implement log1p and log1pf

Author: erikdesjardins

src/lib.rs

@@ -114,7 +114,6 @@ pub trait F32Ext: private::Sealed {
     #[cfg(todo)]
     fn exp_m1(self) -> Self;
 
-    #[cfg(todo)]
     fn ln_1p(self) -> Self;
 
     #[cfg(todo)]
@@ -295,7 +294,6 @@ impl F32Ext for f32 {
         expm1f(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn ln_1p(self) -> Self {
         log1pf(self)
@@ -432,7 +430,6 @@ pub trait F64Ext: private::Sealed {
     #[cfg(todo)]
     fn exp_m1(self) -> Self;
 
-    #[cfg(todo)]
     fn ln_1p(self) -> Self;
 
     #[cfg(todo)]
@@ -616,7 +613,6 @@ impl F64Ext for f64 {
         expm1(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn ln_1p(self) -> Self {
         log1p(self)

src/math/log1p.rs

@@ -0,0 +1,142 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_log1p.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* double log1p(double x)
+ * Return the natural logarithm of 1+x.
+ *
+ * Method :
+ *   1. Argument Reduction: find k and f such that
+ *                      1+x = 2^k * (1+f),
+ *         where  sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ *      Note. If k=0, then f=x is exact. However, if k!=0, then f
+ *      may not be representable exactly. In that case, a correction
+ *      term is need. Let u=1+x rounded. Let c = (1+x)-u, then
+ *      log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
+ *      and add back the correction term c/u.
+ *      (Note: when x > 2**53, one can simply return log(x))
+ *
+ *   2. Approximation of log(1+f): See log.c
+ *
+ *   3. Finally, log1p(x) = k*ln2 + log(1+f) + c/u. See log.c
+ *
+ * Special cases:
+ *      log1p(x) is NaN with signal if x < -1 (including -INF) ;
+ *      log1p(+INF) is +INF; log1p(-1) is -INF with signal;
+ *      log1p(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.
+ *
+ * Note: Assuming log() return accurate answer, the following
+ *       algorithm can be used to compute log1p(x) to within a few ULP:
+ *
+ *              u = 1+x;
+ *              if(u==1.0) return x ; else
+ *                         return log(u)*(x/(u-1.0));
+ *
+ *       See HP-15C Advanced Functions Handbook, p.193.
+ */
+
+use core::f64;
+
+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 */
+
+pub fn log1p(x: f64) -> f64 {
+    let mut ui: u64 = x.to_bits();
+    let hfsq: f64;
+    let mut f: f64 = 0.;
+    let mut c: f64 = 0.;
+    let s: f64;
+    let z: f64;
+    let r: f64;
+    let w: f64;
+    let t1: f64;
+    let t2: f64;
+    let dk: f64;
+    let hx: u32;
+    let mut hu: u32;
+    let mut k: i32;
+
+    hx = (ui >> 32) as u32;
+    k = 1;
+    if hx < 0x3fda827a || (hx >> 31) > 0 {
+        /* 1+x < sqrt(2)+ */
+        if hx >= 0xbff00000 {
+            /* x <= -1.0 */
+            if x == -1. {
+                return x / 0.0; /* log1p(-1) = -inf */
+            }
+            return (x - x) / 0.0; /* log1p(x<-1) = NaN */
+        }
+        if hx << 1 < 0x3ca00000 << 1 {
+            /* |x| < 2**-53 */
+            /* underflow if subnormal */
+            if (hx & 0x7ff00000) == 0 {
+                force_eval!(x as f32);
+            }
+            return x;
+        }
+        if hx <= 0xbfd2bec4 {
+            /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
+            k = 0;
+            c = 0.;
+            f = x;
+        }
+    } else if hx >= 0x7ff00000 {
+        return x;
+    }
+    if k > 0 {
+        ui = (1. + x).to_bits();
+        hu = (ui >> 32) as u32;
+        hu += 0x3ff00000 - 0x3fe6a09e;
+        k = (hu >> 20) as i32 - 0x3ff;
+        /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
+        if k < 54 {
+            c = if k >= 2 {
+                1. - (f64::from_bits(ui) - x)
+            } else {
+                x - (f64::from_bits(ui) - 1.)
+            };
+            c /= f64::from_bits(ui);
+        } else {
+            c = 0.;
+        }
+        /* reduce u into [sqrt(2)/2, sqrt(2)] */
+        hu = (hu & 0x000fffff) + 0x3fe6a09e;
+        ui = (hu as u64) << 32 | (ui & 0xffffffff);
+        f = f64::from_bits(ui) - 1.;
+    }
+    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;
+    dk = k as f64;
+    return s * (hfsq + r) + (dk * LN2_LO + c) - hfsq + f + dk * LN2_HI;
+}

src/math/log1pf.rs

@@ -0,0 +1,97 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use core::f32;
+
+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 */
+
+pub fn log1pf(x: f32) -> f32 {
+    let mut ui: u32 = x.to_bits();
+    let hfsq: f32;
+    let mut f: f32 = 0.;
+    let mut c: f32 = 0.;
+    let s: f32;
+    let z: f32;
+    let r: f32;
+    let w: f32;
+    let t1: f32;
+    let t2: f32;
+    let dk: f32;
+    let ix: u32;
+    let mut iu: u32;
+    let mut k: i32;
+
+    ix = ui;
+    k = 1;
+    if ix < 0x3ed413d0 || (ix >> 31) > 0 {
+        /* 1+x < sqrt(2)+  */
+        if ix >= 0xbf800000 {
+            /* x <= -1.0 */
+            if x == -1. {
+                return x / 0.0; /* log1p(-1)=+inf */
+            }
+            return (x - x) / 0.0; /* log1p(x<-1)=NaN */
+        }
+        if ix << 1 < 0x33800000 << 1 {
+            /* |x| < 2**-24 */
+            /* underflow if subnormal */
+            if (ix & 0x7f800000) == 0 {
+                force_eval!(x * x);
+            }
+            return x;
+        }
+        if ix <= 0xbe95f619 {
+            /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
+            k = 0;
+            c = 0.;
+            f = x;
+        }
+    } else if ix >= 0x7f800000 {
+        return x;
+    }
+    if k > 0 {
+        ui = (1. + x).to_bits();
+        iu = ui;
+        iu += 0x3f800000 - 0x3f3504f3;
+        k = (iu >> 23) as i32 - 0x7f;
+        /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
+        if k < 25 {
+            c = if k >= 2 {
+                1. - (f32::from_bits(ui) - x)
+            } else {
+                x - (f32::from_bits(ui) - 1.)
+            };
+            c /= f32::from_bits(ui);
+        } else {
+            c = 0.;
+        }
+        /* reduce u into [sqrt(2)/2, sqrt(2)] */
+        iu = (iu & 0x007fffff) + 0x3f3504f3;
+        ui = iu;
+        f = f32::from_bits(ui) - 1.;
+    }
+    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;
+    dk = k as f32;
+    return s * (hfsq + r) + (dk * LN2_LO + c) - hfsq + f + dk * LN2_HI;
+}

src/math/mod.rs

@@ -18,6 +18,8 @@ mod hypotf;
 mod log;
 mod log10;
 mod log10f;
+mod log1p;
+mod log1pf;
 mod log2;
 mod log2f;
 mod logf;
@@ -35,9 +37,9 @@ mod truncf;
 
 pub use self::{
     ceilf::ceilf, expf::expf, fabs::fabs, fabsf::fabsf, floor::floor, floorf::floorf, fmodf::fmodf,
-    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,
+    hypot::hypot, hypotf::hypotf, log::log, log10::log10, log10f::log10f, log1p::log1p,
+    log1pf::log1pf, 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

@@ -664,6 +664,7 @@ f32_f32! {
     expf,
     // fdimf,
     log10f,
+    log1pf,
     log2f,
     logf,
     roundf,
@@ -708,7 +709,7 @@ f64_f64! {
     floor,
     log,
     log10,
-    // log1p,
+    log1p,
     log2,
     round,
     // sin,