Merge rust-lang#101

101: implement cbrt and cbrtf r=japaric a=erikdesjardins

closes rust-lang#10, closes rust-lang#43

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

Author: bors[bot]

src/lib.rs

@@ -81,7 +81,6 @@ pub trait F32Ext: private::Sealed {
 
     fn log10(self) -> Self;
 
-    #[cfg(todo)]
     fn cbrt(self) -> Self;
 
     fn hypot(self, other: Self) -> Self;
@@ -241,7 +240,6 @@ impl F32Ext for f32 {
         log10f(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn cbrt(self) -> Self {
         cbrtf(self)
@@ -400,7 +398,6 @@ pub trait F64Ext: private::Sealed {
 
     fn log10(self) -> Self;
 
-    #[cfg(todo)]
     fn cbrt(self) -> Self;
 
     fn hypot(self, other: Self) -> Self;
@@ -561,7 +558,6 @@ impl F64Ext for f64 {
         log10(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn cbrt(self) -> Self {
         cbrt(self)

src/math/cbrt.rs

@@ -0,0 +1,110 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrt.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.
+ * ====================================================
+ *
+ * Optimized by Bruce D. Evans.
+ */
+/* cbrt(x)
+ * Return cube root of x
+ */
+
+use core::f64;
+
+const B1: u32 = 715094163; /* B1 = (1023-1023/3-0.03306235651)*2**20 */
+const B2: u32 = 696219795; /* B2 = (1023-1023/3-54/3-0.03306235651)*2**20 */
+
+/* |1/cbrt(x) - p(x)| < 2**-23.5 (~[-7.93e-8, 7.929e-8]). */
+const P0: f64 = 1.87595182427177009643; /* 0x3ffe03e6, 0x0f61e692 */
+const P1: f64 = -1.88497979543377169875; /* 0xbffe28e0, 0x92f02420 */
+const P2: f64 = 1.621429720105354466140; /* 0x3ff9f160, 0x4a49d6c2 */
+const P3: f64 = -0.758397934778766047437; /* 0xbfe844cb, 0xbee751d9 */
+const P4: f64 = 0.145996192886612446982; /* 0x3fc2b000, 0xd4e4edd7 */
+
+#[inline]
+pub fn cbrt(x: f64) -> f64 {
+    let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54
+
+    let mut ui: u64 = x.to_bits();
+    let mut r: f64;
+    let s: f64;
+    let mut t: f64;
+    let w: f64;
+    let mut hx: u32 = (ui >> 32) as u32 & 0x7fffffff;
+
+    if hx >= 0x7ff00000 {
+        /* cbrt(NaN,INF) is itself */
+        return x + x;
+    }
+
+    /*
+     * Rough cbrt to 5 bits:
+     *    cbrt(2**e*(1+m) ~= 2**(e/3)*(1+(e%3+m)/3)
+     * where e is integral and >= 0, m is real and in [0, 1), and "/" and
+     * "%" are integer division and modulus with rounding towards minus
+     * infinity.  The RHS is always >= the LHS and has a maximum relative
+     * error of about 1 in 16.  Adding a bias of -0.03306235651 to the
+     * (e%3+m)/3 term reduces the error to about 1 in 32. With the IEEE
+     * floating point representation, for finite positive normal values,
+     * ordinary integer divison of the value in bits magically gives
+     * almost exactly the RHS of the above provided we first subtract the
+     * exponent bias (1023 for doubles) and later add it back.  We do the
+     * subtraction virtually to keep e >= 0 so that ordinary integer
+     * division rounds towards minus infinity; this is also efficient.
+     */
+    if hx < 0x00100000 {
+        /* zero or subnormal? */
+        ui = (x * x1p54).to_bits();
+        hx = (ui >> 32) as u32 & 0x7fffffff;
+        if hx == 0 {
+            return x; /* cbrt(0) is itself */
+        }
+        hx = hx / 3 + B2;
+    } else {
+        hx = hx / 3 + B1;
+    }
+    ui &= 1 << 63;
+    ui |= (hx as u64) << 32;
+    t = f64::from_bits(ui);
+
+    /*
+     * New cbrt to 23 bits:
+     *    cbrt(x) = t*cbrt(x/t**3) ~= t*P(t**3/x)
+     * where P(r) is a polynomial of degree 4 that approximates 1/cbrt(r)
+     * to within 2**-23.5 when |r - 1| < 1/10.  The rough approximation
+     * has produced t such than |t/cbrt(x) - 1| ~< 1/32, and cubing this
+     * gives us bounds for r = t**3/x.
+     *
+     * Try to optimize for parallel evaluation as in __tanf.c.
+     */
+    r = (t * t) * (t / x);
+    t = t * ((P0 + r * (P1 + r * P2)) + ((r * r) * r) * (P3 + r * P4));
+
+    /*
+     * Round t away from zero to 23 bits (sloppily except for ensuring that
+     * the result is larger in magnitude than cbrt(x) but not much more than
+     * 2 23-bit ulps larger).  With rounding towards zero, the error bound
+     * would be ~5/6 instead of ~4/6.  With a maximum error of 2 23-bit ulps
+     * in the rounded t, the infinite-precision error in the Newton
+     * approximation barely affects third digit in the final error
+     * 0.667; the error in the rounded t can be up to about 3 23-bit ulps
+     * before the final error is larger than 0.667 ulps.
+     */
+    ui = t.to_bits();
+    ui = (ui + 0x80000000) & 0xffffffffc0000000;
+    t = f64::from_bits(ui);
+
+    /* one step Newton iteration to 53 bits with error < 0.667 ulps */
+    s = t * t; /* t*t is exact */
+    r = x / s; /* error <= 0.5 ulps; |r| < |t| */
+    w = t + t; /* t+t is exact */
+    r = (r - t) / (w + r); /* r-t is exact; w+r ~= 3*t */
+    t = t + t * r; /* error <= 0.5 + 0.5/3 + epsilon */
+    t
+}

src/math/cbrtf.rs

@@ -0,0 +1,72 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
+ * Debugged and optimized by Bruce D. Evans.
+ */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+/* cbrtf(x)
+ * Return cube root of x
+ */
+
+use core::f32;
+
+const B1: u32 = 709958130; /* B1 = (127-127.0/3-0.03306235651)*2**23 */
+const B2: u32 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
+
+#[inline]
+pub fn cbrtf(x: f32) -> f32 {
+    let x1p24 = f32::from_bits(0x4b800000); // 0x1p24f === 2 ^ 24
+
+    let mut r: f64;
+    let mut t: f64;
+    let mut ui: u32 = x.to_bits();
+    let mut hx: u32 = ui & 0x7fffffff;
+
+    if hx >= 0x7f800000 {
+        /* cbrt(NaN,INF) is itself */
+        return x + x;
+    }
+
+    /* rough cbrt to 5 bits */
+    if hx < 0x00800000 {
+        /* zero or subnormal? */
+        if hx == 0 {
+            return x; /* cbrt(+-0) is itself */
+        }
+        ui = (x * x1p24).to_bits();
+        hx = ui & 0x7fffffff;
+        hx = hx / 3 + B2;
+    } else {
+        hx = hx / 3 + B1;
+    }
+    ui &= 0x80000000;
+    ui |= hx;
+
+    /*
+     * First step Newton iteration (solving t*t-x/t == 0) to 16 bits.  In
+     * double precision so that its terms can be arranged for efficiency
+     * without causing overflow or underflow.
+     */
+    t = f32::from_bits(ui) as f64;
+    r = t * t * t;
+    t = t * (x as f64 + x as f64 + r) / (x as f64 + r + r);
+
+    /*
+     * Second step Newton iteration to 47 bits.  In double precision for
+     * efficiency and accuracy.
+     */
+    r = t * t * t;
+    t = t * (x as f64 + x as f64 + r) / (x as f64 + r + r);
+
+    /* rounding to 24 bits is perfect in round-to-nearest mode */
+    t as f32
+}

src/math/mod.rs

@@ -6,6 +6,8 @@ macro_rules! force_eval {
     };
 }
 
+mod cbrt;
+mod cbrtf;
 mod ceil;
 mod ceilf;
 mod cosf;
@@ -39,6 +41,8 @@ mod trunc;
 mod truncf;
 
 // Use separated imports instead of {}-grouped imports for easier merging.
+pub use self::cbrt::cbrt;
+pub use self::cbrtf::cbrtf;
 pub use self::ceil::ceil;
 pub use self::ceilf::ceilf;
 pub use self::cosf::cosf;

test-generator/src/main.rs

@@ -656,7 +656,7 @@ f32_f32! {
     truncf,
     // asinf,
     // atanf,
-    // cbrtf,
+    cbrtf,
     cosf,
     ceilf,
     // coshf,
@@ -699,7 +699,7 @@ f64_f64! {
     // acos,
     // asin,
     // atan,
-    // cbrt,
+    cbrt,
     ceil,
     // cos,
     // cosh,