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/* Translated into C++ by SciPy developers in 2024.
* Original header with Copyright information appears below.
*/
/* sindg.c
*
* Circular sine of angle in degrees
*
*
*
* SYNOPSIS:
*
* double x, y, sindg();
*
* y = sindg( x );
*
*
*
* DESCRIPTION:
*
* Range reduction is into intervals of 45 degrees.
*
* Two polynomial approximating functions are employed.
* Between 0 and pi/4 the sine is approximated by
* x + x**3 P(x**2).
* Between pi/4 and pi/2 the cosine is represented as
* 1 - x**2 P(x**2).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE +-1000 30000 2.3e-16 5.6e-17
*
* ERROR MESSAGES:
*
* message condition value returned
* sindg total loss x > 1.0e14 (IEEE) 0.0
*
*/
/* cosdg.c
*
* Circular cosine of angle in degrees
*
*
*
* SYNOPSIS:
*
* double x, y, cosdg();
*
* y = cosdg( x );
*
*
*
* DESCRIPTION:
*
* Range reduction is into intervals of 45 degrees.
*
* Two polynomial approximating functions are employed.
* Between 0 and pi/4 the cosine is approximated by
* 1 - x**2 P(x**2).
* Between pi/4 and pi/2 the sine is represented as
* x + x**3 P(x**2).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE +-1000 30000 2.1e-16 5.7e-17
* See also sin().
*
*/
/* Cephes Math Library Release 2.0: April, 1987
* Copyright 1985, 1987 by Stephen L. Moshier
* Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */
#pragma once
#include "../config.h"
#include "../error.h"
#include "const.h"
#include "polevl.h"
namespace xsf {
namespace cephes {
namespace detail {
constexpr double sincof[] = {1.58962301572218447952E-10, -2.50507477628503540135E-8,
2.75573136213856773549E-6, -1.98412698295895384658E-4,
8.33333333332211858862E-3, -1.66666666666666307295E-1};
constexpr double coscof[] = {1.13678171382044553091E-11, -2.08758833757683644217E-9, 2.75573155429816611547E-7,
-2.48015872936186303776E-5, 1.38888888888806666760E-3, -4.16666666666666348141E-2,
4.99999999999999999798E-1};
constexpr double sindg_lossth = 1.0e14;
} // namespace detail
XSF_HOST_DEVICE inline double sindg(double x) {
double y, z, zz;
int j, sign;
/* make argument positive but save the sign */
sign = 1;
if (x < 0) {
x = -x;
sign = -1;
}
if (x > detail::sindg_lossth) {
set_error("sindg", SF_ERROR_NO_RESULT, NULL);
return (0.0);
}
y = std::floor(x / 45.0); /* integer part of x/M_PI_4 */
/* strip high bits of integer part to prevent integer overflow */
z = std::ldexp(y, -4);
z = std::floor(z); /* integer part of y/8 */
z = y - std::ldexp(z, 4); /* y - 16 * (y/16) */
j = z; /* convert to integer for tests on the phase angle */
/* map zeros to origin */
if (j & 1) {
j += 1;
y += 1.0;
}
j = j & 07; /* octant modulo 360 degrees */
/* reflect in x axis */
if (j > 3) {
sign = -sign;
j -= 4;
}
z = x - y * 45.0; /* x mod 45 degrees */
z *= detail::PI180; /* multiply by pi/180 to convert to radians */
zz = z * z;
if ((j == 1) || (j == 2)) {
y = 1.0 - zz * polevl(zz, detail::coscof, 6);
} else {
y = z + z * (zz * polevl(zz, detail::sincof, 5));
}
if (sign < 0)
y = -y;
return (y);
}
XSF_HOST_DEVICE inline double cosdg(double x) {
double y, z, zz;
int j, sign;
/* make argument positive */
sign = 1;
if (x < 0)
x = -x;
if (x > detail::sindg_lossth) {
set_error("cosdg", SF_ERROR_NO_RESULT, NULL);
return (0.0);
}
y = std::floor(x / 45.0);
z = std::ldexp(y, -4);
z = std::floor(z); /* integer part of y/8 */
z = y - std::ldexp(z, 4); /* y - 16 * (y/16) */
/* integer and fractional part modulo one octant */
j = z;
if (j & 1) { /* map zeros to origin */
j += 1;
y += 1.0;
}
j = j & 07;
if (j > 3) {
j -= 4;
sign = -sign;
}
if (j > 1)
sign = -sign;
z = x - y * 45.0; /* x mod 45 degrees */
z *= detail::PI180; /* multiply by pi/180 to convert to radians */
zz = z * z;
if ((j == 1) || (j == 2)) {
y = z + z * (zz * polevl(zz, detail::sincof, 5));
} else {
y = 1.0 - zz * polevl(zz, detail::coscof, 6);
}
if (sign < 0)
y = -y;
return (y);
}
/* Degrees, minutes, seconds to radians: */
/* 1 arc second, in radians = 4.848136811095359935899141023579479759563533023727e-6 */
namespace detail {
constexpr double sindg_P64800 = 4.848136811095359935899141023579479759563533023727e-6;
}
XSF_HOST_DEVICE inline double radian(double d, double m, double s) {
return (((d * 60.0 + m) * 60.0 + s) * detail::sindg_P64800);
}
} // namespace cephes
} // namespace xsf
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