fixed errors with infinities
added asin/acos git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@992870 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Luc Maisonobe
parent
99b17c9ce1
commit
c2134b3a90
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@ -204,22 +204,6 @@ public class FastMath {
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private FastMath() {
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}
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/** Compute the arc cosine of a number.
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* @param a number on which evaluation is done
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* @return arc cosine of a
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*/
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public static double acos(final double a) {
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return Math.acos(a);
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}
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/** Compute the arc sine of a number.
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* @param a number on which evaluation is done
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* @return arc sine of a
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*/
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public static double asin(final double a) {
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return Math.asin(a);
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}
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/** Compute the square root of a number.
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* @param a number on which evaluation is done
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* @return square root of a
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@ -441,6 +425,10 @@ public class FastMath {
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intVal = (int) -x;
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if (intVal > 746) {
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if (hiPrec != null) {
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hiPrec[0] = 0.0;
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hiPrec[1] = 0.0;
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}
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return 0.0;
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}
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@ -474,6 +462,10 @@ public class FastMath {
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intVal = (int) x;
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if (intVal > 709) {
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if (hiPrec != null) {
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hiPrec[0] = Double.POSITIVE_INFINITY;
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hiPrec[1] = 0.0;
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}
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return Double.POSITIVE_INFINITY;
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}
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@ -1171,6 +1163,14 @@ public class FastMath {
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double xpa = 1.0 + x;
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double xpb = -(xpa - 1.0 - x);
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if (x == -1) {
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return x/0.0; // -Infinity
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}
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if (x > 0 && 1/x == 0) { // x = Infinity
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return x;
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}
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if (x>1e-6 || x<-1e-6) {
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double hiPrec[] = new double[2];
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@ -1227,22 +1227,28 @@ public class FastMath {
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return 1.0;
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}
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/* Handle special case x<0 */
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if (x < 0) {
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if (y == (long) y) {
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// If y is an integer
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return ((long)y & 1) == 0 ? pow(-x, y) : -pow(-x, y);
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} else {
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return Double.NaN;
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}
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if (x != x) { // X is NaN
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return x;
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}
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if (x == 0) {
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long bits = Double.doubleToLongBits(x);
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if ((bits & 0x8000000000000000L) != 0) {
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// -zero
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if (y < 0 && y == (long)y)
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long yi = (long) y;
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if (y < 0 && y == yi && (yi & 1) == 1) {
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return Double.NEGATIVE_INFINITY;
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}
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if (y < 0 && y == yi && (yi & 1) == 1) {
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return -0.0;
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}
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if (y > 0 && y == yi && (yi & 1) == 1) {
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return -0.0;
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}
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}
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if (y < 0) {
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@ -1256,6 +1262,9 @@ public class FastMath {
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}
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if (x == Double.POSITIVE_INFINITY) {
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if (y != y) { // y is NaN
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return y;
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}
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if (y < 0.0) {
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return 0.0;
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} else {
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@ -1264,6 +1273,9 @@ public class FastMath {
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}
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if (y == Double.POSITIVE_INFINITY) {
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if (x * x == 1.0)
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return Double.NaN;
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if (x * x > 1.0) {
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return Double.POSITIVE_INFINITY;
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} else {
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@ -1271,18 +1283,71 @@ public class FastMath {
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}
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}
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if (x == Double.NEGATIVE_INFINITY) {
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if (y != y) { // y is NaN
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return y;
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}
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if (y < 0) {
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long yi = (long) y;
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if (y == yi && (yi & 1) == 1) {
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return -0.0;
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}
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return 0.0;
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}
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if (y > 0) {
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long yi = (long) y;
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if (y == yi && (yi & 1) == 1) {
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return Double.NEGATIVE_INFINITY;
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}
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return Double.POSITIVE_INFINITY;
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}
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}
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if (y == Double.NEGATIVE_INFINITY) {
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if (x*x < 1.0) {
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return Double.NEGATIVE_INFINITY;
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if (x * x == 1.0) {
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return Double.NaN;
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}
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if (x * x < 1.0) {
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return Double.POSITIVE_INFINITY;
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} else {
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return 0.0;
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}
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}
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/* Handle special case x<0 */
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if (x < 0) {
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// y is an even integer in this case
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if (y >= 4503599627370496.0 || y <= -4503599627370496.0) {
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return pow(-x, y);
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}
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if (y == (long) y) {
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// If y is an integer
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return ((long)y & 1) == 0 ? pow(-x, y) : -pow(-x, y);
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} else {
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return Double.NaN;
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}
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}
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/* Split y into ya and yb such that y = ya+yb */
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double tmp1 = y * 1073741824.0;
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final double ya = y + tmp1 - tmp1;
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final double yb = y - ya;
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double ya;
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double yb;
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if (y < 8e298 && y > -8e298) {
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double tmp1 = y * 1073741824.0;
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ya = y + tmp1 - tmp1;
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yb = y - ya;
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} else {
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double tmp1 = y * 9.31322574615478515625E-10;
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double tmp2 = tmp1 * 9.31322574615478515625E-10;
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ya = (tmp1 + tmp2 - tmp1) * 1073741824.0 * 1073741824.0;
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yb = y - ya;
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}
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/* Compute ln(x) */
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log(x, lns);
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@ -1290,8 +1355,8 @@ public class FastMath {
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double lnb = lns[1];
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/* resplit lns */
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tmp1 = lna * 1073741824.0;
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final double tmp2 = lna + tmp1 - tmp1;
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double tmp1 = lna * 1073741824.0;
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double tmp2 = lna + tmp1 - tmp1;
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lnb += lna - tmp2;
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lna = tmp2;
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@ -2375,8 +2440,8 @@ public class FastMath {
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double b = -(a - pi2a + xa);
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b += pi2b - xb;
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xa = a;
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xb = b;
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xa = a + b;
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xb = -(xa - a - b);
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quadrant ^= 1;
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negative ^= true;
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}
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@ -2412,7 +2477,6 @@ public class FastMath {
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*/
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private static double atan(double xa, double xb, boolean leftPlane) {
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boolean negate = false;
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boolean recip = false;
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int idx;
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if (xa < 0) {
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@ -2519,41 +2583,24 @@ public class FastMath {
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double result;
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double resultb;
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if (recip) {
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final double pi2a = 1.5707963267948966;
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final double pi2b = 6.123233995736766E-17;
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double za = pi2a - ya;
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double zb = -(za - pi2a + ya);
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temp = za - EIGHTHES[idx];
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zb += -(temp - za + EIGHTHES[idx]);
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za = temp;
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//result = yb + eighths[idx] + ya;
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double za = EIGHTHES[idx] + ya;
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double zb = -(za - EIGHTHES[idx] - ya);
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temp = za + yb;
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zb += -(temp - za - yb);
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za = temp;
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zb += pi2b - yb;
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ya = za;
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yb = zb;
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result = yb + ya;
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resultb = -(result - yb - ya);
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} else {
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//result = yb + eighths[idx] + ya;
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double za = EIGHTHES[idx] + ya;
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double zb = -(za - EIGHTHES[idx] - ya);
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temp = za + yb;
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zb += -(temp - za - yb);
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za = temp;
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result = za + zb;
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resultb = -(result - za - zb);
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}
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result = za + zb;
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resultb = -(result - za - zb);
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if (leftPlane) {
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// Result is in the left plane
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final double pia = 1.5707963267948966*2.0;
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final double pib = 6.123233995736766E-17*2.0;
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final double za = pia - result;
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double zb = -(za - pia + result);
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za = pia - result;
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zb = -(za - pia + result);
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zb += pib - resultb;
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result = za + zb;
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@ -2585,7 +2632,11 @@ public class FastMath {
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double invy = 1.0/y;
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if (invx == 0.0) { // X is infinite
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return 0.0;
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if (x > 0) {
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return 0.0;
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} else {
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return Math.PI;
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}
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}
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if (result != result) { // y must be infinite
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@ -2686,6 +2737,155 @@ public class FastMath {
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return result;
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}
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/** Compute the arc sine of a number.
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* @param x number on which evaluation is done
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* @return arc sine of x
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*/
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public static double asin(double x) {
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if (x != x) {
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return Double.NaN;
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}
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if (x > 1.0 || x < -1.0) {
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return Double.NaN;
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}
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if (x == 1.0) {
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return Math.PI/2.0;
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}
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if (x == -1.0) {
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return -Math.PI/2.0;
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}
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/* Compute asin(x) = atan(x/sqrt(1-x*x)) */
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/* Split x */
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double temp = x * 1073741824.0;
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final double xa = x + temp - temp;
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final double xb = x - xa;
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/* Square it */
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double ya = xa*xa;
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double yb = xa*xb*2.0 + xb*xb;
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/* Subtract from 1 */
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ya = -ya;
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yb = -yb;
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double za = 1.0 + ya;
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double zb = -(za - 1.0 - ya);
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temp = za + yb;
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zb += -(temp - za - yb);
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za = temp;
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/* Square root */
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double y;
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y = sqrt(za);
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temp = y * 1073741824.0;
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ya = y + temp - temp;
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yb = y - ya;
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/* Extend precision of sqrt */
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yb += (za - ya*ya - 2*ya*yb - yb*yb) / (2.0*y);
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/* Contribution of zb to sqrt */
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double dx = zb / (2.0*y);
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// Compute ratio r = x/y
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double r = x/y;
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temp = r * 1073741824.0;
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double ra = r + temp - temp;
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double rb = r - ra;
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rb += (x - ra*ya - ra*yb - rb*ya - rb*yb) / y; // Correct for rounding in division
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rb += -x * dx / y / y; // Add in effect additional bits of sqrt.
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temp = ra + rb;
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rb = -(temp - ra - rb);
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ra = temp;
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return atan(ra, rb, false);
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}
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/** Compute the arc cosine of a number.
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* @param x number on which evaluation is done
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* @return arc cosine of x
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*/
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public static double acos(double x) {
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if (x != x) {
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return Double.NaN;
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}
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if (x > 1.0 || x < -1.0) {
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return Double.NaN;
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}
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if (x == -1.0) {
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return Math.PI;
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}
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if (x == 1.0) {
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return 0.0;
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}
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if (x == 0) {
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return Math.PI/2.0;
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}
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/* Compute acos(x) = atan(sqrt(1-x*x)/x) */
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/* Split x */
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double temp = x * 1073741824.0;
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final double xa = x + temp - temp;
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final double xb = x - xa;
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/* Square it */
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double ya = xa*xa;
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double yb = xa*xb*2.0 + xb*xb;
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/* Subtract from 1 */
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ya = -ya;
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yb = -yb;
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double za = 1.0 + ya;
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double zb = -(za - 1.0 - ya);
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temp = za + yb;
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zb += -(temp - za - yb);
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za = temp;
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/* Square root */
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double y = sqrt(za);
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temp = y * 1073741824.0;
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ya = y + temp - temp;
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yb = y - ya;
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/* Extend precision of sqrt */
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yb += (za - ya*ya - 2*ya*yb - yb*yb) / (2.0*y);
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/* Contribution of zb to sqrt */
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yb += zb / (2.0*y);
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y = ya+yb;
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yb = -(y - ya - yb);
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// Compute ratio r = y/x
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double r = y/x;
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temp = r * 1073741824.0;
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double ra = r + temp - temp;
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double rb = r - ra;
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rb += (y - ra*xa - ra*xb - rb*xa - rb*xb) / x; // Correct for rounding in division
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rb += yb / x; // Add in effect additional bits of sqrt.
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temp = ra + rb;
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rb = -(temp - ra - rb);
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ra = temp;
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return atan(ra, rb, x<0);
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}
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/**
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* Convert degrees to radians, with error of less than 0.5 ULP
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* @param x angle in degrees
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@ -2829,15 +3029,23 @@ public class FastMath {
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public static double floor(double x) {
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long y;
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if (x != x) { // NaN
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return x;
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}
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if (x >= 4503599627370496.0 || x <= -4503599627370496.0) {
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return x;
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}
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y = (long) x;
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if (x < 0) {
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if (x < 0 && y != x) {
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y--;
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}
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if (y == 0) {
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return x*y;
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}
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return (double) y;
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}
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@ -2848,12 +3056,22 @@ public class FastMath {
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public static double ceil(double x) {
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double y;
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if (x != x) { // NaN
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return x;
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}
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y = floor(x);
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if (y == x) {
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return y;
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}
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return y + 1.0;
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y += 1.0;
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if (y == 0) {
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return x*y;
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}
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return y;
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}
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/** Get the whole number that is the nearest to x, or the even one if x is exactly half way between two integers.
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