Index: fusl/src/math/log10.c |
diff --git a/fusl/src/math/log10.c b/fusl/src/math/log10.c |
index 81026876b223d4f56d6c2542b18898d6105aa34d..621e15e66c3935aba7a96e09093b6404f943eb95 100644 |
--- a/fusl/src/math/log10.c |
+++ b/fusl/src/math/log10.c |
@@ -20,82 +20,84 @@ |
#include <math.h> |
#include <stdint.h> |
-static const double |
-ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */ |
-ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */ |
-log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ |
-log10_2lo = 3.69423907715893078616e-13, /* 0x3D59FEF3, 0x11F12B36 */ |
-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 ivln10hi = |
+ 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */ |
+ ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */ |
+ log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ |
+ log10_2lo = 3.69423907715893078616e-13, /* 0x3D59FEF3, 0x11F12B36 */ |
+ 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 log10(double x) |
-{ |
- union {double f; uint64_t i;} u = {x}; |
- double_t hfsq,f,s,z,R,w,t1,t2,dk,y,hi,lo,val_hi,val_lo; |
- uint32_t hx; |
- int k; |
+double log10(double x) { |
+ union { |
+ double f; |
+ uint64_t i; |
+ } u = {x}; |
+ double_t hfsq, f, s, z, R, w, t1, t2, dk, 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; |
- /* See log2.c for details. */ |
- /* 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); |
+ /* See log2.c for details. */ |
+ /* 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+val_lo ~ log10(1+f) + k*log10(2) */ |
- val_hi = hi*ivln10hi; |
- dk = k; |
- y = dk*log10_2hi; |
- val_lo = dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi; |
+ /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */ |
+ val_hi = hi * ivln10hi; |
+ dk = k; |
+ y = dk * log10_2hi; |
+ val_lo = dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi; |
- /* |
- * Extra precision in for adding y is not strictly needed |
- * since there is no very large cancellation near x = sqrt(2) or |
- * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs |
- * with some parallelism and it reduces the error for many args. |
- */ |
- w = y + val_hi; |
- val_lo += (y - w) + val_hi; |
- val_hi = w; |
+ /* |
+ * Extra precision in for adding y is not strictly needed |
+ * since there is no very large cancellation near x = sqrt(2) or |
+ * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs |
+ * with some parallelism and it reduces the error for many args. |
+ */ |
+ w = y + val_hi; |
+ val_lo += (y - w) + val_hi; |
+ val_hi = w; |
- return val_lo + val_hi; |
+ return val_lo + val_hi; |
} |