/* See numarray.h for Complex32, Complex64:
typedef struct { Float32 r, i; } Complex32;
typedef struct { Float64 r, i; } Complex64;
*/
typedef struct { Float32 a, theta; } PolarComplex32;
typedef struct { Float64 a, theta; } PolarComplex64;
#define NUM_SQ(x) ((x)*(x))
#define NUM_CABSSQ(p) (NUM_SQ((p).r) + NUM_SQ((p).i))
#define NUM_CABS(p) sqrt(NUM_CABSSQ(p))
#define NUM_C_TO_P(c, p) (p).a = NUM_CABS(c); \
(p).theta = atan2((c).i, (c).r);
#define NUM_P_TO_C(p, c) (c).r = (p).a*cos((p).theta); \
(c).i = (p).a*sin((p).theta);
#define NUM_CASS(p, q) (q).r = (p).r, (q).i = (p).i
#define NUM_CADD(p, q, s) (s).r = (p).r + (q).r, \
(s).i = (p).i + (q).i
#define NUM_CSUB(p, q, s) (s).r = (p).r - (q).r, \
(s).i = (p).i - (q).i
#define NUM_CMUL(p, q, s) \
{ Float64 rp = (p).r; \
Float64 rq = (q).r; \
(s).r = rp*rq - (p).i*(q).i; \
(s).i = rp*(q).i + rq*(p).i; \
}
#define NUM_CDIV(p, q, s) \
{ \
Float64 rp = (p).r; \
Float64 ip = (p).i; \
Float64 rq = (q).r; \
if ((q).i != 0) { \
Float64 temp = NUM_CABSSQ(q); \
(s).r = (rp*rq+(p).i*(q).i)/temp; \
(s).i = (rq*(p).i-(q).i*rp)/temp; \
} else { \
(s).r = rp/rq; \
(s).i = ip/rq; \
} \
}
#define NUM_CREM(p, q, s) \
{ Complex64 r; \
NUM_CDIV(p, q, r); \
r.r = floor(r.r); \
r.i = 0; \
NUM_CMUL(r, q, r); \
NUM_CSUB(p, r, s); \
}
#define NUM_CMINUS(p, s) (s).r = -(p).r; (s).i = -(p).i;
#define NUM_CNEG NUM_CMINUS
#define NUM_CEQ(p, q) (((p).r == (q).r) && ((p).i == (q).i))
#define NUM_CNE(p, q) (((p).r != (q).r) || ((p).i != (q).i))
#define NUM_CLT(p, q) ((p).r < (q).r)
#define NUM_CGT(p, q) ((p).r > (q).r)
#define NUM_CLE(p, q) ((p).r <= (q).r)
#define NUM_CGE(p, q) ((p).r >= (q).r)
/* e**z = e**x * (cos(y)+ i*sin(y)) where z = x + i*y
so e**z = e**x * cos(y) + i * e**x * sin(y)
*/
#define NUM_CEXP(p, s) \
{ Float64 ex = exp((p).r); \
(s).r = ex * cos((p).i); \
(s).i = ex * sin((p).i); \
}
/* e**w = z; w = u + i*v; z = r * e**(i*theta);
e**u * e**(i*v) = r * e**(i*theta);
log(z) = w; log(z) = log(r) + i*theta;
*/
#define NUM_CLOG(p, s) \
{ PolarComplex64 temp; NUM_C_TO_P(p, temp); \
(s).r = num_log(temp.a); \
(s).i = temp.theta; \
}
#define NUM_LOG10_E 0.43429448190325182
#define NUM_CLOG10(p, s) \
{ NUM_CLOG(p, s); \
(s).r *= NUM_LOG10_E; \
(s).i *= NUM_LOG10_E; \
}
/* s = p ** q */
#define NUM_CPOW(p, q, s) { if (NUM_CABSSQ(p) == 0) { \
if ((q).r == 0 && (q).i == 0) { \
(s).r = (s).i = 1; \
} else { \
(s).r = (s).i = 0; \
} \
} else { \
NUM_CLOG(p, s); \
NUM_CMUL(s, q, s); \
NUM_CEXP(s, s); \
} \
}
#define NUM_CSQRT(p, s) { Complex64 temp; temp.r = 0.5; temp.i=0; \
NUM_CPOW(p, temp, s); \
}
#define NUM_CSQR(p, s) { Complex64 temp; temp.r = 2.0; temp.i=0; \
NUM_CPOW(p, temp, s); \
}
#define NUM_CSIN(p, s) { Float64 sp = sin((p).r); \
Float64 cp = cos((p).r); \
(s).r = cosh((p).i) * sp; \
(s).i = sinh((p).i) * cp; \
}
#define NUM_CCOS(p, s) { Float64 sp = sin((p).r); \
Float64 cp = cos((p).r); \
(s).r = cosh((p).i) * cp; \
(s).i = -sinh((p).i) * sp; \
}
#define NUM_CTAN(p, s) { Complex64 ss, cs; \
NUM_CSIN(p, ss); \
NUM_CCOS(p, cs); \
NUM_CDIV(ss, cs, s); \
}
#define NUM_CSINH(p, s) { Float64 sp = sin((p).i); \
Float64 cp = cos((p).i); \
(s).r = sinh((p).r) * cp; \
(s).i = cosh((p).r) * sp; \
}
#define NUM_CCOSH(p, s) { Float64 sp = sin((p).i); \
Float64 cp = cos((p).i); \
(s).r = cosh((p).r) * cp; \
(s).i = sinh((p).r) * sp; \
}
#define NUM_CTANH(p, s) { Complex64 ss, cs; \
NUM_CSINH(p, ss); \
NUM_CCOSH(p, cs); \
NUM_CDIV(ss, cs, s); \
}
#define NUM_CRPOW(p, v, s) { Complex64 cr; cr.r = v; cr.i = 0; \
NUM_CPOW(p,cr,s); \
}
#define NUM_CRMUL(p, v, s) (s).r = (p).r * v; (s).i = (p).i * v;
#define NUM_CIMUL(p, s) { Float64 temp = (s).r; \
(s).r = -(p).i; (s).i = temp; \
}
/* asin(z) = -i * log(i*z + (1 - z**2)**0.5) */
#define NUM_CASIN(p, s) { Complex64 p1; NUM_CASS(p, p1); \
NUM_CIMUL(p, p1); \
NUM_CMUL(p, p, s); \
NUM_CNEG(s, s); \
(s).r += 1; \
NUM_CRPOW(s, 0.5, s); \
NUM_CADD(p1, s, s); \
NUM_CLOG(s, s); \
NUM_CIMUL(s, s); \
NUM_CNEG(s, s); \
}
/* acos(z) = -i * log(z + i*(1 - z**2)**0.5) */
#define NUM_CACOS(p, s) { Complex64 p1; NUM_CASS(p, p1); \
NUM_CMUL(p, p, s); \
NUM_CNEG(s, s); \
(s).r += 1; \
NUM_CRPOW(s, 0.5, s); \
NUM_CIMUL(s, s); \
NUM_CADD(p1, s, s); \
NUM_CLOG(s, s); \
NUM_CIMUL(s, s); \
NUM_CNEG(s, s); \
}
/* atan(z) = i/2 * log( (i+z) / (i - z) ) */
#define NUM_CATAN(p, s) { Complex64 p1, p2; \
NUM_CASS(p, p1); NUM_CNEG(p, p2); \
p1.i += 1; \
p2.i += 1; \
NUM_CDIV(p1, p2, s); \
NUM_CLOG(s, s); \
NUM_CIMUL(s, s); \
NUM_CRMUL(s, 0.5, s); \
}
/* asinh(z) = log( z + (z**2 + 1)**0.5 ) */
#define NUM_CASINH(p, s) { Complex64 p1; NUM_CASS(p, p1); \
NUM_CMUL(p, p, s); \
(s).r += 1; \
NUM_CRPOW(s, 0.5, s); \
NUM_CADD(p1, s, s); \
NUM_CLOG(s, s); \
}
/* acosh(z) = log( z + (z**2 - 1)**0.5 ) */
#define NUM_CACOSH(p, s) { Complex64 p1; NUM_CASS(p, p1); \
NUM_CMUL(p, p, s); \
(s).r -= 1; \
NUM_CRPOW(s, 0.5, s); \
NUM_CADD(p1, s, s); \
NUM_CLOG(s, s); \
}
/* atanh(z) = 1/2 * log( (1+z)/(1-z) ) */
#define NUM_CATANH(p, s) { Complex64 p1, p2; \
NUM_CASS(p, p1); NUM_CNEG(p, p2); \
p1.r += 1; \
p2.r += 1; \
NUM_CDIV(p1, p2, s); \
NUM_CLOG(s, s); \
NUM_CRMUL(s, 0.5, s); \
}
#define NUM_CMIN(p, q) (NUM_CLE(p, q) ? p : q)
#define NUM_CMAX(p, q) (NUM_CGE(p, q) ? p : q)
#define NUM_CNZ(p) (((p).r != 0) || ((p).i != 0))
#define NUM_CLAND(p, q) (NUM_CNZ(p) & NUM_CNZ(q))
#define NUM_CLOR(p, q) (NUM_CNZ(p) | NUM_CNZ(q))
#define NUM_CLXOR(p, q) (NUM_CNZ(p) ^ NUM_CNZ(q))
#define NUM_CLNOT(p) (!NUM_CNZ(p))
#define NUM_CFLOOR(p, s) (s).r = floor((p).r); (s).i = floor((p).i);
#define NUM_CCEIL(p, s) (s).r = ceil((p).r); (s).i = ceil((p).i);
#define NUM_CFABS(p, s) (s).r = fabs((p).r); (s).i = fabs((p).i);
#define NUM_CROUND(p, s) (s).r = num_round((p).r); (s).i = num_round((p).i);
#define NUM_CHYPOT(p, q, s) { Complex64 t; \
NUM_CSQR(p, s); NUM_CSQR(q, t); \
NUM_CADD(s, t, s); \
NUM_CSQRT(s, s); \
}