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8302026: Port fdlibm inverse trig functions (asin, acos, atan) to Java
Reviewed-by: bpb
This commit is contained in:
Joe Darcy
parent
861e302011
commit
3ba156082b
6 changed files with 994 additions and 8 deletions
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@ -60,7 +60,9 @@ package java.lang;
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class FdLibm {
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// Constants used by multiple algorithms
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private static final double INFINITY = Double.POSITIVE_INFINITY;
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private static final double TWO54 = 0x1.0p54; // 1.80143985094819840000e+16
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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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private FdLibm() {
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throw new UnsupportedOperationException("No FdLibm instances for you.");
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@ -102,6 +104,296 @@ class FdLibm {
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( ((long)high)) << 32 );
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}
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/** Returns the arcsine of x.
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*
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* Method :
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* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
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* we approximate asin(x) on [0,0.5] by
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* asin(x) = x + x*x^2*R(x^2)
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* where
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* R(x^2) is a rational approximation of (asin(x)-x)/x^3
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* and its remez error is bounded by
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* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
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*
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* For x in [0.5,1]
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* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
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* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
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* then for x>0.98
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* asin(x) = pi/2 - 2*(s+s*z*R(z))
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* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
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* For x<=0.98, let pio4_hi = pio2_hi/2, then
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* f = hi part of s;
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* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
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* and
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* asin(x) = pi/2 - 2*(s+s*z*R(z))
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* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
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* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
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*
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* Special cases:
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* if x is NaN, return x itself;
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* if |x|>1, return NaN with invalid signal.
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*
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*/
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static class Asin {
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private Asin() {throw new UnsupportedOperationException();}
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private static final double
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pio2_hi = 0x1.921fb54442d18p0, // 1.57079632679489655800e+00
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pio2_lo = 0x1.1a62633145c07p-54, // 6.12323399573676603587e-17
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pio4_hi = 0x1.921fb54442d18p-1, // 7.85398163397448278999e-01
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// coefficient for R(x^2)
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pS0 = 0x1.5555555555555p-3, // 1.66666666666666657415e-01
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pS1 = -0x1.4d61203eb6f7dp-2, // -3.25565818622400915405e-01
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pS2 = 0x1.9c1550e884455p-3, // 2.01212532134862925881e-01
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pS3 = -0x1.48228b5688f3bp-5, // -4.00555345006794114027e-02
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pS4 = 0x1.9efe07501b288p-11, // 7.91534994289814532176e-04
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pS5 = 0x1.23de10dfdf709p-15, // 3.47933107596021167570e-05
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qS1 = -0x1.33a271c8a2d4bp1, // -2.40339491173441421878e+00
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qS2 = 0x1.02ae59c598ac8p1, // 2.02094576023350569471e+00
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qS3 = -0x1.6066c1b8d0159p-1, // -6.88283971605453293030e-01
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qS4 = 0x1.3b8c5b12e9282p-4; // 7.70381505559019352791e-02
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static double compute(double x) {
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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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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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return x*pio2_hi + x*pio2_lo;
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}
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return (x - x)/(x - x); // asin(|x| > 1) is NaN
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} else if (ix < 0x3fe0_0000) { // |x| < 0.5
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if (ix < 0x3e40_0000) { // if |x| < 2**-27
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if (HUGE + x > 1.0) {// return x with inexact if x != 0
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return x;
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}
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} else {
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t = x*x;
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}
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p = t*(pS0 + t*(pS1 + t*(pS2 + t*(pS3 + t*(pS4 + t*pS5)))));
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q = 1.0 + t*(qS1 + t*(qS2 + t*(qS3 + t*qS4)));
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w = p/q;
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return x + x*w;
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}
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// 1 > |x| >= 0.5
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w = 1.0 - Math.abs(x);
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t = w*0.5;
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p = t*(pS0 + t*(pS1 + t*(pS2 + t*(pS3 + t*(pS4 + t*pS5)))));
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q = 1.0 + t*(qS1 + t*(qS2 + t*(qS3 + t*qS4)));
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s = Math.sqrt(t);
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if (ix >= 0x3FEF_3333) { // if |x| > 0.975
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w = p/q;
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t = pio2_hi - (2.0*(s + s*w) - pio2_lo);
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} else {
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w = s;
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w = __LO(w, 0);
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c = (t - w*w)/(s + w);
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r = p/q;
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p = 2.0*s*r - (pio2_lo - 2.0*c);
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q = pio4_hi - 2.0*w;
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t = pio4_hi - (p - q);
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}
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return (hx > 0) ? t : -t;
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}
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}
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/** Returns the arccosine of x.
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* Method :
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* acos(x) = pi/2 - asin(x)
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* acos(-x) = pi/2 + asin(x)
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* For |x| <= 0.5
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* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
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* For x > 0.5
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* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
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* = 2asin(sqrt((1-x)/2))
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* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
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* = 2f + (2c + 2s*z*R(z))
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* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
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* for f so that f+c ~ sqrt(z).
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* For x <- 0.5
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* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
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* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
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*
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* Special cases:
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* if x is NaN, return x itself;
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* if |x|>1, return NaN with invalid signal.
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*
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* Function needed: sqrt
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*/
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static class Acos {
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private Acos() {throw new UnsupportedOperationException();}
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private static final double
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pio2_hi = 0x1.921fb54442d18p0, // 1.57079632679489655800e+00
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pio2_lo = 0x1.1a62633145c07p-54, // 6.12323399573676603587e-17
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pS0 = 0x1.5555555555555p-3, // 1.66666666666666657415e-01
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pS1 = -0x1.4d61203eb6f7dp-2, // -3.25565818622400915405e-01
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pS2 = 0x1.9c1550e884455p-3, // 2.01212532134862925881e-01
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pS3 = -0x1.48228b5688f3bp-5, // -4.00555345006794114027e-02
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pS4 = 0x1.9efe07501b288p-11, // 7.91534994289814532176e-04
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pS5 = 0x1.23de10dfdf709p-15, // 3.47933107596021167570e-05
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qS1 = -0x1.33a271c8a2d4bp1, // -2.40339491173441421878e+00
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qS2 = 0x1.02ae59c598ac8p1, // 2.02094576023350569471e+00
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qS3 = -0x1.6066c1b8d0159p-1, // -6.88283971605453293030e-01
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qS4 = 0x1.3b8c5b12e9282p-4; // 7.70381505559019352791e-02
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static double compute(double x) {
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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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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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return 0.0;
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}else { // acos(-1)= pi
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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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}
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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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return pio2_hi + pio2_lo;
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}
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z = x*x;
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p = z*(pS0 + z*(pS1 + z*(pS2 + z*(pS3 + z*(pS4 + z*pS5)))));
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q = 1.0 + z*(qS1 + z*(qS2 + z*(qS3 + z*qS4)));
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r = p/q;
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return pio2_hi - (x - (pio2_lo - x*r));
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} else if (hx < 0) { // x < -0.5
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z = (1.0 + x)*0.5;
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p = z*(pS0 + z*(pS1 + z*(pS2 + z*(pS3 + z*(pS4 + z*pS5)))));
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q = 1.0 + z*(qS1 + z*(qS2 + z*(qS3 + z*qS4)));
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s = Math.sqrt(z);
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r = p/q;
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w = r*s - pio2_lo;
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return Math.PI - 2.0*(s+w);
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} else { // x > 0.5
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z = (1.0 - x)*0.5;
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s = Math.sqrt(z);
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df = s;
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df = __LO(df, 0);
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c = (z - df*df)/(s + df);
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p = z*(pS0 + z*(pS1 + z*(pS2 + z*(pS3 + z*(pS4 + z*pS5)))));
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q = 1.0 + z*(qS1 + z*(qS2 + z*(qS3 + z*qS4)));
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r = p/q;
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w = r*s + c;
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return 2.0*(df + w);
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}
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}
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}
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/* Returns the arctangent of x.
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* Method
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* 1. Reduce x to positive by atan(x) = -atan(-x).
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* 2. According to the integer k=4t+0.25 chopped, t=x, the argument
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* is further reduced to one of the following intervals and the
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* arctangent of t is evaluated by the corresponding formula:
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*
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* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
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* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
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* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
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* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
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* [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following
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* constants. The decimal values may be used, provided that the
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* compiler will convert from decimal to binary accurately enough
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* to produce the hexadecimal values shown.
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*/
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static class Atan {
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private Atan() {throw new UnsupportedOperationException();}
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private static final double atanhi[] = {
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0x1.dac670561bb4fp-2, // atan(0.5)hi 4.63647609000806093515e-01
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0x1.921fb54442d18p-1, // atan(1.0)hi 7.85398163397448278999e-01
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0x1.f730bd281f69bp-1, // atan(1.5)hi 9.82793723247329054082e-01
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0x1.921fb54442d18p0, // atan(inf)hi 1.57079632679489655800e+00
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};
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private static final double atanlo[] = {
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0x1.a2b7f222f65e2p-56, // atan(0.5)lo 2.26987774529616870924e-17
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0x1.1a62633145c07p-55, // atan(1.0)lo 3.06161699786838301793e-17
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0x1.007887af0cbbdp-56, // atan(1.5)lo 1.39033110312309984516e-17
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0x1.1a62633145c07p-54, // atan(inf)lo 6.12323399573676603587e-17
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};
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private static final double aT[] = {
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0x1.555555555550dp-2, // 3.33333333333329318027e-01
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-0x1.999999998ebc4p-3, // -1.99999999998764832476e-01
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0x1.24924920083ffp-3, // 1.42857142725034663711e-01
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-0x1.c71c6fe231671p-4, // -1.11111104054623557880e-01
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0x1.745cdc54c206ep-4, // 9.09088713343650656196e-02
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-0x1.3b0f2af749a6dp-4, // -7.69187620504482999495e-02
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0x1.10d66a0d03d51p-4, // 6.66107313738753120669e-02
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-0x1.dde2d52defd9ap-5, // -5.83357013379057348645e-02
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0x1.97b4b24760debp-5, // 4.97687799461593236017e-02
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-0x1.2b4442c6a6c2fp-5, // -3.65315727442169155270e-02
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0x1.0ad3ae322da11p-6, // 1.62858201153657823623e-02
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};
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static double compute(double x) {
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double w, s1, s2, z;
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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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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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return x+x; // NaN
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}
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if (hx > 0) {
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return atanhi[3] + atanlo[3];
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} else {
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return -atanhi[3] - atanlo[3];
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}
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} if (ix < 0x3fdc_0000) { // |x| < 0.4375
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if (ix < 0x3e20_0000) { // |x| < 2^-29
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if (HUGE + x > 1.0) { // raise inexact
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return x;
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}
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}
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id = -1;
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} else {
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x = Math.abs(x);
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if (ix < 0x3ff3_0000) { // |x| < 1.1875
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if (ix < 0x3fe60000) { // 7/16 <= |x| < 11/16
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id = 0;
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x = (2.0*x - 1.0)/(2.0 + x);
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} else { // 11/16 <= |x| < 19/16
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id = 1;
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x = (x - 1.0)/(x + 1.0);
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}
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} else {
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if (ix < 0x4003_8000) { // |x| < 2.4375
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id = 2;
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x = (x - 1.5)/(1.0 + 1.5*x);
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} else { // 2.4375 <= |x| < 2^66
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id = 3;
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x = -1.0/x;
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}
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}
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}
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// end of argument reduction
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z = x*x;
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w = z*z;
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// break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly
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s1 = z*(aT[0] + w*(aT[2] + w*(aT[4] + w*(aT[6] + w*(aT[8] + w*aT[10])))));
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s2 = w*(aT[1] + w*(aT[3] + w*(aT[5] + w*(aT[7] + w*aT[9]))));
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if (id < 0) {
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return x - x*(s1 + s2);
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} else {
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z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
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return (hx < 0) ? -z: z;
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}
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}
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}
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/**
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* cbrt(x)
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* Return cube root of x
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@ -164,7 +164,9 @@ public final class StrictMath {
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* @param a the value whose arc sine is to be returned.
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* @return the arc sine of the argument.
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*/
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public static native double asin(double a);
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public static double asin(double a) {
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return FdLibm.Asin.compute(a);
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}
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/**
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* Returns the arc cosine of a value; the returned angle is in the
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@ -177,7 +179,9 @@ public final class StrictMath {
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* @param a the value whose arc cosine is to be returned.
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* @return the arc cosine of the argument.
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*/
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public static native double acos(double a);
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public static double acos(double a) {
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return FdLibm.Acos.compute(a);
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}
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/**
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* Returns the arc tangent of a value; the returned angle is in the
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@ -193,7 +197,9 @@ public final class StrictMath {
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* @param a the value whose arc tangent is to be returned.
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* @return the arc tangent of the argument.
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*/
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public static native double atan(double a);
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public static double atan(double a) {
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return FdLibm.Atan.compute(a);
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}
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/**
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* Converts an angle measured in degrees to an approximately
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177
test/jdk/java/lang/Math/InverseTrigTests.java
Normal file
177
test/jdk/java/lang/Math/InverseTrigTests.java
Normal file
|
|
@ -0,0 +1,177 @@
|
|||
/*
|
||||
* Copyright (c) 2003, 2023, 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.
|
||||
*
|
||||
* This code is distributed in the hope that it will be useful, but WITHOUT
|
||||
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
|
||||
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
|
||||
* version 2 for more details (a copy is included in the LICENSE file that
|
||||
* accompanied this code).
|
||||
*
|
||||
* You should have received a copy of the GNU General Public License version
|
||||
* 2 along with this work; if not, write to the Free Software Foundation,
|
||||
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
|
||||
/*
|
||||
* @test
|
||||
* @bug 8302026
|
||||
* @build Tests
|
||||
* @build InverseTrigTests
|
||||
* @run main InverseTrigTests
|
||||
* @summary Tests for {Math, StrictMath}.{asin, acos, atan}
|
||||
*/
|
||||
|
||||
public class InverseTrigTests {
|
||||
private InverseTrigTests(){}
|
||||
|
||||
public static void main(String... args) {
|
||||
int failures = 0;
|
||||
|
||||
failures += testAsinSpecialCases();
|
||||
failures += testAcosSpecialCases();
|
||||
failures += testAtanSpecialCases();
|
||||
|
||||
if (failures > 0) {
|
||||
System.err.println("Testing inverse trig mthods incurred "
|
||||
+ failures + " failures.");
|
||||
throw new RuntimeException();
|
||||
}
|
||||
}
|
||||
|
||||
private static final double InfinityD = Double.POSITIVE_INFINITY;
|
||||
private static final double NaNd = Double.NaN;
|
||||
|
||||
/**
|
||||
* From the spec for Math.asin:
|
||||
*
|
||||
* "Special cases:
|
||||
*
|
||||
* If the argument is NaN or its absolute value is greater than 1,
|
||||
* then the result is NaN.
|
||||
*
|
||||
* If the argument is zero, then the result is a zero with the
|
||||
* same sign as the argument."
|
||||
*/
|
||||
private static int testAsinSpecialCases() {
|
||||
int failures = 0;
|
||||
|
||||
double [][] testCases = {
|
||||
{NaNd, NaNd},
|
||||
{Math.nextUp(1.0), NaNd},
|
||||
{Math.nextDown(-1.0), NaNd},
|
||||
{ InfinityD, NaNd},
|
||||
{-InfinityD, NaNd},
|
||||
|
||||
{-0.0, -0.0},
|
||||
{+0.0, +0.0},
|
||||
};
|
||||
|
||||
for(int i = 0; i < testCases.length; i++) {
|
||||
failures += testAsinCase(testCases[i][0],
|
||||
testCases[i][1]);
|
||||
}
|
||||
|
||||
return failures;
|
||||
}
|
||||
|
||||
private static int testAsinCase(double input, double expected) {
|
||||
int failures=0;
|
||||
|
||||
failures+=Tests.test("Math.asin", input, Math::asin, expected);
|
||||
failures+=Tests.test("StrictMath.asin", input, StrictMath::asin, expected);
|
||||
|
||||
return failures;
|
||||
}
|
||||
|
||||
/**
|
||||
* From the spec for Math.acos:
|
||||
*
|
||||
* "Special case:
|
||||
*
|
||||
* If the argument is NaN or its absolute value is greater than 1,
|
||||
* then the result is NaN.
|
||||
*
|
||||
* If the argument is 1.0, the result is positive zero."
|
||||
*/
|
||||
private static int testAcosSpecialCases() {
|
||||
int failures = 0;
|
||||
|
||||
double [][] testCases = {
|
||||
{NaNd, NaNd},
|
||||
{Math.nextUp(1.0), NaNd},
|
||||
{Math.nextDown(-1.0), NaNd},
|
||||
{InfinityD, NaNd},
|
||||
{-InfinityD, NaNd},
|
||||
|
||||
{1.0, +0.0},
|
||||
};
|
||||
|
||||
for(int i = 0; i < testCases.length; i++) {
|
||||
failures += testAcosCase(testCases[i][0],
|
||||
testCases[i][1]);
|
||||
}
|
||||
|
||||
return failures;
|
||||
}
|
||||
|
||||
private static int testAcosCase(double input, double expected) {
|
||||
int failures=0;
|
||||
|
||||
failures+=Tests.test("Math.acos", input, Math::acos, expected);
|
||||
failures+=Tests.test("StrictMath.acos", input, StrictMath::acos, expected);
|
||||
|
||||
return failures;
|
||||
}
|
||||
|
||||
/**
|
||||
* From the spec for Math.atan:
|
||||
*
|
||||
* "Special cases:
|
||||
*
|
||||
* If the argument is NaN, then the result is NaN.
|
||||
*
|
||||
* If the argument is zero, then the result is a zero with the
|
||||
* same sign as the argument.
|
||||
*
|
||||
* If the argument is infinite, then the result is the closest
|
||||
* value to pi/2 with the same sign as the input."
|
||||
*/
|
||||
private static int testAtanSpecialCases() {
|
||||
int failures = 0;
|
||||
|
||||
double [][] testCases = {
|
||||
{NaNd, NaNd},
|
||||
|
||||
{-0.0, -0.0},
|
||||
{+0.0, +0.0},
|
||||
|
||||
{ InfinityD, +Math.PI/2.0},
|
||||
{-InfinityD, -Math.PI/2.0},
|
||||
};
|
||||
|
||||
for(int i = 0; i < testCases.length; i++) {
|
||||
failures += testAtanCase(testCases[i][0],
|
||||
testCases[i][1]);
|
||||
}
|
||||
|
||||
return failures;
|
||||
}
|
||||
|
||||
private static int testAtanCase(double input, double expected) {
|
||||
int failures=0;
|
||||
|
||||
failures+=Tests.test("Math.atan", input, Math::atan, expected);
|
||||
failures+=Tests.test("StrictMath.atan", input, StrictMath::atan, expected);
|
||||
|
||||
return failures;
|
||||
}
|
||||
}
|
||||
|
|
@ -23,7 +23,7 @@
|
|||
|
||||
/*
|
||||
* @test
|
||||
* @bug 8301833
|
||||
* @bug 8301833 8302026
|
||||
* @build Tests
|
||||
* @build FdlibmTranslit
|
||||
* @build ExhaustingTests
|
||||
|
|
@ -84,9 +84,9 @@ public class ExhaustingTests {
|
|||
// new UnaryTestCase("cos", FdlibmTranslit::cos, StrictMath::cos, DEFAULT_SHIFT),
|
||||
// new UnaryTestCase("tan", FdlibmTranslit::tan, StrictMath::tan, DEFAULT_SHIFT),
|
||||
|
||||
// new UnaryTestCase("asin", FdlibmTranslit::asin, StrictMath::asin, DEFAULT_SHIFT),
|
||||
// new UnaryTestCase("acos", FdlibmTranslit::acos, StrictMath::acos, DEFAULT_SHIFT),
|
||||
// new UnaryTestCase("atan", FdlibmTranslit::atan, StrictMath::atan, DEFAULT_SHIFT),
|
||||
new UnaryTestCase("asin", FdlibmTranslit::asin, StrictMath::asin, DEFAULT_SHIFT),
|
||||
new UnaryTestCase("acos", FdlibmTranslit::acos, StrictMath::acos, DEFAULT_SHIFT),
|
||||
new UnaryTestCase("atan", FdlibmTranslit::atan, StrictMath::atan, DEFAULT_SHIFT),
|
||||
};
|
||||
|
||||
for (var testCase : testCases) {
|
||||
|
|
|
|||
|
|
@ -70,6 +70,18 @@ public class FdlibmTranslit {
|
|||
( ((long)high)) << 32 );
|
||||
}
|
||||
|
||||
public static double asin(double x) {
|
||||
return Asin.compute(x);
|
||||
}
|
||||
|
||||
public static double acos(double x) {
|
||||
return Acos.compute(x);
|
||||
}
|
||||
|
||||
public static double atan(double x) {
|
||||
return Atan.compute(x);
|
||||
}
|
||||
|
||||
public static double hypot(double x, double y) {
|
||||
return Hypot.compute(x, y);
|
||||
}
|
||||
|
|
@ -94,6 +106,279 @@ public class FdlibmTranslit {
|
|||
return Expm1.compute(x);
|
||||
}
|
||||
|
||||
/** Returns the arcsine of x.
|
||||
*
|
||||
* Method :
|
||||
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
|
||||
* we approximate asin(x) on [0,0.5] by
|
||||
* asin(x) = x + x*x^2*R(x^2)
|
||||
* where
|
||||
* R(x^2) is a rational approximation of (asin(x)-x)/x^3
|
||||
* and its remez error is bounded by
|
||||
* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
|
||||
*
|
||||
* For x in [0.5,1]
|
||||
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
|
||||
* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
|
||||
* then for x>0.98
|
||||
* asin(x) = pi/2 - 2*(s+s*z*R(z))
|
||||
* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
|
||||
* For x<=0.98, let pio4_hi = pio2_hi/2, then
|
||||
* f = hi part of s;
|
||||
* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
|
||||
* and
|
||||
* asin(x) = pi/2 - 2*(s+s*z*R(z))
|
||||
* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
|
||||
* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
|
||||
*
|
||||
* Special cases:
|
||||
* if x is NaN, return x itself;
|
||||
* if |x|>1, return NaN with invalid signal.
|
||||
*
|
||||
*/
|
||||
static class Asin {
|
||||
private static final double
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
huge = 1.000e+300,
|
||||
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
|
||||
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
|
||||
pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
|
||||
/* coefficient for R(x^2) */
|
||||
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
|
||||
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
|
||||
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
|
||||
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
|
||||
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
|
||||
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
|
||||
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
|
||||
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
|
||||
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
|
||||
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
|
||||
|
||||
static double compute(double x) {
|
||||
double t=0,w,p,q,c,r,s;
|
||||
int hx,ix;
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>= 0x3ff00000) { /* |x|>= 1 */
|
||||
if(((ix-0x3ff00000)|__LO(x))==0)
|
||||
/* asin(1)=+-pi/2 with inexact */
|
||||
return x*pio2_hi+x*pio2_lo;
|
||||
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
|
||||
} else if (ix<0x3fe00000) { /* |x|<0.5 */
|
||||
if(ix<0x3e400000) { /* if |x| < 2**-27 */
|
||||
if(huge+x>one) 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 = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
|
||||
w = p/q;
|
||||
return x+x*w;
|
||||
}
|
||||
/* 1> |x|>= 0.5 */
|
||||
w = one-Math.abs(x);
|
||||
t = w*0.5;
|
||||
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
|
||||
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
|
||||
s = Math.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;
|
||||
// __LO(w) = 0;
|
||||
w = __LO(w, 0);
|
||||
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);
|
||||
}
|
||||
if(hx>0) return t; else return -t;
|
||||
}
|
||||
}
|
||||
|
||||
/** Returns the arccosine of x.
|
||||
* Method :
|
||||
* acos(x) = pi/2 - asin(x)
|
||||
* acos(-x) = pi/2 + asin(x)
|
||||
* For |x|<=0.5
|
||||
* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
|
||||
* For x>0.5
|
||||
* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
|
||||
* = 2asin(sqrt((1-x)/2))
|
||||
* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
|
||||
* = 2f + (2c + 2s*z*R(z))
|
||||
* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
|
||||
* for f so that f+c ~ sqrt(z).
|
||||
* For x<-0.5
|
||||
* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
|
||||
* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
|
||||
*
|
||||
* Special cases:
|
||||
* if x is NaN, return x itself;
|
||||
* if |x|>1, return NaN with invalid signal.
|
||||
*
|
||||
* Function needed: sqrt
|
||||
*/
|
||||
static class Acos {
|
||||
private static final double
|
||||
one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
|
||||
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
|
||||
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
|
||||
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
|
||||
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
|
||||
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
|
||||
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
|
||||
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
|
||||
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
|
||||
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
|
||||
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
|
||||
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
|
||||
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
|
||||
|
||||
static double compute(double x) {
|
||||
double z,p,q,r,w,s,c,df;
|
||||
int hx,ix;
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x3ff00000) { /* |x| >= 1 */
|
||||
if(((ix-0x3ff00000)|__LO(x))==0) { /* |x|==1 */
|
||||
if(hx>0) return 0.0; /* acos(1) = 0 */
|
||||
else return pi+2.0*pio2_lo; /* acos(-1)= pi */
|
||||
}
|
||||
return (x-x)/(x-x); /* 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 = one+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 = (one+x)*0.5;
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
s = Math.sqrt(z);
|
||||
r = p/q;
|
||||
w = r*s-pio2_lo;
|
||||
return pi - 2.0*(s+w);
|
||||
} else { /* x > 0.5 */
|
||||
z = (one-x)*0.5;
|
||||
s = Math.sqrt(z);
|
||||
df = s;
|
||||
// __LO(df) = 0;
|
||||
df = __LO(df, 0);
|
||||
c = (z-df*df)/(s+df);
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
r = p/q;
|
||||
w = r*s+c;
|
||||
return 2.0*(df+w);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* Returns the arctangent of x.
|
||||
* Method
|
||||
* 1. Reduce x to positive by atan(x) = -atan(-x).
|
||||
* 2. According to the integer k=4t+0.25 chopped, t=x, the argument
|
||||
* is further reduced to one of the following intervals and the
|
||||
* arctangent of t is evaluated by the corresponding formula:
|
||||
*
|
||||
* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
|
||||
* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
|
||||
* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
|
||||
* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
|
||||
* [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
static class Atan {
|
||||
private static final double atanhi[] = {
|
||||
4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
|
||||
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
|
||||
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
|
||||
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
|
||||
};
|
||||
|
||||
private static final double atanlo[] = {
|
||||
2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
|
||||
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
|
||||
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
|
||||
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
|
||||
};
|
||||
|
||||
private static final double aT[] = {
|
||||
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
|
||||
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
|
||||
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
|
||||
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
|
||||
9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
|
||||
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
|
||||
6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
|
||||
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
|
||||
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
|
||||
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
|
||||
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
|
||||
};
|
||||
|
||||
private static final double
|
||||
one = 1.0,
|
||||
huge = 1.0e300;
|
||||
|
||||
static double compute(double x) {
|
||||
double w,s1,s2,z;
|
||||
int ix,hx,id;
|
||||
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x44100000) { /* if |x| >= 2^66 */
|
||||
if(ix>0x7ff00000||
|
||||
(ix==0x7ff00000&&(__LO(x)!=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>one) 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-one)/(2.0+x);
|
||||
} else { /* 11/16<=|x|< 19/16 */
|
||||
id = 1; x = (x-one)/(x+one);
|
||||
}
|
||||
} else {
|
||||
if (ix < 0x40038000) { /* |x| < 2.4375 */
|
||||
id = 2; x = (x-1.5)/(one+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*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
|
||||
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
|
||||
if (id<0) return x - x*(s1+s2);
|
||||
else {
|
||||
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
|
||||
return (hx<0)? -z:z;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* cbrt(x)
|
||||
* Return cube root of x
|
||||
|
|
|
|||
226
test/jdk/java/lang/StrictMath/InverseTrigTests.java
Normal file
226
test/jdk/java/lang/StrictMath/InverseTrigTests.java
Normal file
|
|
@ -0,0 +1,226 @@
|
|||
/*
|
||||
* Copyright (c) 2003, 2023, 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.
|
||||
*
|
||||
* This code is distributed in the hope that it will be useful, but WITHOUT
|
||||
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
|
||||
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
|
||||
* version 2 for more details (a copy is included in the LICENSE file that
|
||||
* accompanied this code).
|
||||
*
|
||||
* You should have received a copy of the GNU General Public License version
|
||||
* 2 along with this work; if not, write to the Free Software Foundation,
|
||||
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
import jdk.test.lib.RandomFactory;
|
||||
import java.util.function.DoubleUnaryOperator;
|
||||
|
||||
/*
|
||||
* @test
|
||||
* @bug 8302026
|
||||
* @key randomness
|
||||
* @library /test/lib
|
||||
* @build jdk.test.lib.RandomFactory
|
||||
* @build Tests
|
||||
* @build FdlibmTranslit
|
||||
* @build InverseTrigTests
|
||||
* @run main InverseTrigTests
|
||||
* @summary Tests for StrictMath.{asin, acos, atan}
|
||||
*/
|
||||
|
||||
/**
|
||||
* The tests in ../Math/InverseTrigTests.java test properties that
|
||||
* should hold for any implementation of the inverse trig functions
|
||||
* ason, acos, and atan, including the FDLIBM-based ones required by
|
||||
* the StrictMath class. Therefore, the test cases in
|
||||
* ../Math/InverseTrig.java are run against both the Math and
|
||||
* StrictMath versions of the inverse trig methods. The role of this
|
||||
* test is to verify that the FDLIBM algorithms are being used by
|
||||
* running golden file tests on values that may vary from one
|
||||
* conforming implementation of the hyperbolics to another.
|
||||
*/
|
||||
|
||||
public class InverseTrigTests {
|
||||
private InverseTrigTests(){}
|
||||
|
||||
public static void main(String... args) {
|
||||
int failures = 0;
|
||||
|
||||
failures += testAgainstTranslitCommon();
|
||||
|
||||
failures += testAgainstTranslitAsin();
|
||||
failures += testAgainstTranslitAcos();
|
||||
failures += testAgainstTranslitAtan();
|
||||
|
||||
if (failures > 0) {
|
||||
System.err.println("Testing the inverse trig functions incurred "
|
||||
+ failures + " failures.");
|
||||
throw new RuntimeException();
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Bundle together groups of testing methods.
|
||||
*/
|
||||
private static enum InverseTrigTest {
|
||||
ASIN(InverseTrigTests::testAsinCase, FdlibmTranslit::asin),
|
||||
ACOS(InverseTrigTests::testAcosCase, FdlibmTranslit::acos),
|
||||
ATAN(InverseTrigTests::testAtanCase, FdlibmTranslit::atan);
|
||||
|
||||
private DoubleDoubleToInt testCase;
|
||||
private DoubleUnaryOperator transliteration;
|
||||
|
||||
InverseTrigTest(DoubleDoubleToInt testCase, DoubleUnaryOperator transliteration) {
|
||||
this.testCase = testCase;
|
||||
this.transliteration = transliteration;
|
||||
}
|
||||
|
||||
public DoubleDoubleToInt testCase() {return testCase;}
|
||||
public DoubleUnaryOperator transliteration() {return transliteration;}
|
||||
}
|
||||
|
||||
// Initialize shared random number generator
|
||||
private static java.util.Random random = RandomFactory.getRandom();
|
||||
|
||||
/**
|
||||
* Test against shared points of interest.
|
||||
*/
|
||||
private static int testAgainstTranslitCommon() {
|
||||
int failures = 0;
|
||||
double[] pointsOfInterest = {
|
||||
Double.MIN_NORMAL,
|
||||
1.0,
|
||||
Tests.createRandomDouble(random),
|
||||
};
|
||||
|
||||
for (var testMethods : InverseTrigTest.values()) {
|
||||
for (double testPoint : pointsOfInterest) {
|
||||
failures += testRangeMidpoint(testPoint, Math.ulp(testPoint), 1000, testMethods);
|
||||
}
|
||||
}
|
||||
|
||||
return failures;
|
||||
}
|
||||
|
||||
/**
|
||||
* Test StrictMath.asin against transliteration port of asin.
|
||||
*/
|
||||
private static int testAgainstTranslitAsin() {
|
||||
int failures = 0;
|
||||
|
||||
// Probe near decision points in the FDLIBM algorithm.
|
||||
double[] decisionPoints = {
|
||||
0x1p-27,
|
||||
-0x1p-27,
|
||||
|
||||
0.5,
|
||||
-0.5,
|
||||
|
||||
0.975,
|
||||
-0.975,
|
||||
};
|
||||
|
||||
for (double testPoint : decisionPoints) {
|
||||
failures += testRangeMidpoint(testPoint, Math.ulp(testPoint), 1000, InverseTrigTest.ASIN);
|
||||
}
|
||||
|
||||
return failures;
|
||||
}
|
||||
|
||||
/**
|
||||
* Test StrictMath.acos against transliteration port of acos.
|
||||
*/
|
||||
private static int testAgainstTranslitAcos() {
|
||||
int failures = 0;
|
||||
|
||||
// Probe near decision points in the FDLIBM algorithm.
|
||||
double[] decisionPoints = {
|
||||
0.5,
|
||||
-0.5,
|
||||
|
||||
0x1.0p-57,
|
||||
-0x1.0p-57,
|
||||
};
|
||||
|
||||
for (double testPoint : decisionPoints) {
|
||||
failures += testRangeMidpoint(testPoint, Math.ulp(testPoint), 1000, InverseTrigTest.ACOS);
|
||||
}
|
||||
|
||||
return failures;
|
||||
}
|
||||
|
||||
/**
|
||||
* Test StrictMath.atan against transliteration port of atan
|
||||
*/
|
||||
private static int testAgainstTranslitAtan() {
|
||||
int failures = 0;
|
||||
|
||||
// Probe near decision points in the FDLIBM algorithm.
|
||||
double[] decisionPoints = {
|
||||
0.0,
|
||||
|
||||
7.0/16.0,
|
||||
11.0/16.0,
|
||||
19.0/16.0,
|
||||
39.0/16.0,
|
||||
|
||||
0x1.0p66,
|
||||
0x1.0p-29,
|
||||
};
|
||||
|
||||
for (double testPoint : decisionPoints) {
|
||||
failures += testRangeMidpoint(testPoint, Math.ulp(testPoint), 1000, InverseTrigTest.ATAN);
|
||||
}
|
||||
|
||||
return failures;
|
||||
}
|
||||
|
||||
private interface DoubleDoubleToInt {
|
||||
int apply(double x, double y);
|
||||
}
|
||||
|
||||
private static int testRange(double start, double increment, int count,
|
||||
InverseTrigTest testMethods) {
|
||||
int failures = 0;
|
||||
double x = start;
|
||||
for (int i = 0; i < count; i++, x += increment) {
|
||||
failures +=
|
||||
testMethods.testCase().apply(x, testMethods.transliteration().applyAsDouble(x));
|
||||
}
|
||||
return failures;
|
||||
}
|
||||
|
||||
private static int testRangeMidpoint(double midpoint, double increment, int count,
|
||||
InverseTrigTest testMethods) {
|
||||
int failures = 0;
|
||||
double x = midpoint - increment*(count / 2) ;
|
||||
for (int i = 0; i < count; i++, x += increment) {
|
||||
failures +=
|
||||
testMethods.testCase().apply(x, testMethods.transliteration().applyAsDouble(x));
|
||||
}
|
||||
return failures;
|
||||
}
|
||||
|
||||
private static int testAsinCase(double input, double expected) {
|
||||
return Tests.test("StrictMath.asin(double)", input,
|
||||
StrictMath::asin, expected);
|
||||
}
|
||||
|
||||
private static int testAcosCase(double input, double expected) {
|
||||
return Tests.test("StrictMath.acos(double)", input,
|
||||
StrictMath::acos, expected);
|
||||
}
|
||||
|
||||
private static int testAtanCase(double input, double expected) {
|
||||
return Tests.test("StrictMath.atan(double)", input,
|
||||
StrictMath::atan, expected);
|
||||
}
|
||||
}
|
||||
Loading…
Add table
Add a link
Reference in a new issue