/*
* arccosh(x) == log [ x + sqrt(x^2 - 1) ]
*
* x >= 1.0
*/
void m_apm_arccosh(M_APM rr, int places, M_APM aa)
{
M_APM tmp1, tmp2;
int ii;
ii = m_apm_compare(aa, MM_One);
if (ii == -1) /* x < 1 */
{
M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_arccosh\', Argument < 1");
M_set_to_zero(rr);
return;
}
tmp1 = M_get_stack_var();
tmp2 = M_get_stack_var();
m_apm_multiply(tmp1, aa, aa);
m_apm_subtract(tmp2, tmp1, MM_One);
m_apm_sqrt(tmp1, (places + 6), tmp2);
m_apm_add(tmp2, aa, tmp1);
m_apm_log(rr, places, tmp2);
M_restore_stack(2);
}
/*
* arcsinh(x) == log [ x + sqrt(x^2 + 1) ]
*
* also, use arcsinh(-x) == -arcsinh(x)
*/
void m_apm_arcsinh(M_APM rr, int places, M_APM aa)
{
M_APM tmp0, tmp1, tmp2;
/* result is 0 if input is 0 */
if (aa->m_apm_sign == 0)
{
M_set_to_zero(rr);
return;
}
tmp0 = M_get_stack_var();
tmp1 = M_get_stack_var();
tmp2 = M_get_stack_var();
m_apm_absolute_value(tmp0, aa);
m_apm_multiply(tmp1, tmp0, tmp0);
m_apm_add(tmp2, tmp1, MM_One);
m_apm_sqrt(tmp1, (places + 6), tmp2);
m_apm_add(tmp2, tmp0, tmp1);
m_apm_log(rr, places, tmp2);
rr->m_apm_sign = aa->m_apm_sign; /* fix final sign */
M_restore_stack(3);
}
/*
* arctanh(x) == 0.5 * log [ (1 + x) / (1 - x) ]
*
* |x| < 1.0
*/
void m_apm_arctanh(M_APM rr, int places, M_APM aa)
{
M_APM tmp1, tmp2, tmp3;
int ii, local_precision;
tmp1 = M_get_stack_var();
m_apm_absolute_value(tmp1, aa);
ii = m_apm_compare(tmp1, MM_One);
if (ii >= 0) /* |x| >= 1.0 */
{
M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_arctanh\', |Argument| >= 1");
M_set_to_zero(rr);
M_restore_stack(1);
return;
}
tmp2 = M_get_stack_var();
tmp3 = M_get_stack_var();
local_precision = places + 8;
m_apm_add(tmp1, MM_One, aa);
m_apm_subtract(tmp2, MM_One, aa);
m_apm_divide(tmp3, local_precision, tmp1, tmp2);
m_apm_log(tmp2, local_precision, tmp3);
m_apm_multiply(tmp1, tmp2, MM_0_5);
m_apm_round(rr, places, tmp1);
M_restore_stack(3);
}
/*
Calls the LOG function. The formula used is :
log10(x) = A * log(x) where A = log (e) [0.43429448190325...]
10
*/
void m_apm_log10(M_APM rr, int places, M_APM aa)
{
int dplaces;
M_APM tmp8, tmp9;
tmp8 = M_get_stack_var();
tmp9 = M_get_stack_var();
dplaces = places + 4;
M_check_log_places(dplaces + 45);
m_apm_log(tmp9, dplaces, aa);
m_apm_multiply(tmp8, tmp9, MM_lc_log10R);
m_apm_round(rr, places, tmp8);
M_restore_stack(2); /* restore the 2 locals we used here */
}
void m_apm_log_mt(M_APM rr, int places, M_APM aa)
{
m_apm_enter();
m_apm_log(rr,places,aa);
m_apm_leave();
}
/*
Calculate the POW function by calling EXP :
Y A
X = e where A = Y * log(X)
*/
void m_apm_pow(M_APM rr, int places, M_APM xx, M_APM yy)
{
int iflag, pflag;
char sbuf[64];
M_APM tmp8, tmp9;
/* if yy == 0, return 1 */
if (yy->m_apm_sign == 0)
{
m_apm_copy(rr, MM_One);
return;
}
/* if xx == 0, return 0 */
if (xx->m_apm_sign == 0)
{
M_set_to_zero(rr);
return;
}
if (M_size_flag == 0) /* init locals on first call */
{
M_size_flag = M_get_sizeof_int();
M_last_log_digits = 0;
M_last_xx_input = m_apm_init();
M_last_xx_log = m_apm_init();
}
/*
* if 'yy' is a small enough integer, call the more
* efficient _integer_pow function.
*/
if (m_apm_is_integer(yy))
{
iflag = FALSE;
if (M_size_flag == 2) /* 16 bit compilers */
{
if (yy->m_apm_exponent <= 4)
iflag = TRUE;
}
else /* >= 32 bit compilers */
{
if (yy->m_apm_exponent <= 7)
iflag = TRUE;
}
if (iflag)
{
m_apm_to_integer_string(sbuf, yy);
m_apm_integer_pow(rr, places, xx, atoi(sbuf));
return;
}
}
tmp8 = M_get_stack_var();
tmp9 = M_get_stack_var();
/*
* If parameter 'X' is the same this call as it
* was the previous call, re-use the saved log
* calculation from last time.
*/
pflag = FALSE;
if (M_last_log_digits >= places)
{
if (m_apm_compare(xx, M_last_xx_input) == 0)
pflag = TRUE;
}
if (pflag)
{
m_apm_round(tmp9, (places + 8), M_last_xx_log);
}
else
{
m_apm_log(tmp9, (places + 8), xx);
M_last_log_digits = places + 2;
/* save the 'X' input value and the log calculation */
m_apm_copy(M_last_xx_input, xx);
m_apm_copy(M_last_xx_log, tmp9);
}
m_apm_multiply(tmp8, tmp9, yy);
m_apm_exp(rr, places, tmp8);
M_restore_stack(2); /* restore the 2 locals we used here */
}
