add exp and log/ln functions for f32

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

@@ -0,0 +1,49 @@
+const LN2_HI : f32 = 6.9313812256e-01;  /* 0x3f317180 */
+const LN2_LO : f32 = 9.0580006145e-06; /* 0x3717f7d1 */
+/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
+const LG1    : f32 = 0.66666662693;  /*  0xaaaaaa.0p-24*/
+const LG2    : f32 = 0.40000972152;  /*  0xccce13.0p-25 */
+const LG3    : f32 = 0.28498786688;  /*  0x91e9ee.0p-25 */
+const LG4    : f32 = 0.24279078841; /*  0xf89e26.0p-26 */
+
+#[inline]
+pub fn logf(mut x: f32) -> f32 {
+    let x1p25 = f32::from_bits(0x4c000000); // 0x1p24f === 2 ^ 25
+    
+    let mut ix = x.to_bits();
+    let mut k = 0i32;
+    
+    if (ix < 0x00800000) || ((ix>>31) != 0) {  /* x < 2**-126  */
+        if ix<<1 == 0 {
+            return -1./(x*x);  /* log(+-0)=-inf */
+        }
+        if (ix>>31) != 0 {
+            return (x-x)/0.;   /* log(-#) = NaN */
+        }
+        /* subnormal number, scale up x */
+        k -= 25;
+        x *= x1p25;
+        ix = x.to_bits();
+    } else if ix >= 0x7f800000 {
+        return x;
+    } else if ix == 0x3f800000 {
+        return 0.;
+    }
+
+    /* reduce x into [sqrt(2)/2, sqrt(2)] */
+    ix += 0x3f800000 - 0x3f3504f3;
+    k += ((ix>>23) as i32) - 0x7f;
+    ix = (ix & 0x007fffff) + 0x3f3504f3;
+    x =  f32::from_bits(ix);
+
+    let f = x - 1.;
+    let s = f/(2. + f);
+    let z = s*s;
+    let w = z*z;
+    let t1 = w*(LG2+w*LG4);
+    let t2 = z*(LG1+w*LG3);
+    let r = t2 + t1;
+    let hfsq = 0.5*f*f;
+    let dk = k as f32;
+    s*(hfsq+r) + dk*LN2_LO - hfsq + f + dk*LN2_HI
+}