diff options
Diffstat (limited to 'src/math/log2.c')
| -rw-r--r-- | src/math/log2.c | 91 |
1 files changed, 54 insertions, 37 deletions
diff --git a/src/math/log2.c b/src/math/log2.c index 1974215d..0aafad4b 100644 --- a/src/math/log2.c +++ b/src/math/log2.c @@ -10,55 +10,66 @@ * ==================================================== */ /* - * Return the base 2 logarithm of x. See log.c and __log1p.h for most - * comments. + * Return the base 2 logarithm of x. See log.c for most comments. * - * This reduces x to {k, 1+f} exactly as in e_log.c, then calls the kernel, - * then does the combining and scaling steps - * log2(x) = (f - 0.5*f*f + k_log1p(f)) / ln2 + k - * in not-quite-routine extra precision. + * Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2 + * as in log.c, then combine and scale in extra precision: + * log2(x) = (f - f*f/2 + r)/log(2) + k */ -#include "libm.h" -#include "__log1p.h" +#include <math.h> +#include <stdint.h> static const double -two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ ivln2hi = 1.44269504072144627571e+00, /* 0x3ff71547, 0x65200000 */ -ivln2lo = 1.67517131648865118353e-10; /* 0x3de705fc, 0x2eefa200 */ +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) { - double f,hfsq,hi,lo,r,val_hi,val_lo,w,y; - int32_t i,k,hx; - uint32_t lx; - - EXTRACT_WORDS(hx, lx, 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) { /* x < 2**-1022 */ - if (((hx&0x7fffffff)|lx) == 0) - return -two54/0.0; /* log(+-0)=-inf */ - if (hx < 0) - return (x-x)/0.0; /* log(-#) = NaN */ - /* subnormal number, scale up x */ + 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 *= two54; - GET_HIGH_WORD(hx, x); - } - if (hx >= 0x7ff00000) - return x+x; - if (hx == 0x3ff00000 && lx == 0) - return 0.0; /* 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; + 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; + f = x - 1.0; hfsq = 0.5*f*f; - r = __log1p(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 @@ -90,13 +101,19 @@ double log2(double x) * The multi-precision calculations for the multiplications are * routine. */ + + /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */ hi = f - hfsq; - SET_LOW_WORD(hi, 0); - lo = (f - hi) - hfsq + r; + 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; /* 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; |