libm: sync with upstream.
There's potential here to maybe lose some/all of builtins.cpp, but I'll
look at that separately later.
Test: treehugger
Change-Id: I2c2bc1d0753affdd214daeb09fa1ac7cd73db347
diff --git a/libm/upstream-freebsd/lib/msun/bsdsrc/b_log.c b/libm/upstream-freebsd/lib/msun/bsdsrc/b_log.c
index c164dfa..9d09ac7 100644
--- a/libm/upstream-freebsd/lib/msun/bsdsrc/b_log.c
+++ b/libm/upstream-freebsd/lib/msun/bsdsrc/b_log.c
@@ -33,10 +33,6 @@
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
-#include <math.h>
-
-#include "mathimpl.h"
-
/* Table-driven natural logarithm.
*
* This code was derived, with minor modifications, from:
@@ -44,25 +40,27 @@
* Logarithm in IEEE Floating-Point arithmetic." ACM Trans.
* Math Software, vol 16. no 4, pp 378-400, Dec 1990).
*
- * Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256,
+ * Calculates log(2^m*F*(1+f/F)), |f/F| <= 1/256,
* where F = j/128 for j an integer in [0, 128].
*
* log(2^m) = log2_hi*m + log2_tail*m
- * since m is an integer, the dominant term is exact.
+ * The leading term is exact, because m is an integer,
* m has at most 10 digits (for subnormal numbers),
* and log2_hi has 11 trailing zero bits.
*
- * log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h
+ * log(F) = logF_hi[j] + logF_lo[j] is in table below.
* logF_hi[] + 512 is exact.
*
* log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ...
- * the leading term is calculated to extra precision in two
+ *
+ * The leading term is calculated to extra precision in two
* parts, the larger of which adds exactly to the dominant
* m and F terms.
+ *
* There are two cases:
- * 1. when m, j are non-zero (m | j), use absolute
+ * 1. When m and j are non-zero (m | j), use absolute
* precision for the leading term.
- * 2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1).
+ * 2. When m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1).
* In this case, use a relative precision of 24 bits.
* (This is done differently in the original paper)
*
@@ -70,11 +68,21 @@
* 0 return signalling -Inf
* neg return signalling NaN
* +Inf return +Inf
-*/
+ */
#define N 128
-/* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128.
+/*
+ * Coefficients in the polynomial approximation of log(1+f/F).
+ * Domain of x is [0,1./256] with 2**(-64.187) precision.
+ */
+static const double
+ A1 = 8.3333333333333329e-02, /* 0x3fb55555, 0x55555555 */
+ A2 = 1.2499999999943598e-02, /* 0x3f899999, 0x99991a98 */
+ A3 = 2.2321527525957776e-03; /* 0x3f624929, 0xe24e70be */
+
+/*
+ * Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128.
* Used for generation of extend precision logarithms.
* The constant 35184372088832 is 2^45, so the divide is exact.
* It ensures correct reading of logF_head, even for inaccurate
@@ -82,12 +90,7 @@
* right answer for integers less than 2^53.)
* Values for log(F) were generated using error < 10^-57 absolute
* with the bc -l package.
-*/
-static double A1 = .08333333333333178827;
-static double A2 = .01250000000377174923;
-static double A3 = .002232139987919447809;
-static double A4 = .0004348877777076145742;
-
+ */
static double logF_head[N+1] = {
0.,
.007782140442060381246,
@@ -351,118 +354,51 @@
.00000000000025144230728376072,
-.00000000000017239444525614834
};
-
-#if 0
-double
-#ifdef _ANSI_SOURCE
-log(double x)
-#else
-log(x) double x;
-#endif
-{
- int m, j;
- double F, f, g, q, u, u2, v, zero = 0.0, one = 1.0;
- volatile double u1;
-
- /* Catch special cases */
- if (x <= 0)
- if (x == zero) /* log(0) = -Inf */
- return (-one/zero);
- else /* log(neg) = NaN */
- return (zero/zero);
- else if (!finite(x))
- return (x+x); /* x = NaN, Inf */
-
- /* Argument reduction: 1 <= g < 2; x/2^m = g; */
- /* y = F*(1 + f/F) for |f| <= 2^-8 */
-
- m = logb(x);
- g = ldexp(x, -m);
- if (m == -1022) {
- j = logb(g), m += j;
- g = ldexp(g, -j);
- }
- j = N*(g-1) + .5;
- F = (1.0/N) * j + 1; /* F*128 is an integer in [128, 512] */
- f = g - F;
-
- /* Approximate expansion for log(1+f/F) ~= u + q */
- g = 1/(2*F+f);
- u = 2*f*g;
- v = u*u;
- q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
-
- /* case 1: u1 = u rounded to 2^-43 absolute. Since u < 2^-8,
- * u1 has at most 35 bits, and F*u1 is exact, as F has < 8 bits.
- * It also adds exactly to |m*log2_hi + log_F_head[j] | < 750
- */
- if (m | j)
- u1 = u + 513, u1 -= 513;
-
- /* case 2: |1-x| < 1/256. The m- and j- dependent terms are zero;
- * u1 = u to 24 bits.
- */
- else
- u1 = u, TRUNC(u1);
- u2 = (2.0*(f - F*u1) - u1*f) * g;
- /* u1 + u2 = 2f/(2F+f) to extra precision. */
-
- /* log(x) = log(2^m*F*(1+f/F)) = */
- /* (m*log2_hi+logF_head[j]+u1) + (m*log2_lo+logF_tail[j]+q); */
- /* (exact) + (tiny) */
-
- u1 += m*logF_head[N] + logF_head[j]; /* exact */
- u2 = (u2 + logF_tail[j]) + q; /* tiny */
- u2 += logF_tail[N]*m;
- return (u1 + u2);
-}
-#endif
-
/*
* Extra precision variant, returning struct {double a, b;};
- * log(x) = a+b to 63 bits, with a rounded to 26 bits.
+ * log(x) = a+b to 63 bits, with 'a' rounded to 24 bits.
*/
-struct Double
-#ifdef _ANSI_SOURCE
+static struct Double
__log__D(double x)
-#else
-__log__D(x) double x;
-#endif
{
int m, j;
- double F, f, g, q, u, v, u2;
- volatile double u1;
+ double F, f, g, q, u, v, u1, u2;
struct Double r;
- /* Argument reduction: 1 <= g < 2; x/2^m = g; */
- /* y = F*(1 + f/F) for |f| <= 2^-8 */
-
- m = logb(x);
- g = ldexp(x, -m);
+ /*
+ * Argument reduction: 1 <= g < 2; x/2^m = g;
+ * y = F*(1 + f/F) for |f| <= 2^-8
+ */
+ g = frexp(x, &m);
+ g *= 2;
+ m--;
if (m == -1022) {
- j = logb(g), m += j;
+ j = ilogb(g);
+ m += j;
g = ldexp(g, -j);
}
- j = N*(g-1) + .5;
- F = (1.0/N) * j + 1;
+ j = N * (g - 1) + 0.5;
+ F = (1. / N) * j + 1;
f = g - F;
- g = 1/(2*F+f);
- u = 2*f*g;
- v = u*u;
- q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
- if (m | j)
- u1 = u + 513, u1 -= 513;
- else
- u1 = u, TRUNC(u1);
- u2 = (2.0*(f - F*u1) - u1*f) * g;
+ g = 1 / (2 * F + f);
+ u = 2 * f * g;
+ v = u * u;
+ q = u * v * (A1 + v * (A2 + v * A3));
+ if (m | j) {
+ u1 = u + 513;
+ u1 -= 513;
+ } else {
+ u1 = (float)u;
+ }
+ u2 = (2 * (f - F * u1) - u1 * f) * g;
- u1 += m*logF_head[N] + logF_head[j];
+ u1 += m * logF_head[N] + logF_head[j];
- u2 += logF_tail[j]; u2 += q;
- u2 += logF_tail[N]*m;
- r.a = u1 + u2; /* Only difference is here */
- TRUNC(r.a);
+ u2 += logF_tail[j];
+ u2 += q;
+ u2 += logF_tail[N] * m;
+ r.a = (float)(u1 + u2); /* Only difference is here. */
r.b = (u1 - r.a) + u2;
return (r);
}