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8304423: Refactor FdLibm.java
Reviewed-by: bpb
This commit is contained in:
Joe Darcy
parent
28829f308f
commit
d819debaa5
1 changed files with 82 additions and 75 deletions
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@ -64,6 +64,16 @@ class FdLibm {
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private static final double TWO54 = 0x1.0p54; // 1.80143985094819840000e+16
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private static final double HUGE = 1.0e+300;
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/*
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* Constants for bit-wise manipulation of IEEE 754 double
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* values. These constants are for the high-order 32-bits of a
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* 64-bit double value: 1 sign bit as the most significant bit,
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* followed by 11 exponent bits, and then the remaining bits as
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* the significand.
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*/
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private static final int SIGN_BIT = 0x8000_0000;
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private static final int EXP_BITS = 0x7ff0_0000;
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private static final int EXP_SIGNIF_BITS = 0x7fff_ffff;
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private FdLibm() {
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throw new UnsupportedOperationException("No FdLibm instances for you.");
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@ -156,10 +166,10 @@ class FdLibm {
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ix = __HI(x);
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// |x| ~< pi/4
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ix &= 0x7fff_ffff;
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ix &= EXP_SIGNIF_BITS;
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if (ix <= 0x3fe9_21fb) {
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return __kernel_sin(x, z, 0);
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} else if (ix>=0x7ff0_0000) { // sin(Inf or NaN) is NaN
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} else if (ix >= EXP_BITS) { // sin(Inf or NaN) is NaN
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return x - x;
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} else { // argument reduction needed
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n = RemPio2.__ieee754_rem_pio2(x, y);
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@ -211,7 +221,7 @@ class FdLibm {
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static double __kernel_sin(double x, double y, int iy) {
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double z, r, v;
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int ix;
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ix = __HI(x) & 0x7fff_ffff; // high word of x
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ix = __HI(x) & EXP_SIGNIF_BITS; // high word of x
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if (ix < 0x3e40_0000) { // |x| < 2**-27
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if ((int)x == 0) // generate inexact
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return x;
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@ -269,11 +279,11 @@ class FdLibm {
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ix = __HI(x);
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// |x| ~< pi/4
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ix &= 0x7fff_ffff;
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ix &= EXP_SIGNIF_BITS;
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if (ix <= 0x3fe9_21fb) {
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return __kernel_cos(x, z);
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} else if (ix >= 0x7ff0_0000) { // cos(Inf or NaN) is NaN
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return x-x;
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} else if (ix >= EXP_BITS) { // cos(Inf or NaN) is NaN
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return x - x;
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} else { // argument reduction needed
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n = RemPio2.__ieee754_rem_pio2(x,y);
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switch (n & 3) {
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@ -331,7 +341,7 @@ class FdLibm {
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static double __kernel_cos(double x, double y) {
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double a, hz, z, r, qx = 0.0;
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int ix;
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ix = __HI(x) & 0x7fff_ffff; // ix = |x|'s high word
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ix = __HI(x) & EXP_SIGNIF_BITS; // ix = |x|'s high word
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if (ix < 0x3e40_0000) { // if x < 2**27
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if (((int)x) == 0) { // generate inexact
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return 1.0;
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@ -395,11 +405,11 @@ class FdLibm {
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ix = __HI(x);
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// |x| ~< pi/4
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ix &= 0x7fff_ffff;
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ix &= EXP_SIGNIF_BITS;
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if (ix <= 0x3fe9_21fb) {
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return __kernel_tan(x, z, 1);
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} else if (ix >= 0x7ff0_0000) { // tan(Inf or NaN) is NaN
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return x-x; // NaN
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} else if (ix >= EXP_BITS) { // tan(Inf or NaN) is NaN
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return x - x; // NaN
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} else { // argument reduction needed
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n = RemPio2.__ieee754_rem_pio2(x, y);
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return __kernel_tan(y[0], y[1], 1 - ((n & 1) << 1)); // 1 -- n even; -1 -- n odd
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@ -462,7 +472,7 @@ class FdLibm {
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double z, r, v, w, s;
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int ix, hx;
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hx = __HI(x); // high word of x
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ix = hx&0x7fff_ffff; // high word of |x|
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ix = hx & EXP_SIGNIF_BITS; // high word of |x|
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if (ix < 0x3e30_0000) { // x < 2**-28
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if ((int)x == 0) { // generate inexact
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if (((ix | __LO(x)) | (iy + 1)) == 0) {
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@ -584,7 +594,7 @@ class FdLibm {
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int e0, i, j, nx, n, ix, hx;
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hx = __HI(x); // high word of x
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ix = hx & 0x7fff_ffff;
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ix = hx & EXP_SIGNIF_BITS;
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if (ix <= 0x3fe9_21fb) { // |x| ~<= pi/4 , no need for reduction
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y[0] = x;
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y[1] = 0;
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@ -655,13 +665,13 @@ class FdLibm {
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/*
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* all other (large) arguments
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*/
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if (ix >= 0x7ff0_0000) { // x is inf or NaN
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if (ix >= EXP_BITS) { // x is inf or NaN
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y[0] = y[1] = x - x;
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return 0;
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}
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// set z = scalbn(|x|,ilogb(x)-23)
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// set z = scalbn(|x|, ilogb(x)-23)
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z = __LO(z, __LO(x));
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e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */
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e0 = (ix >> 20) - 1046; // e0 = ilogb(z) - 23;
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z = __HI(z, ix - (e0 << 20));
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for (i=0; i < 2; i++) {
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tx[i] = (double)((int)(z));
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@ -859,7 +869,7 @@ class FdLibm {
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// compute n
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z = Math.scalb(z, q0); // actual value of z
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z -= 8.0*Math.floor(z*0.125); // trim off integer >= 8
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z -= 8.0*Math.floor(z*0.125); // trim off integer >= 8
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n = (int) z;
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z -= (double)n;
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ih = 0;
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@ -1071,7 +1081,7 @@ class FdLibm {
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double t = 0, w, p, q, c, r, s;
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int hx, ix;
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hx = __HI(x);
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ix = hx & 0x7fff_ffff;
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ix = hx & EXP_SIGNIF_BITS;
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if (ix >= 0x3ff0_0000) { // |x| >= 1
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if(((ix - 0x3ff0_0000) | __LO(x)) == 0) {
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// asin(1) = +-pi/2 with inexact
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@ -1157,7 +1167,7 @@ class FdLibm {
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double z, p, q, r, w, s, c, df;
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int hx, ix;
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hx = __HI(x);
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ix = hx & 0x7fff_ffff;
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ix = hx & EXP_SIGNIF_BITS;
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if (ix >= 0x3ff0_0000) { // |x| >= 1
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if (((ix - 0x3ff0_0000) | __LO(x)) == 0) { // |x| == 1
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if (hx > 0) {// acos(1) = 0
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@ -1166,7 +1176,7 @@ class FdLibm {
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return Math.PI + 2.0*pio2_lo;
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}
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}
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return (x-x)/(x-x); // acos(|x| > 1) is NaN
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return (x - x)/(x - x); // acos(|x| > 1) is NaN
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}
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if (ix < 0x3fe0_0000) { // |x| < 0.5
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if (ix <= 0x3c60_0000) { // if |x| < 2**-57
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@ -1255,10 +1265,10 @@ class FdLibm {
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int ix, hx, id;
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hx = __HI(x);
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ix = hx & 0x7fff_ffff;
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ix = hx & EXP_SIGNIF_BITS;
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if (ix >= 0x4410_0000) { // if |x| >= 2^66
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if (ix > 0x7ff0_0000 ||
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(ix == 0x7ff0_0000 && (__LO(x) != 0))) {
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if (ix > EXP_BITS ||
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(ix == EXP_BITS && (__LO(x) != 0))) {
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return x+x; // NaN
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}
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if (hx > 0) {
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@ -1352,10 +1362,10 @@ class FdLibm {
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/*unsigned*/ int lx, ly;
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hx = __HI(x);
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ix = hx & 0x7fff_ffff;
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ix = hx & EXP_SIGNIF_BITS;
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lx = __LO(x);
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hy = __HI(y);
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iy = hy&0x7fff_ffff;
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iy = hy & EXP_SIGNIF_BITS;
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ly = __LO(y);
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if (Double.isNaN(x) || Double.isNaN(y))
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return x + y;
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@ -1378,8 +1388,8 @@ class FdLibm {
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}
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// when x is INF
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if (ix == 0x7ff0_0000) {
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if (iy == 0x7ff0_0000) {
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if (ix == EXP_BITS) {
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if (iy == EXP_BITS) {
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switch(m) {
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case 0: return pi_o_4 + tiny; // atan(+INF, +INF)
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case 1: return -pi_o_4 - tiny; // atan(-INF, +INF)
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@ -1396,7 +1406,7 @@ class FdLibm {
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}
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}
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// when y is INF
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if (iy == 0x7ff0_0000) {
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if (iy == EXP_BITS) {
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return (hy < 0)? -pi_o_2 - tiny : pi_o_2 + tiny;
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}
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@ -1494,7 +1504,7 @@ class FdLibm {
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static double compute(double x) {
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double z = 0.0;
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int sign = 0x8000_0000;
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int sign = SIGN_BIT;
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/*unsigned*/ int r, t1, s1, ix1, q1;
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int ix0, s0, q, m, t, i;
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@ -1502,7 +1512,7 @@ class FdLibm {
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ix1 = __LO(x); // low word of x
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// take care of Inf and NaN
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if ((ix0 & 0x7ff0_0000) == 0x7ff0_0000) {
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if ((ix0 & EXP_BITS) == EXP_BITS) {
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return x*x + x; // sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN
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}
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// take care of zero
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@ -1510,7 +1520,7 @@ class FdLibm {
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if (((ix0 & (~sign)) | ix1) == 0)
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return x; // sqrt(+-0) = +-0
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else if (ix0 < 0)
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return (x-x)/(x-x); // sqrt(-ve) = sNaN
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return (x - x)/(x - x); // sqrt(-ve) = sNaN
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}
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// normalize x
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m = (ix0 >> 20);
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@ -2136,7 +2146,7 @@ class FdLibm {
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}
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final int hx = __HI(x);
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int ix = hx & 0x7fffffff;
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int ix = hx & EXP_SIGNIF_BITS;
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/*
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* When x < 0, determine if y is an odd integer:
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@ -2176,7 +2186,7 @@ class FdLibm {
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// (x < 0)**(non-int) is NaN
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if ((n | y_is_int) == 0)
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return (x-x)/(x-x);
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return (x - x)/(x - x);
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s = 1.0; // s (sign of result -ve**odd) = -1 else = 1
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if ( (n | (y_is_int - 1)) == 0)
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@ -2299,7 +2309,7 @@ class FdLibm {
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if (p_l + OVT > z - p_h)
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return s * INFINITY; // Overflow
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}
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} else if ((j & 0x7fffffff) >= 0x4090cc00 ) { // z <= -1075
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} else if ((j & EXP_SIGNIF_BITS) >= 0x4090cc00 ) { // z <= -1075
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if (((j - 0xc090cc00) | i)!=0) // z < -1075
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return s * 0.0; // Underflow
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else {
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@ -2319,12 +2329,12 @@ class FdLibm {
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final double LG2 = 0x1.62e4_2fef_a39efp-1; // 6.93147180559945286227e-01
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final double LG2_H = 0x1.62e43p-1; // 6.93147182464599609375e-01
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final double LG2_L = -0x1.05c6_10ca_86c39p-29; // -1.90465429995776804525e-09
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i = j & 0x7fffffff;
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i = j & EXP_SIGNIF_BITS;
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k = (i >> 20) - 0x3ff;
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n = 0;
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if (i > 0x3fe00000) { // if |z| > 0.5, set n = [z + 0.5]
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n = j + (0x00100000 >> (k + 1));
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k = ((n & 0x7fffffff) >> 20) - 0x3ff; // new k for n
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k = ((n & EXP_SIGNIF_BITS) >> 20) - 0x3ff; // new k for n
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t = 0.0;
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t = __HI(t, (n & ~(0x000fffff >> k)) );
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n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
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@ -2449,7 +2459,7 @@ class FdLibm {
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hx = __HI(x); /* high word of x */
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xsb = (hx >> 31) & 1; /* sign bit of x */
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hx &= 0x7fffffff; /* high word of |x| */
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hx &= EXP_SIGNIF_BITS; /* high word of |x| */
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/* filter out non-finite argument */
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if (hx >= 0x40862E42) { /* if |x| >= 709.78... */
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@ -2568,8 +2578,6 @@ class FdLibm {
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Lg6 = 0x1.39a09d078c69fp-3, // 1.531383769920937332e-01
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Lg7 = 0x1.2f112df3e5244p-3; // 1.479819860511658591e-01
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private static final double zero = 0.0;
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static double compute(double x) {
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double hfsq, f, s, z, R, w, t1, t2, dk;
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int k, hx, i, j;
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@ -2580,17 +2588,17 @@ class FdLibm {
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k=0;
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if (hx < 0x0010_0000) { // x < 2**-1022
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if (((hx & 0x7fff_ffff) | lx) == 0) { // log(+-0) = -inf
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return -TWO54/zero;
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if (((hx & EXP_SIGNIF_BITS) | lx) == 0) { // log(+-0) = -inf
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return -TWO54/0.0;
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}
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if (hx < 0) { // log(-#) = NaN
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return (x - x)/zero;
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return (x - x)/0.0;
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}
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k -= 54;
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x *= TWO54; // subnormal number, scale up x
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hx = __HI(x); // high word of x
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}
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if (hx >= 0x7ff0_0000) {
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if (hx >= EXP_BITS) {
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return x + x;
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}
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k += (hx >> 20) - 1023;
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@ -2600,9 +2608,9 @@ class FdLibm {
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k += (i >> 20);
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f = x - 1.0;
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if ((0x000f_ffff & (2 + hx)) < 3) {// |f| < 2**-20
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if (f == zero) {
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if (f == 0.0) {
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if (k == 0) {
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return zero;
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return 0.0;
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} else {
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dk = (double)k;
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return dk*ln2_hi + dk*ln2_lo;
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@ -2694,7 +2702,7 @@ class FdLibm {
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k=0;
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if (hx < 0x0010_0000) { /* x < 2**-1022 */
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if (((hx & 0x7fff_ffff) | lx) == 0) {
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if (((hx & EXP_SIGNIF_BITS) | lx) == 0) {
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return -TWO54/0.0; /* log(+-0)=-inf */
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}
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if (hx < 0) {
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@ -2705,12 +2713,12 @@ class FdLibm {
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hx = __HI(x);
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}
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if (hx >= 0x7ff0_0000) {
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if (hx >= EXP_BITS) {
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return x + x;
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}
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k += (hx >> 20) - 1023;
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i = (k & 0x8000_0000) >>> 31; // unsigned shift
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i = (k & SIGN_BIT) >>> 31; // unsigned shift
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hx = (hx & 0x000f_ffff) | ((0x3ff - i) << 20);
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y = (double)(k + i);
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x = __HI(x, hx); // replace high word of x with hx
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@ -2800,7 +2808,7 @@ class FdLibm {
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int k, hx, hu=0, ax;
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hx = __HI(x); /* high word of x */
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ax = hx & 0x7fff_ffff;
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ax = hx & EXP_SIGNIF_BITS;
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k = 1;
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if (hx < 0x3FDA_827A) { /* x < 0.41422 */
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@ -2826,7 +2834,7 @@ class FdLibm {
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}
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}
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if (hx >= 0x7ff0_0000) {
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if (hx >= EXP_BITS) {
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return x + x;
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}
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@ -2977,7 +2985,6 @@ class FdLibm {
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* to produce the hexadecimal values shown.
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*/
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static class Expm1 {
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private static final double one = 1.0;
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private static final double huge = 1.0e+300;
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private static final double tiny = 1.0e-300;
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private static final double o_threshold = 0x1.62e42fefa39efp9; // 7.09782712893383973096e+02
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@ -2997,9 +3004,9 @@ class FdLibm {
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/*unsigned*/ int hx;
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hx = __HI(x); // high word of x
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xsb = hx & 0x8000_0000; // sign bit of x
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xsb = hx & SIGN_BIT; // sign bit of x
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y = Math.abs(x);
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hx &= 0x7fff_ffff; // high word of |x|
|
||||
hx &= EXP_SIGNIF_BITS; // high word of |x|
|
||||
|
||||
// filter out huge and non-finite argument
|
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if (hx >= 0x4043_687A) { // if |x| >= 56*ln2
|
||||
|
|
@ -3017,7 +3024,7 @@ class FdLibm {
|
|||
}
|
||||
if (xsb != 0) { // x < -56*ln2, return -1.0 with inexact
|
||||
if (x + tiny < 0.0) { // raise inexact
|
||||
return tiny - one; // return -1
|
||||
return tiny - 1.0; // return -1
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
@ -3052,7 +3059,7 @@ class FdLibm {
|
|||
// x is now in primary range
|
||||
hfx = 0.5*x;
|
||||
hxs = x*hfx;
|
||||
r1 = one + hxs*(Q1 + hxs*(Q2 + hxs*(Q3 + hxs*(Q4 + hxs*Q5))));
|
||||
r1 = 1.0 + 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) {
|
||||
|
|
@ -3067,15 +3074,15 @@ class FdLibm {
|
|||
if (x < -0.25) {
|
||||
return -2.0*(e - (x + 0.5));
|
||||
} else {
|
||||
return one + 2.0*(x - e);
|
||||
return 1.0 + 2.0*(x - e);
|
||||
}
|
||||
}
|
||||
if (k <= -2 || k > 56) { // suffice to return exp(x) - 1
|
||||
y = one - (e - x);
|
||||
y = 1.0 - (e - x);
|
||||
y = __HI(y, __HI(y) + (k << 20)); // add k to y's exponent
|
||||
return y - one;
|
||||
return y - 1.0;
|
||||
}
|
||||
t = one;
|
||||
t = 1.0;
|
||||
if (k < 20) {
|
||||
t = __HI(t, 0x3ff0_0000 - (0x2_00000 >> k)); // t = 1-2^-k
|
||||
y = t - ( e - x);
|
||||
|
|
@ -3083,7 +3090,7 @@ class FdLibm {
|
|||
} else {
|
||||
t = __HI(t, ((0x3ff - k) << 20)); // 2^-k
|
||||
y = x - (e + t);
|
||||
y += one;
|
||||
y += 1.0;
|
||||
y = __HI(y, __HI(y) + (k << 20)); // add k to y's exponent
|
||||
}
|
||||
}
|
||||
|
|
@ -3120,10 +3127,10 @@ class FdLibm {
|
|||
|
||||
// High word of |x|
|
||||
jx = __HI(x);
|
||||
ix = jx & 0x7fff_ffff;
|
||||
ix = jx & EXP_SIGNIF_BITS;
|
||||
|
||||
// x is INF or NaN
|
||||
if (ix >= 0x7ff0_0000) {
|
||||
if (ix >= EXP_BITS) {
|
||||
return x + x;
|
||||
}
|
||||
|
||||
|
|
@ -3196,10 +3203,10 @@ class FdLibm {
|
|||
|
||||
// High word of |x|
|
||||
ix = __HI(x);
|
||||
ix &= 0x7fff_ffff;
|
||||
ix &= EXP_SIGNIF_BITS;
|
||||
|
||||
// x is INF or NaN
|
||||
if (ix >= 0x7ff0_0000) {
|
||||
if (ix >= EXP_BITS) {
|
||||
return x*x;
|
||||
}
|
||||
|
||||
|
|
@ -3273,10 +3280,10 @@ class FdLibm {
|
|||
|
||||
// High word of |x|.
|
||||
jx = __HI(x);
|
||||
ix = jx & 0x7fff_ffff;
|
||||
ix = jx & EXP_SIGNIF_BITS;
|
||||
|
||||
// x is INF or NaN
|
||||
if (ix >= 0x7ff0_0000) {
|
||||
if (ix >= EXP_BITS) {
|
||||
if (jx >= 0) { // tanh(+-inf)=+-1
|
||||
return 1.0/x + 1.0;
|
||||
} else { // tanh(NaN) = NaN
|
||||
|
|
@ -3314,17 +3321,17 @@ class FdLibm {
|
|||
lx = __LO(x); // low word of x
|
||||
hp = __HI(p); // high word of p
|
||||
lp = __LO(p); // low word of p
|
||||
sx = hx & 0x8000_0000;
|
||||
hp &= 0x7fff_ffff;
|
||||
hx &= 0x7fff_ffff;
|
||||
sx = hx & SIGN_BIT;
|
||||
hp &= EXP_SIGNIF_BITS;
|
||||
hx &= EXP_SIGNIF_BITS;
|
||||
|
||||
// purge off exception values
|
||||
if ((hp | lp) == 0) {// p = 0
|
||||
return (x*p)/(x*p);
|
||||
}
|
||||
if ((hx >= 0x7ff0_0000) || // not finite
|
||||
((hp >= 0x7ff0_0000) && // p is NaN
|
||||
(((hp - 0x7ff0_0000) | lp) != 0)))
|
||||
if ((hx >= EXP_BITS) || // not finite
|
||||
((hp >= EXP_BITS) && // p is NaN
|
||||
(((hp - EXP_BITS) | lp) != 0)))
|
||||
return (x*p)/(x*p);
|
||||
|
||||
if (hp <= 0x7fdf_ffff) { // now x < 2p
|
||||
|
|
@ -3362,13 +3369,13 @@ class FdLibm {
|
|||
lx = __LO(x); // low word of x
|
||||
hy = __HI(y); // high word of y
|
||||
ly = __LO(y); // low word of y
|
||||
sx = hx & 0x8000_0000; // sign of x
|
||||
sx = hx & SIGN_BIT; // sign of x
|
||||
hx ^= sx; // |x|
|
||||
hy &= 0x7fff_ffff; // |y|
|
||||
hy &= EXP_SIGNIF_BITS; // |y|
|
||||
|
||||
// purge off exception values
|
||||
if ((hy | ly) == 0 || (hx >= 0x7ff0_0000)|| // y = 0, or x not finite
|
||||
((hy | ((ly | -ly) >>> 31)) > 0x7ff0_0000)) // or y is NaN, unsigned shift
|
||||
if ((hy | ly) == 0 || (hx >= EXP_BITS)|| // y = 0, or x not finite
|
||||
((hy | ((ly | -ly) >>> 31)) > EXP_BITS)) // or y is NaN, unsigned shift
|
||||
return (x*y)/(x*y);
|
||||
if (hx <= hy) {
|
||||
if ((hx < hy) || (Integer.compareUnsigned(lx, ly) < 0)) { // |x| < |y| return x
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue