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; |
} |