implement log10 and log10f

library/compiler-builtins/libm/src/math/log10.rs

@@ -0,0 +1,98 @@
+use core::f64;
+
+const IVLN10HI: f64 = 4.34294481878168880939e-01; /* 0x3fdbcb7b, 0x15200000 */
+const IVLN10LO: f64 = 2.50829467116452752298e-11; /* 0x3dbb9438, 0xca9aadd5 */
+const LOG10_2HI: f64 = 3.01029995663611771306e-01; /* 0x3FD34413, 0x509F6000 */
+const LOG10_2LO: f64 = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
+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 log10(mut x: f64) -> f64 {
+    let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54
+
+    let mut ui: u64 = x.to_bits();
+    let hfsq: f64;
+    let f: f64;
+    let s: f64;
+    let z: f64;
+    let r: f64;
+    let mut w: f64;
+    let t1: f64;
+    let t2: f64;
+    let dk: f64;
+    let y: f64;
+    let mut hi: f64;
+    let lo: f64;
+    let mut val_hi: f64;
+    let mut val_lo: f64;
+    let mut hx: u32;
+    let mut k: i32;
+
+    hx = (ui >> 32) as u32;
+    k = 0;
+    if hx < 0x00100000 || (hx >> 31) > 0 {
+        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);
+
+    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;
+
+    /* See log2.c for details. */
+    /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
+    hi = f - hfsq;
+    ui = hi.to_bits();
+    ui &= (-1i64 as u64) << 32;
+    hi = f64::from_bits(ui);
+    lo = f - hi - hfsq + s * (hfsq + r);
+
+    /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
+    val_hi = hi * IVLN10HI;
+    dk = k as f64;
+    y = dk * LOG10_2HI;
+    val_lo = dk * LOG10_2LO + (lo + hi) * IVLN10LO + lo * IVLN10HI;
+
+    /*
+     * Extra precision in for adding y is not strictly needed
+     * since there is no very large cancellation near x = sqrt(2) or
+     * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
+     * with some parallelism and it reduces the error for many args.
+     */
+    w = y + val_hi;
+    val_lo += (y - w) + val_hi;
+    val_hi = w;
+
+    return val_lo + val_hi;
+}