Log2 and log10 for wordsize-64.
This patch also fixes indentation on default dbl-64 code.
This commit is contained in:
Adhemerval Zanella
parent
02a9193863
commit
9ea01d93f7
@ -1,3 +1,11 @@
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2012-05-15 Adhemerval Zanella <azanella@linux.vnet.ibm.com>
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* sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c: New file.
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* sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c: New file.
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* sysdeps/ieee754/dbl-64/e_log2.c: Fixing indents.
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* sysdeps/ieee754/dbl-64/e_log10.c: Likewise and also
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remove unused global constant.
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2012-05-15 Chris Metcalf <cmetcalf@tilera.com>
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* sysdeps/unix/sysv/linux/getsysstats.c: Remove duplicate
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@ -46,39 +46,40 @@
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#include <math.h>
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#include <math_private.h>
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static const double
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two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
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ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
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log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
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log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
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static const double zero = 0.0;
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static const double two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */
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static const double ivln10 = 4.34294481903251816668e-01; /* 0x3FDBCB7B, 0x1526E50E */
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static const double log10_2hi = 3.01029995663611771306e-01; /* 0x3FD34413, 0x509F6000 */
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static const double log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
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double
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__ieee754_log10(double x)
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__ieee754_log10 (double x)
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{
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double y,z;
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int32_t i,k,hx;
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u_int32_t lx;
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double y, z;
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int32_t i, k, hx;
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u_int32_t lx;
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EXTRACT_WORDS(hx,lx,x);
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EXTRACT_WORDS (hx, lx, x);
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k=0;
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if (hx < 0x00100000) { /* x < 2**-1022 */
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if (__builtin_expect(((hx&0x7fffffff)|lx)==0, 0))
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return -two54/(x-x); /* log(+-0)=-inf */
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if (__builtin_expect(hx<0, 0))
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return (x-x)/(x-x); /* log(-#) = NaN */
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k -= 54; x *= two54; /* subnormal number, scale up x */
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GET_HIGH_WORD(hx,x);
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}
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if (__builtin_expect(hx >= 0x7ff00000, 0)) return x+x;
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k += (hx>>20)-1023;
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i = ((u_int32_t)k&0x80000000)>>31;
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hx = (hx&0x000fffff)|((0x3ff-i)<<20);
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y = (double)(k+i);
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SET_HIGH_WORD(x,hx);
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z = y*log10_2lo + ivln10*__ieee754_log(x);
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return z+y*log10_2hi;
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k = 0;
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if (hx < 0x00100000)
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{ /* x < 2**-1022 */
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if (__builtin_expect (((hx & 0x7fffffff) | lx) == 0, 0))
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return -two54 / (x - x); /* log(+-0)=-inf */
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if (__builtin_expect (hx < 0, 0))
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return (x - x) / (x - x); /* log(-#) = NaN */
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k -= 54;
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x *= two54; /* subnormal number, scale up x */
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GET_HIGH_WORD (hx, x);
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}
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if (__builtin_expect (hx >= 0x7ff00000, 0))
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return x + x;
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k += (hx >> 20) - 1023;
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i = ((u_int32_t) k & 0x80000000) >> 31;
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hx = (hx & 0x000fffff) | ((0x3ff - i) << 20);
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y = (double) (k + i);
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SET_HIGH_WORD (x, hx);
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z = y * log10_2lo + ivln10 * __ieee754_log (x);
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return z + y * log10_2hi;
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}
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strong_alias (__ieee754_log10, __log10_finite)
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@ -57,64 +57,72 @@
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#include <math.h>
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#include <math_private.h>
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static const double
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ln2 = 0.69314718055994530942,
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two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
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Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
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Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
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Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
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Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
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Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
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Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
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Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
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static const double ln2 = 0.69314718055994530942;
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static const double two54 = 1.80143985094819840000e+16; /* 43500000 00000000 */
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static const double Lg1 = 6.666666666666735130e-01; /* 3FE55555 55555593 */
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static const double Lg2 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */
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static const double Lg3 = 2.857142874366239149e-01; /* 3FD24924 94229359 */
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static const double Lg4 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */
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static const double Lg5 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */
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static const double Lg6 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */
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static const double Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
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static const double zero = 0.0;
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static const double zero = 0.0;
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double
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__ieee754_log2(double x)
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__ieee754_log2 (double x)
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{
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double hfsq,f,s,z,R,w,t1,t2,dk;
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int32_t k,hx,i,j;
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u_int32_t lx;
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double hfsq, f, s, z, R, w, t1, t2, dk;
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int32_t k, hx, i, j;
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u_int32_t lx;
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EXTRACT_WORDS(hx,lx,x);
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EXTRACT_WORDS (hx, lx, x);
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k=0;
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if (hx < 0x00100000) { /* x < 2**-1022 */
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if (__builtin_expect(((hx&0x7fffffff)|lx)==0, 0))
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return -two54/(x-x); /* log(+-0)=-inf */
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if (__builtin_expect(hx<0, 0))
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return (x-x)/(x-x); /* log(-#) = NaN */
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k -= 54; x *= two54; /* subnormal number, scale up x */
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GET_HIGH_WORD(hx,x);
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}
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if (__builtin_expect(hx >= 0x7ff00000, 0)) return x+x;
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k += (hx>>20)-1023;
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hx &= 0x000fffff;
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i = (hx+0x95f64)&0x100000;
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SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
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k += (i>>20);
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dk = (double) k;
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f = x-1.0;
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if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
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if(f==zero) return dk;
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R = f*f*(0.5-0.33333333333333333*f);
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return dk-(R-f)/ln2;
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}
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s = f/(2.0+f);
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z = s*s;
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i = hx-0x6147a;
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w = z*z;
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j = 0x6b851-hx;
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t1= w*(Lg2+w*(Lg4+w*Lg6));
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t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
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i |= j;
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R = t2+t1;
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if(i>0) {
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hfsq=0.5*f*f;
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return dk-((hfsq-(s*(hfsq+R)))-f)/ln2;
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} else {
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return dk-((s*(f-R))-f)/ln2;
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}
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k = 0;
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if (hx < 0x00100000)
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{ /* x < 2**-1022 */
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if (__builtin_expect (((hx & 0x7fffffff) | lx) == 0, 0))
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return -two54 / (x - x); /* log(+-0)=-inf */
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if (__builtin_expect (hx < 0, 0))
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return (x - x) / (x - x); /* log(-#) = NaN */
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k -= 54;
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x *= two54; /* subnormal number, scale up x */
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GET_HIGH_WORD (hx, x);
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}
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if (__builtin_expect (hx >= 0x7ff00000, 0))
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return x + x;
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k += (hx >> 20) - 1023;
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hx &= 0x000fffff;
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i = (hx + 0x95f64) & 0x100000;
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SET_HIGH_WORD (x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */
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k += (i >> 20);
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dk = (double) k;
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f = x - 1.0;
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if ((0x000fffff & (2 + hx)) < 3)
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{ /* |f| < 2**-20 */
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if (f == zero)
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return dk;
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R = f * f * (0.5 - 0.33333333333333333 * f);
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return dk - (R - f) / ln2;
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}
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s = f / (2.0 + f);
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z = s * s;
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i = hx - 0x6147a;
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w = z * z;
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j = 0x6b851 - hx;
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t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
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t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
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i |= j;
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R = t2 + t1;
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if (i > 0)
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{
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hfsq = 0.5 * f * f;
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return dk - ((hfsq - (s * (hfsq + R))) - f) / ln2;
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}
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else
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{
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return dk - ((s * (f - R)) - f) / ln2;
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}
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}
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strong_alias (__ieee754_log2, __log2_finite)
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86
sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c
Normal file
86
sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c
Normal file
@ -0,0 +1,86 @@
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/* @(#)e_log10.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* __ieee754_log10(x)
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* Return the base 10 logarithm of x
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*
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* Method :
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* Let log10_2hi = leading 40 bits of log10(2) and
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* log10_2lo = log10(2) - log10_2hi,
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* ivln10 = 1/log(10) rounded.
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* Then
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* n = ilogb(x),
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* if(n<0) n = n+1;
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* x = scalbn(x,-n);
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* log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
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*
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* Note 1:
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* To guarantee log10(10**n)=n, where 10**n is normal, the rounding
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* mode must set to Round-to-Nearest.
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* Note 2:
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* [1/log(10)] rounded to 53 bits has error .198 ulps;
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* log10 is monotonic at all binary break points.
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*
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* Special cases:
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* log10(x) is NaN with signal if x < 0;
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* log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
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* log10(NaN) is that NaN with no signal;
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* log10(10**N) = N for N=0,1,...,22.
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following constants.
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* The decimal values may be used, provided that the compiler will convert
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* from decimal to binary accurately enough to produce the hexadecimal values
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* shown.
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*/
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#include <math.h>
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#include <math_private.h>
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static const double two54 = 1.80143985094819840000e+16; /* 0x4350000000000000 */
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static const double ivln10 = 4.34294481903251816668e-01; /* 0x3FDBCB7B1526E50E */
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static const double log10_2hi = 3.01029995663611771306e-01; /* 0x3FD34413509F6000 */
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static const double log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF311F12B36 */
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double
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__ieee754_log10 (double x)
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{
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double y, z;
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int64_t i, hx;
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int32_t k;
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EXTRACT_WORDS64 (hx, x);
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k = 0;
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if (hx < INT64_C(0x0010000000000000))
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{ /* x < 2**-1022 */
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if (__builtin_expect ((hx & UINT64_C(0x7fffffffffffffff)) == 0, 0))
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return -two54 / (x - x); /* log(+-0)=-inf */
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if (__builtin_expect (hx < 0, 0))
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return (x - x) / (x - x); /* log(-#) = NaN */
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k -= 54;
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x *= two54; /* subnormal number, scale up x */
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EXTRACT_WORDS64 (hx, x);
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}
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/* scale up resulted in a NaN number */
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if (__builtin_expect (hx >= UINT64_C(0x7ff0000000000000), 0))
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return x + x;
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k += (hx >> 52) - 1023;
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i = ((uint64_t) k & UINT64_C(0x8000000000000000)) >> 63;
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hx = (hx & UINT64_C(0x000fffffffffffff)) | ((0x3ff - i) << 52);
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y = (double) (k + i);
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INSERT_WORDS64 (x, hx);
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z = y * log10_2lo + ivln10 * __ieee754_log (x);
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return z + y * log10_2hi;
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}
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strong_alias (__ieee754_log10, __log10_finite)
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128
sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c
Normal file
128
sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c
Normal file
@ -0,0 +1,128 @@
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* __ieee754_log2(x)
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* Return the logarithm to base 2 of x
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*
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* Method :
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* 1. Argument Reduction: find k and f such that
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* x = 2^k * (1+f),
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* where sqrt(2)/2 < 1+f < sqrt(2) .
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*
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* 2. Approximation of log(1+f).
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* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
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* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
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* = 2s + s*R
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* We use a special Reme algorithm on [0,0.1716] to generate
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* a polynomial of degree 14 to approximate R The maximum error
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* of this polynomial approximation is bounded by 2**-58.45. In
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* other words,
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* 2 4 6 8 10 12 14
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* R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
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* (the values of Lg1 to Lg7 are listed in the program)
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* and
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* | 2 14 | -58.45
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* | Lg1*s +...+Lg7*s - R(z) | <= 2
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* | |
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* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
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* In order to guarantee error in log below 1ulp, we compute log
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* by
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* log(1+f) = f - s*(f - R) (if f is not too large)
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* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
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*
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* 3. Finally, log(x) = k + log(1+f).
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* = k+(f-(hfsq-(s*(hfsq+R))))
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*
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* Special cases:
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* log2(x) is NaN with signal if x < 0 (including -INF) ;
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* log2(+INF) is +INF; log(0) is -INF with signal;
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* log2(NaN) is that NaN with no signal.
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following
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* constants. The decimal values may be used, provided that the
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* compiler will convert from decimal to binary accurately enough
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* to produce the hexadecimal values shown.
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*/
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#include <math.h>
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#include <math_private.h>
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static const double ln2 = 0.69314718055994530942;
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static const double two54 = 1.80143985094819840000e+16; /* 4350000000000000 */
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static const double Lg1 = 6.666666666666735130e-01; /* 3FE5555555555593 */
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static const double Lg2 = 3.999999999940941908e-01; /* 3FD999999997FA04 */
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static const double Lg3 = 2.857142874366239149e-01; /* 3FD2492494229359 */
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static const double Lg4 = 2.222219843214978396e-01; /* 3FCC71C51D8E78AF */
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static const double Lg5 = 1.818357216161805012e-01; /* 3FC7466496CB03DE */
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static const double Lg6 = 1.531383769920937332e-01; /* 3FC39A09D078C69F */
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static const double Lg7 = 1.479819860511658591e-01; /* 3FC2F112DF3E5244 */
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static const double zero = 0.0;
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double
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__ieee754_log2 (double x)
|
||||
{
|
||||
double hfsq, f, s, z, R, w, t1, t2, dk;
|
||||
int64_t hx, i, j;
|
||||
int32_t k;
|
||||
|
||||
EXTRACT_WORDS64 (hx, x);
|
||||
|
||||
k = 0;
|
||||
if (hx < INT64_C(0x0010000000000000))
|
||||
{ /* x < 2**-1022 */
|
||||
if (__builtin_expect ((hx & UINT64_C(0x7fffffffffffffff)) == 0, 0))
|
||||
return -two54 / (x - x); /* log(+-0)=-inf */
|
||||
if (__builtin_expect (hx < 0, 0))
|
||||
return (x - x) / (x - x); /* log(-#) = NaN */
|
||||
k -= 54;
|
||||
x *= two54; /* subnormal number, scale up x */
|
||||
EXTRACT_WORDS64 (hx, x);
|
||||
}
|
||||
if (__builtin_expect (hx >= UINT64_C(0x7ff0000000000000), 0))
|
||||
return x + x;
|
||||
k += (hx >> 52) - 1023;
|
||||
hx &= UINT64_C(0x000fffffffffffff);
|
||||
i = (hx + UINT64_C(0x95f6400000000)) & UINT64_C(0x10000000000000);
|
||||
/* normalize x or x/2 */
|
||||
INSERT_WORDS64 (x, hx | (i ^ UINT64_C(0x3ff0000000000000)));
|
||||
k += (i >> 52);
|
||||
dk = (double) k;
|
||||
f = x - 1.0;
|
||||
if ((UINT64_C(0x000fffffffffffff) & (2 + hx)) < 3)
|
||||
{ /* |f| < 2**-20 */
|
||||
if (f == zero)
|
||||
return dk;
|
||||
R = f * f * (0.5 - 0.33333333333333333 * f);
|
||||
return dk - (R - f) / ln2;
|
||||
}
|
||||
s = f / (2.0 + f);
|
||||
z = s * s;
|
||||
i = hx - UINT64_C(0x6147a00000000);
|
||||
w = z * z;
|
||||
j = UINT64_C(0x6b85100000000) - hx;
|
||||
t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
|
||||
t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
|
||||
i |= j;
|
||||
R = t2 + t1;
|
||||
if (i > 0)
|
||||
{
|
||||
hfsq = 0.5 * f * f;
|
||||
return dk - ((hfsq - (s * (hfsq + R))) - f) / ln2;
|
||||
}
|
||||
else
|
||||
{
|
||||
return dk - ((s * (f - R)) - f) / ln2;
|
||||
}
|
||||
}
|
||||
|
||||
strong_alias (__ieee754_log2, __log2_finite)
|
||||
Loading…
x
Reference in New Issue
Block a user