_eighty_deg_t.data.dval = one_eighty_deg; /* various approximations */ mp_new_number (mp, &math->one_k, mp_scaled_type); - math->one_k.data.dval = 1024; + math->one_k.data.dval = 1.0/64 ; mp_new_number (mp, &math->sqrt_8_e_k, mp_scaled_type); - math->sqrt_8_e_k.data.dval = 112429 / 65536.0; /* $2^{16}\sqrt{8/e}\approx 112428.82793$ */ + math->sqrt_8_e_k.data.dval = 1.71552776992141359295 ; /* $2^{16}\sqrt{8/e}\approx 112428.82793$ */ mp_new_number (mp, &math->twelve_ln_2_k, mp_fraction_type); - math->twelve_ln_2_k.data.dval = 139548960 / 65536.0; /* $2^{24}\cdot12\ln2\approx139548959.6165$ */ + math->twelve_ln_2_k.data.dval = 8.31776616671934371292 *256; /* $2^{24}\cdot12\ln2\approx139548959.6165$ */ mp_new_number (mp, &math->coef_bound_k, mp_fraction_type); math->coef_bound_k.data.dval = coef_bound; mp_new_number (mp, &math->coef_bound_minus_1, mp_fraction_type); @@ -260,6 +262,7 @@ 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_norm_rand = mp_double_m_norm_rand; math->pyth_add = mp_double_pyth_add; math->pyth_sub = mp_double_pyth_sub; math->fraction_to_scaled = mp_number_fraction_to_scaled; @@ -1248,4 +1251,87 @@ double modulus(double left, double right) { } void mp_number_modulo (mp_number *a, mp_number b) { a->data.dval = modulus (a->data.dval, b.data.dval); -}
\ No newline at end of file +} + + + + + +@ To consume a random fraction, the program below will say `|next_random|'. + +@c +static void mp_next_random (MP mp, mp_number *ret) { + if ( mp->j_random==0 ) + mp_new_randoms(mp); + else + mp->j_random = mp->j_random-1; + mp_number_clone (ret, mp->randoms[mp->j_random]); +} + + +@ 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\/}). + +@c +static void mp_double_m_norm_rand (MP mp, mp_number *ret) { + mp_number ab_vs_cd; + mp_number abs_x; + mp_number u; + mp_number r; + mp_number la, xa; + new_number (ab_vs_cd); + new_number (la); + new_number (xa); + new_number (abs_x); + new_number (u); + new_number (r); + + do { + do { + mp_number v; + new_number (v); + mp_next_random(mp, &v); + mp_number_substract (&v, ((math_data *)mp->math)->fraction_half_t); + mp_double_number_take_fraction (mp,&xa, ((math_data *)mp->math)->sqrt_8_e_k, v); + free_number (v); + mp_next_random(mp, &u); + mp_number_clone (&abs_x, xa); + mp_double_abs (&abs_x); + } while (!mp_number_less(abs_x, u)); + mp_double_number_make_fraction (mp, &r, xa, u); + mp_number_clone (&xa, r); + mp_double_m_log (mp,&la, u); + mp_set_double_from_substraction(&la, ((math_data *)mp->math)->twelve_ln_2_k, la); + mp_double_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); + free_number (ab_vs_cd); + free_number (r); + free_number (abs_x); + free_number (la); + free_number (xa); + free_number (u); +} + + + + +@ The following subroutine is used only in norm_rand and tests if $ab$ is +greater than, equal to, or less than~$cd$. +The result is $+1$, 0, or~$-1$ in the three respective cases. + +@c +void mp_double_ab_vs_cd (MP mp, mp_number *ret, mp_number a_orig, mp_number b_orig, mp_number c_orig, mp_number d_orig) { + double ab, cd; + (void)mp; + ret->data.dval = 0 ; + ab = a_orig.data.dval*b_orig.data.dval; + cd = c_orig.data.dval*d_orig.data.dval; + if (ab > cd ) + ret->data.dval = 1 ; + else if (ab < cd ) + ret->data.dval = -1 ; + return ; +} + diff --git a/Build/source/texk/web2c/mplibdir/mpost.w b/Build/source/texk/web2c/mplibdir/mpost.w index 7c9e24b6053..cf87cceab7f 100644 --- a/Build/source/texk/web2c/mplibdir/mpost.w +++ b/Build/source/texk/web2c/mplibdir/mpost.w @@ -1,5 +1,3 @@ -% $Id: mpost.w 2048 2014-12-04 10:26:26Z luigi $ -% % This file is part of MetaPost; % the MetaPost program is in the public domain. % See the <Show version...> code below for more info. diff --git a/Build/source/texk/web2c/mplibdir/mpstrings.w b/Build/source/texk/web2c/mplibdir/mpstrings.w index 0ecc4e6ff7e..ff4e5b6b44e 100644 --- a/Build/source/texk/web2c/mplibdir/mpstrings.w +++ b/Build/source/texk/web2c/mplibdir/mpstrings.w @@ -1,5 +1,3 @@ -% $Id: mpstrings.w 1702 2012-09-27 10:31:30Z taco $ -% % This file is part of MetaPost; % the MetaPost program is in the public domain. % See the <Show version...> code in mpost.w for more info. diff --git a/Build/source/texk/web2c/mplibdir/mpxout.w b/Build/source/texk/web2c/mplibdir/mpxout.w index 382b907dbee..8d1dee5ed49 100644 --- a/Build/source/texk/web2c/mplibdir/mpxout.w +++ b/Build/source/texk/web2c/mplibdir/mpxout.w @@ -1,4 +1,3 @@ -% $Id: mpxout.w 2031 2014-06-24 13:38:58Z luigi $ % This file is part of MetaPost; % the MetaPost program is in the public domain. % See the <Show version...> code in mpost.w for more info. diff --git a/Build/source/texk/web2c/mplibdir/pngout.w b/Build/source/texk/web2c/mplibdir/pngout.w index 1ab58d6b015..7a4a0b44006 100644 --- a/Build/source/texk/web2c/mplibdir/pngout.w +++ b/Build/source/texk/web2c/mplibdir/pngout.w @@ -1,5 +1,3 @@ -% $Id: pngout.w 1706 2012-09-28 08:12:34Z taco $ -% % Copyright 2012 Taco Hoekwater. % % This program is free software: you can redistribute it and/or modify diff --git a/Build/source/texk/web2c/mplibdir/psout.w b/Build/source/texk/web2c/mplibdir/psout.w index bc26e0dadcc..e11dca0cc2a 100644 --- a/Build/source/texk/web2c/mplibdir/psout.w +++ b/Build/source/texk/web2c/mplibdir/psout.w @@ -1,4 +1,3 @@ -% $Id: psout.w 2045 2014-11-05 11:33:13Z luigi $ % This file is part of MetaPost; % the MetaPost program is in the public domain. % See the <Show version...> code in mpost.w for more info. diff --git a/Build/source/texk/web2c/mplibdir/svgout.w b/Build/source/texk/web2c/mplibdir/svgout.w index ecc81972124..6ee2c711739 100644 --- a/Build/source/texk/web2c/mplibdir/svgout.w +++ b/Build/source/texk/web2c/mplibdir/svgout.w @@ -1,5 +1,3 @@ -% $Id: svgout.w 2003 2014-04-09 09:48:26Z taco $ -% % Copyright 2008-2009 Taco Hoekwater. % % This program is free software: you can redistribute it and/or modify diff --git a/Build/source/texk/web2c/mplibdir/tfmin.w b/Build/source/texk/web2c/mplibdir/tfmin.w index 0c9e7c5385c..142824258c6 100644 --- a/Build/source/texk/web2c/mplibdir/tfmin.w +++ b/Build/source/texk/web2c/mplibdir/tfmin.w @@ -1,5 +1,3 @@ -% $Id: tfmin.w 1682 2011-05-30 07:24:45Z taco $ -% % Copyright 2008-2009 Taco Hoekwater. % % This program is free software: you can redistribute it and/or modify |