complex math
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Guido van Rossum
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/* Complex math module */
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/* much code borrowed from mathmodule.c */
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#include "allobjects.h"
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#include "complexobject.h"
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#include <errno.h>
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#include "mymath.h"
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#ifdef i860
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/* Cray APP has bogus definition of HUGE_VAL in <math.h> */
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#undef HUGE_VAL
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#endif
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#ifdef HUGE_VAL
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#define CHECK(x) if (errno != 0) ; \
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else if (-HUGE_VAL <= (x) && (x) <= HUGE_VAL) ; \
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else errno = ERANGE
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#else
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#define CHECK(x) /* Don't know how to check */
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#endif
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#ifndef M_PI
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#define M_PI (3.141592653589793239)
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#endif
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/* First, the C functions that do the real work */
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/* constants */
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static complex c_1 = {1., 0.};
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static complex c_half = {0.5, 0.};
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static complex c_i = {0., 1.};
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static complex c_i2 = {0., 0.5};
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static complex c_mi = {0., -1.};
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static complex c_pi2 = {M_PI/2., 0.};
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/* forward declarations */
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complex c_log();
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complex c_prodi();
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complex c_sqrt();
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complex c_acos(x)
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complex x;
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{
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return c_neg(c_prodi(c_log(c_sum(x,c_prod(c_i,
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c_sqrt(c_diff(c_1,c_prod(x,x))))))));
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}
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complex c_acosh(x)
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complex x;
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{
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return c_log(c_sum(x,c_prod(c_i,
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c_sqrt(c_diff(c_1,c_prod(x,x))))));
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}
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complex c_asin(x)
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complex x;
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{
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return c_neg(c_prodi(c_log(c_sum(c_prod(c_i,x),
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c_sqrt(c_diff(c_1,c_prod(x,x)))))));
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}
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complex c_asinh(x)
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complex x;
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{
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return c_neg(c_log(c_diff(c_sqrt(c_sum(c_1,c_prod(x,x))),x)));
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}
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complex c_atan(x)
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complex x;
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{
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return c_prod(c_i2,c_log(c_quot(c_sum(c_i,x),c_diff(c_i,x))));
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}
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complex c_atanh(x)
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complex x;
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{
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return c_prod(c_half,c_log(c_quot(c_sum(c_1,x),c_diff(c_1,x))));
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}
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complex c_cos(x)
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complex x;
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{
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complex r;
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r.real = cos(x.real)*cosh(x.imag);
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r.imag = -sin(x.real)*sinh(x.imag);
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return r;
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}
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complex c_cosh(x)
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complex x;
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{
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complex r;
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r.real = cos(x.imag)*cosh(x.real);
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r.imag = sin(x.imag)*sinh(x.real);
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return r;
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}
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complex c_exp(x)
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complex x;
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{
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complex r;
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double l = exp(x.real);
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r.real = l*cos(x.imag);
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r.imag = l*sin(x.imag);
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return r;
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}
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complex c_log(x)
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complex x;
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{
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complex r;
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double l = hypot(x.real,x.imag);
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r.imag = atan2(x.imag, x.real);
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r.real = log(l);
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return r;
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}
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complex c_log10(x)
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complex x;
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{
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complex r;
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double l = hypot(x.real,x.imag);
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r.imag = atan2(x.imag, x.real)/log(10.);
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r.real = log10(l);
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return r;
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}
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complex c_prodi(x)
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complex x;
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{
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complex r;
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r.real = -x.imag;
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r.imag = x.real;
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return r;
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}
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complex c_sin(x)
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complex x;
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{
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complex r;
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r.real = sin(x.real)*cosh(x.imag);
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r.imag = cos(x.real)*sinh(x.imag);
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return r;
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}
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complex c_sinh(x)
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complex x;
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{
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complex r;
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r.real = cos(x.imag)*sinh(x.real);
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r.imag = sin(x.imag)*cosh(x.real);
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return r;
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}
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complex c_sqrt(x)
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complex x;
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{
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complex r;
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double s,d;
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if (x.real == 0. && x.imag == 0.)
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r = x;
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else {
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s = sqrt(0.5*(fabs(x.real) + hypot(x.real,x.imag)));
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d = 0.5*x.imag/s;
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if (x.real > 0.) {
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r.real = s;
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r.imag = d;
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}
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else if (x.imag >= 0.) {
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r.real = d;
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r.imag = s;
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}
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else {
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r.real = -d;
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r.imag = -s;
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}
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}
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return r;
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}
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complex c_tan(x)
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complex x;
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{
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complex r;
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double sr,cr,shi,chi;
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double rs,is,rc,ic;
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double d;
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sr = sin(x.real);
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cr = cos(x.real);
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shi = sinh(x.imag);
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chi = cosh(x.imag);
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rs = sr*chi;
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is = cr*shi;
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rc = cr*chi;
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ic = -sr*shi;
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d = rc*rc + ic*ic;
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r.real = (rs*rc+is*ic)/d;
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r.imag = (is*rc-rs*ic)/d;
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return r;
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}
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complex c_tanh(x)
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complex x;
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{
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complex r;
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double si,ci,shr,chr;
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double rs,is,rc,ic;
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double d;
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si = sin(x.imag);
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ci = cos(x.imag);
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shr = sinh(x.real);
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chr = cosh(x.real);
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rs = ci*shr;
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is = si*chr;
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rc = ci*chr;
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ic = si*shr;
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d = rc*rc + ic*ic;
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r.real = (rs*rc+is*ic)/d;
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r.imag = (is*rc-rs*ic)/d;
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return r;
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}
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/* And now the glue to make them available from Python: */
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static object *
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math_error()
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{
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if (errno == EDOM)
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err_setstr(ValueError, "math domain error");
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else if (errno == ERANGE)
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err_setstr(OverflowError, "math range error");
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else
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err_errno(ValueError); /* Unexpected math error */
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return NULL;
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}
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static object *
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math_1(args, func)
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object *args;
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complex (*func) FPROTO((complex));
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{
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complex x;
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if (!PyArg_ParseTuple(args, "D", &x))
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return NULL;
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errno = 0;
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x = (*func)(x);
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CHECK(x.real);
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CHECK(x.imag);
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if (errno != 0)
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return math_error();
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else
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return newcomplexobject(x);
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}
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#define FUNC1(stubname, func) \
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static object * stubname(self, args) object *self, *args; { \
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return math_1(args, func); \
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}
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FUNC1(cmath_acos, c_acos)
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FUNC1(cmath_acosh, c_acosh)
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FUNC1(cmath_asin, c_asin)
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FUNC1(cmath_asinh, c_asinh)
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FUNC1(cmath_atan, c_atan)
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FUNC1(cmath_atanh, c_atanh)
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FUNC1(cmath_cos, c_cos)
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FUNC1(cmath_cosh, c_cosh)
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FUNC1(cmath_exp, c_exp)
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FUNC1(cmath_log, c_log)
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FUNC1(cmath_log10, c_log10)
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FUNC1(cmath_sin, c_sin)
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FUNC1(cmath_sinh, c_sinh)
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FUNC1(cmath_sqrt, c_sqrt)
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FUNC1(cmath_tan, c_tan)
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FUNC1(cmath_tanh, c_tanh)
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static struct methodlist cmath_methods[] = {
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{"acos", cmath_acos, 1},
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{"acosh", cmath_acosh, 1},
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{"asin", cmath_asin, 1},
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{"asinh", cmath_asinh, 1},
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{"atan", cmath_atan, 1},
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{"atanh", cmath_atanh, 1},
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{"cos", cmath_cos, 1},
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{"cosh", cmath_cosh, 1},
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{"exp", cmath_exp, 1},
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{"log", cmath_log, 1},
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{"log10", cmath_log10, 1},
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{"sin", cmath_sin, 1},
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{"sinh", cmath_sinh, 1},
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{"sqrt", cmath_sqrt, 1},
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{"tan", cmath_tan, 1},
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{"tanh", cmath_tanh, 1},
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{NULL, NULL} /* sentinel */
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};
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void
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initcmath()
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{
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object *m, *d, *v;
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m = Py_InitModule("cmath", cmath_methods);
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d = getmoduledict(m);
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dictinsert(d, "pi", v = newfloatobject(atan(1.0) * 4.0));
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DECREF(v);
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dictinsert(d, "e", v = newfloatobject(exp(1.0)));
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DECREF(v);
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}
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