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/******************************************************************************
* Project: PROJ
* Purpose: Make C99 math functions available on C89 systems
* Author: Kristian Evers
*
******************************************************************************
* Copyright (c) 2018, Kristian Evers
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included
* in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
* DEALINGS IN THE SOFTWARE.
*****************************************************************************/
#include "proj_math.h"
/* pj_isnan is used in gie.c which means that is has to */
/* be exported in the Windows DLL and therefore needs */
/* to be declared even though we have isnan() on the */
/* system. */
#ifdef HAVE_C99_MATH
int pj_isnan (double x);
#endif
/* Returns 0 if not a NaN and non-zero if val is a NaN */
int pj_isnan (double x) {
/* cppcheck-suppress duplicateExpression */
return x != x;
}
#if !(defined(HAVE_C99_MATH) && HAVE_C99_MATH)
/* Define C99 compatible versions of
* hypot
* log1p
* asinh
* atanh
* copysign
* cbrt
* remainder
* remquo
* round
* lround
*/
/* Compute hypotenuse */
double pj_hypot(double x, double y) {
x = fabs(x);
y = fabs(y);
if (x < y) {
x /= y; /* y is nonzero */
return y * sqrt(1 + x * x);
} else {
y /= (x ? x : 1);
return x * sqrt(1 + y * y);
}
}
/* Compute log(1+x) accurately */
double pj_log1p(double x) {
volatile double
y = 1 + x,
z = y - 1;
/* Here's the explanation for this magic: y = 1 + z, exactly, and z
* approx x, thus log(y)/z (which is nearly constant near z = 0) returns
* a good approximation to the true log(1 + x)/x. The multiplication x *
* (log(y)/z) introduces little additional error. */
return z == 0 ? x : x * log(y) / z;
}
/* Compute asinh(x) accurately */
double pj_asinh(double x) {
double y = fabs(x); /* Enforce odd parity */
y = pj_log1p(y * (1 + y/(pj_hypot(1.0, y) + 1)));
return x > 0 ? y : (x < 0 ? -y : x); /* asinh(-0.0) = -0.0 */
}
/* Compute atanh(x) accurately */
double pj_atanh(double x) {
double y = fabs(x); /* Enforce odd parity */
y = pj_log1p(2 * y/(1 - y))/2;
return x > 0 ? y : (x < 0 ? -y : x); /* atanh(-0.0) = -0.0 */
}
/* Implement copysign(x, y) */
double pj_copysign(double x, double y) {
/* 1/y trick to get the sign of -0.0 */
return fabs(x) * (y < 0 || (y == 0 && 1/y < 0) ? -1 : 1);
}
/* Implement cbrt(x) */
double pj_cbrt(double x) {
double y = pow(fabs(x), 1/3.0); /* Return the real cube root */
return x > 0 ? y : (x < 0 ? -y : x); /* cbrt(-0.0) = -0.0 */
}
/* Implement remainder(x, y) with ties to even */
double pj_remainder(double x, double y) {
double z;
y = fabs(y); /* The result doesn't depend on the sign of y */
z = fmod(x, y);
if (z == 0)
/* This shouldn't be necessary. However, before version 14 (2015),
* Visual Studio had problems dealing with -0.0. Specifically
* VC 10,11,12 and 32-bit compile: fmod(-0.0, 360.0) -> +0.0
* python 2.7 on Windows 32-bit machines has the same problem. */
z = pj_copysign(z, x);
else if (2 * fabs(z) == y)
z -= fmod(x, 2 * y) - z; /* Implement ties to even */
else if (2 * fabs(z) > y)
z += (z < 0 ? y : -y); /* Fold remaining cases to (-y/2, y/2) */
return z;
}
/* Implement remquo(x, y, n) with n giving low 3 bits + sign of x/y */
double pj_remquo(double x, double y, int* n) {
double z = pj_remainder(x, y);
if (n) {
double
a = pj_remainder(x, 2 * y),
b = pj_remainder(x, 4 * y),
c = pj_remainder(x, 8 * y);
*n = (a > z ? 1 : (a < z ? -1 : 0));
*n += (b > a ? 2 : (b < a ? -2 : 0));
*n += (c > b ? 4 : (c < b ? -4 : 0));
if (y < 0) *n *= -1;
if (y != 0) {
if (x/y > 0 && *n <= 0)
*n += 8;
else if (x/y < 0 && *n >= 0)
*n -= 8;
}
}
return z;
}
/* Implement round(x) */
double pj_round(double x) {
/* The handling of corner cases is copied from boost; see
* https://github.com/boostorg/math/pull/8
* with improvements to return -0.0 when appropriate */
double t;
if (0 < x && x < 0.5)
return +0.0;
else if (0 > x && x > -0.5)
return -0.0;
else if (x > 0) {
t = ceil(x);
return 0.5 < t - x ? t - 1 : t;
} else if (x < 0) {
t = floor(x);
return 0.5 < x - t ? t + 1 : t;
} else /* +/-0 and NaN */
return x; /* retain sign of 0 */
}
/* Implement lround(x) */
long pj_lround(double x) {
/* Default value for overflow + NaN + (x == LONG_MIN) */
long r = LONG_MIN;
x = pj_round(x);
if (fabs(x) < -(double)r) /* Assume (double)LONG_MIN is exact */
r = (long)x;
return r;
}
#endif /* !(defined(HAVE_C99_MATH) && HAVE_C99_MATH) */
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