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authorJeff Hao <jeffhao@google.com>2014-08-08 21:20:36 +0000
committerGerrit Code Review <noreply-gerritcodereview@google.com>2014-08-08 17:27:05 +0000
commitcf5219256c9a44e9b215ac645c1823238ebd31d7 (patch)
tree9c8a68034c67a8edf30de11daed545a73f4974e0
parent7033b1a77271044b40c1c598c55b4135fc1a146b (diff)
parent562ef053263cf7efccb6640c027b9d015956741e (diff)
downloadlibcore-cf5219256c9a44e9b215ac645c1823238ebd31d7.zip
libcore-cf5219256c9a44e9b215ac645c1823238ebd31d7.tar.gz
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Merge "Implements some math functions for faster performance"
-rw-r--r--NOTICE11
-rw-r--r--luni/src/main/java/java/lang/StrictMath.java1070
-rw-r--r--luni/src/main/native/java_lang_StrictMath.cpp65
3 files changed, 1017 insertions, 129 deletions
diff --git a/NOTICE b/NOTICE
index 951e506..5136b4b 100644
--- a/NOTICE
+++ b/NOTICE
@@ -104,3 +104,14 @@ WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
See W3C License http://www.w3.org/Consortium/Legal/ for more details.
+
+ =========================================================================
+ == NOTICE file for the fdlibm License. ==
+ =========================================================================
+
+Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+
+Developed at SunSoft, a Sun Microsystems, Inc. business.
+Permission to use, copy, modify, and distribute this
+software is freely granted, provided that this notice
+is preserved.
diff --git a/luni/src/main/java/java/lang/StrictMath.java b/luni/src/main/java/java/lang/StrictMath.java
index f409c06..2e848f2 100644
--- a/luni/src/main/java/java/lang/StrictMath.java
+++ b/luni/src/main/java/java/lang/StrictMath.java
@@ -15,6 +15,18 @@
* limitations under the License.
*/
+/*
+ * acos, asin, atan, cosh, sinh, tanh, exp, expm1, log, log10, log1p, and cbrt
+ * have been implemented with the following license.
+ * ====================================================
+ * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
package java.lang;
/**
@@ -102,6 +114,21 @@ public final class StrictMath {
return Math.abs(l);
}
+ private static final double PIO2_HI = 1.57079632679489655800e+00;
+ private static final double PIO2_LO = 6.12323399573676603587e-17;
+ private static final double PS0 = 1.66666666666666657415e-01;
+ private static final double PS1 = -3.25565818622400915405e-01;
+ private static final double PS2 = 2.01212532134862925881e-01;
+ private static final double PS3 = -4.00555345006794114027e-02;
+ private static final double PS4 = 7.91534994289814532176e-04;
+ private static final double PS5 = 3.47933107596021167570e-05;
+ private static final double QS1 = -2.40339491173441421878e+00;
+ private static final double QS2 = 2.02094576023350569471e+00;
+ private static final double QS3 = -6.88283971605453293030e-01;
+ private static final double QS4 = 7.70381505559019352791e-02;
+ private static final double HUGE = 1.000e+300;
+ private static final double PIO4_HI = 7.85398163397448278999e-01;
+
/**
* Returns the closest double approximation of the arc cosine of the
* argument within the range {@code [0..pi]}.
@@ -113,11 +140,62 @@ public final class StrictMath {
* <li>{@code acos(NaN) = NaN}</li>
* </ul>
*
- * @param d
+ * @param x
* the value to compute arc cosine of.
* @return the arc cosine of the argument.
*/
- public static native double acos(double d);
+ public static double acos(double x) {
+ double z, p, q, r, w, s, c, df;
+ int hx, ix;
+ final long bits = Double.doubleToRawLongBits(x);
+ hx = (int) (bits >>> 32);
+ ix = hx & 0x7fffffff;
+ if (ix >= 0x3ff00000) { /* |x| >= 1 */
+ if ((((ix - 0x3ff00000) | ((int) bits))) == 0) { /* |x|==1 */
+ if (hx > 0) {
+ return 0.0; /* ieee_acos(1) = 0 */
+ } else {
+ return 3.14159265358979311600e+00 + 2.0 * PIO2_LO; /* ieee_acos(-1)= pi */
+ }
+ }
+ return (x - x) / (x - x); /* ieee_acos(|x|>1) is NaN */
+ }
+
+ if (ix < 0x3fe00000) { /* |x| < 0.5 */
+ if (ix <= 0x3c600000) {
+ return PIO2_HI + PIO2_LO;/* if|x|<2**-57 */
+ }
+
+ z = x * x;
+ p = z * (PS0 + z
+ * (PS1 + z * (PS2 + z * (PS3 + z * (PS4 + z * PS5)))));
+ q = 1.00000000000000000000e+00 + z * (QS1 + z * (QS2 + z * (QS3 + z * QS4)));
+ r = p / q;
+ return PIO2_HI - (x - (PIO2_LO - x * r));
+ } else if (hx < 0) { /* x < -0.5 */
+ z = (1.00000000000000000000e+00 + x) * 0.5;
+ p = z * (PS0 + z
+ * (PS1 + z * (PS2 + z * (PS3 + z * (PS4 + z * PS5)))));
+ q = 1.00000000000000000000e+00 + z * (QS1 + z * (QS2 + z * (QS3 + z * QS4)));
+ s = StrictMath.sqrt(z);
+ r = p / q;
+ w = r * s - PIO2_LO;
+ return 3.14159265358979311600e+00 - 2.0 * (s + w);
+ } else { /* x > 0.5 */
+ z = (1.00000000000000000000e+00 - x) * 0.5;
+ s = StrictMath.sqrt(z);
+ df = s;
+ df = Double.longBitsToDouble(
+ Double.doubleToRawLongBits(df) & 0xffffffffL << 32);
+ c = (z - df * df) / (s + df);
+ p = z * (PS0 + z
+ * (PS1 + z * (PS2 + z * (PS3 + z * (PS4 + z * PS5)))));
+ q = 1.00000000000000000000e+00 + z * (QS1 + z * (QS2 + z * (QS3 + z * QS4)));
+ r = p / q;
+ w = r * s + c;
+ return 2.0 * (df + w);
+ }
+ }
/**
* Returns the closest double approximation of the arc sine of the argument
@@ -130,11 +208,75 @@ public final class StrictMath {
* <li>{@code asin(NaN) = NaN}</li>
* </ul>
*
- * @param d
+ * @param x
* the value whose arc sine has to be computed.
* @return the arc sine of the argument.
*/
- public static native double asin(double d);
+ public static double asin(double x) {
+ double t, w, p, q, c, r, s;
+ int hx, ix;
+ final long bits = Double.doubleToRawLongBits(x);
+ hx = (int) (bits >>> 32);
+ ix = hx & 0x7fffffff;
+ if (ix >= 0x3ff00000) { /* |x|>= 1 */
+ if ((((ix - 0x3ff00000) | ((int) bits))) == 0) {
+ /* ieee_asin(1)=+-pi/2 with inexact */
+ return x * PIO2_HI + x * PIO2_LO;
+ }
+ return (x - x) / (x - x); /* ieee_asin(|x|>1) is NaN */
+ } else if (ix < 0x3fe00000) { /* |x|<0.5 */
+ if (ix < 0x3e400000) { /* if |x| < 2**-27 */
+ if (HUGE + x > 1.00000000000000000000e+00) {
+ return x;/* return x with inexact if x!=0 */
+ }
+ } else {
+ t = x * x;
+ p = t * (PS0 + t
+ * (PS1 + t * (PS2 + t * (PS3 + t * (PS4 + t * PS5)))));
+ q = 1.00000000000000000000e+00 + t * (QS1 + t * (QS2 + t * (QS3 + t * QS4)));
+ w = p / q;
+ return x + x * w;
+ }
+ }
+ /* 1> |x|>= 0.5 */
+ w = 1.00000000000000000000e+00 - Math.abs(x);
+ t = w * 0.5;
+ p = t * (PS0 + t * (PS1 + t * (PS2 + t * (PS3 + t * (PS4 + t * PS5)))));
+ q = 1.00000000000000000000e+00 + t * (QS1 + t * (QS2 + t * (QS3 + t * QS4)));
+ s = StrictMath.sqrt(t);
+ if (ix >= 0x3FEF3333) { /* if |x| > 0.975 */
+ w = p / q;
+ t = PIO2_HI - (2.0 * (s + s * w) - PIO2_LO);
+ } else {
+ w = s;
+ w = Double.longBitsToDouble(
+ Double.doubleToRawLongBits(w) & 0xffffffffL << 32);
+ c = (t - w * w) / (s + w);
+ r = p / q;
+ p = 2.0 * s * r - (PIO2_LO - 2.0 * c);
+ q = PIO4_HI - 2.0 * w;
+ t = PIO4_HI - (p - q);
+ }
+ return (hx > 0) ? t : -t;
+ }
+
+ private static final double[] ATANHI = { 4.63647609000806093515e-01,
+ 7.85398163397448278999e-01, 9.82793723247329054082e-01,
+ 1.57079632679489655800e+00 };
+ private static final double[] ATANLO = { 2.26987774529616870924e-17,
+ 3.06161699786838301793e-17, 1.39033110312309984516e-17,
+ 6.12323399573676603587e-17 };
+ private static final double AT0 = 3.33333333333329318027e-01;
+ private static final double AT1 = -1.99999999998764832476e-01;
+ private static final double AT2 = 1.42857142725034663711e-01;
+ private static final double AT3 = -1.11111104054623557880e-01;
+ private static final double AT4 = 9.09088713343650656196e-02;
+ private static final double AT5 = -7.69187620504482999495e-02;
+ private static final double AT6 = 6.66107313738753120669e-02;
+ private static final double AT7= -5.83357013379057348645e-02;
+ private static final double AT8 = 4.97687799461593236017e-02;
+ private static final double AT9 = -3.65315727442169155270e-02;
+ private static final double AT10 = 1.62858201153657823623e-02;
/**
* Returns the closest double approximation of the arc tangent of the
@@ -149,11 +291,73 @@ public final class StrictMath {
* <li>{@code atan(NaN) = NaN}</li>
* </ul>
*
- * @param d
+ * @param x
* the value whose arc tangent has to be computed.
* @return the arc tangent of the argument.
*/
- public static native double atan(double d);
+ public static double atan(double x) {
+ double w, s1, s2, z;
+ int ix, hx, id;
+
+ final long bits = Double.doubleToRawLongBits(x);
+ hx = (int) (bits >>> 32);
+ ix = hx & 0x7fffffff;
+ if (ix >= 0x44100000) { /* if |x| >= 2^66 */
+ if (ix > 0x7ff00000 || (ix == 0x7ff00000 && (((int) bits) != 0))) {
+ return x + x; /* NaN */
+ }
+ if (hx > 0) {
+ return ATANHI[3] + ATANLO[3];
+ } else {
+ return -ATANHI[3] - ATANLO[3];
+ }
+ }
+ if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
+ if (ix < 0x3e200000) { /* |x| < 2^-29 */
+ if (HUGE + x > 1.00000000000000000000e+00) {
+ return x; /* raise inexact */
+ }
+ }
+ id = -1;
+ } else {
+ x = Math.abs(x);
+ if (ix < 0x3ff30000) { /* |x| < 1.1875 */
+ if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
+ id = 0;
+ x = (2.0 * x - 1.00000000000000000000e+00) / (2.0 + x);
+ } else { /* 11/16<=|x|< 19/16 */
+ id = 1;
+ x = (x - 1.00000000000000000000e+00) / (x + 1.00000000000000000000e+00);
+ }
+ } else {
+ if (ix < 0x40038000) { /* |x| < 2.4375 */
+ id = 2;
+ x = (x - 1.5) / (1.00000000000000000000e+00 + 1.5 * x);
+ } else { /* 2.4375 <= |x| < 2^66 */
+ id = 3;
+ x = -1.0 / x;
+ }
+ }
+ }
+
+ /* end of argument reduction */
+ z = x * x;
+ w = z * z;
+ /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
+ s1 = z * (AT0 + w * (AT2 + w
+ * (AT4 + w * (AT6 + w * (AT8 + w * AT10)))));
+ s2 = w * (AT1 + w * (AT3 + w * (AT5 + w * (AT7 + w * AT9))));
+ if (id < 0) {
+ return x - x * (s1 + s2);
+ } else {
+ z = ATANHI[id] - ((x * (s1 + s2) - ATANLO[id]) - x);
+ return (hx < 0) ? -z : z;
+ }
+ }
+
+ private static final double PI_O_4 = 7.8539816339744827900E-01;
+ private static final double PI_O_2 = 1.5707963267948965580E+00;
+ private static final double PI_LO = 1.2246467991473531772E-16;
/**
* Returns the closest double approximation of the arc tangent of
@@ -192,7 +396,108 @@ public final class StrictMath {
* the denominator of the value whose atan has to be computed.
* @return the arc tangent of {@code y/x}.
*/
- public static native double atan2(double y, double x);
+ public static double atan2(double y, double x) {
+ double z;
+ int k, m, hx, hy, ix, iy;
+ int lx, ly; // watch out, should be unsigned
+
+ final long yBits = Double.doubleToRawLongBits(y);
+ final long xBits = Double.doubleToRawLongBits(x);
+
+ hx = (int) (xBits >>> 32); // __HI(x);
+ ix = hx & 0x7fffffff;
+ lx = (int) xBits; // __LO(x);
+ hy = (int) (yBits >>> 32); // __HI(y);
+ iy = hy & 0x7fffffff;
+ ly = (int) yBits; // __LO(y);
+ if (((ix | ((lx | -lx) >> 31)) > 0x7ff00000)
+ || ((iy | ((ly | -ly) >> 31)) > 0x7ff00000)) { /* x or y is NaN */
+ return x + y;
+ }
+ if ((hx - 0x3ff00000 | lx) == 0) {
+ return StrictMath.atan(y); /* x=1.0 */
+ }
+
+ m = ((hy >> 31) & 1) | ((hx >> 30) & 2); /* 2*sign(x)+sign(y) */
+
+ /* when y = 0 */
+ if ((iy | ly) == 0) {
+ switch (m) {
+ case 0:
+ case 1:
+ return y; /* ieee_atan(+-0,+anything)=+-0 */
+ case 2:
+ return 3.14159265358979311600e+00 + TINY;/* ieee_atan(+0,-anything) = pi */
+ case 3:
+ return -3.14159265358979311600e+00 - TINY;/* ieee_atan(-0,-anything) =-pi */
+ }
+ }
+ /* when x = 0 */
+ if ((ix | lx) == 0)
+ return (hy < 0) ? -PI_O_2 - TINY : PI_O_2 + TINY;
+
+ /* when x is INF */
+ if (ix == 0x7ff00000) {
+ if (iy == 0x7ff00000) {
+ switch (m) {
+ case 0:
+ return PI_O_4 + TINY;/* ieee_atan(+INF,+INF) */
+ case 1:
+ return -PI_O_4 - TINY;/* ieee_atan(-INF,+INF) */
+ case 2:
+ return 3.0 * PI_O_4 + TINY;/* ieee_atan(+INF,-INF) */
+ case 3:
+ return -3.0 * PI_O_4 - TINY;/* ieee_atan(-INF,-INF) */
+ }
+ } else {
+ switch (m) {
+ case 0:
+ return 0.0; /* ieee_atan(+...,+INF) */
+ case 1:
+ return -0.0; /* ieee_atan(-...,+INF) */
+ case 2:
+ return 3.14159265358979311600e+00 + TINY; /* ieee_atan(+...,-INF) */
+ case 3:
+ return -3.14159265358979311600e+00 - TINY; /* ieee_atan(-...,-INF) */
+ }
+ }
+ }
+ /* when y is INF */
+ if (iy == 0x7ff00000)
+ return (hy < 0) ? -PI_O_2 - TINY : PI_O_2 + TINY;
+
+ /* compute y/x */
+ k = (iy - ix) >> 20;
+ if (k > 60) {
+ z = PI_O_2 + 0.5 * PI_LO; /* |y/x| > 2**60 */
+ } else if (hx < 0 && k < -60) {
+ z = 0.0; /* |y|/x < -2**60 */
+ } else {
+ z = StrictMath.atan(Math.abs(y / x)); /* safe to do y/x */
+ }
+
+ switch (m) {
+ case 0:
+ return z; /* ieee_atan(+,+) */
+ case 1:
+ // __HI(z) ^= 0x80000000;
+ z = Double.longBitsToDouble(
+ Double.doubleToRawLongBits(z) ^ (0x80000000L << 32));
+ return z; /* ieee_atan(-,+) */
+ case 2:
+ return 3.14159265358979311600e+00 - (z - PI_LO);/* ieee_atan(+,-) */
+ default: /* case 3 */
+ return (z - PI_LO) - 3.14159265358979311600e+00;/* ieee_atan(-,-) */
+ }
+ }
+
+ private static final int B1 = 715094163;
+ private static final int B2 = 696219795;
+ private static final double C = 5.42857142857142815906e-01;
+ private static final double D = -7.05306122448979611050e-01;
+ private static final double CBRTE = 1.41428571428571436819e+00;
+ private static final double F = 1.60714285714285720630e+00;
+ private static final double G = 3.57142857142857150787e-01;
/**
* Returns the closest double approximation of the cube root of the
@@ -207,11 +512,79 @@ public final class StrictMath {
* <li>{@code cbrt(NaN) = NaN}</li>
* </ul>
*
- * @param d
+ * @param x
* the value whose cube root has to be computed.
* @return the cube root of the argument.
*/
- public static native double cbrt(double d);
+ public static double cbrt(double x) {
+ if (x < 0) {
+ return -cbrt(-x);
+ }
+ int hx;
+ double r, s, w;
+ int sign; // caution: should be unsigned
+ long bits = Double.doubleToRawLongBits(x);
+
+ hx = (int) (bits >>> 32);
+ sign = hx & 0x80000000; /* sign= sign(x) */
+ hx ^= sign;
+ if (hx >= 0x7ff00000) {
+ return (x + x); /* ieee_cbrt(NaN,INF) is itself */
+ }
+
+ if ((hx | ((int) bits)) == 0) {
+ return x; /* ieee_cbrt(0) is itself */
+ }
+
+ // __HI(x) = hx; /* x <- |x| */
+ bits &= 0x00000000ffffffffL;
+ bits |= ((long) hx << 32);
+
+ long tBits = Double.doubleToRawLongBits(0.0) & 0x00000000ffffffffL;
+ double t = 0.0;
+ /* rough cbrt to 5 bits */
+ if (hx < 0x00100000) { /* subnormal number */
+ // __HI(t)=0x43500000; /*set t= 2**54*/
+ tBits |= 0x43500000L << 32;
+ t = Double.longBitsToDouble(tBits);
+ t *= x;
+
+ // __HI(t)=__HI(t)/3+B2;
+ tBits = Double.doubleToRawLongBits(t);
+ long tBitsHigh = tBits >> 32;
+ tBits &= 0x00000000ffffffffL;
+ tBits |= ((tBitsHigh / 3) + B2) << 32;
+ t = Double.longBitsToDouble(tBits);
+
+ } else {
+ // __HI(t)=hx/3+B1;
+ tBits |= ((long) ((hx / 3) + B1)) << 32;
+ t = Double.longBitsToDouble(tBits);
+ }
+
+ /* new cbrt to 23 bits, may be implemented in single precision */
+ r = t * t / x;
+ s = C + r * t;
+ t *= G + F / (s + CBRTE + D / s);
+
+ /* chopped to 20 bits and make it larger than ieee_cbrt(x) */
+ tBits = Double.doubleToRawLongBits(t);
+ tBits &= 0xFFFFFFFFL << 32;
+ tBits += 0x00000001L << 32;
+ t = Double.longBitsToDouble(tBits);
+
+ /* one step newton iteration to 53 bits with error less than 0.667 ulps */
+ s = t * t; /* t*t is exact */
+ r = x / s;
+ w = t + t;
+ r = (r - t) / (w + r); /* r-s is exact */
+ t = t + t * r;
+
+ /* retore the sign bit */
+ tBits = Double.doubleToRawLongBits(t);
+ tBits |= ((long) sign) << 32;
+ return Double.longBitsToDouble(tBits);
+ }
/**
* Returns the double conversion of the most negative (closest to negative
@@ -229,6 +602,8 @@ public final class StrictMath {
*/
public static native double ceil(double d);
+ private static final long ONEBITS = Double.doubleToRawLongBits(1.00000000000000000000e+00)
+ & 0x00000000ffffffffL;
/**
* Returns the closest double approximation of the hyperbolic cosine of the
@@ -241,11 +616,54 @@ public final class StrictMath {
* <li>{@code cosh(NaN) = NaN}</li>
* </ul>
*
- * @param d
+ * @param x
* the value whose hyperbolic cosine has to be computed.
* @return the hyperbolic cosine of the argument.
*/
- public static native double cosh(double d);
+ public static double cosh(double x) {
+ double t, w;
+ int ix;
+ final long bits = Double.doubleToRawLongBits(x);
+ ix = (int) (bits >>> 32) & 0x7fffffff;
+
+ /* x is INF or NaN */
+ if (ix >= 0x7ff00000) {
+ return x * x;
+ }
+
+ /* |x| in [0,0.5*ln2], return 1+ieee_expm1(|x|)^2/(2*ieee_exp(|x|)) */
+ if (ix < 0x3fd62e43) {
+ t = expm1(Math.abs(x));
+ w = 1.00000000000000000000e+00 + t;
+ if (ix < 0x3c800000)
+ return w; /* ieee_cosh(tiny) = 1 */
+ return 1.00000000000000000000e+00 + (t * t) / (w + w);
+ }
+
+ /* |x| in [0.5*ln2,22], return (ieee_exp(|x|)+1/ieee_exp(|x|)/2; */
+ if (ix < 0x40360000) {
+ t = exp(Math.abs(x));
+ return 0.5 * t + 0.5 / t;
+ }
+
+ /* |x| in [22, ieee_log(maxdouble)] return half*ieee_exp(|x|) */
+ if (ix < 0x40862E42) {
+ return 0.5 * exp(Math.abs(x));
+ }
+
+ /* |x| in [log(maxdouble), overflowthresold] */
+ final long lx = ((ONEBITS >>> 29) + ((int) bits)) & 0x00000000ffffffffL;
+ // watch out: lx should be an unsigned int
+ // lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
+ if (ix < 0x408633CE || (ix == 0x408633ce) && (lx <= 0x8fb9f87dL)) {
+ w = exp(0.5 * Math.abs(x));
+ t = 0.5 * w;
+ return t * w;
+ }
+
+ /* |x| > overflowthresold, ieee_cosh(x) overflow */
+ return HUGE * HUGE;
+ }
/**
* Returns the closest double approximation of the cosine of the argument.
@@ -263,6 +681,19 @@ public final class StrictMath {
*/
public static native double cos(double d);
+ private static final double TWON24 = 5.96046447753906250000e-08;
+ private static final double TWO54 = 1.80143985094819840000e+16,
+ TWOM54 = 5.55111512312578270212e-17;
+ private static final double TWOM1000 = 9.33263618503218878990e-302;
+ private static final double O_THRESHOLD = 7.09782712893383973096e+02;
+ private static final double U_THRESHOLD = -7.45133219101941108420e+02;
+ private static final double INVLN2 = 1.44269504088896338700e+00;
+ private static final double P1 = 1.66666666666666019037e-01;
+ private static final double P2 = -2.77777777770155933842e-03;
+ private static final double P3 = 6.61375632143793436117e-05;
+ private static final double P4 = -1.65339022054652515390e-06;
+ private static final double P5 = 4.13813679705723846039e-08;
+
/**
* Returns the closest double approximation of the raising "e" to the power
* of the argument.
@@ -274,11 +705,88 @@ public final class StrictMath {
* <li>{@code exp(NaN) = NaN}</li>
* </ul>
*
- * @param d
+ * @param x
* the value whose exponential has to be computed.
* @return the exponential of the argument.
*/
- public static native double exp(double d);
+ public static double exp(double x) {
+ double y, c, t;
+ double hi = 0, lo = 0;
+ int k = 0, xsb;
+ int hx; // should be unsigned, be careful!
+ final long bits = Double.doubleToRawLongBits(x);
+ int lowBits = (int) bits;
+ int highBits = (int) (bits >>> 32);
+ hx = highBits & 0x7fffffff;
+ xsb = (highBits >>> 31) & 1;
+
+ /* filter out non-finite argument */
+ if (hx >= 0x40862E42) { /* if |x|>=709.78... */
+ if (hx >= 0x7ff00000) {
+ if (((hx & 0xfffff) | lowBits) != 0) {
+ return x + x; /* NaN */
+ } else {
+ return (xsb == 0) ? x : 0.0; /* ieee_exp(+-inf)={inf,0} */
+ }
+ }
+
+ if (x > O_THRESHOLD) {
+ return HUGE * HUGE; /* overflow */
+ }
+
+ if (x < U_THRESHOLD) {
+ return TWOM1000 * TWOM1000; /* underflow */
+ }
+ }
+
+ /* argument reduction */
+ if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
+ if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
+ hi = x - ((xsb == 0) ? 6.93147180369123816490e-01 :
+ -6.93147180369123816490e-01); // LN2HI[xsb];
+ lo = (xsb == 0) ? 1.90821492927058770002e-10 :
+ -1.90821492927058770002e-10; // LN2LO[xsb];
+ k = 1 - xsb - xsb;
+ } else {
+ k = (int) (INVLN2 * x + ((xsb == 0) ? 0.5 : -0.5 ));//halF[xsb]);
+ t = k;
+ hi = x - t * 6.93147180369123816490e-01; //ln2HI[0]; /* t*ln2HI is exact here */
+ lo = t * 1.90821492927058770002e-10; //ln2LO[0];
+ }
+ x = hi - lo;
+ } else if (hx < 0x3e300000) { /* when |x|<2**-28 */
+ if (HUGE + x > 1.00000000000000000000e+00)
+ return 1.00000000000000000000e+00 + x;/* trigger inexact */
+ } else {
+ k = 0;
+ }
+
+ /* x is now in primary range */
+ t = x * x;
+ c = x - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
+ if (k == 0) {
+ return 1.00000000000000000000e+00 - ((x * c) / (c - 2.0) - x);
+ } else {
+ y = 1.00000000000000000000e+00 - ((lo - (x * c) / (2.0 - c)) - hi);
+ }
+ long yBits = Double.doubleToRawLongBits(y);
+ if (k >= -1021) {
+ yBits += ((long) (k << 20)) << 32; /* add k to y's exponent */
+ return Double.longBitsToDouble(yBits);
+ } else {
+ yBits += ((long) ((k + 1000) << 20)) << 32;/* add k to y's exponent */
+ return Double.longBitsToDouble(yBits) * TWOM1000;
+ }
+ }
+
+ private static final double TINY = 1.0e-300;
+ private static final double LN2_HI = 6.93147180369123816490e-01;
+ private static final double LN2_LO = 1.90821492927058770002e-10;
+ private static final double Q1 = -3.33333333333331316428e-02;
+ private static final double Q2 = 1.58730158725481460165e-03;
+ private static final double Q3 = -7.93650757867487942473e-05;
+ private static final double Q4 = 4.00821782732936239552e-06;
+ private static final double Q5 = -2.01099218183624371326e-07;
/**
* Returns the closest double approximation of <i>{@code e}</i><sup>
@@ -295,17 +803,124 @@ public final class StrictMath {
* <li>{@code expm1(NaN) = NaN}</li>
* </ul>
*
- * @param d
+ * @param x
* the value to compute the <i>{@code e}</i><sup>{@code d}</sup>
* {@code - 1} of.
- * @return the <i>{@code e}</i><sup>{@code d}</sup>{@code - 1} value
- * of the argument.
+ * @return the <i>{@code e}</i><sup>{@code d}</sup>{@code - 1} value of the
+ * argument.
*/
- public static native double expm1(double d);
+ public static double expm1(double x) {
+ double y, hi, lo, t, e, hxs, hfx, r1, c = 0.0;
+ int k, xsb;
+ long yBits = 0;
+ final long bits = Double.doubleToRawLongBits(x);
+ int highBits = (int) (bits >>> 32);
+ int lowBits = (int) (bits);
+ int hx = highBits & 0x7fffffff; // caution: should be unsigned!
+ xsb = highBits & 0x80000000; /* sign bit of x */
+ y = xsb == 0 ? x : -x; /* y = |x| */
+
+ /* filter out huge and non-finite argument */
+ if (hx >= 0x4043687A) { /* if |x|>=56*ln2 */
+ if (hx >= 0x40862E42) { /* if |x|>=709.78... */
+ if (hx >= 0x7ff00000) {
+ if (((hx & 0xfffff) | lowBits) != 0) {
+ return x + x; /* NaN */
+ } else {
+ return (xsb == 0) ? x : -1.0;/* ieee_exp(+-inf)={inf,-1} */
+ }
+ }
+ if (x > O_THRESHOLD) {
+ return HUGE * HUGE; /* overflow */
+ }
+ }
+ if (xsb != 0) { /* x < -56*ln2, return -1.0 with inexact */
+ if (x + TINY < 0.0) { /* raise inexact */
+ return TINY - 1.00000000000000000000e+00; /* return -1 */
+ }
+ }
+ }
+ /* argument reduction */
+ if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
+ if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
+ if (xsb == 0) {
+ hi = x - LN2_HI;
+ lo = LN2_LO;
+ k = 1;
+ } else {
+ hi = x + LN2_HI;
+ lo = -LN2_LO;
+ k = -1;
+ }
+ } else {
+ k = (int) (INVLN2 * x + ((xsb == 0) ? 0.5 : -0.5));
+ t = k;
+ hi = x - t * LN2_HI; /* t*ln2_hi is exact here */
+ lo = t * LN2_LO;
+ }
+ x = hi - lo;
+ c = (hi - x) - lo;
+ } else if (hx < 0x3c900000) { /* when |x|<2**-54, return x */
+ // t = huge+x; /* return x with inexact flags when x!=0 */
+ // return x - (t-(huge+x));
+ return x; // inexact flag is not set, but Java ignors this flag
+ // anyway
+ } else {
+ k = 0;
+ }
+
+ /* x is now in primary range */
+ hfx = 0.5 * x;
+ hxs = x * hfx;
+ r1 = 1.00000000000000000000e+00 + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
+ t = 3.0 - r1 * hfx;
+ e = hxs * ((r1 - t) / (6.0 - x * t));
+ if (k == 0) {
+ return x - (x * e - hxs); /* c is 0 */
+ } else {
+ e = (x * (e - c) - c);
+ e -= hxs;
+ if (k == -1) {
+ return 0.5 * (x - e) - 0.5;
+ }
+
+ if (k == 1) {
+ if (x < -0.25) {
+ return -2.0 * (e - (x + 0.5));
+ } else {
+ return 1.00000000000000000000e+00 + 2.0 * (x - e);
+ }
+ }
+
+ if (k <= -2 || k > 56) { /* suffice to return ieee_exp(x)-1 */
+ y = 1.00000000000000000000e+00 - (e - x);
+ yBits = Double.doubleToRawLongBits(y);
+ yBits += (((long) k) << 52); /* add k to y's exponent */
+ return Double.longBitsToDouble(yBits) - 1.00000000000000000000e+00;
+ }
+
+ long tBits = Double.doubleToRawLongBits(1.00000000000000000000e+00) & 0x00000000ffffffffL;
+
+ if (k < 20) {
+ tBits |= (((long) 0x3ff00000) - (0x200000 >> k)) << 32;
+ y = Double.longBitsToDouble(tBits) - (e - x);
+ yBits = Double.doubleToRawLongBits(y);
+ yBits += (((long) k) << 52); /* add k to y's exponent */
+ return Double.longBitsToDouble(yBits);
+ } else {
+ tBits |= ((((long) 0x3ff) - k) << 52); /* 2^-k */
+ y = x - (e + Double.longBitsToDouble(tBits));
+ y += 1.00000000000000000000e+00;
+ yBits = Double.doubleToRawLongBits(y);
+ yBits += (((long) k) << 52); /* add k to y's exponent */
+ return Double.longBitsToDouble(yBits);
+ }
+ }
+ }
/**
- * Returns the double conversion of the most positive (closest to
- * positive infinity) integer less than or equal to the argument.
+ * Returns the double conversion of the most positive (closest to positive
+ * infinity) integer less than or equal to the argument.
* <p>
* Special cases:
* <ul>
@@ -319,9 +934,9 @@ public final class StrictMath {
public static native double floor(double d);
/**
- * Returns {@code sqrt(}<i>{@code x}</i><sup>{@code 2}</sup>{@code +}
- * <i> {@code y}</i><sup>{@code 2}</sup>{@code )}. The final result is
- * without medium underflow or overflow.
+ * Returns {@code sqrt(}<i>{@code x}</i><sup>{@code 2}</sup>{@code +} <i>
+ * {@code y}</i><sup>{@code 2}</sup>{@code )}. The final result is without
+ * medium underflow or overflow.
* <p>
* Special cases:
* <ul>
@@ -369,6 +984,14 @@ public final class StrictMath {
*/
public static native double IEEEremainder(double x, double y);
+ private static final double LG1 = 6.666666666666735130e-01;
+ private static final double LG2 = 3.999999999940941908e-01;
+ private static final double LG3 = 2.857142874366239149e-01;
+ private static final double LG4 = 2.222219843214978396e-01;
+ private static final double LG5 = 1.818357216161805012e-01;
+ private static final double LG6 = 1.531383769920937332e-01;
+ private static final double LG7 = 1.479819860511658591e-01;
+
/**
* Returns the closest double approximation of the natural logarithm of the
* argument.
@@ -383,11 +1006,95 @@ public final class StrictMath {
* <li>{@code log(NaN) = NaN}</li>
* </ul>
*
- * @param d
+ * @param x
* the value whose log has to be computed.
* @return the natural logarithm of the argument.
*/
- public static native double log(double d);
+ public static double log(double x) {
+ double hfsq, f, s, z, R, w, t1, t2, dk;
+ int hx, i, j, k = 0;
+ int lx; // watch out, should be unsigned
+
+ long bits = Double.doubleToRawLongBits(x);
+ hx = (int) (bits >>> 32); /* high word of x */
+ lx = (int) bits; /* low word of x */
+
+ if (hx < 0x00100000) { /* x < 2**-1022 */
+ if (((hx & 0x7fffffff) | lx) == 0) {
+ return -TWO54 / 0.0; /* ieee_log(+-0)=-inf */
+ }
+
+ if (hx < 0) {
+ return (x - x) / 0.0; /* ieee_log(-#) = NaN */
+ }
+
+ k -= 54;
+ x *= TWO54; /* subnormal number, scale up x */
+ bits = Double.doubleToRawLongBits(x);
+ hx = (int) (bits >>> 32); /* high word of x */
+ }
+
+ if (hx >= 0x7ff00000) {
+ return x + x;
+ }
+
+ k += (hx >> 20) - 1023;
+ hx &= 0x000fffff;
+ bits &= 0x00000000ffffffffL;
+ i = (hx + 0x95f64) & 0x100000;
+ bits |= ((long) hx | (i ^ 0x3ff00000)) << 32; /* normalize x or x/2 */
+ x = Double.longBitsToDouble(bits);
+ k += (i >> 20);
+ f = x - 1.0;
+
+ if ((0x000fffff & (2 + hx)) < 3) { /* |f| < 2**-20 */
+ if (f == 0.0) {
+ if (k == 0) {
+ return 0.0;
+ } else {
+ dk = k;
+ }
+ return dk * LN2_HI + dk * LN2_LO;
+ }
+
+ R = f * f * (0.5 - 0.33333333333333333 * f);
+ if (k == 0) {
+ return f - R;
+ } else {
+ dk = k;
+ return dk * LN2_HI - ((R - dk * LN2_LO) - f);
+ }
+ }
+ s = f / (2.0 + f);
+ dk = k;
+ z = s * s;
+ i = hx - 0x6147a;
+ w = z * z;
+ j = 0x6b851 - hx;
+ t1 = w * (LG2 + w * (LG4 + w * LG6));
+ t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
+ i |= j;
+ R = t2 + t1;
+ if (i > 0) {
+ hfsq = 0.5 * f * f;
+ if (k == 0) {
+ return f - (hfsq - s * (hfsq + R));
+ } else {
+ return dk * LN2_HI
+ - ((hfsq - (s * (hfsq + R) + dk * LN2_LO)) - f);
+ }
+ } else {
+ if (k == 0) {
+ return f - s * (f - R);
+ } else {
+ return dk * LN2_HI - ((s * (f - R) - dk * LN2_LO) - f);
+ }
+ }
+ }
+
+ private static final double IVLN10 = 4.34294481903251816668e-01;
+ private static final double LOG10_2HI = 3.01029995663611771306e-01;
+ private static final double LOG10_2LO = 3.69423907715893078616e-13;
/**
* Returns the closest double approximation of the base 10 logarithm of the
@@ -403,11 +1110,54 @@ public final class StrictMath {
* <li>{@code log10(NaN) = NaN}</li>
* </ul>
*
- * @param d
+ * @param x
* the value whose base 10 log has to be computed.
- * @return the natural logarithm of the argument.
+ * @return the the base 10 logarithm of x
*/
- public static native double log10(double d);
+ public static double log10(double x) {
+ double y, z;
+ int i, k = 0, hx;
+ int lx; // careful: lx should be unsigned!
+ long bits = Double.doubleToRawLongBits(x);
+ hx = (int) (bits >> 32); /* high word of x */
+ lx = (int) bits; /* low word of x */
+ if (hx < 0x00100000) { /* x < 2**-1022 */
+ if (((hx & 0x7fffffff) | lx) == 0) {
+ return -TWO54 / 0.0; /* ieee_log(+-0)=-inf */
+ }
+
+ if (hx < 0) {
+ return (x - x) / 0.0; /* ieee_log(-#) = NaN */
+ }
+
+ k -= 54;
+ x *= TWO54; /* subnormal number, scale up x */
+ bits = Double.doubleToRawLongBits(x);
+ hx = (int) (bits >> 32); /* high word of x */
+ }
+
+ if (hx >= 0x7ff00000) {
+ return x + x;
+ }
+
+ k += (hx >> 20) - 1023;
+ i = (int) (((k & 0x00000000ffffffffL) & 0x80000000) >>> 31);
+ hx = (hx & 0x000fffff) | ((0x3ff - i) << 20);
+ y = k + i;
+ bits &= 0x00000000ffffffffL;
+ bits |= ((long) hx) << 32;
+ x = Double.longBitsToDouble(bits); // __HI(x) = hx;
+ z = y * LOG10_2LO + IVLN10 * log(x);
+ return z + y * LOG10_2HI;
+ }
+
+ private static final double LP1 = 6.666666666666735130e-01,
+ LP2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
+ LP3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
+ LP4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
+ LP5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
+ LP6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
+ LP7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
/**
* Returns the closest double approximation of the natural logarithm of the
@@ -426,11 +1176,107 @@ public final class StrictMath {
* <li>{@code log1p(NaN) = NaN}</li>
* </ul>
*
- * @param d
+ * @param x
* the value to compute the {@code ln(1+d)} of.
* @return the natural logarithm of the sum of the argument and 1.
*/
- public static native double log1p(double d);
+
+ public static double log1p(double x) {
+ double hfsq, f = 0.0, c = 0.0, s, z, R, u = 0.0;
+ int k, hx, hu = 0, ax;
+
+ final long bits = Double.doubleToRawLongBits(x);
+ hx = (int) (bits >>> 32); /* high word of x */
+ ax = hx & 0x7fffffff;
+
+ k = 1;
+ if (hx < 0x3FDA827A) { /* x < 0.41422 */
+ if (ax >= 0x3ff00000) { /* x <= -1.0 */
+ if (x == -1.0) {
+ return -TWO54 / 0.0; /* ieee_log1p(-1)=+inf */
+ } else {
+ return (x - x) / (x - x); /* ieee_log1p(x<-1)=NaN */
+ }
+ }
+ if (ax < 0x3e200000) {
+ if (TWO54 + x > 0.0 && ax < 0x3c900000) {
+ return x;
+ } else {
+ return x - x * x * 0.5;
+ }
+ }
+ if (hx > 0 || hx <= 0xbfd2bec3) {
+ k = 0;
+ f = x;
+ hu = 1;
+ } /* -0.2929<x<0.41422 */
+ }
+
+ if (hx >= 0x7ff00000) {
+ return x + x;
+ }
+
+ if (k != 0) {
+ long uBits;
+ if (hx < 0x43400000) {
+ u = 1.0 + x;
+ uBits = Double.doubleToRawLongBits(u);
+ hu = (int) (uBits >>> 32);
+ k = (hu >> 20) - 1023;
+ c = (k > 0) ? 1.0 - (u - x) : x - (u - 1.0);/* correction term */
+ c /= u;
+ } else {
+ uBits = Double.doubleToRawLongBits(x);
+ hu = (int) (uBits >>> 32);
+ k = (hu >> 20) - 1023;
+ c = 0;
+ }
+ hu &= 0x000fffff;
+ if (hu < 0x6a09e) {
+ // __HI(u) = hu|0x3ff00000; /* normalize u */
+ uBits &= 0x00000000ffffffffL;
+ uBits |= ((long) hu | 0x3ff00000) << 32;
+ u = Double.longBitsToDouble(uBits);
+ } else {
+ k += 1;
+ // __HI(u) = hu|0x3fe00000; /* normalize u/2 */
+ uBits &= 0xffffffffL;
+ uBits |= ((long) hu | 0x3fe00000) << 32;
+ u = Double.longBitsToDouble(uBits);
+ hu = (0x00100000 - hu) >> 2;
+ }
+ f = u - 1.0;
+ }
+ hfsq = 0.5 * f * f;
+ if (hu == 0) { /* |f| < 2**-20 */
+ if (f == 0.0) {
+ if (k == 0) {
+ return 0.0;
+ } else {
+ c += k * LN2_LO;
+ return k * LN2_HI + c;
+ }
+ }
+
+ R = hfsq * (1.0 - 0.66666666666666666 * f);
+ if (k == 0) {
+ return f - R;
+ } else {
+ return k * LN2_HI - ((R - (k * LN2_LO + c)) - f);
+ }
+ }
+
+ s = f / (2.0 + f);
+ z = s * s;
+ R = z * (LP1 + z * (LP2 + z
+ * (LP3 + z * (LP4 + z * (LP5 + z * (LP6 + z * LP7))))));
+ if (k == 0) {
+ return f - (hfsq - s * (hfsq + R));
+ } else {
+ return k * LN2_HI
+ - ((hfsq - (s * (hfsq + R) + (k * LN2_LO + c))) - f);
+ }
+ }
/**
* Returns the most positive (closest to positive infinity) of the two
@@ -453,8 +1299,8 @@ public final class StrictMath {
if (d1 != d2)
return Double.NaN;
/* max( +0.0,-0.0) == +0.0 */
- if (d1 == 0.0
- && ((Double.doubleToLongBits(d1) & Double.doubleToLongBits(d2)) & 0x8000000000000000L) == 0)
+ if (d1 == 0.0 &&
+ ((Double.doubleToLongBits(d1) & Double.doubleToLongBits(d2)) & 0x8000000000000000L) == 0)
return 0.0;
return d1;
}
@@ -480,8 +1326,8 @@ public final class StrictMath {
if (f1 != f2)
return Float.NaN;
/* max( +0.0,-0.0) == +0.0 */
- if (f1 == 0.0f
- && ((Float.floatToIntBits(f1) & Float.floatToIntBits(f2)) & 0x80000000) == 0)
+ if (f1 == 0.0f &&
+ ((Float.floatToIntBits(f1) & Float.floatToIntBits(f2)) & 0x80000000) == 0)
return 0.0f;
return f1;
}
@@ -523,8 +1369,8 @@ public final class StrictMath {
if (d1 != d2)
return Double.NaN;
/* min( +0.0,-0.0) == -0.0 */
- if (d1 == 0.0
- && ((Double.doubleToLongBits(d1) | Double.doubleToLongBits(d2)) & 0x8000000000000000l) != 0)
+ if (d1 == 0.0 &&
+ ((Double.doubleToLongBits(d1) | Double.doubleToLongBits(d2)) & 0x8000000000000000l) != 0)
return 0.0 * (-1.0);
return d1;
}
@@ -550,8 +1396,8 @@ public final class StrictMath {
if (f1 != f2)
return Float.NaN;
/* min( +0.0,-0.0) == -0.0 */
- if (f1 == 0.0f
- && ((Float.floatToIntBits(f1) | Float.floatToIntBits(f2)) & 0x80000000) != 0)
+ if (f1 == 0.0f &&
+ ((Float.floatToIntBits(f1) | Float.floatToIntBits(f2)) & 0x80000000) != 0)
return 0.0f * (-1.0f);
return f1;
}
@@ -706,7 +1552,7 @@ public final class StrictMath {
* the value whose signum has to be computed.
* @return the value of the signum function.
*/
- public static double signum(double d){
+ public static double signum(double d) {
return Math.signum(d);
}
@@ -729,10 +1575,12 @@ public final class StrictMath {
* the value whose signum has to be computed.
* @return the value of the signum function.
*/
- public static float signum(float f){
+ public static float signum(float f) {
return Math.signum(f);
}
+ private static final double shuge = 1.0e307;
+
/**
* Returns the closest double approximation of the hyperbolic sine of the
* argument.
@@ -746,11 +1594,57 @@ public final class StrictMath {
* <li>{@code sinh(NaN) = NaN}</li>
* </ul>
*
- * @param d
+ * @param x
* the value whose hyperbolic sine has to be computed.
* @return the hyperbolic sine of the argument.
*/
- public static native double sinh(double d);
+ public static double sinh(double x) {
+ double t, w, h;
+ int ix, jx;
+ final long bits = Double.doubleToRawLongBits(x);
+
+ jx = (int) (bits >>> 32);
+ ix = jx & 0x7fffffff;
+
+ /* x is INF or NaN */
+ if (ix >= 0x7ff00000) {
+ return x + x;
+ }
+
+ h = 0.5;
+ if (jx < 0) {
+ h = -h;
+ }
+
+ /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
+ if (ix < 0x40360000) { /* |x|<22 */
+ if (ix < 0x3e300000) /* |x|<2**-28 */
+ if (shuge + x > 1.00000000000000000000e+00) {
+ return x;/* ieee_sinh(tiny) = tiny with inexact */
+ }
+ t = expm1(Math.abs(x));
+ if (ix < 0x3ff00000)
+ return h * (2.0 * t - t * t / (t + 1.00000000000000000000e+00));
+ return h * (t + t / (t + 1.00000000000000000000e+00));
+ }
+
+ /* |x| in [22, ieee_log(maxdouble)] return 0.5*ieee_exp(|x|) */
+ if (ix < 0x40862E42) {
+ return h * exp(Math.abs(x));
+ }
+
+ /* |x| in [log(maxdouble), overflowthresold] */
+ final long lx = ((ONEBITS >>> 29) + ((int) bits)) & 0x00000000ffffffffL;
+ // lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
+ if (ix < 0x408633CE || (ix == 0x408633ce) && (lx <= 0x8fb9f87dL)) {
+ w = exp(0.5 * Math.abs(x));
+ t = h * w;
+ return t * w;
+ }
+
+ /* |x| > overflowthresold, ieee_sinh(x) overflow */
+ return x * shuge;
+ }
/**
* Returns the closest double approximation of the sine of the argument.
@@ -816,11 +1710,47 @@ public final class StrictMath {
* <li>{@code tanh(NaN) = NaN}</li>
* </ul>
*
- * @param d
+ * @param x
* the value whose hyperbolic tangent has to be computed.
* @return the hyperbolic tangent of the argument
*/
- public static native double tanh(double d);
+ public static double tanh(double x) {
+ double t, z;
+ int jx, ix;
+
+ final long bits = Double.doubleToRawLongBits(x);
+ /* High word of |x|. */
+ jx = (int) (bits >>> 32);
+ ix = jx & 0x7fffffff;
+
+ /* x is INF or NaN */
+ if (ix >= 0x7ff00000) {
+ if (jx >= 0) {
+ return 1.00000000000000000000e+00 / x + 1.00000000000000000000e+00; /* ieee_tanh(+-inf)=+-1 */
+ } else {
+ return 1.00000000000000000000e+00 / x - 1.00000000000000000000e+00; /* ieee_tanh(NaN) = NaN */
+ }
+ }
+
+ /* |x| < 22 */
+ if (ix < 0x40360000) { /* |x|<22 */
+ if (ix < 0x3c800000) { /* |x|<2**-55 */
+ return x * (1.00000000000000000000e+00 + x);/* ieee_tanh(small) = small */
+ }
+
+ if (ix >= 0x3ff00000) { /* |x|>=1 */
+ t = Math.expm1(2.0 * Math.abs(x));
+ z = 1.00000000000000000000e+00 - 2.0 / (t + 2.0);
+ } else {
+ t = Math.expm1(-2.0 * Math.abs(x));
+ z = -t / (t + 2.0);
+ }
+ /* |x| > 22, return +-1 */
+ } else {
+ z = 1.00000000000000000000e+00 - TINY; /* raised inexact flag */
+ }
+ return (jx >= 0) ? z : -z;
+ }
/**
* Returns the measure in degrees of the supplied radian angle. The result
@@ -922,6 +1852,7 @@ public final class StrictMath {
/**
* Returns a double with the given magnitude and the sign of {@code sign}.
* If {@code sign} is NaN, the sign of the result is positive.
+ *
* @since 1.6
*/
public static double copySign(double magnitude, double sign) {
@@ -932,13 +1863,15 @@ public final class StrictMath {
// (Tested on a Nexus One.)
long magnitudeBits = Double.doubleToRawLongBits(magnitude);
long signBits = Double.doubleToRawLongBits((sign != sign) ? 1.0 : sign);
- magnitudeBits = (magnitudeBits & ~Double.SIGN_MASK) | (signBits & Double.SIGN_MASK);
+ magnitudeBits = (magnitudeBits & ~Double.SIGN_MASK)
+ | (signBits & Double.SIGN_MASK);
return Double.longBitsToDouble(magnitudeBits);
}
/**
- * Returns a float with the given magnitude and the sign of {@code sign}.
- * If {@code sign} is NaN, the sign of the result is positive.
+ * Returns a float with the given magnitude and the sign of {@code sign}. If
+ * {@code sign} is NaN, the sign of the result is positive.
+ *
* @since 1.6
*/
public static float copySign(float magnitude, float sign) {
@@ -949,12 +1882,14 @@ public final class StrictMath {
// (Tested on a Nexus One.)
int magnitudeBits = Float.floatToRawIntBits(magnitude);
int signBits = Float.floatToRawIntBits((sign != sign) ? 1.0f : sign);
- magnitudeBits = (magnitudeBits & ~Float.SIGN_MASK) | (signBits & Float.SIGN_MASK);
+ magnitudeBits = (magnitudeBits & ~Float.SIGN_MASK)
+ | (signBits & Float.SIGN_MASK);
return Float.intBitsToFloat(magnitudeBits);
}
/**
* Returns the exponent of float {@code f}.
+ *
* @since 1.6
*/
public static int getExponent(float f) {
@@ -963,14 +1898,17 @@ public final class StrictMath {
/**
* Returns the exponent of double {@code d}.
+ *
* @since 1.6
*/
- public static int getExponent(double d){
+ public static int getExponent(double d) {
return Math.getExponent(d);
}
/**
- * Returns the next double after {@code start} in the given {@code direction}.
+ * Returns the next double after {@code start} in the given
+ * {@code direction}.
+ *
* @since 1.6
*/
public static double nextAfter(double start, double direction) {
@@ -981,7 +1919,9 @@ public final class StrictMath {
}
/**
- * Returns the next float after {@code start} in the given {@code direction}.
+ * Returns the next float after {@code start} in the given {@code direction}
+ * .
+ *
* @since 1.6
*/
public static float nextAfter(float start, double direction) {
@@ -990,6 +1930,7 @@ public final class StrictMath {
/**
* Returns the next double larger than {@code d}.
+ *
* @since 1.6
*/
public static double nextUp(double d) {
@@ -998,6 +1939,7 @@ public final class StrictMath {
/**
* Returns the next float larger than {@code f}.
+ *
* @since 1.6
*/
public static float nextUp(float f) {
@@ -1006,6 +1948,7 @@ public final class StrictMath {
/**
* Returns {@code d} * 2^{@code scaleFactor}. The result may be rounded.
+ *
* @since 1.6
*/
public static double scalb(double d, int scaleFactor) {
@@ -1049,12 +1992,10 @@ public final class StrictMath {
} else {
if (Math.abs(d) >= Double.MIN_NORMAL) {
// common situation
- result = ((factor + Double.EXPONENT_BIAS) << Double.MANTISSA_BITS)
- | (bits & Double.MANTISSA_MASK);
+ result = ((factor + Double.EXPONENT_BIAS) << Double.MANTISSA_BITS) | (bits & Double.MANTISSA_MASK);
} else {
// origin d is sub-normal, change mantissa to normal style
- result = ((factor + Double.EXPONENT_BIAS) << Double.MANTISSA_BITS)
- | ((bits << (subNormalFactor + 1)) & Double.MANTISSA_MASK);
+ result = ((factor + Double.EXPONENT_BIAS) << Double.MANTISSA_BITS) | ((bits << (subNormalFactor + 1)) & Double.MANTISSA_MASK);
}
}
return Double.longBitsToDouble(result | sign);
@@ -1062,6 +2003,7 @@ public final class StrictMath {
/**
* Returns {@code d} * 2^{@code scaleFactor}. The result may be rounded.
+ *
* @since 1.6
*/
public static float scalb(float d, int scaleFactor) {
@@ -1073,8 +2015,7 @@ public final class StrictMath {
int factor = ((bits & Float.EXPONENT_MASK) >> Float.MANTISSA_BITS)
- Float.EXPONENT_BIAS + scaleFactor;
// calculates the factor of sub-normal values
- int subNormalFactor = Integer.numberOfLeadingZeros(bits & ~Float.SIGN_MASK)
- - Float.EXPONENT_BITS;
+ int subNormalFactor = Integer.numberOfLeadingZeros(bits & ~Float.SIGN_MASK) - Float.EXPONENT_BITS;
if (subNormalFactor < 0) {
// not sub-normal values
subNormalFactor = 0;
@@ -1105,8 +2046,9 @@ public final class StrictMath {
| (bits & Float.MANTISSA_MASK);
} else {
// origin d is sub-normal, change mantissa to normal style
- result = ((factor + Float.EXPONENT_BIAS) << Float.MANTISSA_BITS)
- | ((bits << (subNormalFactor + 1)) & Float.MANTISSA_MASK);
+ result = ((factor + Float.EXPONENT_BIAS)
+ << Float.MANTISSA_BITS) | (
+ (bits << (subNormalFactor + 1)) & Float.MANTISSA_MASK);
}
}
return Float.intBitsToFloat(result | sign);
@@ -1120,10 +2062,10 @@ public final class StrictMath {
}
// change it to positive
int absDigits = -digits;
- if (Integer.numberOfLeadingZeros(bits & ~Float.SIGN_MASK) <= (32 - absDigits)) {
+ if (Integer.numberOfLeadingZeros(bits & ~Float.SIGN_MASK)
+ <= (32 - absDigits)) {
// some bits will remain after shifting, calculates its carry
- if ((((bits >> (absDigits - 1)) & 0x1) == 0)
- || Integer.numberOfTrailingZeros(bits) == (absDigits - 1)) {
+ if ((((bits >> (absDigits - 1)) & 0x1) == 0) || Integer.numberOfTrailingZeros(bits) == (absDigits - 1)) {
return bits >> absDigits;
}
return ((bits >> absDigits) + 1);
@@ -1139,10 +2081,10 @@ public final class StrictMath {
}
// change it to positive
long absDigits = -digits;
- if (Long.numberOfLeadingZeros(bits & ~Double.SIGN_MASK) <= (64 - absDigits)) {
+ if (Long.numberOfLeadingZeros(bits & ~Double.SIGN_MASK)
+ <= (64 - absDigits)) {
// some bits will remain after shifting, calculates its carry
- if ((((bits >> (absDigits - 1)) & 0x1) == 0)
- || Long.numberOfTrailingZeros(bits) == (absDigits - 1)) {
+ if ((((bits >> (absDigits - 1)) & 0x1) == 0) || Long.numberOfTrailingZeros(bits) == (absDigits - 1)) {
return bits >> absDigits;
}
return ((bits >> absDigits) + 1);
diff --git a/luni/src/main/native/java_lang_StrictMath.cpp b/luni/src/main/native/java_lang_StrictMath.cpp
index cfe375e..e8c6dfb 100644
--- a/luni/src/main/native/java_lang_StrictMath.cpp
+++ b/luni/src/main/native/java_lang_StrictMath.cpp
@@ -34,26 +34,6 @@ static jdouble StrictMath_tan(JNIEnv*, jclass, jdouble a) {
return ieee_tan(a);
}
-static jdouble StrictMath_asin(JNIEnv*, jclass, jdouble a) {
- return ieee_asin(a);
-}
-
-static jdouble StrictMath_acos(JNIEnv*, jclass, jdouble a) {
- return ieee_acos(a);
-}
-
-static jdouble StrictMath_atan(JNIEnv*, jclass, jdouble a) {
- return ieee_atan(a);
-}
-
-static jdouble StrictMath_exp(JNIEnv*, jclass, jdouble a) {
- return ieee_exp(a);
-}
-
-static jdouble StrictMath_log(JNIEnv*, jclass, jdouble a) {
- return ieee_log(a);
-}
-
static jdouble StrictMath_sqrt(JNIEnv*, jclass, jdouble a) {
return ieee_sqrt(a);
}
@@ -74,75 +54,30 @@ static jdouble StrictMath_rint(JNIEnv*, jclass, jdouble a) {
return ieee_rint(a);
}
-static jdouble StrictMath_atan2(JNIEnv*, jclass, jdouble a, jdouble b) {
- return ieee_atan2(a, b);
-}
-
static jdouble StrictMath_pow(JNIEnv*, jclass, jdouble a, jdouble b) {
return ieee_pow(a,b);
}
-static jdouble StrictMath_sinh(JNIEnv*, jclass, jdouble a) {
- return ieee_sinh(a);
-}
-
-static jdouble StrictMath_tanh(JNIEnv*, jclass, jdouble a) {
- return ieee_tanh(a);
-}
-
-static jdouble StrictMath_cosh(JNIEnv*, jclass, jdouble a) {
- return ieee_cosh(a);
-}
-
-static jdouble StrictMath_log10(JNIEnv*, jclass, jdouble a) {
- return ieee_log10(a);
-}
-
-static jdouble StrictMath_cbrt(JNIEnv*, jclass, jdouble a) {
- return ieee_cbrt(a);
-}
-
-static jdouble StrictMath_expm1(JNIEnv*, jclass, jdouble a) {
- return ieee_expm1(a);
-}
-
static jdouble StrictMath_hypot(JNIEnv*, jclass, jdouble a, jdouble b) {
return ieee_hypot(a, b);
}
-static jdouble StrictMath_log1p(JNIEnv*, jclass, jdouble a) {
- return ieee_log1p(a);
-}
-
static jdouble StrictMath_nextafter(JNIEnv*, jclass, jdouble a, jdouble b) {
return ieee_nextafter(a, b);
}
static JNINativeMethod gMethods[] = {
NATIVE_METHOD(StrictMath, IEEEremainder, "!(DD)D"),
- NATIVE_METHOD(StrictMath, acos, "!(D)D"),
- NATIVE_METHOD(StrictMath, asin, "!(D)D"),
- NATIVE_METHOD(StrictMath, atan, "!(D)D"),
- NATIVE_METHOD(StrictMath, atan2, "!(DD)D"),
- NATIVE_METHOD(StrictMath, cbrt, "!(D)D"),
NATIVE_METHOD(StrictMath, ceil, "!(D)D"),
NATIVE_METHOD(StrictMath, cos, "!(D)D"),
- NATIVE_METHOD(StrictMath, cosh, "!(D)D"),
- NATIVE_METHOD(StrictMath, exp, "!(D)D"),
- NATIVE_METHOD(StrictMath, expm1, "!(D)D"),
NATIVE_METHOD(StrictMath, floor, "!(D)D"),
NATIVE_METHOD(StrictMath, hypot, "!(DD)D"),
- NATIVE_METHOD(StrictMath, log, "!(D)D"),
- NATIVE_METHOD(StrictMath, log10, "!(D)D"),
- NATIVE_METHOD(StrictMath, log1p, "!(D)D"),
NATIVE_METHOD(StrictMath, nextafter, "!(DD)D"),
NATIVE_METHOD(StrictMath, pow, "!(DD)D"),
NATIVE_METHOD(StrictMath, rint, "!(D)D"),
NATIVE_METHOD(StrictMath, sin, "!(D)D"),
- NATIVE_METHOD(StrictMath, sinh, "!(D)D"),
NATIVE_METHOD(StrictMath, sqrt, "!(D)D"),
NATIVE_METHOD(StrictMath, tan, "!(D)D"),
- NATIVE_METHOD(StrictMath, tanh, "!(D)D"),
};
void register_java_lang_StrictMath(JNIEnv* env) {
jniRegisterNativeMethods(env, "java/lang/StrictMath", gMethods, NELEM(gMethods));