diff options
Diffstat (limited to 'src/math.cpp')
| -rw-r--r-- | src/math.cpp | 131 |
1 files changed, 102 insertions, 29 deletions
diff --git a/src/math.cpp b/src/math.cpp index 540ab9eb..0ec4f57f 100644 --- a/src/math.cpp +++ b/src/math.cpp @@ -44,64 +44,137 @@ int pj_isnan (double 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; - return ( y * sqrt( 1. + x * x ) ); - } else { - y /= (x != 0.0 ? x : 1.0); - return ( x * sqrt( 1. + y * 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; + 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 = log1p(y * (1 + y/(hypot(1.0, y) + 1))); - return x > 0 ? y : (x < 0 ? -y : 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 (x == 0) - return x; /* Retain sign of 0 */ - else if (0 < x && x < 0.5) + if (0 < x && x < 0.5) return +0.0; else if (0 > x && x > -0.5) return -0.0; - else if (x > 0) { + else if (x > 0) { t = ceil(x); return 0.5 < t - x ? t - 1 : t; - } else { /* Includes NaN */ + } 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 = round(x); - if (fabs(x) < -(double)LONG_MIN) /* Assume (double)LONG_MIN is exact */ - r = (int)x; + x = pj_round(x); + if (fabs(x) < -(double)r) /* Assume (double)LONG_MIN is exact */ + r = (long)x; return r; } |