Add a "fork" of musl as //fusl.

fusl/src/math/log.c

+/* origin: FreeBSD /usr/src/lib/msun/src/e_log.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* log(x)
+ * Return the logarithm 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 Remez 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*ln2 + log(1+f).
+ *                          = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
+ *         Here ln2 is split into two floating point number:
+ *                      ln2_hi + ln2_lo,
+ *         where n*ln2_hi is always exact for |n| < 2000.
+ *
+ * Special cases:
+ *      log(x) is NaN with signal if x < 0 (including -INF) ;
+ *      log(+INF) is +INF; log(0) is -INF with signal;
+ *      log(NaN) is that NaN with no signal.
+ *
+ * Accuracy:
+ *      according to an error analysis, the error is always less than
+ *      1 ulp (unit in the last place).
+ *
+ * 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 <stdint.h>
+
+static const double
+ln2_hi = 6.93147180369123816490e-01,  /* 3fe62e42 fee00000 */
+ln2_lo = 1.90821492927058770002e-10,  /* 3dea39ef 35793c76 */
+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 log(double x)
+{
+        union {double f; uint64_t i;} u = {x};
+        double_t hfsq,f,s,z,R,w,t1,t2,dk;
+        uint32_t hx;
+        int k;
+
+        hx = u.i>>32;
+        k = 0;
+        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 *= 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;
+        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;
+        dk = k;
+        return s*(hfsq+R) + dk*ln2_lo - hfsq + f + dk*ln2_hi;
+}