generating and testing the quad-precision constants

include/universal/number/qd/qd_impl.hpp

@@ -393,12 +393,12 @@ class qd {
 
 		u = quick_two_sum(u, v, v);
 
-		double x[4] = { 0.0, 0.0, 0.0, 0.0 };
+		double c[4] = { 0.0, 0.0, 0.0, 0.0 };
 		while (k < 4) {
 			if (i >= 4 && j >= 4) {
-				x[k] = u;
+				c[k] = u;
 				if (k < 3) {
-					x[++k] = v;
+					c[++k] = v;
 				}
 				break;
 			}
@@ -419,16 +419,16 @@ class qd {
 			double s = quick_three_accumulation(u, v, t);
 
 			if (s != 0.0) {
-				x[k++] = s;
+				c[k++] = s;
 			}
 		}
 
 		// add the rest
-		for (k = i; k < 4; k++) x[3] += a[k];
-		for (k = j; k < 4; k++) x[3] += b[k];
+		for (k = i; k < 4; k++) c[3] += a[k];
+		for (k = j; k < 4; k++) c[3] += b[k];
 
-		sw::universal::renorm(x[0], x[1], x[2], x[3]);
-		return qd(x[0], x[1], x[2], x[3]);
+		sw::universal::renorm(c[0], c[1], c[2], c[3]);
+		return qd(c[0], c[1], c[2], c[3]);
 	}
 
 	qd approximate_addition(const qd& a, const qd& b) {
@@ -1057,35 +1057,43 @@ class qd {
 
 ////////////////////////  precomputed constants of note  /////////////////////////////////
 
-// precomputed quad-double constants 
-
-constexpr qd qd_2pi   (6.283185307179586232e+00,  2.449293598294706414e-16);
-constexpr qd qd_pi    (3.141592653589793116e+00,  1.224646799147353207e-16);
-constexpr qd qd_pi2   (1.570796326794896558e+00,  6.123233995736766036e-17);
-constexpr qd qd_pi4   (7.853981633974482790e-01,  3.061616997868383018e-17);
-constexpr qd qd_3pi4  (2.356194490192344837e+00,  9.1848509936051484375e-17);
-constexpr qd qd_e     (2.718281828459045091e+00,  1.445646891729250158e-16);
-constexpr qd qd_log2  (6.931471805599452862e-01,  2.319046813846299558e-17);
-constexpr qd qd_log10 (2.302585092994045901e+00, -2.170756223382249351e-16);
-
-constexpr qd qd_max     (1.79769313486231570815e+308, 9.97920154767359795037e+291);
-constexpr qd qd_safe_max(1.7976931080746007281e+308, 9.97920154767359795037e+291);
-
-
 // precomputed quad-double constants courtesy of constants example program
 
-constexpr qd qd_ln2      (0.69314718055994529e+00,  2.3190468138462996e-17);
-constexpr qd qd_ln10     (2.30258509299404590e+00, -2.1707562233822494e-16);
-constexpr qd qd_lge      (1.44269504088896340e+00,  2.0355273740931027e-17);
-constexpr qd qd_lg10     (3.32192809488736220e+00,  1.6616175169735918e-16);
-constexpr qd qd_loge     (0.43429448190325182e+00,  1.0983196502167652e-17);
-
-constexpr qd qd_sqrt2    (1.41421356237309510e+00, -9.6672933134529122e-17);
+// Golden ratio PHI
+constexpr qd qd_phi    (1.6180339887498949, -5.4321152036825061e-17, 2.6543252083815655e-33, -3.3049919975020988e-50);
+constexpr qd qd_inv_phi(0.6180339887498949, -5.4321152036825061e-17, 2.6543252083815655e-33, -3.3049919975021111e-50);
+// Euler's number e
+constexpr qd qd_e      (2.7182818284590451, 1.4456468917292502e-16, -2.1277171080381768e-33, 1.515630159841219e-49);
+constexpr qd qd_inv_e  (0.36787944117144233, -1.2428753672788363e-17, -5.830044851072742e-34, -2.8267977849017436e-50);
+
+// pi multiples and fractions
+constexpr qd qd_2pi    (6.2831853071795862, 2.4492935982947064e-16, -5.9895396194366793e-33, 2.2249084417267313e-49);
+constexpr qd qd_pi     (3.1415926535897931, 1.2246467991473532e-16, -2.9947698097183397e-33, 1.1124542208633657e-49);
+constexpr qd qd_pi2    (1.5707963267948966, 6.123233995736766e-17, -1.4973849048591698e-33, 5.5622711043168283e-50);
+constexpr qd qd_pi4    (0.78539816339744828, 3.061616997868383e-17, -7.4869245242958492e-34, 2.7811355521584142e-50);
+constexpr qd qd_3pi4   (2.3561944901923448, 9.1848509936051484e-17, 3.9168984647504003e-33, -2.586798163270486e-49);
+constexpr qd qd_inv_pi (0.31830988618379069, -1.9678676675182486e-17, -1.0721436282893004e-33, 8.053563926594112e-50);
+constexpr qd qd_inv_pi2(0.63661977236758138, -3.9357353350364972e-17, -2.1442872565786008e-33, 1.6107127853188224e-49);
+
+// natural logarithm (base = e)
+constexpr qd qd_ln2    (0.69314718055994529, 2.3190468138462996e-17, 5.7077084384162121e-34, -3.5824322106018105e-50);
+constexpr qd qd_lne    (1.0, 0.0, 0.0, 0.0);
+constexpr qd qd_ln10   (2.3025850929940459, -2.1707562233822494e-16, -9.9842624544657766e-33, -4.0233574544502071e-49);
+// binary logarithm (base = 2)
+constexpr qd qd_lg2    (1.0, 0.0, 0.0, 0.0);
+constexpr qd qd_lge    (1.4426950408889634, 2.0355273740931033e-17, -1.0614659956117258e-33, -1.3836716780181395e-50);
+constexpr qd qd_lg10   (3.3219280948873622, 1.661617516973592e-16, 1.2215512178458181e-32, 5.9551189702782481e-49);
+// common logarithm (base = 10)
+constexpr qd qd_log2   (0.3010299956639812, -2.8037281277851704e-18, 5.4719484023146385e-35, 5.1051389831070996e-51);
+constexpr qd qd_loge   (0.43429448190325182, 1.0983196502167651e-17, 3.717181233110959e-34, 7.7344843465042927e-51);
+constexpr qd qd_log10  (1.0, 0.0, 0.0, 0.0);
+
+constexpr qd qd_sqrt2    (1.4142135623730951, -9.6672933134529135e-17, 4.1386753086994136e-33, 4.9355469914683538e-50);
+constexpr qd qd_inv_sqrt2(0.70710678118654757, -4.8336466567264567e-17, 2.0693376543497068e-33, 2.4677734957341745e-50);
+
+
+constexpr qd qd_max(1.79769313486231570815e+308, 9.97920154767359795037e+291);
 
-constexpr qd qd_inv_pi   (0.31830988618379069e+00, -1.9678676675182486e-17);
-constexpr qd qd_inv_pi2  (0.63661977236758138e+00, -3.9357353350364972e-17);
-constexpr qd qd_inv_e    (0.36787944117144233e+00, -1.2428753672788364e-17);
-constexpr qd qd_inv_sqrt2(0.70710678118654757e+00, -4.8336466567264561e-17);
 
 ////////////////////////    helper functions   /////////////////////////////////