Fix spurious and extra underflows and resulting inaccuracies for some cases
with 1 huge component and 1 tiny (but nowhere near denormal) component. Rescale earlier so that a scale factor of 2 can be combined with a non- scale divisor of 2, so that the division doesn't shift out a bit. In the usual case where the scale factor is just 1, the division may shift out a bit, but then the underflow is not spurious and the inaccuracies are harder to fix.
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@ -99,15 +99,15 @@ csqrt(double complex z)
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/* Algorithm 312, CACM vol 10, Oct 1967. */
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if (a >= 0) {
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t = sqrt((a + hypot(a, b)) * 0.5);
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rx = t;
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ry = b / (2 * t);
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rx = scale * t;
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ry = scale * b / (2 * t);
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} else {
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t = sqrt((-a + hypot(a, b)) * 0.5);
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rx = fabs(b) / (2 * t);
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ry = copysign(t, b);
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rx = scale * fabs(b) / (2 * t);
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ry = copysign(scale * t, b);
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}
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return (CMPLX(rx * scale, ry * scale));
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return (CMPLX(rx, ry));
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}
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#if LDBL_MANT_DIG == 53
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@ -114,13 +114,13 @@ csqrtl(long double complex z)
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/* Algorithm 312, CACM vol 10, Oct 1967. */
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if (a >= 0) {
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t = sqrtl((a + hypotl(a, b)) * 0.5);
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rx = t;
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ry = b / (2 * t);
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rx = scale * t;
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ry = scale * b / (2 * t);
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} else {
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t = sqrtl((-a + hypotl(a, b)) * 0.5);
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rx = fabsl(b) / (2 * t);
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ry = copysignl(t, b);
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rx = scale * fabsl(b) / (2 * t);
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ry = copysignl(scale * t, b);
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}
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return (CMPLXL(rx * scale, ry * scale));
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return (CMPLXL(rx, ry));
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}
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