MATH-476 FastMath code contains 'magic' numbers
Extracted "splitter" value as a constant git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1061621 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Sebastian Bazley
parent
64a0eee333
commit
d4005bbd6e
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@ -161,6 +161,11 @@ public class FastMath {
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1.2599210498948732,
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1.2599210498948732,
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1.5874010519681994 };
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1.5874010519681994 };
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/**
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* 0x40000000 - used to split a double into two parts, both with the low order bits cleared.
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*/
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private static final double HEX_40000000 = 1073741824.0;
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// Initialize tables
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// Initialize tables
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static {
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static {
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int i;
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int i;
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@ -245,13 +250,13 @@ public class FastMath {
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double ya = hiPrec[0] + hiPrec[1];
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double ya = hiPrec[0] + hiPrec[1];
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double yb = -(ya - hiPrec[0] - hiPrec[1]);
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double yb = -(ya - hiPrec[0] - hiPrec[1]);
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double temp = ya * 1073741824.0;
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double temp = ya * HEX_40000000;
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double yaa = ya + temp - temp;
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double yaa = ya + temp - temp;
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double yab = ya - yaa;
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double yab = ya - yaa;
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// recip = 1/y
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// recip = 1/y
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double recip = 1.0/ya;
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double recip = 1.0/ya;
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temp = recip * 1073741824.0;
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temp = recip * HEX_40000000;
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double recipa = recip + temp - temp;
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double recipa = recip + temp - temp;
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double recipb = recip - recipa;
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double recipb = recip - recipa;
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@ -309,13 +314,13 @@ public class FastMath {
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double ya = hiPrec[0] + hiPrec[1];
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double ya = hiPrec[0] + hiPrec[1];
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double yb = -(ya - hiPrec[0] - hiPrec[1]);
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double yb = -(ya - hiPrec[0] - hiPrec[1]);
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double temp = ya * 1073741824.0;
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double temp = ya * HEX_40000000;
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double yaa = ya + temp - temp;
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double yaa = ya + temp - temp;
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double yab = ya - yaa;
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double yab = ya - yaa;
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// recip = 1/y
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// recip = 1/y
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double recip = 1.0/ya;
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double recip = 1.0/ya;
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temp = recip * 1073741824.0;
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temp = recip * HEX_40000000;
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double recipa = recip + temp - temp;
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double recipa = recip + temp - temp;
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double recipb = recip - recipa;
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double recipb = recip - recipa;
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@ -350,11 +355,11 @@ public class FastMath {
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double denomr = 1.0 / denom;
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double denomr = 1.0 / denom;
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double denomb = -(denom - 1.0 - ya) + yb;
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double denomb = -(denom - 1.0 - ya) + yb;
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double ratio = ya * denomr;
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double ratio = ya * denomr;
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double temp = ratio * 1073741824.0;
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double temp = ratio * HEX_40000000;
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double ra = ratio + temp - temp;
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double ra = ratio + temp - temp;
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double rb = ratio - ra;
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double rb = ratio - ra;
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temp = denom * 1073741824.0;
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temp = denom * HEX_40000000;
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double za = denom + temp - temp;
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double za = denom + temp - temp;
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double zb = denom - za;
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double zb = denom - za;
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@ -434,13 +439,13 @@ public class FastMath {
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db += -(temp - da - yb);
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db += -(temp - da - yb);
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da = temp;
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da = temp;
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temp = da * 1073741824.0;
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temp = da * HEX_40000000;
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double daa = da + temp - temp;
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double daa = da + temp - temp;
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double dab = da - daa;
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double dab = da - daa;
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// ratio = na/da
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// ratio = na/da
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double ratio = na/da;
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double ratio = na/da;
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temp = ratio * 1073741824.0;
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temp = ratio * HEX_40000000;
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double ratioa = ratio + temp - temp;
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double ratioa = ratio + temp - temp;
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double ratiob = ratio - ratioa;
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double ratiob = ratio - ratioa;
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@ -473,13 +478,13 @@ public class FastMath {
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db += -(temp - da - yb);
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db += -(temp - da - yb);
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da = temp;
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da = temp;
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temp = da * 1073741824.0;
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temp = da * HEX_40000000;
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double daa = da + temp - temp;
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double daa = da + temp - temp;
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double dab = da - daa;
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double dab = da - daa;
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// ratio = na/da
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// ratio = na/da
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double ratio = na/da;
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double ratio = na/da;
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temp = ratio * 1073741824.0;
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temp = ratio * HEX_40000000;
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double ratioa = ratio + temp - temp;
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double ratioa = ratio + temp - temp;
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double ratiob = ratio - ratioa;
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double ratiob = ratio - ratioa;
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@ -814,7 +819,7 @@ public class FastMath {
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tempB = -(temp - tempA - tempB);
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tempB = -(temp - tempA - tempB);
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tempA = temp;
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tempA = temp;
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temp = tempA * 1073741824.0;
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temp = tempA * HEX_40000000;
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baseA = tempA + temp - temp;
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baseA = tempA + temp - temp;
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baseB = tempB + (tempA - baseA);
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baseB = tempB + (tempA - baseA);
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@ -835,7 +840,7 @@ public class FastMath {
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zb = -(temp - za - zb);
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zb = -(temp - za - zb);
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za = temp;
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za = temp;
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temp = za * 1073741824.0;
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temp = za * HEX_40000000;
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temp = za + temp - temp;
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temp = za + temp - temp;
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zb += za - temp;
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zb += za - temp;
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za = temp;
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za = temp;
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@ -882,11 +887,11 @@ public class FastMath {
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double denomr = 1.0 / denom;
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double denomr = 1.0 / denom;
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double denomb = -(denom - 1.0 - ya) + yb;
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double denomb = -(denom - 1.0 - ya) + yb;
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double ratio = ya * denomr;
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double ratio = ya * denomr;
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temp = ratio * 1073741824.0;
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temp = ratio * HEX_40000000;
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final double ra = ratio + temp - temp;
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final double ra = ratio + temp - temp;
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double rb = ratio - ra;
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double rb = ratio - ra;
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temp = denom * 1073741824.0;
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temp = denom * HEX_40000000;
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za = denom + temp - temp;
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za = denom + temp - temp;
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zb = denom - za;
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zb = denom - za;
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@ -960,12 +965,12 @@ public class FastMath {
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*/
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*/
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private static void split(final double d, final double split[]) {
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private static void split(final double d, final double split[]) {
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if (d < 8e298 && d > -8e298) {
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if (d < 8e298 && d > -8e298) {
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final double a = d * 1073741824.0;
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final double a = d * HEX_40000000;
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split[0] = (d + a) - a;
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split[0] = (d + a) - a;
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split[1] = d - split[0];
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split[1] = d - split[0];
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} else {
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} else {
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final double a = d * 9.31322574615478515625E-10;
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final double a = d * 9.31322574615478515625E-10;
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split[0] = (d + a - d) * 1073741824.0;
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split[0] = (d + a - d) * HEX_40000000;
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split[1] = d - split[0];
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split[1] = d - split[0];
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}
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}
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}
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}
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@ -979,12 +984,12 @@ public class FastMath {
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final double d = -(c - a[0] - a[1]);
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final double d = -(c - a[0] - a[1]);
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if (c < 8e298 && c > -8e298) {
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if (c < 8e298 && c > -8e298) {
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double z = c * 1073741824.0;
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double z = c * HEX_40000000;
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a[0] = (c + z) - z;
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a[0] = (c + z) - z;
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a[1] = c - a[0] + d;
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a[1] = c - a[0] + d;
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} else {
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} else {
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double z = c * 9.31322574615478515625E-10;
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double z = c * 9.31322574615478515625E-10;
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a[0] = (c + z - c) * 1073741824.0;
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a[0] = (c + z - c) * HEX_40000000;
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a[1] = c - a[0] + d;
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a[1] = c - a[0] + d;
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}
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}
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}
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}
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@ -1235,7 +1240,7 @@ public class FastMath {
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/* Compute x - 1.0 and split it */
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/* Compute x - 1.0 and split it */
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double xa = x - 1.0;
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double xa = x - 1.0;
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double xb = xa - x + 1.0;
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double xb = xa - x + 1.0;
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double tmp = xa * 1073741824.0;
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double tmp = xa * HEX_40000000;
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double aa = xa + tmp - tmp;
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double aa = xa + tmp - tmp;
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double ab = xa - aa;
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double ab = xa - aa;
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xa = aa;
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xa = aa;
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@ -1249,7 +1254,7 @@ public class FastMath {
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aa = ya * xa;
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aa = ya * xa;
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ab = ya * xb + yb * xa + yb * xb;
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ab = ya * xb + yb * xa + yb * xb;
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/* split, so now y = a */
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/* split, so now y = a */
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tmp = aa * 1073741824.0;
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tmp = aa * HEX_40000000;
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ya = aa + tmp - tmp;
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ya = aa + tmp - tmp;
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yb = aa - ya + ab;
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yb = aa - ya + ab;
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@ -1257,7 +1262,7 @@ public class FastMath {
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aa = ya + LN_QUICK_COEF[i][0];
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aa = ya + LN_QUICK_COEF[i][0];
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ab = yb + LN_QUICK_COEF[i][1];
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ab = yb + LN_QUICK_COEF[i][1];
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/* Split y = a */
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/* Split y = a */
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tmp = aa * 1073741824.0;
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tmp = aa * HEX_40000000;
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ya = aa + tmp - tmp;
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ya = aa + tmp - tmp;
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yb = aa - ya + ab;
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yb = aa - ya + ab;
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}
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}
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@ -1266,7 +1271,7 @@ public class FastMath {
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aa = ya * xa;
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aa = ya * xa;
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ab = ya * xb + yb * xa + yb * xb;
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ab = ya * xb + yb * xa + yb * xb;
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/* split, so now y = a */
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/* split, so now y = a */
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tmp = aa * 1073741824.0;
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tmp = aa * HEX_40000000;
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ya = aa + tmp - tmp;
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ya = aa + tmp - tmp;
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yb = aa - ya + ab;
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yb = aa - ya + ab;
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@ -1293,7 +1298,7 @@ public class FastMath {
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if (hiPrec != null) {
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if (hiPrec != null) {
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/* split epsilon -> x */
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/* split epsilon -> x */
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double tmp = epsilon * 1073741824.0;
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double tmp = epsilon * HEX_40000000;
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double aa = epsilon + tmp - tmp;
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double aa = epsilon + tmp - tmp;
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double ab = epsilon - aa;
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double ab = epsilon - aa;
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double xa = aa;
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double xa = aa;
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@ -1314,7 +1319,7 @@ public class FastMath {
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aa = ya * xa;
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aa = ya * xa;
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ab = ya * xb + yb * xa + yb * xb;
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ab = ya * xb + yb * xa + yb * xb;
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/* split, so now y = a */
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/* split, so now y = a */
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tmp = aa * 1073741824.0;
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tmp = aa * HEX_40000000;
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ya = aa + tmp - tmp;
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ya = aa + tmp - tmp;
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yb = aa - ya + ab;
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yb = aa - ya + ab;
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@ -1322,7 +1327,7 @@ public class FastMath {
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aa = ya + LN_HI_PREC_COEF[i][0];
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aa = ya + LN_HI_PREC_COEF[i][0];
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ab = yb + LN_HI_PREC_COEF[i][1];
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ab = yb + LN_HI_PREC_COEF[i][1];
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/* Split y = a */
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/* Split y = a */
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tmp = aa * 1073741824.0;
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tmp = aa * HEX_40000000;
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ya = aa + tmp - tmp;
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ya = aa + tmp - tmp;
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yb = aa - ya + ab;
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yb = aa - ya + ab;
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}
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}
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@ -1454,7 +1459,7 @@ public class FastMath {
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return lores;
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return lores;
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}
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}
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final double tmp = hiPrec[0] * 1073741824.0;
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final double tmp = hiPrec[0] * HEX_40000000;
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final double lna = hiPrec[0] + tmp - tmp;
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final double lna = hiPrec[0] + tmp - tmp;
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final double lnb = hiPrec[0] - lna + hiPrec[1];
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final double lnb = hiPrec[0] - lna + hiPrec[1];
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@ -1590,13 +1595,13 @@ public class FastMath {
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double ya;
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double ya;
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double yb;
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double yb;
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if (y < 8e298 && y > -8e298) {
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if (y < 8e298 && y > -8e298) {
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double tmp1 = y * 1073741824.0;
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double tmp1 = y * HEX_40000000;
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ya = y + tmp1 - tmp1;
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ya = y + tmp1 - tmp1;
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yb = y - ya;
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yb = y - ya;
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} else {
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} else {
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double tmp1 = y * 9.31322574615478515625E-10;
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double tmp1 = y * 9.31322574615478515625E-10;
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double tmp2 = tmp1 * 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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ya = (tmp1 + tmp2 - tmp1) * HEX_40000000 * HEX_40000000;
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yb = y - ya;
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yb = y - ya;
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}
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}
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@ -1610,7 +1615,7 @@ public class FastMath {
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double lnb = lns[1];
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double lnb = lns[1];
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/* resplit lns */
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/* resplit lns */
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double tmp1 = lna * 1073741824.0;
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double tmp1 = lna * HEX_40000000;
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double tmp2 = lna + tmp1 - tmp1;
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double tmp2 = lna + tmp1 - tmp1;
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lnb += lna - tmp2;
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lnb += lna - tmp2;
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lna = tmp2;
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lna = tmp2;
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@ -1941,7 +1946,7 @@ public class FastMath {
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final double cosEpsB = polyCosine(epsilon);
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final double cosEpsB = polyCosine(epsilon);
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// Split epsilon xa + xb = x
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// Split epsilon xa + xb = x
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final double temp = sinEpsA * 1073741824.0;
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final double temp = sinEpsA * HEX_40000000;
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double temp2 = (sinEpsA + temp) - temp;
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double temp2 = (sinEpsA + temp) - temp;
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sinEpsB += sinEpsA - temp2;
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sinEpsB += sinEpsA - temp2;
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sinEpsA = temp2;
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sinEpsA = temp2;
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@ -2085,7 +2090,7 @@ public class FastMath {
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final double cosEpsB = polyCosine(epsilon);
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final double cosEpsB = polyCosine(epsilon);
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// Split epsilon xa + xb = x
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// Split epsilon xa + xb = x
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double temp = sinEpsA * 1073741824.0;
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double temp = sinEpsA * HEX_40000000;
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double temp2 = (sinEpsA + temp) - temp;
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double temp2 = (sinEpsA + temp) - temp;
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sinEpsB += sinEpsA - temp2;
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sinEpsB += sinEpsA - temp2;
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sinEpsA = temp2;
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sinEpsA = temp2;
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@ -2177,11 +2182,11 @@ public class FastMath {
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double est = sina/cosa;
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double est = sina/cosa;
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/* Split the estimate to get more accurate read on division rounding */
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/* Split the estimate to get more accurate read on division rounding */
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temp = est * 1073741824.0;
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temp = est * HEX_40000000;
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double esta = (est + temp) - temp;
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double esta = (est + temp) - temp;
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double estb = est - esta;
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double estb = est - esta;
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temp = cosa * 1073741824.0;
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temp = cosa * HEX_40000000;
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double cosaa = (cosa + temp) - temp;
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double cosaa = (cosa + temp) - temp;
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double cosab = cosa - cosaa;
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double cosab = cosa - cosaa;
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@ -2765,7 +2770,7 @@ public class FastMath {
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epsA = temp;
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epsA = temp;
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/* Compute eps = eps / (1.0 + xa*tangent) */
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/* Compute eps = eps / (1.0 + xa*tangent) */
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temp = xa * 1073741824.0;
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temp = xa * HEX_40000000;
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double ya = xa + temp - temp;
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double ya = xa + temp - temp;
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double yb = xb + xa - ya;
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double yb = xb + xa - ya;
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xa = ya;
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xa = ya;
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@ -2791,11 +2796,11 @@ public class FastMath {
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zb += xb * TANGENT_TABLE_B[idx];
|
zb += xb * TANGENT_TABLE_B[idx];
|
||||||
ya = epsA / za;
|
ya = epsA / za;
|
||||||
|
|
||||||
temp = ya * 1073741824.0;
|
temp = ya * HEX_40000000;
|
||||||
final double yaa = (ya + temp) - temp;
|
final double yaa = (ya + temp) - temp;
|
||||||
final double yab = ya - yaa;
|
final double yab = ya - yaa;
|
||||||
|
|
||||||
temp = za * 1073741824.0;
|
temp = za * HEX_40000000;
|
||||||
final double zaa = (za + temp) - temp;
|
final double zaa = (za + temp) - temp;
|
||||||
final double zab = za - zaa;
|
final double zab = za - zaa;
|
||||||
|
|
||||||
|
|
@ -2974,13 +2979,13 @@ public class FastMath {
|
||||||
}
|
}
|
||||||
|
|
||||||
// Split y
|
// Split y
|
||||||
double temp = x * 1073741824.0;
|
double temp = x * HEX_40000000;
|
||||||
final double xa = x + temp - temp;
|
final double xa = x + temp - temp;
|
||||||
final double xb = x - xa;
|
final double xb = x - xa;
|
||||||
|
|
||||||
// Compute ratio r = x/y
|
// Compute ratio r = x/y
|
||||||
final double r = y/x;
|
final double r = y/x;
|
||||||
temp = r * 1073741824.0;
|
temp = r * HEX_40000000;
|
||||||
double ra = r + temp - temp;
|
double ra = r + temp - temp;
|
||||||
double rb = r - ra;
|
double rb = r - ra;
|
||||||
|
|
||||||
|
|
@ -3024,7 +3029,7 @@ public class FastMath {
|
||||||
/* Compute asin(x) = atan(x/sqrt(1-x*x)) */
|
/* Compute asin(x) = atan(x/sqrt(1-x*x)) */
|
||||||
|
|
||||||
/* Split x */
|
/* Split x */
|
||||||
double temp = x * 1073741824.0;
|
double temp = x * HEX_40000000;
|
||||||
final double xa = x + temp - temp;
|
final double xa = x + temp - temp;
|
||||||
final double xb = x - xa;
|
final double xb = x - xa;
|
||||||
|
|
||||||
|
|
@ -3046,7 +3051,7 @@ public class FastMath {
|
||||||
/* Square root */
|
/* Square root */
|
||||||
double y;
|
double y;
|
||||||
y = sqrt(za);
|
y = sqrt(za);
|
||||||
temp = y * 1073741824.0;
|
temp = y * HEX_40000000;
|
||||||
ya = y + temp - temp;
|
ya = y + temp - temp;
|
||||||
yb = y - ya;
|
yb = y - ya;
|
||||||
|
|
||||||
|
|
@ -3058,7 +3063,7 @@ public class FastMath {
|
||||||
|
|
||||||
// Compute ratio r = x/y
|
// Compute ratio r = x/y
|
||||||
double r = x/y;
|
double r = x/y;
|
||||||
temp = r * 1073741824.0;
|
temp = r * HEX_40000000;
|
||||||
double ra = r + temp - temp;
|
double ra = r + temp - temp;
|
||||||
double rb = r - ra;
|
double rb = r - ra;
|
||||||
|
|
||||||
|
|
@ -3100,7 +3105,7 @@ public class FastMath {
|
||||||
/* Compute acos(x) = atan(sqrt(1-x*x)/x) */
|
/* Compute acos(x) = atan(sqrt(1-x*x)/x) */
|
||||||
|
|
||||||
/* Split x */
|
/* Split x */
|
||||||
double temp = x * 1073741824.0;
|
double temp = x * HEX_40000000;
|
||||||
final double xa = x + temp - temp;
|
final double xa = x + temp - temp;
|
||||||
final double xb = x - xa;
|
final double xb = x - xa;
|
||||||
|
|
||||||
|
|
@ -3121,7 +3126,7 @@ public class FastMath {
|
||||||
|
|
||||||
/* Square root */
|
/* Square root */
|
||||||
double y = sqrt(za);
|
double y = sqrt(za);
|
||||||
temp = y * 1073741824.0;
|
temp = y * HEX_40000000;
|
||||||
ya = y + temp - temp;
|
ya = y + temp - temp;
|
||||||
yb = y - ya;
|
yb = y - ya;
|
||||||
|
|
||||||
|
|
@ -3141,8 +3146,8 @@ public class FastMath {
|
||||||
return Math.PI/2; // so return the appropriate value
|
return Math.PI/2; // so return the appropriate value
|
||||||
}
|
}
|
||||||
|
|
||||||
if (abs(r) < Double.MAX_VALUE/1073741824.0){ // is it safe to split r ?
|
if (abs(r) < Double.MAX_VALUE/HEX_40000000){ // is it safe to split r ?
|
||||||
temp = r * 1073741824.0;
|
temp = r * HEX_40000000;
|
||||||
} else {
|
} else {
|
||||||
temp = 0.0;
|
temp = 0.0;
|
||||||
}
|
}
|
||||||
|
|
@ -3214,13 +3219,13 @@ public class FastMath {
|
||||||
est += (xs - est*est*est) / (3*est*est);
|
est += (xs - est*est*est) / (3*est*est);
|
||||||
|
|
||||||
// Do one round of Newton's method in extended precision to get the last bit right.
|
// Do one round of Newton's method in extended precision to get the last bit right.
|
||||||
double temp = est * 1073741824.0;
|
double temp = est * HEX_40000000;
|
||||||
double ya = est + temp - temp;
|
double ya = est + temp - temp;
|
||||||
double yb = est - ya;
|
double yb = est - ya;
|
||||||
|
|
||||||
double za = ya * ya;
|
double za = ya * ya;
|
||||||
double zb = ya * yb * 2.0 + yb * yb;
|
double zb = ya * yb * 2.0 + yb * yb;
|
||||||
temp = za * 1073741824.0;
|
temp = za * HEX_40000000;
|
||||||
double temp2 = za + temp - temp;
|
double temp2 = za + temp - temp;
|
||||||
zb += za - temp2;
|
zb += za - temp2;
|
||||||
za = temp2;
|
za = temp2;
|
||||||
|
|
@ -3255,12 +3260,13 @@ public class FastMath {
|
||||||
return x;
|
return x;
|
||||||
}
|
}
|
||||||
|
|
||||||
|
// These are PI/180 split into high and low order bits
|
||||||
final double facta = 0.01745329052209854;
|
final double facta = 0.01745329052209854;
|
||||||
final double factb = 1.997844754509471E-9;
|
final double factb = 1.997844754509471E-9;
|
||||||
|
|
||||||
double temp = 0;
|
double temp = 0;
|
||||||
if (abs(x) < Double.MAX_VALUE/1073741824.0) { // prevent overflow to infinity
|
if (abs(x) < Double.MAX_VALUE/HEX_40000000) { // prevent overflow to infinity
|
||||||
temp = x * 1073741824.0;
|
temp = x * HEX_40000000;
|
||||||
}
|
}
|
||||||
double xa = x + temp - temp;
|
double xa = x + temp - temp;
|
||||||
double xb = x - xa;
|
double xb = x - xa;
|
||||||
|
|
@ -3283,12 +3289,13 @@ public class FastMath {
|
||||||
return x;
|
return x;
|
||||||
}
|
}
|
||||||
|
|
||||||
|
// These are 180/PI split into high and low order bits
|
||||||
final double facta = 57.2957763671875;
|
final double facta = 57.2957763671875;
|
||||||
final double factb = 3.145894820876798E-6;
|
final double factb = 3.145894820876798E-6;
|
||||||
|
|
||||||
double temp = 0;
|
double temp = 0;
|
||||||
if (abs(x) < Double.MAX_VALUE/1073741824.0) { // prevent overflow to infinity
|
if (abs(x) < Double.MAX_VALUE/HEX_40000000) { // prevent overflow to infinity
|
||||||
temp = x * 1073741824.0;
|
temp = x * HEX_40000000;
|
||||||
}
|
}
|
||||||
double xa = x + temp - temp;
|
double xa = x + temp - temp;
|
||||||
double xb = x - xa;
|
double xb = x - xa;
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue