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-rw-r--r--libjava/classpath/java/lang/StrictMath.java418
1 files changed, 209 insertions, 209 deletions
diff --git a/libjava/classpath/java/lang/StrictMath.java b/libjava/classpath/java/lang/StrictMath.java
index 6eb1cb2..88f5e57 100644
--- a/libjava/classpath/java/lang/StrictMath.java
+++ b/libjava/classpath/java/lang/StrictMath.java
@@ -658,12 +658,12 @@ public final strictfp class StrictMath
// 1. Replace x by |x| (sinh(-x) = -sinh(x)).
// 2.
// E + E/(E+1)
- // 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
- // 2
+ // 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) := +inf (overflow)
+ // ln2ovft < x : sinh(x) := +inf (overflow)
double t, w, h;
@@ -691,15 +691,15 @@ public final strictfp class StrictMath
// |x| in [0, 22], return sign(x) * 0.5 * (E+E/(E+1))
if (h_bits < 0x40360000L) // |x| < 22
{
- if (h_bits < 0x3e300000L) // |x| < 2^-28
- return x; // for tiny arguments return x
+ if (h_bits < 0x3e300000L) // |x| < 2^-28
+ return x; // for tiny arguments return x
- t = expm1(abs(x));
+ t = expm1(abs(x));
- if (h_bits < 0x3ff00000L)
- return h * (2.0 * t - t * t / (t + 1.0));
+ if (h_bits < 0x3ff00000L)
+ return h * (2.0 * t - t * t / (t + 1.0));
- return h * (t + t / (t + 1.0));
+ return h * (t + t / (t + 1.0));
}
// |x| in [22, log(Double.MAX_VALUE)], return 0.5 * exp(|x|)
@@ -708,12 +708,12 @@ public final strictfp class StrictMath
// |x| in [log(Double.MAX_VALUE), overflowthreshold]
if ((h_bits < 0x408633ceL)
- || ((h_bits == 0x408633ceL) && (l_bits <= 0x8fb9f87dL)))
+ || ((h_bits == 0x408633ceL) && (l_bits <= 0x8fb9f87dL)))
{
- w = exp(0.5 * abs(x));
- t = h * w;
+ w = exp(0.5 * abs(x));
+ t = h * w;
- return t * w;
+ return t * w;
}
// |x| > overflowthershold
@@ -749,12 +749,12 @@ public final strictfp class StrictMath
// 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
// 2*exp(x)
//
- // exp(x) + 1/exp(x)
+ // exp(x) + 1/exp(x)
// ln2/2 <= x <= 22 : cosh(x) := ------------------
- // 2
+ // 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) := +inf (overflow)
+ // ln2ovft < x : cosh(x) := +inf (overflow)
double t, w;
long bits;
@@ -776,22 +776,22 @@ public final strictfp class StrictMath
// |x| in [0, 0.5 * ln(2)], return 1 + expm1(|x|)^2 / (2 * exp(|x|))
if (hx < 0x3fd62e43L)
{
- t = expm1(abs(x));
- w = 1.0 + t;
+ t = expm1(abs(x));
+ w = 1.0 + t;
- // for tiny arguments return 1.
- if (hx < 0x3c800000L)
- return w;
+ // for tiny arguments return 1.
+ if (hx < 0x3c800000L)
+ return w;
- return 1.0 + (t * t) / (w + w);
+ return 1.0 + (t * t) / (w + w);
}
// |x| in [0.5 * ln(2), 22], return exp(|x|)/2 + 1 / (2 * exp(|x|))
if (hx < 0x40360000L)
{
- t = exp(abs(x));
+ t = exp(abs(x));
- return 0.5 * t + 0.5 / t;
+ return 0.5 * t + 0.5 / t;
}
// |x| in [22, log(Double.MAX_VALUE)], return 0.5 * exp(|x|)
@@ -801,12 +801,12 @@ public final strictfp class StrictMath
// |x| in [log(Double.MAX_VALUE), overflowthreshold],
// return exp(x/2)/2 * exp(x/2)
if ((hx < 0x408633ceL)
- || ((hx == 0x408633ceL) && (lx <= 0x8fb9f87dL)))
+ || ((hx == 0x408633ceL) && (lx <= 0x8fb9f87dL)))
{
- w = exp(0.5 * abs(x));
- t = 0.5 * w;
+ w = exp(0.5 * abs(x));
+ t = 0.5 * w;
- return t * w;
+ return t * w;
}
// |x| > overflowthreshold
@@ -862,22 +862,22 @@ public final strictfp class StrictMath
if (h_bits < 0x40360000L) // |x| < 22
{
- if (h_bits < 0x3c800000L) // |x| < 2^-55
- return x * (1.0 + x);
-
- if (h_bits >= 0x3ff00000L) // |x| >= 1
- {
- t = expm1(2.0 * abs(x));
- z = 1.0 - 2.0 / (t + 2.0);
- }
- else // |x| < 1
- {
- t = expm1(-2.0 * abs(x));
- z = -t / (t + 2.0);
- }
+ if (h_bits < 0x3c800000L) // |x| < 2^-55
+ return x * (1.0 + x);
+
+ if (h_bits >= 0x3ff00000L) // |x| >= 1
+ {
+ t = expm1(2.0 * abs(x));
+ z = 1.0 - 2.0 / (t + 2.0);
+ }
+ else // |x| < 1
+ {
+ t = expm1(-2.0 * abs(x));
+ z = -t / (t + 2.0);
+ }
}
else // |x| >= 22
- z = 1.0;
+ z = 1.0;
return (x >= 0) ? z : -z;
}
@@ -909,7 +909,7 @@ public final strictfp class StrictMath
private static double buildDouble(long lowDWord, long highDWord)
{
return Double.longBitsToDouble(((highDWord & 0xffffffffL) << 32)
- | (lowDWord & 0xffffffffL));
+ | (lowDWord & 0xffffffffL));
}
/**
@@ -960,26 +960,26 @@ public final strictfp class StrictMath
if (bits < 0x0010000000000000L) // subnormal number
{
- t = TWO_54;
- t *= x;
+ t = TWO_54;
+ t *= x;
- // __HI(t)=__HI(t)/3+B2;
- bits = Double.doubleToLongBits(t);
- h = getHighDWord(bits);
- l = getLowDWord(bits);
+ // __HI(t)=__HI(t)/3+B2;
+ bits = Double.doubleToLongBits(t);
+ h = getHighDWord(bits);
+ l = getLowDWord(bits);
- h = h / 3 + CBRT_B2;
+ h = h / 3 + CBRT_B2;
- t = buildDouble(l, h);
+ t = buildDouble(l, h);
}
else
{
- // __HI(t)=__HI(x)/3+B1;
- h = getHighDWord(bits);
- l = 0;
+ // __HI(t)=__HI(x)/3+B1;
+ h = getHighDWord(bits);
+ l = 0;
- h = h / 3 + CBRT_B1;
- t = buildDouble(l, h);
+ h = h / 3 + CBRT_B1;
+ t = buildDouble(l, h);
}
// new cbrt to 23 bits
@@ -998,7 +998,7 @@ public final strictfp class StrictMath
t = buildDouble(l, h);
// one step newton iteration to 53 bits with error less than 0.667 ulps
- s = t * t; // t * t is exact
+ s = t * t; // t * t is exact
r = x / s;
w = t + t;
r = (r - t) / (w + r); // r - t is exact
@@ -1087,75 +1087,75 @@ public final strictfp class StrictMath
{
// Method
// 1. Argument reduction:
- // Given x, find r and integer k such that
+ // Given x, find r and integer k such that
//
// x = k * ln(2) + r, |r| <= 0.5 * ln(2)
//
// Here a correction term c will be computed to compensate
- // the error in r when rounded to a floating-point number.
+ // the error in r when rounded to a floating-point number.
//
// 2. Approximating expm1(r) by a special rational function on
- // the interval [0, 0.5 * ln(2)]:
- // Since
- // r*(exp(r)+1)/(exp(r)-1) = 2 + r^2/6 - r^4/360 + ...
- // we define R1(r*r) by
- // r*(exp(r)+1)/(exp(r)-1) = 2 + r^2/6 * R1(r*r)
- // That is,
- // R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
- // = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
- // = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
+ // the interval [0, 0.5 * ln(2)]:
+ // Since
+ // r*(exp(r)+1)/(exp(r)-1) = 2 + r^2/6 - r^4/360 + ...
+ // we define R1(r*r) by
+ // r*(exp(r)+1)/(exp(r)-1) = 2 + r^2/6 * R1(r*r)
+ // That is,
+ // R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
+ // = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
+ // = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
// We use a special Remes algorithm on [0, 0.347] to generate
- // a polynomial of degree 5 in r*r to approximate R1. The
- // maximum error of this polynomial approximation is bounded
- // by 2**-61. In other words,
- // R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
- // where Q1 = -1.6666666666666567384E-2,
- // Q2 = 3.9682539681370365873E-4,
- // Q3 = -9.9206344733435987357E-6,
- // Q4 = 2.5051361420808517002E-7,
- // Q5 = -6.2843505682382617102E-9;
- // (where z=r*r, and Q1 to Q5 are called EXPM1_Qx in the source)
- // with error bounded by
- // | 5 | -61
- // | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
- // | |
+ // a polynomial of degree 5 in r*r to approximate R1. The
+ // maximum error of this polynomial approximation is bounded
+ // by 2**-61. In other words,
+ // R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
+ // where Q1 = -1.6666666666666567384E-2,
+ // Q2 = 3.9682539681370365873E-4,
+ // Q3 = -9.9206344733435987357E-6,
+ // Q4 = 2.5051361420808517002E-7,
+ // Q5 = -6.2843505682382617102E-9;
+ // (where z=r*r, and Q1 to Q5 are called EXPM1_Qx in the source)
+ // with error bounded by
+ // | 5 | -61
+ // | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
+ // | |
//
- // expm1(r) = exp(r)-1 is then computed by the following
- // specific way which minimize the accumulation rounding error:
- // 2 3
- // r r [ 3 - (R1 + R1*r/2) ]
- // expm1(r) = r + --- + --- * [--------------------]
- // 2 2 [ 6 - r*(3 - R1*r/2) ]
+ // expm1(r) = exp(r)-1 is then computed by the following
+ // specific way which minimize the accumulation rounding error:
+ // 2 3
+ // r r [ 3 - (R1 + R1*r/2) ]
+ // expm1(r) = r + --- + --- * [--------------------]
+ // 2 2 [ 6 - r*(3 - R1*r/2) ]
//
- // To compensate the error in the argument reduction, we use
- // expm1(r+c) = expm1(r) + c + expm1(r)*c
- // ~ expm1(r) + c + r*c
- // Thus c+r*c will be added in as the correction terms for
- // expm1(r+c). Now rearrange the term to avoid optimization
- // screw up:
- // ( 2 2 )
- // ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
- // expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
- // ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
+ // To compensate the error in the argument reduction, we use
+ // expm1(r+c) = expm1(r) + c + expm1(r)*c
+ // ~ expm1(r) + c + r*c
+ // Thus c+r*c will be added in as the correction terms for
+ // expm1(r+c). Now rearrange the term to avoid optimization
+ // screw up:
+ // ( 2 2 )
+ // ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
+ // expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
+ // ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
// ( )
//
- // = r - E
+ // = r - E
// 3. Scale back to obtain expm1(x):
- // From step 1, we have
- // expm1(x) = either 2^k*[expm1(r)+1] - 1
- // = or 2^k*[expm1(r) + (1-2^-k)]
+ // From step 1, we have
+ // expm1(x) = either 2^k*[expm1(r)+1] - 1
+ // = or 2^k*[expm1(r) + (1-2^-k)]
// 4. Implementation notes:
- // (A). To save one multiplication, we scale the coefficient Qi
- // to Qi*2^i, and replace z by (x^2)/2.
- // (B). To achieve maximum accuracy, we compute expm1(x) by
- // (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
- // (ii) if k=0, return r-E
- // (iii) if k=-1, return 0.5*(r-E)-0.5
- // (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
- // else return 1.0+2.0*(r-E);
- // (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
- // (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
- // (vii) return 2^k(1-((E+2^-k)-r))
+ // (A). To save one multiplication, we scale the coefficient Qi
+ // to Qi*2^i, and replace z by (x^2)/2.
+ // (B). To achieve maximum accuracy, we compute expm1(x) by
+ // (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
+ // (ii) if k=0, return r-E
+ // (iii) if k=-1, return 0.5*(r-E)-0.5
+ // (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
+ // else return 1.0+2.0*(r-E);
+ // (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
+ // (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
+ // (vii) return 2^k(1-((E+2^-k)-r))
boolean negative = (x < 0);
double y, hi, lo, c, t, e, hxs, hfx, r1;
@@ -1175,52 +1175,52 @@ public final strictfp class StrictMath
// handle special cases and large arguments
if (h_bits >= 0x4043687aL) // if |x| >= 56 * ln(2)
{
- if (h_bits >= 0x40862e42L) // if |x| >= EXP_LIMIT_H
- {
- if (h_bits >= 0x7ff00000L)
- {
- if (((h_bits & 0x000fffffL) | (l_bits & 0xffffffffL)) != 0)
- return x; // exp(NaN) = NaN
- else
- return negative ? -1.0 : x; // exp({+-inf}) = {+inf, -1}
- }
-
- if (x > EXP_LIMIT_H)
- return Double.POSITIVE_INFINITY; // overflow
- }
-
- if (negative) // x <= -56 * ln(2)
- return -1.0;
+ if (h_bits >= 0x40862e42L) // if |x| >= EXP_LIMIT_H
+ {
+ if (h_bits >= 0x7ff00000L)
+ {
+ if (((h_bits & 0x000fffffL) | (l_bits & 0xffffffffL)) != 0)
+ return x; // exp(NaN) = NaN
+ else
+ return negative ? -1.0 : x; // exp({+-inf}) = {+inf, -1}
+ }
+
+ if (x > EXP_LIMIT_H)
+ return Double.POSITIVE_INFINITY; // overflow
+ }
+
+ if (negative) // x <= -56 * ln(2)
+ return -1.0;
}
// argument reduction
if (h_bits > 0x3fd62e42L) // |x| > 0.5 * ln(2)
{
- if (h_bits < 0x3ff0a2b2L) // |x| < 1.5 * ln(2)
- {
- if (negative)
- {
- hi = x + LN2_H;
- lo = -LN2_L;
- k = -1;
- }
- else
- {
- hi = x - LN2_H;
- lo = LN2_L;
- k = 1;
- }
- }
- else
- {
- k = (int) (INV_LN2 * x + (negative ? - 0.5 : 0.5));
- t = k;
- hi = x - t * LN2_H;
- lo = t * LN2_L;
- }
-
- x = hi - lo;
- c = (hi - x) - lo;
+ if (h_bits < 0x3ff0a2b2L) // |x| < 1.5 * ln(2)
+ {
+ if (negative)
+ {
+ hi = x + LN2_H;
+ lo = -LN2_L;
+ k = -1;
+ }
+ else
+ {
+ hi = x - LN2_H;
+ lo = LN2_L;
+ k = 1;
+ }
+ }
+ else
+ {
+ k = (int) (INV_LN2 * x + (negative ? - 0.5 : 0.5));
+ t = k;
+ hi = x - t * LN2_H;
+ lo = t * LN2_L;
+ }
+
+ x = hi - lo;
+ c = (hi - x) - lo;
}
else if (h_bits < 0x3c900000L) // |x| < 2^-54 return x
@@ -1232,85 +1232,85 @@ public final strictfp class StrictMath
hfx = 0.5 * x;
hxs = x * hfx;
r1 = 1.0 + hxs * (EXPM1_Q1
- + hxs * (EXPM1_Q2
+ + hxs * (EXPM1_Q2
+ hxs * (EXPM1_Q3
- + hxs * (EXPM1_Q4
- + hxs * EXPM1_Q5))));
+ + hxs * (EXPM1_Q4
+ + hxs * EXPM1_Q5))));
t = 3.0 - r1 * hfx;
e = hxs * ((r1 - t) / (6.0 - x * t));
if (k == 0)
{
- return x - (x * e - hxs); // c == 0
+ return x - (x * e - hxs); // c == 0
}
else
{
- e = x * (e - c) - c;
- e -= hxs;
+ e = x * (e - c) - c;
+ e -= hxs;
- if (k == -1)
- return 0.5 * (x - e) - 0.5;
+ 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 1.0 + 2.0 * (x - e);
- }
+ if (k == 1)
+ {
+ if (x < - 0.25)
+ return -2.0 * (e - (x + 0.5));
+ else
+ return 1.0 + 2.0 * (x - e);
+ }
- if (k <= -2 || k > 56) // sufficient to return exp(x) - 1
- {
- y = 1.0 - (e - x);
+ if (k <= -2 || k > 56) // sufficient to return exp(x) - 1
+ {
+ y = 1.0 - (e - x);
- bits = Double.doubleToLongBits(y);
- h_bits = getHighDWord(bits);
- l_bits = getLowDWord(bits);
+ bits = Double.doubleToLongBits(y);
+ h_bits = getHighDWord(bits);
+ l_bits = getLowDWord(bits);
- h_bits += (k << 20); // add k to y's exponent
+ h_bits += (k << 20); // add k to y's exponent
- y = buildDouble(l_bits, h_bits);
+ y = buildDouble(l_bits, h_bits);
- return y - 1.0;
- }
+ return y - 1.0;
+ }
- t = 1.0;
- if (k < 20)
- {
- bits = Double.doubleToLongBits(t);
- h_bits = 0x3ff00000L - (0x00200000L >> k);
- l_bits = getLowDWord(bits);
+ t = 1.0;
+ if (k < 20)
+ {
+ bits = Double.doubleToLongBits(t);
+ h_bits = 0x3ff00000L - (0x00200000L >> k);
+ l_bits = getLowDWord(bits);
- t = buildDouble(l_bits, h_bits); // t = 1 - 2^(-k)
- y = t - (e - x);
+ t = buildDouble(l_bits, h_bits); // t = 1 - 2^(-k)
+ y = t - (e - x);
- bits = Double.doubleToLongBits(y);
- h_bits = getHighDWord(bits);
- l_bits = getLowDWord(bits);
+ bits = Double.doubleToLongBits(y);
+ h_bits = getHighDWord(bits);
+ l_bits = getLowDWord(bits);
- h_bits += (k << 20); // add k to y's exponent
+ h_bits += (k << 20); // add k to y's exponent
- y = buildDouble(l_bits, h_bits);
- }
- else
- {
- bits = Double.doubleToLongBits(t);
- h_bits = (0x000003ffL - k) << 20;
- l_bits = getLowDWord(bits);
+ y = buildDouble(l_bits, h_bits);
+ }
+ else
+ {
+ bits = Double.doubleToLongBits(t);
+ h_bits = (0x000003ffL - k) << 20;
+ l_bits = getLowDWord(bits);
- t = buildDouble(l_bits, h_bits); // t = 2^(-k)
+ t = buildDouble(l_bits, h_bits); // t = 2^(-k)
- y = x - (e + t);
- y += 1.0;
+ y = x - (e + t);
+ y += 1.0;
- bits = Double.doubleToLongBits(y);
- h_bits = getHighDWord(bits);
- l_bits = getLowDWord(bits);
+ bits = Double.doubleToLongBits(y);
+ h_bits = getHighDWord(bits);
+ l_bits = getLowDWord(bits);
- h_bits += (k << 20); // add k to y's exponent
+ h_bits += (k << 20); // add k to y's exponent
- y = buildDouble(l_bits, h_bits);
- }
+ y = buildDouble(l_bits, h_bits);
+ }
}
return y;
@@ -2504,7 +2504,7 @@ public final strictfp class StrictMath
* <li>If <code>a</code> is positive or negative zero, the result is the
* same.</li>
* </ul>
- *
+ *
* @param a the numeric argument.
* @return the sign of the argument.
* @since 1.5.
@@ -2526,7 +2526,7 @@ public final strictfp class StrictMath
* <li>If <code>a</code> is positive or negative zero, the result is the
* same.</li>
* </ul>
- *
+ *
* @param a the numeric argument.
* @return the sign of the argument.
* @since 1.5.
generated by cgit v1.1 at 2025-03-20 11:21:26 +0000