add exp and log/ln functions for f32

Author: burrbull

src/lib.rs

@@ -71,16 +71,13 @@ pub trait F32Ext {
 
     fn sqrt(self) -> Self;
 
-    #[cfg(todo)]
     fn exp(self) -> Self;
 
     #[cfg(todo)]
     fn exp2(self) -> Self;
 
-    #[cfg(todo)]
     fn ln(self) -> Self;
 
-    #[cfg(todo)]
     fn log(self, base: Self) -> Self;
 
     #[cfg(todo)]
@@ -220,7 +217,6 @@ impl F32Ext for f32 {
         sqrtf(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn exp(self) -> Self {
         expf(self)
@@ -232,13 +228,11 @@ impl F32Ext for f32 {
         exp2f(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn ln(self) -> Self {
         logf(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn log(self, base: Self) -> Self {
         self.ln() / base.ln()

src/math/expf.rs

@@ -0,0 +1,76 @@
+use super::scalbnf;
+
+const HALF    : [f32; 2] = [0.5,-0.5];
+const LN2_HI  : f32      = 6.9314575195e-01;  /* 0x3f317200 */
+const LN2_LO  : f32      = 1.4286067653e-06;  /* 0x35bfbe8e */
+const INV_LN2 : f32      = 1.4426950216e+00;  /* 0x3fb8aa3b */
+/*
+ * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
+ * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
+ */
+const P1 : f32 =  1.6666625440e-1;    /*  0xaaaa8f.0p-26 */
+const P2 : f32 = -2.7667332906e-3;    /* -0xb55215.0p-32 */
+
+#[inline]
+pub fn expf(mut x: f32) -> f32 {
+    let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127
+    let x1p_126 = f32::from_bits(0x800000); // 0x1p-126f === 2 ^ -126  /*original 0x1p-149f    ??????????? */
+    
+    let mut hx = x.to_bits() as i32;
+    let sign = (hx >> 31) as i32;   /* sign bit of x */
+    let signb : bool = sign != 0;
+    hx &= 0x7fffffff;  /* high word of |x| */
+    
+    /* special cases */
+    if hx >= 0x42aeac50 {  /* if |x| >= -87.33655f or NaN */
+        if hx > 0x7f800000 {/* NaN */
+            return x;
+        }
+        if (hx >= 0x42b17218) && (!signb) {  /* x >= 88.722839f */
+            /* overflow */
+            x *= x1p127;
+            return x;
+        }
+        if signb {
+            /* underflow */
+            force_eval!(-x1p_126/x);
+            if hx >= 0x42cff1b5 { /* x <= -103.972084f */
+                return 0.
+            }
+        }
+    }
+    
+    /* argument reduction */
+    let k  : i32;
+    let hi : f32;
+    let lo : f32;
+    if hx > 0x3eb17218 {     /* if |x| > 0.5 ln2 */
+        if hx > 0x3f851592 { /* if |x| > 1.5 ln2 */
+            k = (INV_LN2*x + HALF[sign as usize]) as i32;
+        } else {
+            k = 1 - sign - sign;
+        }
+        let kf = k as f32;
+        hi = x - kf*LN2_HI;  /* k*ln2hi is exact here */
+        lo = kf*LN2_LO;
+        x = hi - lo;
+    } else if hx > 0x39000000 {  /* |x| > 2**-14 */
+        k = 0;
+        hi = x;
+        lo = 0.;
+    } else {
+        /* raise inexact */
+        force_eval!(x1p127 + x);
+        return 1. + x;
+    }
+    
+    /* x is now in primary range */
+    let xx = x*x;
+    let c = x - xx*(P1+xx*P2);
+    let y = 1. + (x*c/(2.-c) - lo + hi);
+    if k == 0 {
+        y
+    } else {
+        scalbnf(y, k)
+    }
+}

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
+}

src/math/mod.rs

@@ -11,6 +11,8 @@ mod powf;
 mod round;
 mod scalbnf;
 mod sqrtf;
+mod logf;
+mod expf;
 
 pub use self::fabs::fabs;
 pub use self::fabsf::fabsf;
@@ -19,6 +21,8 @@ pub use self::powf::powf;
 pub use self::round::round;
 pub use self::scalbnf::scalbnf;
 pub use self::sqrtf::sqrtf;
+pub use self::logf::logf;
+pub use self::expf::expf;
 
 fn isnanf(x: f32) -> bool {
     x.to_bits() & 0x7fffffff > 0x7f800000