/*
* hash_complex - hash a COMPLEX
*
* given:
* type - hash type (see hash.h)
* c - the COMPLEX
* state - the state to hash or NULL
*
* returns:
* the new state
*/
HASH *
hash_complex(int type, void *c, HASH *state)
{
COMPLEX *complex = (COMPLEX *)c; /* c as a COMPLEX pointer */
/*
* initialize if state is NULL
*/
if (state == NULL) {
state = hash_init(type, NULL);
}
/*
* setup for the COMPLEX hash
*/
(state->chkpt)(state);
state->bytes = FALSE;
/*
* catch the zero special case
*/
if (ciszero(complex)) {
/* note a zero numeric value and return */
(state->note)(HASH_ZERO(state->base), state);
return state;
}
/*
* process the real value if not pure imaginary
*
* We will ignore the real part if the value is of the form 0+xi.
*/
if (!qiszero(complex->real)) {
state = hash_number(type, complex->real, state);
}
/*
* if the NUMBER is not real, process the imaginary value
*
* We will ignore the imaginary part of the value is of the form x+0i.
*/
if (!cisreal(complex)) {
/* note the sqrt(-1) */
(state->note)(HASH_COMPLEX(state->base), state);
/* hash the imaginary value */
state = hash_number(type, complex->imag, state);
}
/*
* all done
*/
return state;
}
/*
* Add two complex numbers.
*/
COMPLEX *
cadd(COMPLEX *c1, COMPLEX *c2)
{
COMPLEX *r;
if (ciszero(c1))
return clink(c2);
if (ciszero(c2))
return clink(c1);
r = comalloc();
if (!qiszero(c1->real) || !qiszero(c2->real)) {
qfree(r->real);
r->real = qqadd(c1->real, c2->real);
}
if (!qiszero(c1->imag) || !qiszero(c2->imag)) {
qfree(r->imag);
r->imag = qqadd(c1->imag, c2->imag);
}
return r;
}
/*
* Multiply two complex numbers.
* This saves one multiplication over the obvious algorithm by
* trading it for several extra additions, as follows. Let
* q1 = (a + b) * (c + d)
* q2 = a * c
* q3 = b * d
* Then (a+bi) * (c+di) = (q2 - q3) + (q1 - q2 - q3)i.
*/
COMPLEX *
cmul(COMPLEX *c1, COMPLEX *c2)
{
COMPLEX *r;
NUMBER *q1, *q2, *q3, *q4;
if (ciszero(c1) || ciszero(c2))
return clink(&_czero_);
if (cisone(c1))
return clink(c2);
if (cisone(c2))
return clink(c1);
if (cisreal(c2))
return cmulq(c1, c2->real);
if (cisreal(c1))
return cmulq(c2, c1->real);
/*
* Need to do the full calculation.
*/
r = comalloc();
q2 = qqadd(c1->real, c1->imag);
q3 = qqadd(c2->real, c2->imag);
q1 = qmul(q2, q3);
qfree(q2);
qfree(q3);
q2 = qmul(c1->real, c2->real);
q3 = qmul(c1->imag, c2->imag);
q4 = qqadd(q2, q3);
qfree(r->real);
r->real = qsub(q2, q3);
qfree(r->imag);
r->imag = qsub(q1, q4);
qfree(q1);
qfree(q2);
qfree(q3);
qfree(q4);
return r;
}
/*
* Scale a complex number by a power of two.
*/
COMPLEX *
cscale(COMPLEX *c, long n)
{
COMPLEX *r;
if (ciszero(c) || (n == 0))
return clink(c);
r = comalloc();
qfree(r->real);
qfree(r->imag);
r->real = qscale(c->real, n);
r->imag = qscale(c->imag, n);
return r;
}
/*
* Negate a complex number.
*/
COMPLEX *
cneg(COMPLEX *c)
{
COMPLEX *r;
if (ciszero(c))
return clink(&_czero_);
r = comalloc();
if (!qiszero(c->real)) {
qfree(r->real);
r->real = qneg(c->real);
}
if (!qiszero(c->imag)) {
qfree(r->imag);
r->imag = qneg(c->imag);
}
return r;
}
/*
* Subtract two complex numbers.
*/
COMPLEX *
csub(COMPLEX *c1, COMPLEX *c2)
{
COMPLEX *r;
if ((c1->real == c2->real) && (c1->imag == c2->imag))
return clink(&_czero_);
if (ciszero(c2))
return clink(c1);
r = comalloc();
if (!qiszero(c1->real) || !qiszero(c2->real)) {
qfree(r->real);
r->real = qsub(c1->real, c2->real);
}
if (!qiszero(c1->imag) || !qiszero(c2->imag)) {
qfree(r->imag);
r->imag = qsub(c1->imag, c2->imag);
}
return r;
}
/*
* Invert a complex number.
*/
COMPLEX *
cinv(COMPLEX *c)
{
COMPLEX *r;
NUMBER *q1, *q2, *den;
if (ciszero(c)) {
math_error("Inverting zero");
/*NOTREACHED*/
}
r = comalloc();
if (cisreal(c)) {
qfree(r->real);
r->real = qinv(c->real);
return r;
}
if (cisimag(c)) {
q1 = qinv(c->imag);
qfree(r->imag);
r->imag = qneg(q1);
qfree(q1);
return r;
}
q1 = qsquare(c->real);
q2 = qsquare(c->imag);
den = qqadd(q1, q2);
qfree(q1);
qfree(q2);
qfree(r->real);
r->real = qqdiv(c->real, den);
q1 = qqdiv(c->imag, den);
qfree(r->imag);
r->imag = qneg(q1);
qfree(q1);
qfree(den);
return r;
}
/*
* Square a complex number.
*/
COMPLEX *
csquare(COMPLEX *c)
{
COMPLEX *r;
NUMBER *q1, *q2;
if (ciszero(c))
return clink(&_czero_);
if (cisrunit(c))
return clink(&_cone_);
if (cisiunit(c))
return clink(&_cnegone_);
r = comalloc();
if (cisreal(c)) {
qfree(r->real);
r->real = qsquare(c->real);
return r;
}
if (cisimag(c)) {
qfree(r->real);
q1 = qsquare(c->imag);
r->real = qneg(q1);
qfree(q1);
return r;
}
q1 = qsquare(c->real);
q2 = qsquare(c->imag);
qfree(r->real);
r->real = qsub(q1, q2);
qfree(q1);
qfree(q2);
qfree(r->imag);
q1 = qmul(c->real, c->imag);
r->imag = qscale(q1, 1L);
qfree(q1);
return r;
}
/*
* Divide two complex numbers.
*/
COMPLEX *
cdiv(COMPLEX *c1, COMPLEX *c2)
{
COMPLEX *r;
NUMBER *q1, *q2, *q3, *den;
if (ciszero(c2)) {
math_error("Division by zero");
/*NOTREACHED*/
}
if ((c1->real == c2->real) && (c1->imag == c2->imag))
return clink(&_cone_);
r = comalloc();
if (cisreal(c1) && cisreal(c2)) {
qfree(r->real);
r->real = qqdiv(c1->real, c2->real);
return r;
}
if (cisimag(c1) && cisimag(c2)) {
qfree(r->real);
r->real = qqdiv(c1->imag, c2->imag);
return r;
}
if (cisimag(c1) && cisreal(c2)) {
qfree(r->imag);
r->imag = qqdiv(c1->imag, c2->real);
return r;
}
if (cisreal(c1) && cisimag(c2)) {
qfree(r->imag);
q1 = qqdiv(c1->real, c2->imag);
r->imag = qneg(q1);
qfree(q1);
return r;
}
if (cisreal(c2)) {
qfree(r->real);
qfree(r->imag);
r->real = qqdiv(c1->real, c2->real);
r->imag = qqdiv(c1->imag, c2->real);
return r;
}
q1 = qsquare(c2->real);
q2 = qsquare(c2->imag);
den = qqadd(q1, q2);
qfree(q1);
qfree(q2);
q1 = qmul(c1->real, c2->real);
q2 = qmul(c1->imag, c2->imag);
q3 = qqadd(q1, q2);
qfree(q1);
qfree(q2);
qfree(r->real);
r->real = qqdiv(q3, den);
qfree(q3);
q1 = qmul(c1->real, c2->imag);
q2 = qmul(c1->imag, c2->real);
q3 = qsub(q2, q1);
qfree(q1);
qfree(q2);
qfree(r->imag);
r->imag = qqdiv(q3, den);
qfree(q3);
qfree(den);
return r;
}
