mirror of
https://github.com/openjdk/jdk.git
synced 2025-08-27 06:45:07 +02:00
8301444: Port fdlibm hyperbolic transcendental functions to Java
Reviewed-by: bpb
This commit is contained in:
Joe Darcy
parent
b242eef93e
commit
655a71277d
6 changed files with 656 additions and 50 deletions
|
|
@ -950,8 +950,9 @@ class FdLibm {
|
|||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
static class Exp {
|
||||
private static final double one = 1.0;
|
||||
static final class Exp {
|
||||
private Exp() {throw new UnsupportedOperationException();}
|
||||
|
||||
private static final double[] half = {0.5, -0.5,};
|
||||
private static final double huge = 1.0e+300;
|
||||
private static final double twom1000= 0x1.0p-1000; // 9.33263618503218878990e-302 = 2^-1000
|
||||
|
|
@ -969,10 +970,6 @@ class FdLibm {
|
|||
private static final double P4 = -0x1.bbd41c5d26bf1p-20; // -1.65339022054652515390e-06
|
||||
private static final double P5 = 0x1.6376972bea4d0p-25; // 4.13813679705723846039e-08
|
||||
|
||||
private Exp() {
|
||||
throw new UnsupportedOperationException();
|
||||
}
|
||||
|
||||
public static double compute(double x) {
|
||||
double y;
|
||||
double hi = 0.0;
|
||||
|
|
@ -1015,8 +1012,8 @@ class FdLibm {
|
|||
}
|
||||
x = hi - lo;
|
||||
} else if (hx < 0x3e300000) { /* when |x|<2**-28 */
|
||||
if (huge + x > one)
|
||||
return one + x; /* trigger inexact */
|
||||
if (huge + x > 1.0)
|
||||
return 1.0 + x; /* trigger inexact */
|
||||
} else {
|
||||
k = 0;
|
||||
}
|
||||
|
|
@ -1025,9 +1022,9 @@ class FdLibm {
|
|||
t = x * x;
|
||||
c = x - t*(P1 + t*(P2 + t*(P3 + t*(P4 + t*P5))));
|
||||
if (k == 0)
|
||||
return one - ((x*c)/(c - 2.0) - x);
|
||||
return 1.0 - ((x*c)/(c - 2.0) - x);
|
||||
else
|
||||
y = one - ((lo - (x*c)/(2.0 - c)) - hi);
|
||||
y = 1.0 - ((lo - (x*c)/(2.0 - c)) - hi);
|
||||
|
||||
if(k >= -1021) {
|
||||
y = __HI(y, __HI(y) + (k << 20)); /* add k to y's exponent */
|
||||
|
|
@ -1626,4 +1623,215 @@ class FdLibm {
|
|||
return y;
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Method :
|
||||
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
|
||||
* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
|
||||
* 2.
|
||||
* E + E/(E+1)
|
||||
* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
|
||||
* 2
|
||||
*
|
||||
* 22 <= x <= lnovft : sinh(x) := exp(x)/2
|
||||
* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
|
||||
* ln2ovft < x : sinh(x) := x*shuge (overflow)
|
||||
*
|
||||
* Special cases:
|
||||
* sinh(x) is |x| if x is +INF, -INF, or NaN.
|
||||
* only sinh(0)=0 is exact for finite x.
|
||||
*/
|
||||
static final class Sinh {
|
||||
private Sinh() {throw new UnsupportedOperationException();}
|
||||
|
||||
private static final double shuge = 1.0e307;
|
||||
|
||||
static double compute(double x) {
|
||||
double t, w, h;
|
||||
int ix, jx;
|
||||
/* unsigned */ int lx;
|
||||
|
||||
// High word of |x|
|
||||
jx = __HI(x);
|
||||
ix = jx & 0x7fff_ffff;
|
||||
|
||||
// x is INF or NaN
|
||||
if (ix >= 0x7ff0_0000) {
|
||||
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 < 0x4036_0000) { // |x| < 22
|
||||
if (ix < 0x3e30_0000) // |x| < 2**-28
|
||||
if (shuge + x > 1.0) { // sinh(tiny) = tiny with inexact
|
||||
return x;
|
||||
}
|
||||
t = StrictMath.expm1(Math.abs(x));
|
||||
if (ix < 0x3ff0_0000) {
|
||||
return h*(2.0 * t - t*t/(t + 1.0));
|
||||
}
|
||||
return h*(t + t/(t + 1.0));
|
||||
}
|
||||
|
||||
// |x| in [22, log(maxdouble)] return 0.5*exp(|x|)
|
||||
if (ix < 0x4086_2E42) {
|
||||
return h*StrictMath.exp(Math.abs(x));
|
||||
}
|
||||
|
||||
// |x| in [log(maxdouble), overflowthresold]
|
||||
lx = __LO(x);
|
||||
if (ix < 0x4086_33CE ||
|
||||
((ix == 0x4086_33ce) &&
|
||||
(Long.compareUnsigned(lx, 0x8fb9_f87d) <= 0 ))) {
|
||||
w = StrictMath.exp(0.5 * Math.abs(x));
|
||||
t = h * w;
|
||||
return t * w;
|
||||
}
|
||||
|
||||
// |x| > overflowthresold, sinh(x) overflow
|
||||
return x * shuge;
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Method :
|
||||
* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
|
||||
* 1. Replace x by |x| (cosh(x) = cosh(-x)).
|
||||
* 2.
|
||||
* [ exp(x) - 1 ]^2
|
||||
* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
|
||||
* 2*exp(x)
|
||||
*
|
||||
* exp(x) + 1/exp(x)
|
||||
* ln2/2 <= x <= 22 : cosh(x) := -------------------
|
||||
* 2
|
||||
* 22 <= x <= lnovft : cosh(x) := exp(x)/2
|
||||
* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
|
||||
* ln2ovft < x : cosh(x) := huge*huge (overflow)
|
||||
*
|
||||
* Special cases:
|
||||
* cosh(x) is |x| if x is +INF, -INF, or NaN.
|
||||
* only cosh(0)=1 is exact for finite x.
|
||||
*/
|
||||
static final class Cosh {
|
||||
private Cosh() {throw new UnsupportedOperationException();}
|
||||
|
||||
private static final double huge = 1.0e300;
|
||||
|
||||
static double compute(double x) {
|
||||
double t, w;
|
||||
int ix;
|
||||
/*unsigned*/ int lx;
|
||||
|
||||
// High word of |x|
|
||||
ix = __HI(x);
|
||||
ix &= 0x7fff_ffff;
|
||||
|
||||
// x is INF or NaN
|
||||
if (ix >= 0x7ff0_0000) {
|
||||
return x*x;
|
||||
}
|
||||
|
||||
// |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|))
|
||||
if (ix < 0x3fd6_2e43) {
|
||||
t = StrictMath.expm1(Math.abs(x));
|
||||
w = 1.0 + t;
|
||||
if (ix < 0x3c80_0000) { // cosh(tiny) = 1
|
||||
return w;
|
||||
}
|
||||
return 1.0 + (t * t)/(w + w);
|
||||
}
|
||||
|
||||
// |x| in [0.5*ln2, 22], return (exp(|x|) + 1/exp(|x|)/2
|
||||
if (ix < 0x4036_0000) {
|
||||
t = StrictMath.exp(Math.abs(x));
|
||||
return 0.5*t + 0.5/t;
|
||||
}
|
||||
|
||||
// |x| in [22, log(maxdouble)] return 0.5*exp(|x|)
|
||||
if (ix < 0x4086_2E42) {
|
||||
return 0.5*StrictMath.exp(Math.abs(x));
|
||||
}
|
||||
|
||||
// |x| in [log(maxdouble), overflowthresold]
|
||||
lx = __LO(x);
|
||||
if (ix<0x4086_33CE ||
|
||||
((ix == 0x4086_33ce) &&
|
||||
(Integer.compareUnsigned(lx, 0x8fb9_f87d) <= 0))) {
|
||||
w = StrictMath.exp(0.5*Math.abs(x));
|
||||
t = 0.5*w;
|
||||
return t*w;
|
||||
}
|
||||
|
||||
// |x| > overflowthresold, cosh(x) overflow
|
||||
return huge*huge;
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Return the Hyperbolic Tangent of x
|
||||
*
|
||||
* Method :
|
||||
* x -x
|
||||
* e - e
|
||||
* 0. tanh(x) is defined to be -----------
|
||||
* x -x
|
||||
* e + e
|
||||
* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
|
||||
* 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
|
||||
* -t
|
||||
* 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
|
||||
* t + 2
|
||||
* 2
|
||||
* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
|
||||
* t + 2
|
||||
* 22.0 < x <= INF : tanh(x) := 1.
|
||||
*
|
||||
* Special cases:
|
||||
* tanh(NaN) is NaN;
|
||||
* only tanh(0)=0 is exact for finite argument.
|
||||
*/
|
||||
static final class Tanh {
|
||||
private Tanh() {throw new UnsupportedOperationException();}
|
||||
|
||||
private static final double tiny = 1.0e-300;
|
||||
|
||||
static double compute(double x) {
|
||||
double t, z;
|
||||
int jx, ix;
|
||||
|
||||
// High word of |x|.
|
||||
jx = __HI(x);
|
||||
ix = jx & 0x7fff_ffff;
|
||||
|
||||
// x is INF or NaN
|
||||
if (ix >= 0x7ff0_0000) {
|
||||
if (jx >= 0) { // tanh(+-inf)=+-1
|
||||
return 1.0/x + 1.0;
|
||||
} else { // tanh(NaN) = NaN
|
||||
return 1.0/x - 1.0;
|
||||
}
|
||||
}
|
||||
|
||||
// |x| < 22
|
||||
if (ix < 0x4036_0000) { // |x| < 22
|
||||
if (ix<0x3c80_0000) // |x| < 2**-55
|
||||
return x*(1.0 + x); // tanh(small) = small
|
||||
if (ix>=0x3ff0_0000) { // |x| >= 1
|
||||
t = StrictMath.expm1(2.0*Math.abs(x));
|
||||
z = 1.0 - 2.0/(t + 2.0);
|
||||
} else {
|
||||
t = StrictMath.expm1(-2.0*Math.abs(x));
|
||||
z= -t/(t + 2.0);
|
||||
}
|
||||
} else { // |x| > 22, return +-1
|
||||
z = 1.0 - tiny; // raised inexact flag
|
||||
}
|
||||
return (jx >= 0)? z: -z;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue