diff options
Diffstat (limited to 'lib/msun/src/e_log10.c')
| -rw-r--r-- | lib/msun/src/e_log10.c | 51 |
1 files changed, 37 insertions, 14 deletions
diff --git a/lib/msun/src/e_log10.c b/lib/msun/src/e_log10.c index 135f0dc..104d257 100644 --- a/lib/msun/src/e_log10.c +++ b/lib/msun/src/e_log10.c @@ -15,7 +15,11 @@ __FBSDID("$FreeBSD$"); /* - * Return the base 10 logarithm of x. See k_log.c for details on the algorithm. + * Return the base 10 logarithm of x. See e_log.c and k_log.h for most + * comments. + * + * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2) + * in not-quite-routine extra precision. */ #include "math.h" @@ -34,31 +38,50 @@ static const double zero = 0.0; double __ieee754_log10(double x) { - double f,hi,lo,y,z; + double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2; int32_t i,k,hx; u_int32_t lx; EXTRACT_WORDS(hx,lx,x); - k=0; - if (hx < 0x00100000) { /* x < 2**-1022 */ - if (((hx&0x7fffffff)|lx)==0) - return -two54/zero; /* log(+-0)=-inf */ - if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ - k -= 54; x *= two54; /* subnormal number, scale up x */ + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ GET_HIGH_WORD(hx,x); - } + } if (hx >= 0x7ff00000) return x+x; + if (hx == 0x3ff00000 && lx == 0) + return zero; /* log(1) = +0 */ k += (hx>>20)-1023; hx &= 0x000fffff; i = (hx+0x95f64)&0x100000; SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ k += (i>>20); y = (double)k; - f = __kernel_log(x); - hi = x = x - 1; + f = x - 1.0; + hfsq = 0.5*f*f; + r = k_log1p(f); + + /* See e_log2.c for most details. */ + hi = f - hfsq; SET_LOW_WORD(hi,0); - lo = x - hi; - z = y*log10_2lo + (x+f)*ivln10lo + (lo+f)*ivln10hi + hi*ivln10hi; - return z+y*log10_2hi; + lo = (f - hi) - hfsq + r; + val_hi = hi*ivln10hi; + y2 = y*log10_2hi; + val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi; + + /* + * Extra precision in for adding y*log10_2hi 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 = y2 + val_hi; + val_lo += (y2 - w) + val_hi; + val_hi = w; + + return val_lo + val_hi; } |
