| Index: fusl/src/math/log2.c
|
| diff --git a/fusl/src/math/log2.c b/fusl/src/math/log2.c
|
| index 0aafad4b86c1cd3bf7b69090534aa1f5a05fda36..1ee2ea0d3fee375fb1ebe4f4cffe01dd698d512a 100644
|
| --- a/fusl/src/math/log2.c
|
| +++ b/fusl/src/math/log2.c
|
| @@ -20,103 +20,105 @@
|
| #include <math.h>
|
| #include <stdint.h>
|
|
|
| -static const double
|
| -ivln2hi = 1.44269504072144627571e+00, /* 0x3ff71547, 0x65200000 */
|
| -ivln2lo = 1.67517131648865118353e-10, /* 0x3de705fc, 0x2eefa200 */
|
| -Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
|
| -Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
|
| -Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
|
| -Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
|
| -Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
|
| -Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
|
| -Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
|
| +static const double ivln2hi =
|
| + 1.44269504072144627571e+00, /* 0x3ff71547, 0x65200000 */
|
| + ivln2lo = 1.67517131648865118353e-10, /* 0x3de705fc, 0x2eefa200 */
|
| + Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
|
| + Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
|
| + Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
|
| + Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
|
| + Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
|
| + Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
|
| + Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
|
|
|
| -double log2(double x)
|
| -{
|
| - union {double f; uint64_t i;} u = {x};
|
| - double_t hfsq,f,s,z,R,w,t1,t2,y,hi,lo,val_hi,val_lo;
|
| - uint32_t hx;
|
| - int k;
|
| +double log2(double x) {
|
| + union {
|
| + double f;
|
| + uint64_t i;
|
| + } u = {x};
|
| + double_t hfsq, f, s, z, R, w, t1, t2, y, hi, lo, val_hi, val_lo;
|
| + uint32_t hx;
|
| + int k;
|
|
|
| - hx = u.i>>32;
|
| - k = 0;
|
| - if (hx < 0x00100000 || hx>>31) {
|
| - if (u.i<<1 == 0)
|
| - return -1/(x*x); /* log(+-0)=-inf */
|
| - if (hx>>31)
|
| - return (x-x)/0.0; /* log(-#) = NaN */
|
| - /* subnormal number, scale x up */
|
| - k -= 54;
|
| - x *= 0x1p54;
|
| - u.f = x;
|
| - hx = u.i>>32;
|
| - } else if (hx >= 0x7ff00000) {
|
| - return x;
|
| - } else if (hx == 0x3ff00000 && u.i<<32 == 0)
|
| - return 0;
|
| + hx = u.i >> 32;
|
| + k = 0;
|
| + if (hx < 0x00100000 || hx >> 31) {
|
| + if (u.i << 1 == 0)
|
| + return -1 / (x * x); /* log(+-0)=-inf */
|
| + if (hx >> 31)
|
| + return (x - x) / 0.0; /* log(-#) = NaN */
|
| + /* subnormal number, scale x up */
|
| + k -= 54;
|
| + x *= 0x1p54;
|
| + u.f = x;
|
| + hx = u.i >> 32;
|
| + } else if (hx >= 0x7ff00000) {
|
| + return x;
|
| + } else if (hx == 0x3ff00000 && u.i << 32 == 0)
|
| + return 0;
|
|
|
| - /* reduce x into [sqrt(2)/2, sqrt(2)] */
|
| - hx += 0x3ff00000 - 0x3fe6a09e;
|
| - k += (int)(hx>>20) - 0x3ff;
|
| - hx = (hx&0x000fffff) + 0x3fe6a09e;
|
| - u.i = (uint64_t)hx<<32 | (u.i&0xffffffff);
|
| - x = u.f;
|
| + /* reduce x into [sqrt(2)/2, sqrt(2)] */
|
| + hx += 0x3ff00000 - 0x3fe6a09e;
|
| + k += (int)(hx >> 20) - 0x3ff;
|
| + hx = (hx & 0x000fffff) + 0x3fe6a09e;
|
| + u.i = (uint64_t)hx << 32 | (u.i & 0xffffffff);
|
| + x = u.f;
|
|
|
| - f = x - 1.0;
|
| - hfsq = 0.5*f*f;
|
| - s = f/(2.0+f);
|
| - z = s*s;
|
| - w = z*z;
|
| - t1 = w*(Lg2+w*(Lg4+w*Lg6));
|
| - t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
|
| - R = t2 + t1;
|
| + f = x - 1.0;
|
| + hfsq = 0.5 * f * f;
|
| + s = f / (2.0 + f);
|
| + z = s * s;
|
| + w = z * z;
|
| + t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
|
| + t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
|
| + R = t2 + t1;
|
|
|
| - /*
|
| - * f-hfsq must (for args near 1) be evaluated in extra precision
|
| - * to avoid a large cancellation when x is near sqrt(2) or 1/sqrt(2).
|
| - * This is fairly efficient since f-hfsq only depends on f, so can
|
| - * be evaluated in parallel with R. Not combining hfsq with R also
|
| - * keeps R small (though not as small as a true `lo' term would be),
|
| - * so that extra precision is not needed for terms involving R.
|
| - *
|
| - * Compiler bugs involving extra precision used to break Dekker's
|
| - * theorem for spitting f-hfsq as hi+lo, unless double_t was used
|
| - * or the multi-precision calculations were avoided when double_t
|
| - * has extra precision. These problems are now automatically
|
| - * avoided as a side effect of the optimization of combining the
|
| - * Dekker splitting step with the clear-low-bits step.
|
| - *
|
| - * y must (for args near sqrt(2) and 1/sqrt(2)) be added in extra
|
| - * precision to avoid a very large cancellation when x is very near
|
| - * these values. Unlike the above cancellations, this problem is
|
| - * specific to base 2. It is strange that adding +-1 is so much
|
| - * harder than adding +-ln2 or +-log10_2.
|
| - *
|
| - * This uses Dekker's theorem to normalize y+val_hi, so the
|
| - * compiler bugs are back in some configurations, sigh. And I
|
| - * don't want to used double_t to avoid them, since that gives a
|
| - * pessimization and the support for avoiding the pessimization
|
| - * is not yet available.
|
| - *
|
| - * The multi-precision calculations for the multiplications are
|
| - * routine.
|
| - */
|
| + /*
|
| + * f-hfsq must (for args near 1) be evaluated in extra precision
|
| + * to avoid a large cancellation when x is near sqrt(2) or 1/sqrt(2).
|
| + * This is fairly efficient since f-hfsq only depends on f, so can
|
| + * be evaluated in parallel with R. Not combining hfsq with R also
|
| + * keeps R small (though not as small as a true `lo' term would be),
|
| + * so that extra precision is not needed for terms involving R.
|
| + *
|
| + * Compiler bugs involving extra precision used to break Dekker's
|
| + * theorem for spitting f-hfsq as hi+lo, unless double_t was used
|
| + * or the multi-precision calculations were avoided when double_t
|
| + * has extra precision. These problems are now automatically
|
| + * avoided as a side effect of the optimization of combining the
|
| + * Dekker splitting step with the clear-low-bits step.
|
| + *
|
| + * y must (for args near sqrt(2) and 1/sqrt(2)) be added in extra
|
| + * precision to avoid a very large cancellation when x is very near
|
| + * these values. Unlike the above cancellations, this problem is
|
| + * specific to base 2. It is strange that adding +-1 is so much
|
| + * harder than adding +-ln2 or +-log10_2.
|
| + *
|
| + * This uses Dekker's theorem to normalize y+val_hi, so the
|
| + * compiler bugs are back in some configurations, sigh. And I
|
| + * don't want to used double_t to avoid them, since that gives a
|
| + * pessimization and the support for avoiding the pessimization
|
| + * is not yet available.
|
| + *
|
| + * The multi-precision calculations for the multiplications are
|
| + * routine.
|
| + */
|
|
|
| - /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
|
| - hi = f - hfsq;
|
| - u.f = hi;
|
| - u.i &= (uint64_t)-1<<32;
|
| - hi = u.f;
|
| - lo = f - hi - hfsq + s*(hfsq+R);
|
| + /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
|
| + hi = f - hfsq;
|
| + u.f = hi;
|
| + u.i &= (uint64_t)-1 << 32;
|
| + hi = u.f;
|
| + lo = f - hi - hfsq + s * (hfsq + R);
|
|
|
| - val_hi = hi*ivln2hi;
|
| - val_lo = (lo+hi)*ivln2lo + lo*ivln2hi;
|
| + val_hi = hi * ivln2hi;
|
| + val_lo = (lo + hi) * ivln2lo + lo * ivln2hi;
|
|
|
| - /* spadd(val_hi, val_lo, y), except for not using double_t: */
|
| - y = k;
|
| - w = y + val_hi;
|
| - val_lo += (y - w) + val_hi;
|
| - val_hi = w;
|
| + /* spadd(val_hi, val_lo, y), except for not using double_t: */
|
| + y = k;
|
| + w = y + val_hi;
|
| + val_lo += (y - w) + val_hi;
|
| + val_hi = w;
|
|
|
| - return val_lo + val_hi;
|
| + return val_lo + val_hi;
|
| }
|
|
|