Merge rust-lang#81

81: implement log2 and log2f r=japaric a=erikdesjardins

closes rust-lang#27, closes rust-lang#28

Co-authored-by: Erik <[email protected]>

Author: bors[bot]

src/lib.rs

@@ -75,7 +75,6 @@ pub trait F32Ext: private::Sealed {
 
     fn log(self, base: Self) -> Self;
 
-    #[cfg(todo)]
     fn log2(self) -> Self;
 
     #[cfg(todo)]
@@ -228,7 +227,6 @@ impl F32Ext for f32 {
         self.ln() / base.ln()
     }
 
-    #[cfg(todo)]
     #[inline]
     fn log2(self) -> Self {
         log2f(self)
@@ -399,7 +397,6 @@ pub trait F64Ext: private::Sealed {
     #[cfg(todo)]
     fn log(self, base: Self) -> Self;
 
-    #[cfg(todo)]
     fn log2(self) -> Self;
 
     #[cfg(todo)]
@@ -557,7 +554,6 @@ impl F64Ext for f64 {
         self.ln() / base.ln()
     }
 
-    #[cfg(todo)]
     #[inline]
     fn log2(self) -> Self {
         log2(self)

src/math/log2.rs

@@ -0,0 +1,86 @@
+use core::f64;
+
+const IVLN2HI: f64 = 1.44269504072144627571e+00; /* 0x3ff71547, 0x65200000 */
+const IVLN2LO: f64 = 1.67517131648865118353e-10; /* 0x3de705fc, 0x2eefa200 */
+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 */
+
+pub fn log2(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 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;
+
+    /* 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 = hi * IVLN2HI;
+    val_lo = (lo + hi) * IVLN2LO + lo * IVLN2HI;
+
+    /* spadd(val_hi, val_lo, y), except for not using double_t: */
+    y = k.into();
+    w = y + val_hi;
+    val_lo += (y - w) + val_hi;
+    val_hi = w;
+
+    return val_lo + val_hi;
+}

src/math/log2f.rs

@@ -0,0 +1,71 @@
+use core::f32;
+
+const IVLN2HI: f32 = 1.4428710938e+00; /* 0x3fb8b000 */
+const IVLN2LO: f32 = -1.7605285393e-04; /* 0xb9389ad4 */
+/* |(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 */
+
+pub fn log2f(mut x: f32) -> f32 {
+    let x1p25f = f32::from_bits(0x4c000000); // 0x1p25f === 2 ^ 25
+
+    let mut ui: u32 = x.to_bits();
+    let hfsq: f32;
+    let f: f32;
+    let s: f32;
+    let z: f32;
+    let r: f32;
+    let w: f32;
+    let t1: f32;
+    let t2: f32;
+    let mut hi: f32;
+    let lo: f32;
+    let mut ix: u32;
+    let mut k: i32;
+
+    ix = ui;
+    k = 0;
+    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) / 0.0; /* log(-#) = NaN */
+        }
+        /* subnormal number, scale up x */
+        k -= 25;
+        x *= x1p25f;
+        ui = x.to_bits();
+        ix = ui;
+    } 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;
+    ui = ix;
+    x = f32::from_bits(ui);
+
+    f = x - 1.0;
+    s = f / (2.0 + f);
+    z = s * s;
+    w = z * z;
+    t1 = w * (LG2 + w * LG4);
+    t2 = z * (LG1 + w * LG3);
+    r = t2 + t1;
+    hfsq = 0.5 * f * f;
+
+    hi = f - hfsq;
+    ui = hi.to_bits();
+    ui &= 0xfffff000;
+    hi = f32::from_bits(ui);
+    lo = f - hi - hfsq + s * (hfsq + r);
+    return (lo + hi) * IVLN2LO + lo * IVLN2HI + hi * IVLN2HI + k as f32;
+}

src/math/mod.rs

@@ -15,6 +15,8 @@ mod floorf;
 mod fmodf;
 mod hypot;
 mod hypotf;
+mod log2;
+mod log2f;
 mod logf;
 mod powf;
 mod round;
@@ -30,8 +32,9 @@ mod truncf;
 
 pub use self::{
     ceilf::ceilf, expf::expf, fabs::fabs, fabsf::fabsf, floor::floor, floorf::floorf, fmodf::fmodf,
-    hypot::hypot, hypotf::hypotf, logf::logf, powf::powf, round::round, roundf::roundf,
-    scalbn::scalbn, scalbnf::scalbnf, sqrt::sqrt, sqrtf::sqrtf, trunc::trunc, truncf::truncf,
+    hypot::hypot, hypotf::hypotf, log2::log2, log2f::log2f, logf::logf, powf::powf, round::round,
+    roundf::roundf, scalbn::scalbn, scalbnf::scalbnf, sqrt::sqrt, sqrtf::sqrtf, trunc::trunc,
+    truncf::truncf,
 };
 
 fn isnanf(x: f32) -> bool {

test-generator/src/main.rs

@@ -664,7 +664,7 @@ f32_f32! {
     expf,
     // fdimf,
     // log10f,
-    // log2f,
+    log2f,
     logf,
     roundf,
     // sinf,
@@ -709,7 +709,7 @@ f64_f64! {
     // log,
     // log10,
     // log1p,
-    // log2,
+    log2,
     round,
     // sin,
     // sinh,