This is the mail archive of the
libc-alpha@sourceware.org
mailing list for the glibc project.
[PATCH] log2 and log10 for wordsize-64
- From: Adhemerval Zanella <azanella at linux dot vnet dot ibm dot com>
- To: "GNU C. Library" <libc-alpha at sourceware dot org>
- Date: Mon, 14 May 2012 12:31:25 -0300
- Subject: [PATCH] log2 and log10 for wordsize-64
These were in my backlog for while. On x86_64 I observed an improvement of about 7%
for log10 and about 20% for log2. And on PPC64 I observed an improvement of about
20% for log10 and about 30 for log2.
Tested on ppc64 and x86_64.
---
2012-05-14 Adhemerval Zanella <azanella@linux.vnet.ibm.com>
* sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c: New file.
* sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c: New file.
diff --git a/sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c b/sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c
new file mode 100644
index 0000000..2562a49
--- /dev/null
+++ b/sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c
@@ -0,0 +1,88 @@
+/* @(#)e_log10.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/* __ieee754_log10(x)
+ * Return the base 10 logarithm of x
+ *
+ * Method :
+ * Let log10_2hi = leading 40 bits of log10(2) and
+ * log10_2lo = log10(2) - log10_2hi,
+ * ivln10 = 1/log(10) rounded.
+ * Then
+ * n = ilogb(x),
+ * if(n<0) n = n+1;
+ * x = scalbn(x,-n);
+ * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
+ *
+ * Note 1:
+ * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
+ * mode must set to Round-to-Nearest.
+ * Note 2:
+ * [1/log(10)] rounded to 53 bits has error .198 ulps;
+ * log10 is monotonic at all binary break points.
+ *
+ * Special cases:
+ * log10(x) is NaN with signal if x < 0;
+ * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
+ * log10(NaN) is that NaN with no signal;
+ * log10(10**N) = N for N=0,1,...,22.
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following constants.
+ * The decimal values may be used, provided that the compiler will convert
+ * from decimal to binary accurately enough to produce the hexadecimal values
+ * shown.
+ */
+
+#include <math.h>
+#include <math_private.h>
+
+static const double two54 = 1.80143985094819840000e+16; /* 0x4350000000000000 */
+static const double ivln10 = 4.34294481903251816668e-01; /* 0x3FDBCB7B1526E50E */
+static const double log10_2hi = 3.01029995663611771306e-01; /* 0x3FD34413509F6000 */
+static const double log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF311F12B36 */
+
+static const double zero = 0.0;
+
+double
+__ieee754_log10 (double x)
+{
+ double y, z;
+ int64_t i, hx;
+ 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);
+ }
+ /* scale up resulted in a NaN number */
+ if (__builtin_expect (hx >= UINT64_C(0x7ff0000000000000), 0))
+ return x + x;
+ k += (hx >> 52) - 1023;
+ i = ((uint64_t) k & UINT64_C(0x8000000000000000)) >> 63;
+ hx = (hx & UINT64_C(0x000fffffffffffff)) | ((0x3ff - i) << 52);
+ y = (double)(k+i);
+ INSERT_WORDS64 (x, hx);
+ z = y * log10_2lo + ivln10 * __ieee754_log (x);
+ return z + y * log10_2hi;
+}
+
+strong_alias (__ieee754_log10, __log10_finite)
diff --git a/sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c b/sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c
new file mode 100644
index 0000000..d532f1f
--- /dev/null
+++ b/sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c
@@ -0,0 +1,129 @@
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/* __ieee754_log2(x)
+ * Return the logarithm to base 2 of x
+ *
+ * Method :
+ * 1. Argument Reduction: find k and f such that
+ * x = 2^k * (1+f),
+ * where sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ * 2. Approximation of log(1+f).
+ * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
+ * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
+ * = 2s + s*R
+ * We use a special Reme algorithm on [0,0.1716] to generate
+ * a polynomial of degree 14 to approximate R The maximum error
+ * of this polynomial approximation is bounded by 2**-58.45. In
+ * other words,
+ * 2 4 6 8 10 12 14
+ * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
+ * (the values of Lg1 to Lg7 are listed in the program)
+ * and
+ * | 2 14 | -58.45
+ * | Lg1*s +...+Lg7*s - R(z) | <= 2
+ * | |
+ * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
+ * In order to guarantee error in log below 1ulp, we compute log
+ * by
+ * log(1+f) = f - s*(f - R) (if f is not too large)
+ * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
+ *
+ * 3. Finally, log(x) = k + log(1+f).
+ * = k+(f-(hfsq-(s*(hfsq+R))))
+ *
+ * Special cases:
+ * log2(x) is NaN with signal if x < 0 (including -INF) ;
+ * log2(+INF) is +INF; log(0) is -INF with signal;
+ * log2(NaN) is that NaN with no signal.
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include <math.h>
+#include <math_private.h>
+
+static const double ln2 = 0.69314718055994530942;
+static const double two1ln2 = 1.4426950408889636;
+static const double two54 = 1.80143985094819840000e+16; /* 4350000000000000 */
+static const double Lg1 = 6.666666666666735130e-01; /* 3FE5555555555593 */
+static const double Lg2 = 3.999999999940941908e-01; /* 3FD999999997FA04 */
+static const double Lg3 = 2.857142874366239149e-01; /* 3FD2492494229359 */
+static const double Lg4 = 2.222219843214978396e-01; /* 3FCC71C51D8E78AF */
+static const double Lg5 = 1.818357216161805012e-01; /* 3FC7466496CB03DE */
+static const double Lg6 = 1.531383769920937332e-01; /* 3FC39A09D078C69F */
+static const double Lg7 = 1.479819860511658591e-01; /* 3FC2F112DF3E5244 */
+
+static const double zero = 0.0;
+
+double
+__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) * two1ln2;
+ }
+ 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) * two1ln2;
+ }
+ else
+ {
+ return dk - ((s * (f - R)) - f) * two1ln2;
+ }
+}
+
+strong_alias (__ieee754_log2, __log2_finite)
--
1.7.9.5
--
Adhemerval Zanella Netto
Software Engineer
Linux Technology Center Brazil
Toolchain / GLIBC on Power Architecture
azanella@linux.vnet.ibm.com / azanella@br.ibm.com
+55 61 8642-9890