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texpand.c
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texpand.c
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/* This file is part of the MAYLIB libray.
Copyright 2007-2018 Patrick Pelissier
This Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.
This Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with th Library; see the file COPYING.LESSER.txt.
If not, write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */
#include "may-impl.h"
static may_t cos_expand (may_t x);
static may_t sin_expand (may_t x);
static may_t tan_expand (may_t x);
static may_t cosh_expand (may_t x);
static may_t sinh_expand (may_t x);
static may_t tanh_expand (may_t x);
/* Construct the tchebycheff polynomial */
static void
tchebycheff (long n, long b[n+1], int first_kind)
{
long a[n+1], c[n+1];
long i, k, t;
MAY_ASSERT (n >= 1);
memset (a, 0, sizeof a);
memset (b, 0, sizeof a);
memset (c, 0, sizeof a);
a[0] = 1;
if (first_kind) {
/* T0 = 1 T1=X */
b[1] = 1;
} else {
/* U0 = 1 U1 = 2*X */
b[1] = 2;
}
t = 2;
for (k = 1; k < n; k++) {
/* Un+1 = 2*X*Un -Un-1 */
c[0] = -a[0];
for (i = 0; i < t; i++)
c[i+1] = 2*b[i] - a[i+1];
t++;
MAY_ASSERT (t <= n+1);
memcpy (a, b, t*sizeof (long));
memcpy (b, c, t*sizeof (long));
}
return;
}
/* Front ent to tchebycheff */
static may_t
tchebycheff_var (long n, int first_kind, int askabs, may_t arg)
{
MAY_ASSERT (n >= 1);
long coeff[n+1];
tchebycheff (n, coeff, first_kind);
may_t r = MAY_NODE_C (MAY_SUM_T, n+1);
long i;
for (i = 0; i <= n; i++)
MAY_SET_AT (r, i, may_mul_c (may_set_si (askabs ? labs (coeff[i]) : coeff[i] ),
may_pow_si_c (arg, i)));
return may_eval (r);
}
/* Expand sin:
- sin(A+B)=sin(A)*cos(B) + cos(A)*sin(B) */
static may_t
sin_expand (may_t x)
{
may_t a, b;
if (may_sum_extract(&a, &b, x)) {
return may_add_c (may_mul_c (sin_expand (a), cos_expand (b)),
may_mul_c (cos_expand (a), sin_expand (b)));
}
if (may_product_extract(&a, &b, x)) {
if (MAY_TYPE (a) == MAY_INT_T
&& mpz_fits_sshort_p (MAY_INT (a))) {
long n = mpz_get_si (MAY_INT (a)), m;
may_t arg = may_sin (b);
int first_kind;
int sign = 0;
MAY_ASSERT (n != 0);
if (n < 0) {
sign = 1;
n = -n;
}
if (MAY_UNLIKELY (n == 1))
return may_neg (arg);
MAY_ASSERT (n >= 2);
if ((n & 1) == 0) {
m = n - 1;
first_kind = 0;
} else {
m = n;
first_kind = 1;
}
arg = tchebycheff_var (m, first_kind, 0, arg);
if ( (((n+1)&3) <= 1 && sign == 0)
|| (((n+1)&3) >= 2 && sign == 1))
arg = may_neg_c (arg);
if ( (n&1) == 0)
arg = may_mul_c (arg, may_cos_c (MAY_AT (x, 1)));
return may_eval (arg);
}
}
return may_sin_c (x);
}
/* Expand cos */
static may_t
cos_expand (may_t x)
{
may_t a, b;
if (may_sum_extract(&a, &b, x)) {
return may_sub_c (may_mul_c (cos_expand (a), cos_expand (b)),
may_mul_c (sin_expand (a), sin_expand (b)));
}
if (may_product_extract(&a, &b, x)
&& MAY_TYPE (a) == MAY_INT_T
&& mpz_fits_sshort_p (MAY_INT (a))) {
long n = labs (mpz_get_si (MAY_INT (a)));
may_t arg = may_cos (b);
if (MAY_UNLIKELY (n == 1))
return arg;
MAY_ASSERT (n >= 2);
arg = tchebycheff_var (n, 1, 0, arg);
return may_eval (arg);
}
return may_cos_c (x);
}
/* Hyperbolic functions are nearly identical */
/* sinh_expand is nearly identical to sin_expand.
We don't inverse the sign for (n+1)%3 <= 1. */
static may_t
sinh_expand (may_t x)
{
may_t a, b;
if (may_sum_extract(&a, &b, x)) {
return may_add_c (may_mul_c (sinh_expand (a), cosh_expand (b)),
may_mul_c (cosh_expand (a), sinh_expand (b)));
}
if (may_product_extract(&a, &b, x)
&& MAY_TYPE (a) == MAY_INT_T
&& mpz_fits_sshort_p (MAY_INT (a))) {
long n = mpz_get_si (MAY_INT (a)), m;
may_t arg = may_sinh (b);
int first_kind;
int sign = 0;
MAY_ASSERT (n != 0);
if (n < 0) {
sign = 1;
n = -n;
}
if (MAY_UNLIKELY (n == 1))
return may_neg (arg);
MAY_ASSERT (n >= 2);
if ((n & 1) == 0) {
m = n - 1;
first_kind = 0;
} else {
m = n;
first_kind = 1;
}
arg = tchebycheff_var (m, first_kind, 1, arg);
if (sign == 1)
arg = may_neg_c (arg);
if ( (n&1) == 0)
arg = may_mul_c (arg, may_cosh_c (MAY_AT (x, 1)));
return may_eval (arg);
}
return may_sinh_c (x);
}
/* It is identical to cos_expand except that
cosh(a+b) = cosh(a)*cosh(b)+sinh(a)+sinh(b) */
static may_t
cosh_expand (may_t x)
{
may_t a, b;
if (may_sum_extract(&a, &b, x)) {
return may_add_c (may_mul_c (cosh_expand (a), cosh_expand (b)),
may_mul_c (sinh_expand (a), sinh_expand (b)));
}
if (may_product_extract(&a, &b, x)
&& MAY_TYPE (a) == MAY_INT_T
&& mpz_fits_sshort_p (MAY_INT (a))) {
long n = labs (mpz_get_si (MAY_INT (a)));
may_t arg = may_cosh (b);
if (MAY_UNLIKELY (n == 1))
return arg;
MAY_ASSERT (n >= 2);
arg = tchebycheff_var (n, 1, 0, arg);
return may_eval (arg);
}
return may_cosh_c (x);
}
static may_t
tan_expand (may_t x)
{
may_t a, b;
if (may_sum_extract(&a, &b, x)) {
may_t first = tan_expand (may_eval (a));
may_t last = tan_expand (may_eval (b));
return may_div_c (may_add_c (first, last), may_sub_c (MAY_ONE,may_mul_c (first, last)));
}
if (may_product_extract(&a, &b, x)
&& MAY_TYPE (a) == MAY_INT_T
&& mpz_fits_sshort_p (MAY_INT (a))) {
/* Pure lazyness */
may_t g = may_eval (may_div_c (sin_expand (x), cos_expand (x)));
g = may_sin2tancos (g);
g = may_rewrite (g,
may_parse_str ("cos($1)^$2"),
may_parse_str ("(1+tan($1)^2)^(-$2/2)"));
return g;
}
return may_tan_c (x);
}
static may_t
tanh_expand (may_t x)
{
may_t a, b;
if (may_sum_extract(&a, &b, x)) {
may_t first = tanh_expand (may_eval(a));
may_t last = tanh_expand (may_eval(b));
return may_div_c (may_add_c (first, last), may_add_c (MAY_ONE,may_mul_c (first, last)));
}
if (may_product_extract(&a, &b, x)
&& MAY_TYPE (a) == MAY_INT_T
&& mpz_fits_sshort_p (MAY_INT (a))) {
/* Pure lazyness */
may_t g = may_eval (may_div_c (sinh_expand (x), cosh_expand (x)));
g = may_sin2tancos (g);
g = may_rewrite (g,
may_parse_str ("cosh($1)^$2"),
may_parse_str ("(1-tanh($1)^2)^(-$2/2)"));
return g;
}
return may_tanh (x);
}
static const char *const texpand_name[] = {
may_sin_name, may_cos_name, may_tan_name,
may_sinh_name, may_cosh_name, may_tanh_name
};
static const void *const texpand_func[] = {
sin_expand, cos_expand, tan_expand,
sinh_expand, cosh_expand, tanh_expand
};
may_t
may_texpand (may_t x)
{
MAY_ASSERT (MAY_EVAL_P (x));
MAY_ASSERT (numberof (texpand_name) == numberof (texpand_func));
MAY_LOG_FUNC (("%Y", x));
may_mark();
may_t y = may_subs_c (x, 1, numberof (texpand_name),
texpand_name, texpand_func);
return may_keep (may_eval (y));
}
/* FIXME: Semantic to define */
static may_t
exp_expand (may_t x)
{
may_t y, a, b;
if (may_sum_p (x)) {
may_iterator_t it;
y = may_sum_iterator_init(it, x);
y = exp_expand(y);
while (may_sum_iterator_end(&a, &b, it)) {
y = may_mulinc_c (y, may_pow_c (exp_expand (b), a));
may_sum_iterator_next(it);
}
} else if (may_product_extract(&a, &b, x) && MAY_INT_P (a)) {
y = may_pow_c (exp_expand (b), a);
} else if (may_purenum_p (x) && may_num_neg_p (x)) {
y = may_pow_c (may_exp_c (may_num_abs (MAY_DUMMY, x)), MAY_N_ONE);
} else
y = may_exp_c (x);
return may_eval (y);
}
static const char *const eexpand_name[] = {
may_exp_name
};
static const void *const eexpand_func[] = {
exp_expand
};
may_t
may_eexpand (may_t x)
{
MAY_ASSERT (MAY_EVAL_P (x));
MAY_ASSERT (numberof (eexpand_name) == numberof (eexpand_func));
MAY_LOG_FUNC (("%Y", x));
may_mark();
may_t y = may_subs_c (x, 1, numberof (eexpand_name),
eexpand_name, eexpand_func);
return may_keep (may_eval(y));
}