Add log implementation.

Fixes rust-lang#23

Author: software-opal

src/lib.rs

@@ -389,10 +389,8 @@ pub trait F64Ext: private::Sealed {
     #[cfg(todo)]
     fn exp2(self) -> Self;
 
-    #[cfg(todo)]
     fn ln(self) -> Self;
 
-    #[cfg(todo)]
     fn log(self, base: Self) -> Self;
 
     fn log2(self) -> Self;
@@ -539,13 +537,11 @@ impl F64Ext for f64 {
         exp2(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn ln(self) -> Self {
         log(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn log(self, base: Self) -> Self {
         self.ln() / base.ln()

src/math/log.rs

@@ -0,0 +1,117 @@
+/* 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.
+ */
+
+const LN2_HI: f64 = 6.93147180369123816490e-01; /* 3fe62e42 fee00000 */
+const LN2_LO: f64 = 1.90821492927058770002e-10; /* 3dea39ef 35793c76 */
+const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */
+const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */
+const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */
+const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */
+const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */
+const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */
+const LG7: f64 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
+
+#[inline]
+pub fn log(mut x: f64) -> f64 {
+    let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54
+
+    let mut ui = x.to_bits();
+    let mut hx: u32 = (ui >> 32) as u32;
+    let mut k: i32 = 0;
+
+    if (hx < 0x00100000) || ((hx >> 31) != 0) {
+        /* x < 2**-126  */
+        if ui << 1 == 0 {
+            return -1. / (x * x); /* log(+-0)=-inf */
+        }
+        if hx >> 31 != 0 {
+            return (x - x) / 0.0; /* log(-#) = NaN */
+        }
+        /* subnormal number, scale x up */
+        k -= 54;
+        x *= x1p54;
+        ui = x.to_bits();
+        hx = (ui >> 32) as u32;
+    } else if hx >= 0x7ff00000 {
+        return x;
+    } else if hx == 0x3ff00000 && ui << 32 == 0 {
+        return 0.;
+    }
+
+    /* reduce x into [sqrt(2)/2, sqrt(2)] */
+    hx += 0x3ff00000 - 0x3fe6a09e;
+    k += ((hx >> 20) as i32) - 0x3ff;
+    hx = (hx & 0x000fffff) + 0x3fe6a09e;
+    ui = ((hx as u64) << 32) | (ui & 0xffffffff);
+    x = f64::from_bits(ui);
+
+    let f: f64 = x - 1.0;
+    let hfsq: f64 = 0.5 * f * f;
+    let s: f64 = f / (2.0 + f);
+    let z: f64 = s * s;
+    let w: f64 = z * z;
+    let t1: f64 = w * (LG2 + w * (LG4 + w * LG6));
+    let t2: f64 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
+    let r: f64 = t2 + t1;
+    let dk: f64 = k as f64;
+    return s * (hfsq + r) + dk * LN2_LO - hfsq + f + dk * LN2_HI;
+}

src/math/mod.rs

@@ -15,6 +15,7 @@ mod floorf;
 mod fmodf;
 mod hypot;
 mod hypotf;
+mod log;
 mod log10;
 mod log10f;
 mod log2;
@@ -34,7 +35,7 @@ mod truncf;
 
 pub use self::{
     ceilf::ceilf, expf::expf, fabs::fabs, fabsf::fabsf, floor::floor, floorf::floorf, fmodf::fmodf,
-    hypot::hypot, hypotf::hypotf, log10::log10, log10f::log10f, log2::log2, log2f::log2f,
+    hypot::hypot, hypotf::hypotf, log::log, log10::log10, log10f::log10f, log2::log2, log2f::log2f,
     logf::logf, powf::powf, round::round, roundf::roundf, scalbn::scalbn, scalbnf::scalbnf,
     sqrt::sqrt, sqrtf::sqrtf, trunc::trunc, truncf::truncf,
 };

test-generator/src/main.rs

@@ -706,7 +706,7 @@ f64_f64! {
     // exp2,
     // expm1,
     floor,
-    // log,
+    log,
     log10,
     // log1p,
     log2,