8302040: Port fdlibm sqrt to Java
Reviewed-by: bpb, thartmann, aturbanov
This commit is contained in:
parent
6423065b7d
commit
61e8867591
src
hotspot/share
java.base/share/classes/java/lang
test/jdk/java/lang
@ -202,8 +202,8 @@ class methodHandle;
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do_intrinsic(_maxF_strict, java_lang_StrictMath, max_name, float2_float_signature, F_S) \
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do_intrinsic(_minD_strict, java_lang_StrictMath, min_name, double2_double_signature, F_S) \
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do_intrinsic(_maxD_strict, java_lang_StrictMath, max_name, double2_double_signature, F_S) \
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/* Special flavor of dsqrt intrinsic to handle the "native" method in StrictMath. Otherwise the same as in Math. */ \
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do_intrinsic(_dsqrt_strict, java_lang_StrictMath, sqrt_name, double_double_signature, F_SN) \
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/* Additional dsqrt intrinsic to directly handle the sqrt method in StrictMath. Otherwise the same as in Math. */ \
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do_intrinsic(_dsqrt_strict, java_lang_StrictMath, sqrt_name, double_double_signature, F_S) \
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\
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do_intrinsic(_floatIsInfinite, java_lang_Float, isInfinite_name, float_bool_signature, F_S) \
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do_name( isInfinite_name, "isInfinite") \
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@ -148,7 +148,7 @@ AbstractInterpreter::MethodKind AbstractInterpreter::method_kind(const methodHan
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case vmIntrinsics::_fmaD: return java_lang_math_fmaD;
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case vmIntrinsics::_fmaF: return java_lang_math_fmaF;
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case vmIntrinsics::_dsqrt: return java_lang_math_sqrt;
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case vmIntrinsics::_dsqrt_strict: return native;
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case vmIntrinsics::_dsqrt_strict: return java_lang_math_sqrt;
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case vmIntrinsics::_Reference_get: return java_lang_ref_reference_get;
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case vmIntrinsics::_Object_init:
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if (RegisterFinalizersAtInit && m->code_size() == 1) {
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@ -104,6 +104,15 @@ class FdLibm {
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( ((long)high)) << 32 );
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}
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/**
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* Return a double with its high-order bits of the first argument
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* and the low-order bits of the second argument..
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*/
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private static double __HI_LO(int high, int low) {
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return Double.longBitsToDouble(((long)high << 32) |
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(low & 0xffff_ffffL));
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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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@ -504,6 +513,449 @@ class FdLibm {
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}
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}
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/**
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* Return correctly rounded sqrt.
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* ------------------------------------------
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* | Use the hardware sqrt if you have one |
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* ------------------------------------------
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* Method:
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* Bit by bit method using integer arithmetic. (Slow, but portable)
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* 1. Normalization
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* Scale x to y in [1,4) with even powers of 2:
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* find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
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* sqrt(x) = 2^k * sqrt(y)
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* 2. Bit by bit computation
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* Let q = sqrt(y) truncated to i bit after binary point (q = 1),
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* i 0
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* i+1 2
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* s = 2*q , and y = 2 * ( y - q ). (1)
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* i i i i
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*
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* To compute q from q , one checks whether
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* i+1 i
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*
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* -(i+1) 2
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* (q + 2 ) <= y. (2)
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* i
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* -(i+1)
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* If (2) is false, then q = q ; otherwise q = q + 2 .
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* i+1 i i+1 i
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*
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* With some algebraic manipulation, it is not difficult to see
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* that (2) is equivalent to
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* -(i+1)
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* s + 2 <= y (3)
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* i i
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*
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* The advantage of (3) is that s and y can be computed by
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* i i
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* the following recurrence formula:
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* if (3) is false
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*
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* s = s , y = y ; (4)
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* i+1 i i+1 i
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*
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* otherwise,
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* -i -(i+1)
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* s = s + 2 , y = y - s - 2 (5)
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* i+1 i i+1 i i
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*
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* One may easily use induction to prove (4) and (5).
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* Note. Since the left hand side of (3) contain only i+2 bits,
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* it does not necessary to do a full (53-bit) comparison
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* in (3).
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* 3. Final rounding
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* After generating the 53 bits result, we compute one more bit.
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* Together with the remainder, we can decide whether the
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* result is exact, bigger than 1/2ulp, or less than 1/2ulp
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* (it will never equal to 1/2ulp).
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* The rounding mode can be detected by checking whether
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* huge + tiny is equal to huge, and whether huge - tiny is
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* equal to huge for some floating point number "huge" and "tiny".
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*
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* Special cases:
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* sqrt(+-0) = +-0 ... exact
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* sqrt(inf) = inf
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* sqrt(-ve) = NaN ... with invalid signal
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* sqrt(NaN) = NaN ... with invalid signal for signaling NaN
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*
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* Other methods : see the appended file at the end of the program below.
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*---------------
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*/
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static class Sqrt {
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private Sqrt() {throw new UnsupportedOperationException();}
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private static final double tiny = 1.0e-300;
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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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/*unsigned*/ int r, t1, s1, ix1, q1;
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int ix0, s0, q, m, t, i;
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ix0 = __HI(x); // high word of x
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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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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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if (ix0 <= 0) {
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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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}
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// normalize x
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m = (ix0 >> 20);
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if (m == 0) { // subnormal x
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while (ix0 == 0) {
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m -= 21;
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ix0 |= (ix1 >>> 11); // unsigned shift
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ix1 <<= 21;
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}
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for(i = 0; (ix0 & 0x0010_0000) == 0; i++) {
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ix0 <<= 1;
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}
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m -= i-1;
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ix0 |= (ix1 >>> (32 - i)); // unsigned shift
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ix1 <<= i;
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}
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m -= 1023; // unbias exponent */
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ix0 = (ix0 & 0x000f_ffff) | 0x0010_0000;
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if ((m & 1) != 0){ // odd m, double x to make it even
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ix0 += ix0 + ((ix1 & sign) >>> 31); // unsigned shift
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ix1 += ix1;
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}
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m >>= 1; // m = [m/2]
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// generate sqrt(x) bit by bit
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ix0 += ix0 + ((ix1 & sign) >>> 31); // unsigned shift
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ix1 += ix1;
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q = q1 = s0 = s1 = 0; // [q,q1] = sqrt(x)
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r = 0x0020_0000; // r = moving bit from right to left
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while (r != 0) {
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t = s0 + r;
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if (t <= ix0) {
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s0 = t + r;
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ix0 -= t;
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q += r;
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}
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ix0 += ix0 + ((ix1 & sign) >>> 31); // unsigned shift
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ix1 += ix1;
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r >>>= 1; // unsigned shift
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}
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r = sign;
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while (r != 0) {
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t1 = s1 + r;
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t = s0;
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if ((t < ix0) ||
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((t == ix0) && (Integer.compareUnsigned(t1, ix1) <= 0 ))) { // t1 <= ix1
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s1 = t1 + r;
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if (((t1 & sign) == sign) && (s1 & sign) == 0) {
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s0 += 1;
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}
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ix0 -= t;
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if (Integer.compareUnsigned(ix1, t1) < 0) { // ix1 < t1
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ix0 -= 1;
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}
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ix1 -= t1;
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q1 += r;
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}
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ix0 += ix0 + ((ix1 & sign) >>> 31); // unsigned shift
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ix1 += ix1;
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r >>>= 1; // unsigned shift
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}
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// use floating add to find out rounding direction
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if ((ix0 | ix1) != 0) {
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z = 1.0 - tiny; // trigger inexact flag
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if (z >= 1.0) {
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z = 1.0 + tiny;
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if (q1 == 0xffff_ffff) {
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q1 = 0;
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q += 1;
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} else if (z > 1.0) {
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if (q1 == 0xffff_fffe) {
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q += 1;
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}
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q1 += 2;
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} else {
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q1 += (q1 & 1);
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}
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}
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}
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ix0 = (q >> 1) + 0x3fe0_0000;
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ix1 = q1 >>> 1; // unsigned shift
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if ((q & 1) == 1) {
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ix1 |= sign;
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}
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ix0 += (m << 20);
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return __HI_LO(ix0, ix1);
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}
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}
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// The following comment is supplementary information from the FDLIBM sources.
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/*
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* Other methods (use floating-point arithmetic)
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* -------------
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* (This is a copy of a drafted paper by Prof W. Kahan
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* and K.C. Ng, written in May, 1986)
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*
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* Two algorithms are given here to implement sqrt(x)
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* (IEEE double precision arithmetic) in software.
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* Both supply sqrt(x) correctly rounded. The first algorithm (in
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* Section A) uses newton iterations and involves four divisions.
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* The second one uses reciproot iterations to avoid division, but
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* requires more multiplications. Both algorithms need the ability
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* to chop results of arithmetic operations instead of round them,
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* and the INEXACT flag to indicate when an arithmetic operation
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* is executed exactly with no roundoff error, all part of the
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* standard (IEEE 754-1985). The ability to perform shift, add,
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* subtract and logical AND operations upon 32-bit words is needed
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* too, though not part of the standard.
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*
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* A. sqrt(x) by Newton Iteration
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*
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* (1) Initial approximation
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*
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* Let x0 and x1 be the leading and the trailing 32-bit words of
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* a floating point number x (in IEEE double format) respectively
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*
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* 1 11 52 ...widths
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* ------------------------------------------------------
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* x: |s| e | f |
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* ------------------------------------------------------
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* msb lsb msb lsb ...order
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*
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*
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* ------------------------ ------------------------
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* x0: |s| e | f1 | x1: | f2 |
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* ------------------------ ------------------------
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*
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* By performing shifts and subtracts on x0 and x1 (both regarded
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* as integers), we obtain an 8-bit approximation of sqrt(x) as
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* follows.
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*
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* k := (x0>>1) + 0x1ff80000;
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* y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits
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* Here k is a 32-bit integer and T1[] is an integer array containing
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* correction terms. Now magically the floating value of y (y's
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* leading 32-bit word is y0, the value of its trailing word is 0)
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* approximates sqrt(x) to almost 8-bit.
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*
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* Value of T1:
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* static int T1[32]= {
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* 0, 1024, 3062, 5746, 9193, 13348, 18162, 23592,
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* 29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215,
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* 83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581,
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* 16499, 12183, 8588, 5674, 3403, 1742, 661, 130,};
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*
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* (2) Iterative refinement
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*
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* Apply Heron's rule three times to y, we have y approximates
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* sqrt(x) to within 1 ulp (Unit in the Last Place):
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*
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* y := (y+x/y)/2 ... almost 17 sig. bits
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* y := (y+x/y)/2 ... almost 35 sig. bits
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* y := y-(y-x/y)/2 ... within 1 ulp
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*
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*
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* Remark 1.
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* Another way to improve y to within 1 ulp is:
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*
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* y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x)
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* y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x)
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*
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* 2
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* (x-y )*y
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* y := y + 2* ---------- ...within 1 ulp
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* 2
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* 3y + x
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*
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*
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* This formula has one division fewer than the one above; however,
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* it requires more multiplications and additions. Also x must be
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* scaled in advance to avoid spurious overflow in evaluating the
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* expression 3y*y+x. Hence it is not recommended uless division
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* is slow. If division is very slow, then one should use the
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* reciproot algorithm given in section B.
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*
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* (3) Final adjustment
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*
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* By twiddling y's last bit it is possible to force y to be
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* correctly rounded according to the prevailing rounding mode
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* as follows. Let r and i be copies of the rounding mode and
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* inexact flag before entering the square root program. Also we
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* use the expression y+-ulp for the next representable floating
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* numbers (up and down) of y. Note that y+-ulp = either fixed
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* point y+-1, or multiply y by nextafter(1,+-inf) in chopped
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* mode.
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*
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* I := FALSE; ... reset INEXACT flag I
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* R := RZ; ... set rounding mode to round-toward-zero
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* z := x/y; ... chopped quotient, possibly inexact
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* If(not I) then { ... if the quotient is exact
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* if(z=y) {
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* I := i; ... restore inexact flag
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* R := r; ... restore rounded mode
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* return sqrt(x):=y.
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* } else {
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* z := z - ulp; ... special rounding
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* }
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* }
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* i := TRUE; ... sqrt(x) is inexact
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* If (r=RN) then z=z+ulp ... rounded-to-nearest
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* If (r=RP) then { ... round-toward-+inf
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* y = y+ulp; z=z+ulp;
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* }
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* y := y+z; ... chopped sum
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* y0:=y0-0x00100000; ... y := y/2 is correctly rounded.
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* I := i; ... restore inexact flag
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* R := r; ... restore rounded mode
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* return sqrt(x):=y.
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*
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* (4) Special cases
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*
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* Square root of +inf, +-0, or NaN is itself;
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* Square root of a negative number is NaN with invalid signal.
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*
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*
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* B. sqrt(x) by Reciproot Iteration
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*
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* (1) Initial approximation
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*
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* Let x0 and x1 be the leading and the trailing 32-bit words of
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* a floating point number x (in IEEE double format) respectively
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* (see section A). By performing shifs and subtracts on x0 and y0,
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* we obtain a 7.8-bit approximation of 1/sqrt(x) as follows.
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*
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* k := 0x5fe80000 - (x0>>1);
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* y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits
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*
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* Here k is a 32-bit integer and T2[] is an integer array
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* containing correction terms. Now magically the floating
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* value of y (y's leading 32-bit word is y0, the value of
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* its trailing word y1 is set to zero) approximates 1/sqrt(x)
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* to almost 7.8-bit.
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*
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* Value of T2:
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* static int T2[64]= {
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* 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
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* 0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
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* 0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
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* 0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
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* 0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
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* 0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
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* 0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
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* 0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,};
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*
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* (2) Iterative refinement
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*
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* Apply Reciproot iteration three times to y and multiply the
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* result by x to get an approximation z that matches sqrt(x)
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* to about 1 ulp. To be exact, we will have
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* -1ulp < sqrt(x)-z<1.0625ulp.
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*
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* ... set rounding mode to Round-to-nearest
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* y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x)
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* y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x)
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* ... special arrangement for better accuracy
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* z := x*y ... 29 bits to sqrt(x), with z*y<1
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* z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x)
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*
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* Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that
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* (a) the term z*y in the final iteration is always less than 1;
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* (b) the error in the final result is biased upward so that
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* -1 ulp < sqrt(x) - z < 1.0625 ulp
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* instead of |sqrt(x)-z|<1.03125ulp.
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*
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* (3) Final adjustment
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*
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* By twiddling y's last bit it is possible to force y to be
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* correctly rounded according to the prevailing rounding mode
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* as follows. Let r and i be copies of the rounding mode and
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* inexact flag before entering the square root program. Also we
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* use the expression y+-ulp for the next representable floating
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* numbers (up and down) of y. Note that y+-ulp = either fixed
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* point y+-1, or multiply y by nextafter(1,+-inf) in chopped
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* mode.
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||||
*
|
||||
* R := RZ; ... set rounding mode to round-toward-zero
|
||||
* switch(r) {
|
||||
* case RN: ... round-to-nearest
|
||||
* if(x<= z*(z-ulp)...chopped) z = z - ulp; else
|
||||
* if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp;
|
||||
* break;
|
||||
* case RZ:case RM: ... round-to-zero or round-to--inf
|
||||
* R:=RP; ... reset rounding mod to round-to-+inf
|
||||
* if(x<z*z ... rounded up) z = z - ulp; else
|
||||
* if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp;
|
||||
* break;
|
||||
* case RP: ... round-to-+inf
|
||||
* if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else
|
||||
* if(x>z*z ...chopped) z = z+ulp;
|
||||
* break;
|
||||
* }
|
||||
*
|
||||
* Remark 3. The above comparisons can be done in fixed point. For
|
||||
* example, to compare x and w=z*z chopped, it suffices to compare
|
||||
* x1 and w1 (the trailing parts of x and w), regarding them as
|
||||
* two's complement integers.
|
||||
*
|
||||
* ...Is z an exact square root?
|
||||
* To determine whether z is an exact square root of x, let z1 be the
|
||||
* trailing part of z, and also let x0 and x1 be the leading and
|
||||
* trailing parts of x.
|
||||
*
|
||||
* If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0
|
||||
* I := 1; ... Raise Inexact flag: z is not exact
|
||||
* else {
|
||||
* j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2
|
||||
* k := z1 >> 26; ... get z's 25-th and 26-th
|
||||
* fraction bits
|
||||
* I := i or (k&j) or ((k&(j+j+1))!=(x1&3));
|
||||
* }
|
||||
* R:= r ... restore rounded mode
|
||||
* return sqrt(x):=z.
|
||||
*
|
||||
* If multiplication is cheaper then the foregoing red tape, the
|
||||
* Inexact flag can be evaluated by
|
||||
*
|
||||
* I := i;
|
||||
* I := (z*z!=x) or I.
|
||||
*
|
||||
* Note that z*z can overwrite I; this value must be sensed if it is
|
||||
* True.
|
||||
*
|
||||
* Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be
|
||||
* zero.
|
||||
*
|
||||
* --------------------
|
||||
* z1: | f2 |
|
||||
* --------------------
|
||||
* bit 31 bit 0
|
||||
*
|
||||
* Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd
|
||||
* or even of logb(x) have the following relations:
|
||||
*
|
||||
* -------------------------------------------------
|
||||
* bit 27,26 of z1 bit 1,0 of x1 logb(x)
|
||||
* -------------------------------------------------
|
||||
* 00 00 odd and even
|
||||
* 01 01 even
|
||||
* 10 10 odd
|
||||
* 10 00 even
|
||||
* 11 01 even
|
||||
* -------------------------------------------------
|
||||
*
|
||||
* (4) Special cases (see (4) of Section A).
|
||||
*/
|
||||
|
||||
/**
|
||||
* cbrt(x)
|
||||
* Return cube root of x
|
||||
|
@ -310,7 +310,9 @@ public final class StrictMath {
|
||||
* @return the positive square root of {@code a}.
|
||||
*/
|
||||
@IntrinsicCandidate
|
||||
public static native double sqrt(double a);
|
||||
public static double sqrt(double a) {
|
||||
return FdLibm.Sqrt.compute(a);
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns the cube root of a {@code double} value. For
|
||||
|
105
test/jdk/java/lang/Math/SqrtTests.java
Normal file
105
test/jdk/java/lang/Math/SqrtTests.java
Normal file
@ -0,0 +1,105 @@
|
||||
/*
|
||||
* 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
|
||||
* @library /test/lib
|
||||
* @build Tests
|
||||
* @run main SqrtTests
|
||||
* @bug 8302040
|
||||
* @summary Tests for {Math, StrictMath}.sqrt
|
||||
*/
|
||||
|
||||
public class SqrtTests {
|
||||
private SqrtTests(){}
|
||||
|
||||
public static void main(String... argv) {
|
||||
int failures = 0;
|
||||
|
||||
failures += testSqrt();
|
||||
|
||||
if (failures > 0) {
|
||||
System.err.println("Testing sqrt incurred "
|
||||
+ failures + " failures.");
|
||||
throw new RuntimeException();
|
||||
}
|
||||
}
|
||||
|
||||
private static final double InfinityD = Double.POSITIVE_INFINITY;
|
||||
private static final double NaNd = Double.NaN;
|
||||
|
||||
/**
|
||||
* "Returns the correctly rounded positive square root of a double value. Special cases:
|
||||
*
|
||||
* If the argument is NaN or less than zero, then the result is NaN.
|
||||
*
|
||||
* If the argument is positive infinity, then the result is positive infinity.
|
||||
*
|
||||
* If the argument is positive zero or negative zero, then the
|
||||
* result is the same as the argument.
|
||||
*
|
||||
* Otherwise, the result is the double value closest to the true
|
||||
* mathematical square root of the argument value."
|
||||
*/
|
||||
private static int testSqrt() {
|
||||
int failures = 0;
|
||||
|
||||
for(double nan : Tests.NaNs) {
|
||||
failures += testSqrtCase(nan, NaNd);
|
||||
}
|
||||
|
||||
double [][] testCases = {
|
||||
{InfinityD, InfinityD},
|
||||
|
||||
{-Double.MIN_VALUE, NaNd},
|
||||
{-Double.MIN_NORMAL, NaNd},
|
||||
{-Double.MAX_VALUE, NaNd},
|
||||
{-InfinityD, NaNd},
|
||||
|
||||
{+0.0, +0.0},
|
||||
{-0.0, -0.0},
|
||||
|
||||
// Test some notable perfect squares
|
||||
{+0.25, +0.5},
|
||||
{+1.0, +1.0},
|
||||
{+4.0, +2.0},
|
||||
{+9.0, +3.0},
|
||||
{+0x1.ffffff0000002p1023, +0x1.ffffff8p511}
|
||||
};
|
||||
|
||||
for(int i = 0; i < testCases.length; i++) {
|
||||
failures += testSqrtCase(testCases[i][0], testCases[i][1]);
|
||||
}
|
||||
|
||||
return failures;
|
||||
}
|
||||
|
||||
private static int testSqrtCase(double input, double expected) {
|
||||
int failures=0;
|
||||
|
||||
failures+=Tests.test("Math.sqrt", input, Math::sqrt, expected);
|
||||
failures+=Tests.test("StrictMath.sqrt", input, StrictMath::sqrt, expected);
|
||||
|
||||
return failures;
|
||||
}
|
||||
}
|
@ -23,7 +23,7 @@
|
||||
|
||||
/*
|
||||
* @test
|
||||
* @bug 8301833 8302026 8301444 8302028
|
||||
* @bug 8301833 8302026 8301444 8302028 8302040
|
||||
* @build Tests
|
||||
* @build FdlibmTranslit
|
||||
* @build ExhaustingTests
|
||||
@ -66,7 +66,11 @@ public class ExhaustingTests {
|
||||
private static long testUnaryMethods() {
|
||||
long failures = 0;
|
||||
UnaryTestCase[] testCases = {
|
||||
// new UnaryTestCase("sqrt", FdlibmTranslit::sqrt, StrictMath::sqrt, DEFAULT_SHIFT),
|
||||
// Since sqrt is correctly rounded and thus for each input
|
||||
// there is one well-defined correct result, additional
|
||||
// comparison of the transliteration sqrt or StrictMath
|
||||
// sqrt could be made against Math::sqrt.
|
||||
new UnaryTestCase("sqrt", FdlibmTranslit::sqrt, StrictMath::sqrt, DEFAULT_SHIFT),
|
||||
new UnaryTestCase("cbrt", FdlibmTranslit::cbrt, StrictMath::cbrt, DEFAULT_SHIFT),
|
||||
|
||||
new UnaryTestCase("log", FdlibmTranslit::log, StrictMath::log, DEFAULT_SHIFT),
|
||||
|
@ -90,6 +90,10 @@ public class FdlibmTranslit {
|
||||
return Hypot.compute(x, y);
|
||||
}
|
||||
|
||||
public static double sqrt(double x) {
|
||||
return Sqrt.compute(x);
|
||||
}
|
||||
|
||||
public static double cbrt(double x) {
|
||||
return Cbrt.compute(x);
|
||||
}
|
||||
@ -504,6 +508,178 @@ public class FdlibmTranslit {
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Return correctly rounded sqrt.
|
||||
* ------------------------------------------
|
||||
* | Use the hardware sqrt if you have one |
|
||||
* ------------------------------------------
|
||||
* Method:
|
||||
* Bit by bit method using integer arithmetic. (Slow, but portable)
|
||||
* 1. Normalization
|
||||
* Scale x to y in [1,4) with even powers of 2:
|
||||
* find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
|
||||
* sqrt(x) = 2^k * sqrt(y)
|
||||
* 2. Bit by bit computation
|
||||
* Let q = sqrt(y) truncated to i bit after binary point (q = 1),
|
||||
* i 0
|
||||
* i+1 2
|
||||
* s = 2*q , and y = 2 * ( y - q ). (1)
|
||||
* i i i i
|
||||
*
|
||||
* To compute q from q , one checks whether
|
||||
* i+1 i
|
||||
*
|
||||
* -(i+1) 2
|
||||
* (q + 2 ) <= y. (2)
|
||||
* i
|
||||
* -(i+1)
|
||||
* If (2) is false, then q = q ; otherwise q = q + 2 .
|
||||
* i+1 i i+1 i
|
||||
*
|
||||
* With some algebraic manipulation, it is not difficult to see
|
||||
* that (2) is equivalent to
|
||||
* -(i+1)
|
||||
* s + 2 <= y (3)
|
||||
* i i
|
||||
*
|
||||
* The advantage of (3) is that s and y can be computed by
|
||||
* i i
|
||||
* the following recurrence formula:
|
||||
* if (3) is false
|
||||
*
|
||||
* s = s , y = y ; (4)
|
||||
* i+1 i i+1 i
|
||||
*
|
||||
* otherwise,
|
||||
* -i -(i+1)
|
||||
* s = s + 2 , y = y - s - 2 (5)
|
||||
* i+1 i i+1 i i
|
||||
*
|
||||
* One may easily use induction to prove (4) and (5).
|
||||
* Note. Since the left hand side of (3) contain only i+2 bits,
|
||||
* it does not necessary to do a full (53-bit) comparison
|
||||
* in (3).
|
||||
* 3. Final rounding
|
||||
* After generating the 53 bits result, we compute one more bit.
|
||||
* Together with the remainder, we can decide whether the
|
||||
* result is exact, bigger than 1/2ulp, or less than 1/2ulp
|
||||
* (it will never equal to 1/2ulp).
|
||||
* The rounding mode can be detected by checking whether
|
||||
* huge + tiny is equal to huge, and whether huge - tiny is
|
||||
* equal to huge for some floating point number "huge" and "tiny".
|
||||
*
|
||||
* Special cases:
|
||||
* sqrt(+-0) = +-0 ... exact
|
||||
* sqrt(inf) = inf
|
||||
* sqrt(-ve) = NaN ... with invalid signal
|
||||
* sqrt(NaN) = NaN ... with invalid signal for signaling NaN
|
||||
*
|
||||
* Other methods : see the appended file at the end of the program below.
|
||||
*---------------
|
||||
*/
|
||||
static class Sqrt {
|
||||
private static final double one = 1.0, tiny=1.0e-300;
|
||||
|
||||
public static double compute(double x) {
|
||||
double z = 0.0;
|
||||
int sign = (int)0x80000000;
|
||||
/*unsigned*/ int r,t1,s1,ix1,q1;
|
||||
int ix0,s0,q,m,t,i;
|
||||
|
||||
ix0 = __HI(x); /* high word of x */
|
||||
ix1 = __LO(x); /* low word of x */
|
||||
|
||||
/* take care of Inf and NaN */
|
||||
if((ix0&0x7ff00000)==0x7ff00000) {
|
||||
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
|
||||
sqrt(-inf)=sNaN */
|
||||
}
|
||||
/* take care of zero */
|
||||
if(ix0<=0) {
|
||||
if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
|
||||
else if(ix0<0)
|
||||
return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
|
||||
}
|
||||
/* normalize x */
|
||||
m = (ix0>>20);
|
||||
if(m==0) { /* subnormal x */
|
||||
while(ix0==0) {
|
||||
m -= 21;
|
||||
ix0 |= (ix1>>>11); ix1 <<= 21; // unsigned shift
|
||||
}
|
||||
for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
|
||||
m -= i-1;
|
||||
ix0 |= (ix1>>>(32-i)); // unsigned shift
|
||||
ix1 <<= i;
|
||||
}
|
||||
m -= 1023; /* unbias exponent */
|
||||
ix0 = (ix0&0x000fffff)|0x00100000;
|
||||
if((m&1) != 0){ /* odd m, double x to make it even */
|
||||
ix0 += ix0 + ((ix1&sign)>>>31); // unsigned shift
|
||||
ix1 += ix1;
|
||||
}
|
||||
m >>= 1; /* m = [m/2] */
|
||||
|
||||
/* generate sqrt(x) bit by bit */
|
||||
ix0 += ix0 + ((ix1&sign)>>>31); // unsigned shift
|
||||
ix1 += ix1;
|
||||
q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
|
||||
r = 0x00200000; /* r = moving bit from right to left */
|
||||
|
||||
while(r!=0) {
|
||||
t = s0+r;
|
||||
if(t<=ix0) {
|
||||
s0 = t+r;
|
||||
ix0 -= t;
|
||||
q += r;
|
||||
}
|
||||
ix0 += ix0 + ((ix1&sign)>>>31); // unsigned shift
|
||||
ix1 += ix1;
|
||||
r>>>=1; // unsigned shift
|
||||
}
|
||||
|
||||
r = sign;
|
||||
while(r!=0) {
|
||||
t1 = s1+r;
|
||||
t = s0;
|
||||
if((t<ix0)||((t==ix0)&&(Integer.compareUnsigned(t1, ix1) <= 0 ))) { // t1<=ix1
|
||||
s1 = t1+r;
|
||||
if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
|
||||
ix0 -= t;
|
||||
if (Integer.compareUnsigned(ix1, t1) < 0) ix0 -= 1; // ix1 < t1
|
||||
ix1 -= t1;
|
||||
q1 += r;
|
||||
}
|
||||
ix0 += ix0 + ((ix1&sign)>>>31); // unsigned shift
|
||||
ix1 += ix1;
|
||||
r>>>=1; // unsigned shift
|
||||
}
|
||||
|
||||
/* use floating add to find out rounding direction */
|
||||
if((ix0|ix1)!=0) {
|
||||
z = one-tiny; /* trigger inexact flag */
|
||||
if (z>=one) {
|
||||
z = one+tiny;
|
||||
if (q1==0xffffffff) { q1=0; q += 1;}
|
||||
else if (z>one) {
|
||||
if (q1==0xfffffffe) q+=1;
|
||||
q1+=2;
|
||||
} else
|
||||
q1 += (q1&1);
|
||||
}
|
||||
}
|
||||
ix0 = (q>>1)+0x3fe00000;
|
||||
ix1 = q1>>>1; // unsigned shift
|
||||
if ((q&1)==1) ix1 |= sign;
|
||||
ix0 += (m <<20);
|
||||
// __HI(z) = ix0;
|
||||
z = __HI(z, ix0);
|
||||
// __LO(z) = ix1;
|
||||
z = __LO(z, ix1);
|
||||
return z;
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* cbrt(x)
|
||||
* Return cube root of x
|
||||
|
130
test/jdk/java/lang/StrictMath/SqrtTests.java
Normal file
130
test/jdk/java/lang/StrictMath/SqrtTests.java
Normal file
@ -0,0 +1,130 @@
|
||||
/*
|
||||
* 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 8302040
|
||||
* @key randomness
|
||||
* @library /test/lib
|
||||
* @build jdk.test.lib.RandomFactory
|
||||
* @build Tests
|
||||
* @build FdlibmTranslit
|
||||
* @build SqrtTests
|
||||
* @run main SqrtTests
|
||||
* @summary Tests for StrictMath.sqrt
|
||||
*/
|
||||
import jdk.test.lib.RandomFactory;
|
||||
|
||||
/**
|
||||
* The tests in ../Math/SqrtTests.java test properties that should
|
||||
* hold for any sqrt implementation, including the FDLIBM-based one
|
||||
* required for StrictMath.sqrt. Therefore, the test cases in
|
||||
* ../Math/SqrtTests.java are run against both the Math and
|
||||
* StrictMath versions of sqrt. The role of this test is to verify
|
||||
* that the FDLIBM sqrt algorithm is being used by running golden
|
||||
* file tests on values that may vary from one conforming sqrt
|
||||
* implementation to another.
|
||||
*/
|
||||
|
||||
public class SqrtTests {
|
||||
private SqrtTests(){}
|
||||
|
||||
public static void main(String... args) {
|
||||
int failures = 0;
|
||||
|
||||
failures += testAgainstTranslit();
|
||||
|
||||
if (failures > 0) {
|
||||
System.err.println("Testing sqrt incurred "
|
||||
+ failures + " failures.");
|
||||
throw new RuntimeException();
|
||||
}
|
||||
}
|
||||
|
||||
// Initialize shared random number generator
|
||||
private static java.util.Random random = RandomFactory.getRandom();
|
||||
|
||||
/**
|
||||
* Test StrictMath.sqrt against transliteration port of sqrt.
|
||||
*/
|
||||
private static int testAgainstTranslit() {
|
||||
int failures = 0;
|
||||
double x;
|
||||
|
||||
// Test just above subnormal threshold...
|
||||
x = Double.MIN_NORMAL;
|
||||
failures += testRange(x, Math.ulp(x), 1000);
|
||||
|
||||
// ... and just below subnormal threshold ...
|
||||
x = Math.nextDown(Double.MIN_NORMAL);
|
||||
failures += testRange(x, -Math.ulp(x), 1000);
|
||||
|
||||
// ... and near 1.0 ...
|
||||
failures += testRangeMidpoint(1.0, Math.ulp(x), 2000);
|
||||
// (Note: probes every-other value less than 1.0 due to
|
||||
// change in the size of an ulp at 1.0.
|
||||
|
||||
// Probe near decision points in the FDLIBM algorithm.
|
||||
double[] decisionPoints = {
|
||||
Double.MIN_VALUE,
|
||||
Double.MAX_VALUE,
|
||||
};
|
||||
|
||||
for (double testPoint : decisionPoints) {
|
||||
failures += testRangeMidpoint(testPoint, Math.ulp(testPoint), 1000);
|
||||
}
|
||||
|
||||
x = Tests.createRandomDouble(random);
|
||||
|
||||
// Make the increment twice the ulp value in case the random
|
||||
// value is near an exponent threshold. Don't worry about test
|
||||
// elements overflowing to infinity if the starting value is
|
||||
// near Double.MAX_VALUE.
|
||||
failures += testRange(x, 2.0 * Math.ulp(x), 1000);
|
||||
|
||||
return failures;
|
||||
}
|
||||
|
||||
private static int testRange(double start, double increment, int count) {
|
||||
int failures = 0;
|
||||
double x = start;
|
||||
for (int i = 0; i < count; i++, x += increment) {
|
||||
failures += testSqrtCase(x, FdlibmTranslit.sqrt(x));
|
||||
}
|
||||
return failures;
|
||||
}
|
||||
|
||||
private static int testRangeMidpoint(double midpoint, double increment, int count) {
|
||||
int failures = 0;
|
||||
double x = midpoint - increment*(count / 2) ;
|
||||
for (int i = 0; i < count; i++, x += increment) {
|
||||
failures += testSqrtCase(x, FdlibmTranslit.sqrt(x));
|
||||
}
|
||||
return failures;
|
||||
}
|
||||
|
||||
private static int testSqrtCase(double input, double expected) {
|
||||
return Tests.test("StrictMath.sqrt(double)", input,
|
||||
StrictMath::sqrt, expected);
|
||||
}
|
||||
}
|
Loading…
x
Reference in New Issue
Block a user