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src/java.base/share/classes/java/lang/FdLibm.java
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*** 1,8 ****
-
/*
! * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
--- 1,7 ----
/*
! * Copyright (c) 1998, 2015, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
*** 22,99 ****
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
! #include "fdlibm.h"
! /* cbrt(x)
* Return cube root of x
*/
! #ifdef __STDC__
! static const unsigned
! #else
! static unsigned
! #endif
! B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
! B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
!
! #ifdef __STDC__
! static const double
! #else
! static double
! #endif
! C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
! D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
! E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
! F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
! G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
!
! #ifdef __STDC__
! double cbrt(double x)
! #else
! double cbrt(x)
! double x;
! #endif
! {
int hx;
! double r,s,t=0.0,w;
! unsigned sign;
! hx = __HI(x); /* high word of x */
! sign=hx&0x80000000; /* sign= sign(x) */
! hx ^=sign;
! if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
! if((hx|__LO(x))==0)
! return(x); /* cbrt(0) is itself */
!
! __HI(x) = hx; /* x <- |x| */
! /* rough cbrt to 5 bits */
! if(hx<0x00100000) /* subnormal number */
! {__HI(t)=0x43500000; /* set t= 2**54 */
! t*=x; __HI(t)=__HI(t)/3+B2;
}
else
! __HI(t)=hx/3+B1;
! /* new cbrt to 23 bits, may be implemented in single precision */
! r=t*t/x;
! s=C+r*t;
! t*=G+F/(s+E+D/s);
! /* chopped to 20 bits and make it larger than cbrt(x) */
! __LO(t)=0; __HI(t)+=0x00000001;
! /* 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 */
! __HI(t) |= sign;
! return(t);
}
--- 21,586 ----
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
! package java.lang;
!
! /**
! * Port of the "Freely Distributable Math Library", version 5.3, from
! * C to Java.
! *
! * <p>The C version of fdlibm relied on the idiom of pointer aliasing
! * a 64-bit double floating-point value as a two-element array of
! * 32-bit integers and reading and writing the two halves of the
! * double independently. This coding pattern was problematic to C
! * optimizers and not directly expressible in Java. Therefore, rather
! * than a memory level overlay, if portions of a double need to be
! * operated on as integer values, the standard library methods for
! * bitwise floating-point to integer conversion,
! * Double.longBitsToDouble and Double.doubleToRawLongBits, are directly
! * or indirectly used.
! *
! * <p>The C version of fdlibm also took some pains to signal the
! * correct IEEE 754 exceptional conditions divide by zero, invalid,
! * overflow and underflow. For example, overflow would be signaled by
! * {@code huge * huge} where {@code huge} was a large constant that
! * would overflow when squared. Since IEEE floating-point exceptional
! * handling is not supported natively in the JVM, such coding patterns
! * have been omitted from this port. For example, rather than {@code
! * return huge * huge}, this port will use {@code return INFINITY}.
! *
! * <p>Various comparison and arithmetic operations in fdlibm could be
! * done either based on the integer view of a value or directly on the
! * floating-point representation. Which idiom is faster may depend on
! * platform specific factors. However, for code clarity if no other
! * reason, this port will favor expressing the semantics of those
! * operations in terms of floating-point operations when convenient to
! * do so.
! */
! class FdLibm {
! // Constants used by multiple algorithms
! private static final double INFINITY = Double.POSITIVE_INFINITY;
!
! private FdLibm() {
! throw new UnsupportedOperationException("No FdLibm instances for you.");
! }
! /**
! * Return the low-order 32 bits of the double argument as an int.
! */
! private static int __LO(double x) {
! long transducer = Double.doubleToRawLongBits(x);
! return (int)transducer;
! }
!
! /**
! * Return a double with its low-order bits of the second argument
! * and the high-order bits of the first argument..
! */
! private static double __LO(double x, int low) {
! long transX = Double.doubleToRawLongBits(x);
! return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L)|low );
! }
!
! /**
! * Return the high-order 32 bits of the double argument as an int.
! */
! private static int __HI(double x) {
! long transducer = Double.doubleToRawLongBits(x);
! return (int)(transducer >> 32);
! }
!
! /**
! * Return a double with its high-order bits of the second argument
! * and the low-order bits of the first argument..
! */
! private static double __HI(double x, int high) {
! long transX = Double.doubleToRawLongBits(x);
! return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL)|( ((long)high)) << 32 );
! }
!
! /**
! * cbrt(x)
* Return cube root of x
*/
! public static class Cbrt {
! // unsigned
! private static final int B1 = 715094163; /* B1 = (682-0.03306235651)*2**20 */
! private static final int B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
!
! private static final double C = 5.42857142857142815906e-01; /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
! private static final double D = -7.05306122448979611050e-01; /* -864/1225 = 0xBFE691DE, 0x2532C834 */
! private static final double E = 1.41428571428571436819e+00; /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
! private static final double F = 1.60714285714285720630e+00; /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
! private static final double G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
!
! public static strictfp double compute(double x) {
int hx;
! double r, s, t=0.0, w;
! int sign; // unsigned
+ hx = __HI(x); // high word of x
+ sign = hx & 0x80000000; // sign= sign(x)
+ hx ^= sign;
+ if (hx >= 0x7ff00000)
+ return (x+x); // cbrt(NaN,INF) is itself
+ if ((hx | __LO(x)) == 0)
+ return(x); // cbrt(0) is itself
+
+ x = __HI(x, hx); // x <- |x|
+ // rough cbrt to 5 bits
+ if (hx < 0x00100000) { // subnormal number
+ t = __HI(t, 0x43500000); // set t= 2**54
+ t *= x;
+ t = __HI(t, __HI(t)/3+B2);
+ } else {
+ t = __HI(t, hx/3+B1);
+ }
! // new cbrt to 23 bits, may be implemented in single precision
! r = t * t/x;
! s = C + r*t;
! t *= G + F/(s + E + D/s);
!
! // chopped to 20 bits and make it larger than cbrt(x)
! t = __LO(t, 0);
! t = __HI(t, __HI(t)+0x00000001);
!
!
! // 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
! t = __HI(t, __HI(t) | sign);
! return(t);
}
+ }
+
+ /**
+ * hypot(x,y)
+ *
+ * Method :
+ * If (assume round-to-nearest) z = x*x + y*y
+ * has error less than sqrt(2)/2 ulp, than
+ * sqrt(z) has error less than 1 ulp (exercise).
+ *
+ * So, compute sqrt(x*x + y*y) with some care as
+ * follows to get the error below 1 ulp:
+ *
+ * Assume x > y > 0;
+ * (if possible, set rounding to round-to-nearest)
+ * 1. if x > 2y use
+ * x1*x1 + (y*y + (x2*(x + x1))) for x*x + y*y
+ * where x1 = x with lower 32 bits cleared, x2 = x - x1; else
+ * 2. if x <= 2y use
+ * t1*y1 + ((x-y) * (x-y) + (t1*y2 + t2*y))
+ * where t1 = 2x with lower 32 bits cleared, t2 = 2x - t1,
+ * y1= y with lower 32 bits chopped, y2 = y - y1.
+ *
+ * NOTE: scaling may be necessary if some argument is too
+ * large or too tiny
+ *
+ * Special cases:
+ * hypot(x,y) is INF if x or y is +INF or -INF; else
+ * hypot(x,y) is NAN if x or y is NAN.
+ *
+ * Accuracy:
+ * hypot(x,y) returns sqrt(x^2 + y^2) with error less
+ * than 1 ulp (unit in the last place)
+ */
+ public static class Hypot {
+ public static final double TWO_MINUS_600 = 0x1.0p-600;
+ public static final double TWO_PLUS_600 = 0x1.0p+600;
+
+ public static strictfp double compute(double x, double y) {
+ double a = Math.abs(x);
+ double b = Math.abs(y);
+
+ if (!Double.isFinite(a) || !Double.isFinite(b)) {
+ if (a == INFINITY || b == INFINITY)
+ return INFINITY;
else
! return a + b; // Propagate NaN significand bits
! }
+ if (b > a) {
+ double tmp = a;
+ a = b;
+ b = tmp;
+ }
+ assert a >= b;
! // Doing bitwise conversion after screening for NaN allows
! // the code to not worry about the possibility of
! // "negative" NaN values.
!
! // Note: the ha and hb variables are the high-order
! // 32-bits of a and b stored as integer values. The ha and
! // hb values are used first for a rough magnitude
! // comparison of a and b and second for simulating higher
! // precision by allowing a and b, respectively, to be
! // decomposed into non-overlapping portions. Both of these
! // uses could be eliminated. The magnitude comparison
! // could be eliminated by extracting and comparing the
! // exponents of a and b or just be performing a
! // floating-point divide. Splitting a floating-point
! // number into non-overlapping portions can be
! // accomplished by judicious use of multiplies and
! // additions. For details see T. J. Dekker, A Floating
! // Point Technique for Extending the Available Precision ,
! // Numerische Mathematik, vol. 18, 1971, pp.224-242 and
! // subsequent work.
! int ha = __HI(a); // high word of a
! int hb = __HI(b); // high word of b
+ if ((ha - hb) > 0x3c00000) {
+ return a + b; // x / y > 2**60
+ }
! int k = 0;
! if (a > 0x1.00000_ffff_ffffp500) { // a > ~2**500
! // scale a and b by 2**-600
! ha -= 0x25800000;
! hb -= 0x25800000;
! a = a * TWO_MINUS_600;
! b = b * TWO_MINUS_600;
! k += 600;
! }
! double t1, t2;
! if (b < 0x1.0p-500) { // b < 2**-500
! if (b < Double.MIN_NORMAL) { // subnormal b or 0 */
! if (b == 0.0)
! return a;
! t1 = 0x1.0p1022; // t1 = 2^1022
! b *= t1;
! a *= t1;
! k -= 1022;
! } else { // scale a and b by 2^600
! ha += 0x25800000; // a *= 2^600
! hb += 0x25800000; // b *= 2^600
! a = a * TWO_PLUS_600;
! b = b * TWO_PLUS_600;
! k -= 600;
! }
! }
! // medium size a and b
! double w = a - b;
! if (w > b) {
! t1 = 0;
! t1 = __HI(t1, ha);
! t2 = a - t1;
! w = Math.sqrt(t1*t1 - (b*(-b) - t2 * (a + t1)));
! } else {
! double y1, y2;
! a = a + a;
! y1 = 0;
! y1 = __HI(y1, hb);
! y2 = b - y1;
! t1 = 0;
! t1 = __HI(t1, ha + 0x00100000);
! t2 = a - t1;
! w = Math.sqrt(t1*y1 - (w*(-w) - (t1*y2 + t2*b)));
! }
! if (k != 0) {
! return Math.powerOfTwoD(k) * w;
! } else
! return w;
! }
! }
! /**
! * Compute x**y
! * n
! * Method: Let x = 2 * (1+f)
! * 1. Compute and return log2(x) in two pieces:
! * log2(x) = w1 + w2,
! * where w1 has 53 - 24 = 29 bit trailing zeros.
! * 2. Perform y*log2(x) = n+y' by simulating multi-precision
! * arithmetic, where |y'| <= 0.5.
! * 3. Return x**y = 2**n*exp(y'*log2)
! *
! * Special cases:
! * 1. (anything) ** 0 is 1
! * 2. (anything) ** 1 is itself
! * 3. (anything) ** NAN is NAN
! * 4. NAN ** (anything except 0) is NAN
! * 5. +-(|x| > 1) ** +INF is +INF
! * 6. +-(|x| > 1) ** -INF is +0
! * 7. +-(|x| < 1) ** +INF is +0
! * 8. +-(|x| < 1) ** -INF is +INF
! * 9. +-1 ** +-INF is NAN
! * 10. +0 ** (+anything except 0, NAN) is +0
! * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
! * 12. +0 ** (-anything except 0, NAN) is +INF
! * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
! * 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
! * 15. +INF ** (+anything except 0,NAN) is +INF
! * 16. +INF ** (-anything except 0,NAN) is +0
! * 17. -INF ** (anything) = -0 ** (-anything)
! * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
! * 19. (-anything except 0 and inf) ** (non-integer) is NAN
! *
! * Accuracy:
! * pow(x,y) returns x**y nearly rounded. In particular
! * pow(integer,integer)
! * always returns the correct integer provided it is
! * representable.
! */
! public static class Pow {
! public static strictfp double compute(final double x, final double y) {
! double z;
! double r, s, t, u, v, w;
! int i, j, k, n;
!
! // y == zero: x**0 = 1
! if (y == 0.0)
! return 1.0;
!
! // +/-NaN return x + y to propagate NaN significands
! if (Double.isNaN(x) || Double.isNaN(y))
! return x + y;
!
! final double y_abs = Math.abs(y);
! double x_abs = Math.abs(x);
! // Special values of y
! if (y == 2.0) {
! return x * x;
! } else if (y == 0.5) {
! if (x >= -Double.MAX_VALUE) // Handle x == -infinity later
! return Math.sqrt(x + 0.0); // Add 0.0 to properly handle x == -0.0
! } else if (y_abs == 1.0) { // y is +/-1
! return (y == 1.0) ? x : 1.0 / x;
! } else if (y_abs == INFINITY) { // y is +/-infinity
! if (x_abs == 1.0)
! return y - y; // inf**+/-1 is NaN
! else if (x_abs > 1.0) // (|x| > 1)**+/-inf = inf, 0
! return (y >= 0) ? y : 0.0;
! else // (|x| < 1)**-/+inf = inf, 0
! return (y < 0) ? -y : 0.0;
! }
!
! final int hx = __HI(x);
! int ix = hx & 0x7fffffff;
!
! /*
! * When x < 0, determine if y is an odd integer:
! * y_is_int = 0 ... y is not an integer
! * y_is_int = 1 ... y is an odd int
! * y_is_int = 2 ... y is an even int
! */
! int y_is_int = 0;
! if (hx < 0) {
! if (y_abs >= 0x1.0p53) // |y| >= 2^53 = 9.007199254740992E15
! y_is_int = 2; // y is an even integer since ulp(2^53) = 2.0
! else if (y_abs >= 1.0) { // |y| >= 1.0
! long y_abs_as_long = (long) y_abs;
! if ( ((double) y_abs_as_long) == y_abs) {
! y_is_int = 2 - (int)(y_abs_as_long & 0x1L);
! }
! }
! }
!
! // Special value of x
! if (x_abs == 0.0 ||
! x_abs == INFINITY ||
! x_abs == 1.0) {
! z = x_abs; // x is +/-0, +/-inf, +/-1
! if (y < 0.0)
! z = 1.0/z; // z = (1/|x|)
! if (hx < 0) {
! if (((ix - 0x3ff00000) | y_is_int) == 0) {
! z = (z-z)/(z-z); // (-1)**non-int is NaN
! } else if (y_is_int == 1)
! z = -1.0 * z; // (x < 0)**odd = -(|x|**odd)
! }
! return z;
! }
!
! n = (hx >> 31) + 1;
!
! // (x < 0)**(non-int) is NaN
! if ((n | y_is_int) == 0)
! return (x-x)/(x-x);
!
! s = 1.0; // s (sign of result -ve**odd) = -1 else = 1
! if ( (n | (y_is_int - 1)) == 0)
! s = -1.0; // (-ve)**(odd int)
!
! double p_h, p_l, t1, t2;
! // |y| is huge
! if (y_abs > 0x1.00000_ffff_ffffp31) { // if |y| > ~2**31
! final double INV_LN2 = 0x1.7154_7652_b82fep0; // 1.44269504088896338700e+00 = 1/ln2
! final double INV_LN2_H = 0x1.715476p0; // 1.44269502162933349609e+00 = 24 bits of 1/ln2
! final double INV_LN2_L = 0x1.4ae0_bf85_ddf44p-26; // 1.92596299112661746887e-08 = 1/ln2 tail
!
! // Over/underflow if x is not close to one
! if (x_abs < 0x1.fffff_0000_0000p-1) // |x| < ~0.9999995231628418
! return (y < 0.0) ? s * INFINITY : s * 0.0;
! if (x_abs > 0x1.00000_ffff_ffffp0) // |x| > ~1.0
! return (y > 0.0) ? s * INFINITY : s * 0.0;
! /*
! * now |1-x| is tiny <= 2**-20, sufficient to compute
! * log(x) by x - x^2/2 + x^3/3 - x^4/4
! */
! t = x_abs - 1.0; // t has 20 trailing zeros
! w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
! u = INV_LN2_H * t; // INV_LN2_H has 21 sig. bits
! v = t * INV_LN2_L - w * INV_LN2;
! t1 = u + v;
! t1 =__LO(t1, 0);
! t2 = v - (t1 - u);
! } else {
! final double CP = 0x1.ec70_9dc3_a03fdp-1; // 9.61796693925975554329e-01 = 2/(3ln2)
! final double CP_H = 0x1.ec709ep-1; // 9.61796700954437255859e-01 = (float)cp
! final double CP_L = -0x1.e2fe_0145_b01f5p-28; // -7.02846165095275826516e-09 = tail of CP_H
!
! double z_h, z_l, ss, s2, s_h, s_l, t_h, t_l;
! n = 0;
! // Take care of subnormal numbers
! if (ix < 0x00100000) {
! x_abs *= 0x1.0p53; // 2^53 = 9007199254740992.0
! n -= 53;
! ix = __HI(x_abs);
! }
! n += ((ix) >> 20) - 0x3ff;
! j = ix & 0x000fffff;
! // Determine interval
! ix = j | 0x3ff00000; // Normalize ix
! if (j <= 0x3988E)
! k = 0; // |x| <sqrt(3/2)
! else if (j < 0xBB67A)
! k = 1; // |x| <sqrt(3)
! else {
! k = 0;
! n += 1;
! ix -= 0x00100000;
! }
! x_abs = __HI(x_abs, ix);
!
! // Compute ss = s_h + s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5)
!
! final double BP[] = {1.0,
! 1.5};
! final double DP_H[] = {0.0,
! 0x1.2b80_34p-1}; // 5.84962487220764160156e-01
! final double DP_L[] = {0.0,
! 0x1.cfde_b43c_fd006p-27};// 1.35003920212974897128e-08
!
! // Poly coefs for (3/2)*(log(x)-2s-2/3*s**3
! final double L1 = 0x1.3333_3333_33303p-1; // 5.99999999999994648725e-01
! final double L2 = 0x1.b6db_6db6_fabffp-2; // 4.28571428578550184252e-01
! final double L3 = 0x1.5555_5518_f264dp-2; // 3.33333329818377432918e-01
! final double L4 = 0x1.1746_0a91_d4101p-2; // 2.72728123808534006489e-01
! final double L5 = 0x1.d864_a93c_9db65p-3; // 2.30660745775561754067e-01
! final double L6 = 0x1.a7e2_84a4_54eefp-3; // 2.06975017800338417784e-01
! u = x_abs - BP[k]; // BP[0]=1.0, BP[1]=1.5
! v = 1.0 / (x_abs + BP[k]);
! ss = u * v;
! s_h = ss;
! s_h = __LO(s_h, 0);
! // t_h=x_abs + BP[k] High
! t_h = 0.0;
! t_h = __HI(t_h, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18) );
! t_l = x_abs - (t_h - BP[k]);
! s_l = v * ((u - s_h * t_h) - s_h * t_l);
! // Compute log(x_abs)
! s2 = ss * ss;
! r = s2 * s2* (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
! r += s_l * (s_h + ss);
! s2 = s_h * s_h;
! t_h = 3.0 + s2 + r;
! t_h = __LO(t_h, 0);
! t_l = r - ((t_h - 3.0) - s2);
! // u+v = ss*(1+...)
! u = s_h * t_h;
! v = s_l * t_h + t_l * ss;
! // 2/(3log2)*(ss + ...)
! p_h = u + v;
! p_h = __LO(p_h, 0);
! p_l = v - (p_h - u);
! z_h = CP_H * p_h; // CP_H + CP_L = 2/(3*log2)
! z_l = CP_L * p_h + p_l * CP + DP_L[k];
! // log2(x_abs) = (ss + ..)*2/(3*log2) = n + DP_H + z_h + z_l
! t = (double)n;
! t1 = (((z_h + z_l) + DP_H[k]) + t);
! t1 = __LO(t1, 0);
! t2 = z_l - (((t1 - t) - DP_H[k]) - z_h);
! }
!
! // Split up y into (y1 + y2) and compute (y1 + y2) * (t1 + t2)
! double y1 = y;
! y1 = __LO(y1, 0);
! p_l = (y - y1) * t1 + y * t2;
! p_h = y1 * t1;
! z = p_l + p_h;
! j = __HI(z);
! i = __LO(z);
! if (j >= 0x40900000) { // z >= 1024
! if (((j - 0x40900000) | i)!=0) // if z > 1024
! return s * INFINITY; // Overflow
! else {
! final double OVT = 8.0085662595372944372e-0017; // -(1024-log2(ovfl+.5ulp))
! if (p_l + OVT > z - p_h)
! return s * INFINITY; // Overflow
! }
! } else if ((j & 0x7fffffff) >= 0x4090cc00 ) { // z <= -1075
! if (((j - 0xc090cc00) | i)!=0) // z < -1075
! return s * 0.0; // Underflow
! else {
! if (p_l <= z - p_h)
! return s * 0.0; // Underflow
! }
! }
! /*
! * Compute 2**(p_h+p_l)
! */
! // Poly coefs for (3/2)*(log(x)-2s-2/3*s**3
! final double P1 = 0x1.5555_5555_5553ep-3; // 1.66666666666666019037e-01
! final double P2 = -0x1.6c16_c16b_ebd93p-9; // -2.77777777770155933842e-03
! final double P3 = 0x1.1566_aaf2_5de2cp-14; // 6.61375632143793436117e-05
! final double P4 = -0x1.bbd4_1c5d_26bf1p-20; // -1.65339022054652515390e-06
! final double P5 = 0x1.6376_972b_ea4d0p-25; // 4.13813679705723846039e-08
! final double LG2 = 0x1.62e4_2fef_a39efp-1; // 6.93147180559945286227e-01
! final double LG2_H = 0x1.62e43p-1; // 6.93147182464599609375e-01
! final double LG2_L = -0x1.05c6_10ca_86c39p-29; // -1.90465429995776804525e-09
! i = j & 0x7fffffff;
! k = (i >> 20) - 0x3ff;
! n = 0;
! if (i > 0x3fe00000) { // if |z| > 0.5, set n = [z + 0.5]
! n = j + (0x00100000 >> (k + 1));
! k = ((n & 0x7fffffff) >> 20) - 0x3ff; // new k for n
! t = 0.0;
! t = __HI(t, (n & ~(0x000fffff >> k)) );
! n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
! if (j < 0)
! n = -n;
! p_h -= t;
! }
! t = p_l + p_h;
! t = __LO(t, 0);
! u = t * LG2_H;
! v = (p_l - (t - p_h)) * LG2 + t * LG2_L;
! z = u + v;
! w = v - (z - u);
! t = z * z;
! t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
! r = (z * t1)/(t1 - 2.0) - (w + z * w);
! z = 1.0 - (r - z);
! j = __HI(z);
! j += (n << 20);
! if ((j >> 20) <= 0)
! z = Math.scalb(z, n); // subnormal output
! else {
! int z_hi = __HI(z);
! z_hi += (n << 20);
! z = __HI(z, z_hi);
! }
! return s * z;
! }
! }
}
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