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Man Pages
mathi.h(3) FreeBSD Library Functions Manual mathi.h(3)

mathi.h - Complex numbers math library


union complex
 


double csgn (complex z)
 
Complex signum. double cabs (complex z)
 
Absolute value of complex number. double creal (complex z)
 
Real part of complex number. double cimag (complex z)
 
Imaginary part of complex number. complex cpack (double x, double y)
 
Pack two real numbers into a complex number. complex cadd ( complex a, complex z)
 
Addition of two complex numbers. complex csub (complex a, complex z)
 
Subtraction of two complex numbers. complex cmul (complex a, complex z)
 
Multiplication of two complex numbers. complex cdiv (complex a, complex z)
 
Division of two complex numbers. complex cpow (complex x, complex z)
 
Complex number raised to a power. complex cceil (complex z)
 
Ceiling value of complex number. complex cfloor (complex z)
 
Floor value of complex number. complex ctrunc (complex z)
 
Truncated value of complex number. complex cround (complex z)
 
Division of two complex numbers. complex creci (complex z)
 
Reciprocal value of complex number. complex conj (complex z)
 
complex cexp (complex z)
 
Returns e to the power of a complex number. complex csqrt ( complex z)
 
Square root of complex number. complex ccbrt (complex z)
 
Cube root of complex number. complex clog (complex z)
 
Natural logarithm of a complex number. complex clogb (complex z)
 
Base 2 logarithmic value of complex number. complex clog10 ( complex z)
 
Base 10 logarithmic value of complex number. complex ccos ( complex z)
 
Cosine of complex number. complex csin (complex z)
 
Sine of a complex number. complex ctan (complex z)
 
Tangent of a complex number. complex csec (complex z)
 
Secant of a complex number. complex ccsc (complex z)
 
Cosecant of a complex number. complex ccot (complex z)
 
Cotangent of a complex number. complex cacos (complex z)
 
Inverse cosine of complex number. complex casin (complex z)
 
Inverse sine of complex number. complex catan (complex z)
 
Inverse tangent of complex number. complex casec (complex z)
 
Inverse secant expressed using complex logarithms: complex cacsc ( complex z)
 
Inverse cosecant of complex number. complex cacot (complex z)
 
Inverse cotangent of complex number. complex ccosh (complex z)
 
Hyperbolic cosine of a complex number. complex csinh (complex z)
 
Hyperbolic sine of a complex number. complex ctanh (complex z)
 
Hyperbolic tangent of a complex number. complex csech (complex z)
 
Hyperbolic secant of a complex number. complex ccsch (complex z)
 
Hyperbolic secant of a complex number. complex ccoth (complex z)
 
Hyperbolic cotangent of a complex number. complex cacosh (complex z)
 
Inverse hyperbolic cosine of complex number. complex casinh ( complex z)
 
Inverse hyperbolic sine of complex number. complex catanh ( complex z)
 
Inverse hyperbolic tangent of complex number. complex casech ( complex z)
 
Inverse hyperbolic secant of complex numbers. complex cacsch ( complex z)
 
Inverse hyperbolic cosecant of complex number. complex cacoth ( complex z)
 
Inverse hyperbolic cotangent of complex number.

Functions for handling complex numbers. Mostly as specified in IEEE Std 1003.1, 2013 Edition:
 
http://pubs.opengroup.org/onlinepubs/9699919799/basedefs/complex.h.html
Definition in file mathi.h.

Absolute value of complex number.
Definition at line 57 of file prim.c.
58 {
59     return hypot(creal(z), cimag(z));
60 }

Inverse cosine of complex number.
Version:
1.0
Date:
14/09/15
Inverse cosine expressed using complex logarithms:
arccos z = -i * log(z + i * sqrt(1 - z * z))

More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Inverse_trigonometric_functions#Logarithmic_forms
Definition at line 44 of file cacos.c.
45 {
46     complex a = cpack(1.0, 0.0);
47     complex i = cpack(0.0, 1.0);
48     complex j = cpack(0.0, -1.0);
49     complex p = csub(a, cmul(z, z));
50     complex q = clog(cadd(z, cmul(i, csqrt(p))));
51     complex w = cmul(j, q);
52     return w;
53 }

Inverse hyperbolic cosine of complex number.
Version:
1.1
Date:
15/03/03
Inverse hyperbolic cosine expressed using complex logarithms:
acosh(z) = log(z + sqrt(z*z - 1))

More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Inverse_hyperbolic_function#Logarithmic_representation
Definition at line 44 of file cacosh.c.
45 {
46     complex one = cpack(1.0, 0.0);
47     complex a = csub(cmul(z, z), one);
48     complex b = cadd(z, csqrt(a));
49     complex w = clog(b);
50     return w;
51 }

Inverse cotangent of complex number.
Version:
1.1
Date:
14/10/01
Inverse cotangent expressed using complex logarithms:
arccot z = i/2 * (log(1 - i/z) - log(1 + i/z))

More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Inverse_trigonometric_functions#Logarithmic_forms
Definition at line 44 of file cacot.c.
45 {
46     complex one = cpack(1.0, 0.0);
47     complex two = cpack(2.0, 0.0);
48     complex i = cpack(0.0, 1.0);
49     complex iz = cdiv(i, z);
50     complex p = clog(csub(one, iz));
51     complex q = clog(cadd(one, iz));
52     complex w = cmul(cdiv(i, two), csub(p, q));
53     return w;
54 }

Inverse hyperbolic cotangent of complex number.
Version:
1.0
Date:
14/09/15
Inverse hyperbolic cotangent expressed using complex logarithms:
acoth(z) = 1/2 * ((log(z + 1) - log(z - 1))

More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Inverse_hyperbolic_function#Logarithmic_representation
Definition at line 44 of file cacoth.c.
45 {
46     complex half = cpack(0.5, 0.0);
47     complex one = cpack(1.0, 0.0);
48     complex a = clog(cadd(z, one));
49     complex b = clog(csub(z, one));
50     complex c = csub(a, b);
51     complex w = cmul(half, c);
52     return w;
53 }

Inverse cosecant of complex number.
Version:
1.1
Date:
14/10/01
Inverse cosecant expressed using complex logarithms:
arccsc z = -i * log(sqr(1 - 1/(z*z)) + i/z)

More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Inverse_trigonometric_functions#Logarithmic_forms
Definition at line 44 of file cacsc.c.
45 {
46     complex one = cpack(1.0, 0.0);
47     complex i = cpack(0.0, 1.0);
48     complex j = cpack(0.0, -1.0);
49     complex iz = cdiv(i, z);
50     complex z2 = cmul(z, z);
51     complex p = cdiv(one, z2);
52     complex q = csqrt(csub(one, p));
53     complex w = cmul(j, clog(cadd(q, iz)));
54     return w;
55 }

Inverse hyperbolic cosecant of complex number.
Version:
1.0
Date:
14/09/15
Inverse hyperbolic cosecant expressed using complex logarithms:
acsch(z) = log(sqrt(1 + 1 / (z * z)) + 1/z)

More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Inverse_hyperbolic_function#Logarithmic_representation
Definition at line 44 of file cacsch.c.
45 {
46     complex one = cpack(1.0, 0.0);
47     complex a = creci(cmul(z, z));
48     complex b = csqrt(cadd(one, a));
49     complex c = cadd(b, creci(z));
50     complex w = clog(c);
51     return w;
52 }

Addition of two complex numbers.
Definition at line 129 of file prim.c.
130 {
131     complex w;
132     w = cpack(creal(y) + creal(z), cimag(y) + cimag(z));
133     return w;
134 }

Inverse secant expressed using complex logarithms:
Version:
1.1
Date:
14/10/01
Inverse secant expressed using complex logarithms:
arcsec z = -i * log(i * sqr(1 - 1/(z*z)) + 1/z)

More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Inverse_trigonometric_functions#Logarithmic_forms
Definition at line 44 of file casec.c.
45 {
46     complex one = cpack(1.0, 0.0);
47     complex i = cpack(0.0, 1.0);
48     complex j = cpack(0.0, -1.0);
49     complex rz = creci(z);
50     complex z2 = cmul(z, z);
51     complex p = cdiv(one, z2);
52     complex q = csqrt(csub(one, p));
53     complex w = cmul(j, clog(cadd(cmul(i, q), rz)));
54     return w;
55 }

Inverse hyperbolic secant of complex numbers.
Version:
1.1
Date:
15/03/03
Inverse hyperbolic secant expressed using complex logarithms:
asech(z) = log(sqrt(1 / (z * z) - 1) + 1/z)


More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Inverse_hyperbolic_function#Logarithmic_representation
Definition at line 45 of file casech.c.
46 {
47     complex one = cpack(1.0, 0.0);
48     complex a = creci(cmul(z, z));
49     complex b = csqrt(csub(a, one));
50     complex c = cadd(b, creci(z));
51     complex w = clog(c);
52     return w;
53 }

Inverse sine of complex number.
Version:
1.1
Date:
14/10/01
Inverse sine expressed using complex logarithms:
arcsin z = -i * log(iz + sqrt(1 - z*z))

More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Inverse_trigonometric_functions#Logarithmic_forms
Definition at line 44 of file casin.c.
45 {
46     complex one = cpack(1.0, 0.0);
47     complex i = cpack(0.0, 1.0);
48     complex j = cpack(0.0, -1.0);
49     complex iz = cmul(i, z);
50     complex z2 = cmul(z, z);
51     complex p = csqrt(csub(one, z2));
52     complex q = clog(cadd(iz, p));
53     complex w = cmul(j, q);
54     return w;
55 }

Inverse hyperbolic sine of complex number.
Version:
1.0
Date:
14/09/15
Inverse hyperbolic sine expressed using complex logarithms:
asinh(z) = log(z + sqrt(z*z + 1))
With branch cuts: -i INF to -i and i to i INF
Domain: -INF to INF
Range:  -INF to INF

More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Inverse_hyperbolic_function#Logarithmic_representation
Definition at line 49 of file casinh.c.
50 {
51     complex one = cpack(1.0, 0.0);
52     complex a = cadd(cmul(z, z), one);
53     complex b = cadd(z, csqrt(a));
54     complex w = clog(b);
55     return w;
56 }

Inverse tangent of complex number.
Version:
1.1
Date:
14/10/01
Inverse tangent expressed using complex logarithms:
atan(z) = i/2 * (log(1 - i * z) - log(1 + i * z))

More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Inverse_trigonometric_functions#Logarithmic_forms
Definition at line 44 of file catan.c.
45 {
46     complex one = cpack(1.0, 0.0);
47     complex two = cpack(2.0, 0.0);
48     complex i = cpack(0.0, 1.0);
49     complex iz = cmul(i, z);
50     complex p = clog(csub(one, iz));
51     complex q = clog(cadd(one, iz));
52     complex w = cmul(cdiv(i, two), csub(p, q));
53     return w;
54 }

Inverse hyperbolic tangent of complex number.
Version:
1.0
Date:
14/09/15
Inverse hyperbolic tangent expressed using complex logarithms:
atanh(z) = 1/2 * ((log(1 + z) - log(1 - z))

More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Inverse_hyperbolic_function#Logarithmic_representation
Definition at line 44 of file catanh.c.
45 {
46     complex half = cpack(0.5, 0.0);
47     complex one = cpack(1.0, 0.0);
48     complex a = clog(cadd(one, z));
49     complex b = clog(csub(one, z));
50     complex c = csub(a, b);
51     complex w = cmul(half, c);
52     return w;
53 }

Cube root of complex number.
cbrt z = exp(1/3 * log(z))

More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Cube_root
Definition at line 41 of file ccbrt.c.
42 {
43     complex onethird = cpack(1.0 / 3.0, 0.0);
44     complex a = cmul(onethird, clog(z));
45     complex w = cexp(a);
46     return w;
47 }

Ceiling value of complex number.
Definition at line 107 of file prim.c.
108 {
109     complex w;
110     w = cpack(ceil(creal(z)), ceil(cimag(z)));
111     return w;
112 }

Cosine of complex number.
Version:
1.1
Date:
2007/08/20
a+bi
real =  cos(a) * cosh(b)
imag = -sin(a) * sinh(b)
Definition at line 47 of file ccos.c.
48 {
49     complex w;
50     double a, b;
51     double ch, sh;
52 
53     a = creal(z);
54     b = cimag(z);
55     cchsh(b, &ch, &sh);
56     w = cpack((cos(a) * ch), (-sin(a) * sh));
57 
58     return w;
59 }

Hyperbolic cosine of a complex number.
Version:
1.1
Date:
2007/08/20
a+bi
real = cosh(a) * cos(b)
imag = sinh(a) * sin(b)
Definition at line 50 of file ccosh.c.
51 {
52     complex w;
53     double a, b;
54     double ch, sh;
55 
56     a = creal(z);
57     b = cimag(z);
58     cchsh(a, &ch, &sh);
59     w = cpack(cos(b) * ch, sin(b) * sh);
60 
61     return w;
62 }

Cotangent of a complex number. Calculated as in Open Office:
a+bi
                sin(2.0 * a)
real  = ------------------------------
         cosh(2.0 * b) - cos(2.0 * a)
               -sinh(2.0 * b)
imag  = ------------------------------
         cosh(2.0 * b) - cos(2.0 * a)

https://wiki.openoffice.org/wiki/Documentation/How_Tos/Calc:_IMCOT_function
Definition at line 48 of file ccot.c.
49 {
50     complex w;
51     double a, b;
52     double d;
53 
54     a = creal(z);
55     b = cimag(z);
56     d = cosh(2.0 * b) - cos(2.0 * a);
57 
58     if (d == 0.0)
59     {
60         w = cpack((double)INFP, (double)INFP);
61     }
62     else
63     {
64         w = cpack((sin(2.0 * a) / d), (-sinh(2.0 * b) / d));
65     }
66 
67     return w;
68 }

Hyperbolic cotangent of a complex number.
acoth(z) = 0.5 * (log(1 + 1/z) - log(1 - 1/z))

or
a+bi sinh(2.0 * a) real = ------------------------------ cosh(2.0 * a) - cos(2.0 * b)
  -sin(2.0 * b)
imag = ------------------------------
cosh(2.0 * a) - cos(2.0 * b)
Definition at line 50 of file ccoth.c.
51 {
52     complex w;
53     double a, b;
54     double d;
55 
56     a = creal(z);
57     b = cimag(z);
58     d = cosh(2.0 * a) - cos(2.0 * b);
59     w = cpack(sinh(2.0 * a) / d, -sin(2.0 * b) / d);
60 
61     return w;
62 }

Cosecant of a complex number. Calculated as in Open Office:
a+bi 2.0 * sin(a) * cosh(b) real = ------------------------------ cosh(2.0 * b) - cos(2.0 * a)
           -2.0 * cos(a) * sinh(b)
imag  = ------------------------------
         cosh(2.0 * b) - cos(2.0 * a)

https://wiki.openoffice.org/wiki/Documentation/How_Tos/Calc:_IMCSC_function
Definition at line 48 of file ccsc.c.
49 {
50     complex w;
51     double a, b;
52     double d;
53 
54     a = creal(z);
55     b = cimag(z);
56     d = cosh(2.0 * b) - cos(2.0 * a);
57 
58     if (d == 0.0)
59     {
60         w = cpack((double)INFP, (double)INFP);
61     }
62     else
63     {
64         w = cpack((2.0 * sin(a) * cosh(b) / d), (-2.0 * cos(a) * sinh(b) / d));
65     }
66 
67     return w;
68 }

Hyperbolic secant of a complex number. Calculated as in Open Office:
 
https://wiki.openoffice.org/wiki/Documentation/How_Tos/Calc:_IMCSCH_function
a+bi
            2.0 * sinh(a) * cos(b)
real  = ------------------------------
         cosh(2.0 * a) - cos(2.0 * b)
        -2.0 * cosh(2.0 * a) * sin(b)
imag  = ------------------------------
         cosh(2.0 * a) - cos(2.0 * b)
Definition at line 48 of file ccsch.c.
49 {
50     complex w;
51     double a, b;
52     double d;
53 
54     a = creal(z);
55     b = cimag(z);
56     d = cosh(2.0 * a) - cos(2.0 * b);
57     w = cpack((2.0 * sinh(a) * cos(b) / d), (-2.0 * cosh(a) * sin(b) / d));
58 
59     return w;
60 }

Division of two complex numbers.
Definition at line 171 of file prim.c.
172 {
173     complex w;
174     double a, b, c, d;
175     double q, v, x;
176 
177     a = creal(y);
178     b = cimag(y);
179     c = creal(z);
180     d = cimag(z);
181 
182     q = c * c + d * d;
183     v = a * c + b * d;
184     x = b * c - a * d;
185 
186     w = cpack(v / q, x / q);
187     return w;
188 }

Returns e to the power of a complex number.
Version:
1.1
Date:
2007/08/20
Definition at line 45 of file cexp.c.
46 {
47     complex w;
48     double r, x, y;
49     x = creal(z);
50     y = cimag(z);
51     r = exp(x);
52     w = cpack(r * cos(y), r * sin(y));
53     return w;
54 }

Floor value of complex number.
Definition at line 96 of file prim.c.
97 {
98     complex w;
99     w = cpack(floor(creal(z)), floor(cimag(z)));
100     return w;
101 }

Imaginary part of complex number.
Definition at line 48 of file prim.c.
49 {
50     return (IMAG_PART(z));
51 }

Natural logarithm of a complex number.
Version:
1.1
Date:
2007/08/20
Definition at line 45 of file clog.c.
46 {
47     complex w;
48     double p, q;
49     p = log(cabs(z));
50     q = atan2(cimag(z), creal(z));
51     w = cpack(p, q);
52     return w;
53 }

Base 10 logarithmic value of complex number.
log z = log(z) / log(10)

More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Complex_logarithm
Definition at line 41 of file clog10.c.
42 {
43     complex teen = cpack(10.0, 0.0);
44     complex w = cdiv(clog(z), clog(teen));
45     return w;
46 }

Base 2 logarithmic value of complex number.
lb z = log(z) / log(2)

More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Complex_logarithm
Definition at line 41 of file clogb.c.
42 {
43     complex two = cpack(2.0, 0.0);
44     complex w = cdiv(clog(z), clog(two));
45     return w;
46 }

Multiplication of two complex numbers.
Definition at line 151 of file prim.c.
152 {
153     complex w;
154     double a, b, c, d;
155 
156     // (a+bi)(c+di)
157     a = creal(y);
158     b = cimag(y);
159     c = creal(z);
160     d = cimag(z);
161 
162     // (ac -bd) + (ad + bc)i
163     w = cpack(a * c - b * d, a * d + b * c);
164     return w;
165 }

Definition at line 62 of file prim.c.
63 {
64     IMAG_PART(z) = -IMAG_PART(z);
65     return cpack(REAL_PART(z), IMAG_PART(z));
66 }

Pack two real numbers into a complex number.
Definition at line 72 of file prim.c.
73 {
74     complex z;
75 
76     REAL_PART(z) = x;
77     IMAG_PART(z) = y;
78     return (z);
79 }

Complex number raised to a power.
Version:
1.1
Date:
2007/08/20
Definition at line 45 of file cpow.c.
46 {
47     complex w;
48     double x, y, r, theta, absa, arga;
49 
50     x = creal(z);
51     y = cimag(z);
52     absa = cabs(a);
53     if (absa == 0.0)
54     {
55         return cpack(0.0, + 0.0);
56     }
57     arga = atan2(cimag(a), creal(a));
58 
59     r = pow(absa, x);
60     theta = x * arga;
61     if (y != 0.0)
62     {
63         r = r * exp(-y * arga);
64         theta = theta + y * log(absa);
65     }
66 
67     w = cpack(r * cos(theta), r * sin(theta));
68     return w;
69 }

Real part of complex number.
Definition at line 39 of file prim.c.
40 {
41     return (REAL_PART(z));
42 }

Reciprocal value of complex number.
Definition at line 194 of file prim.c.
195 {
196     complex w;
197     double q, a, b;
198 
199     a = creal(z);
200     b = cimag(conj(z));
201     q = a * a + b * b;
202     w = cpack(a / q, b / q);
203 
204     return w;
205 }

Division of two complex numbers.
Definition at line 118 of file prim.c.
119 {
120     complex w;
121     w = cpack(round(creal(z)), round(cimag(z)));
122     return w;
123 }

Secant of a complex number. Calculated as in Open Office:
 

https://wiki.openoffice.org/wiki/Documentation/How_Tos/Calc:_IMSEC_function
a+bi 2.0 * cos(a) * cosh(b) real = ------------------------------ cosh(2.0 * b) + cos(2.0 * a)
            2.0 * sin(a) * sinh(b)
imag  = ------------------------------
         cosh(2.0 * b) + cos(2.0 * a)
Definition at line 48 of file csec.c.
49 {
50     complex w;
51     double a, b;
52     double d;
53 
54     a = creal(z);
55     b = cimag(z);
56     d = cosh(2.0 * b) + cos(2.0 * a);
57 
58     if (d == 0.0)
59     {
60         w = cpack((double)INFP, (double)INFP);
61     }
62     else
63     {
64         w = cpack((2.0 * cos(a) * cosh(b) / d), (2.0 * sin(a) * sinh(b) / d));
65     }
66 
67     return w;
68 }

Hyperbolic secant of a complex number. Calculated as in Open Office:
 

https://wiki.openoffice.org/wiki/Documentation/How_Tos/Calc:_IMSECH_function
a+bi 2.0 * cosh(a) * cos(b) real = ------------------------------ cosh(2.0 * a) + cos(2.0 * b)
        -2.0 * sinh(2.0 * a) * sin(b)
imag  = ------------------------------
         cosh(2.0 * a) + cos(2.0 * b)
Definition at line 48 of file csech.c.
49 {
50     complex w;
51     double a, b;
52     double d;
53 
54     a = creal(z);
55     b = cimag(z);
56     d = cosh(2.0 * a) + cos(2.0 * b);
57     w = cpack((2.0 * cosh(a) * cos(b) / d), (-2.0 * sinh(a) * sin(b) / d));
58 
59     return w;
60 }

Complex signum. More info is available at Wikipedia:
 

https://wikipedia.org/wiki/Sign_function#Complex_signum
Definition at line 39 of file csgn.c.
40 {
41     double a = creal(z);
42 
43     if (a > 0.0)
44     {
45         return 1.0;
46     }
47     else if (a < 0.0)
48     {
49         return -1.0;
50     }
51     else
52     {
53         double b = cimag(z);
54         return b > 0.0 ? 1.0 : b < 0.0 ? -1.0 : 0.0;
55     }
56 }

Sine of a complex number.
Version:
1.1
Date:
2007/08/20
Calculated according to description at wikipedia:
 

https://wikipedia.org/wiki/Sine#Sine_with_a_complex_argument
a+bi real = sin(a) * cosh(b) imag = cos(a) * sinh(b)
Definition at line 52 of file csin.c.
53 {
54     complex w;
55     double a, b;
56     double ch, sh;
57 
58     a = creal(z);
59     b = cimag(z);
60     cchsh(b, &ch, &sh);
61     w = cpack((sin(a) * ch), (cos(a) * sh));
62 
63     return w;
64 }

Hyperbolic sine of a complex number.
Version:
1.1
Date:
2007/08/20
Calculated as in Open Office:
 

https://wiki.openoffice.org/wiki/Documentation/How_Tos/Calc:_IMSINH_function
a+bi real = sinh(a) * cos(b) imag = cosh(a) * sin(b)
Definition at line 52 of file csinh.c.
53 {
54     complex w;
55     double a, b;
56     double ch, sh;
57 
58     a = creal(z);
59     b = cimag(z);
60     cchsh(a, &ch, &sh);
61     w = cpack(cos(b) * sh, sin(b) * ch);
62 
63     return w;
64 }

Square root of complex number.
Version:
1.1
Date:
2007/08/20
Definition at line 45 of file csqrt.c.
46 {
47     complex w;
48     double x, y, r, t, scale;
49 
50     x = creal(z);
51     y = cimag(z);
52 
53     if (y == 0.0)
54     {
55         if (x == 0.0)
56         {
57             w = cpack(0.0, y);
58         }
59         else
60         {
61             r = fabs(x);
62             r = sqrt(r);
63             if (x < 0.0)
64             {
65                 w = cpack(0.0, r);
66             }
67             else
68             {
69                 w = cpack(r, y);
70             }
71         }
72         return w;
73     }
74     if (x == 0.0)
75     {
76         r = fabs(y);
77         r = sqrt(0.5 * r);
78         if (y > 0)
79             w = cpack(r, r);
80         else
81             w = cpack(r, -r);
82         return w;
83     }
84     /* Rescale to avoid internal overflow or underflow.  */
85     if ((fabs(x) > 4.0) || (fabs(y) > 4.0))
86     {
87         x *= 0.25;
88         y *= 0.25;
89         scale = 2.0;
90     }
91     else
92     {
93 #if 1
94         x *= 1.8014398509481984e16; /* 2^54 */
95         y *= 1.8014398509481984e16;
96         scale = 7.450580596923828125e-9; /* 2^-27 */
97 #else
98         x *= 4.0;
99         y *= 4.0;
100         scale = 0.5;
101 #endif
102     }
103     w = cpack(x, y);
104     r = cabs(w);
105     if (x > 0)
106     {
107         t = sqrt(0.5 * r + 0.5 * x);
108         r = scale * fabs((0.5 * y) / t);
109         t *= scale;
110     }
111     else
112     {
113         r = sqrt(0.5 * r - 0.5 * x);
114         t = scale * fabs((0.5 * y) / r);
115         r *= scale;
116     }
117     if (y < 0)
118         w = cpack(t, -r);
119     else
120         w = cpack(t, r);
121     return w;
122 }

Subtraction of two complex numbers.
Definition at line 140 of file prim.c.
141 {
142     complex w;
143     w = cpack(creal(y) - creal(z), cimag(y) - cimag(z));
144     return w;
145 }

Tangent of a complex number.
Version:
1.1
Date:
2007/08/20
Calculated as in Open Office:
 

https://wiki.openoffice.org/wiki/Documentation/How_Tos/Calc:_IMTAN_function
a+bi sin(2.0 * a) real = ------------------------------ cos(2.0 * a) + cosh(2.0 * b)
  sinh(2.0 * b)
imag = ------------------------------
cos(2.0 * a) + cosh(2.0 * b)
Definition at line 57 of file ctan.c.
58 {
59     complex w;
60     double a, b;
61     double d;
62 
63     a = creal(z);
64     b = cimag(z);
65     d = cos(2.0 * a) + cosh(2.0 * b);
66 
67     if (d == 0.0)
68     {
69         w = cpack((double)INFP, (double)INFP);
70     }
71     else
72     {
73         w = cpack((sin(2.0 * a) / d), (sinh(2.0 * b) / d));
74     }
75 
76     return w;
77 }

Hyperbolic tangent of a complex number.
Version:
1.1
Date:
2007/08/20
a+bi sinh(2.0 * a) real = ------------------------------ cosh(2.0 * a) + cos(2.0 * b)
  sin(2.0 * b)
imag = ------------------------------
cosh(2.0 * a) + cos(2.0 * b)
Definition at line 55 of file ctanh.c.
56 {
57     complex w;
58     double a, b;
59     double d;
60 
61     a = creal(z);
62     b = cimag(z);
63     d = cosh(2.0 * a) + cos(2.0 * b);
64     w = cpack((sinh(2.0 * a) / d), (sin(2.0 * b) / d));
65 
66     return w;
67 }

Truncated value of complex number.
Definition at line 85 of file prim.c.
86 {
87     complex w;
88     w = cpack(trunc(creal(z)), trunc(cimag(z)));
89     return w;
90 }

https://amath.innolan.net/

Written by Carsten Sonne Larsen <cs@innolan.net>. Some code in the library is derived from software written by Stephen L. Moshier.

Copyright (c) 2014-2018 Carsten Sonne Larsen <cs@innolan.net>
 
Copyright (c) 2007 The NetBSD Foundation, Inc.

amath(1), amathc(3), amathr(3)
Version 1.8.5 August 07 2018

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