Data Structures

Functions

double cabs (complex z)

Definition at line 57 of file prim.c.

58 {
59     return hypot(creal(z), cimag(z));
60 }

complex cacos (complex z)

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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 }

complex cacosh (complex z)

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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 }

complex cacot (complex z)

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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 }

complex cacoth (complex z)

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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 }

complex cacsc (complex z)

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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 }

complex cacsch (complex z)

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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 }

complex cadd (complex a, complex z)

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 }

complex casec (complex z)

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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 }

complex casech (complex z)

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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 }

complex casin (complex z)

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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 }

complex casinh (complex z)

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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 }

complex catan (complex z)

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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 }

complex catanh (complex z)

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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 }

complex ccbrt (complex z)

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 }

complex cceil (complex z)

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 }

complex ccos (complex z)

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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 }

complex ccosh (complex z)

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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 }

complex ccot (complex z)

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 }

complex ccoth (complex z)

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 }

complex ccsc (complex z)

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 }

complex ccsch (complex z)

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)

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 }

complex cdiv (complex a, complex z)

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 }

complex cexp (complex z)

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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 }

complex cfloor (complex z)

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 }

double cimag (complex z)

Definition at line 48 of file prim.c.

49 {
50     return (IMAG_PART(z));
51 }

complex clog (complex z)

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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 }

complex clog10 (complex z)

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 }

complex clogb (complex z)

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 }

complex cmul (complex a, complex z)

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 }

complex conj (complex z)

63 {
64     IMAG_PART(z) = -IMAG_PART(z);
65     return cpack(REAL_PART(z), IMAG_PART(z));
66 }

complex cpack (double x, double y)

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 cpow (complex a, complex z)

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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 }

double creal (complex z)

Definition at line 39 of file prim.c.

40 {
41     return (REAL_PART(z));
42 }

complex creci (complex z)

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 }

complex cround (complex z)

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 }

complex csec (complex z)

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 }

complex csech (complex z)

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 }

double csgn (complex z)

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 }

complex csin (complex z)

Version:

Date:

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 }

complex csinh (complex z)

Version:

Date:

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 }

complex csqrt (complex z)

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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 }

complex csub (complex a, complex z)

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 }

complex ctan (complex z)

Version:

Date:

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 }

complex ctanh (complex z)

Version:

Date:

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 }

complex ctrunc (complex z)

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 }