fix bit shifting error

Author: Veykril

src/lib.rs

@@ -70,7 +70,6 @@ pub trait F32Ext: private::Sealed {
 
     fn exp(self) -> Self;
 
-    #[cfg(todo)]
     fn exp2(self) -> Self;
 
     fn ln(self) -> Self;
@@ -81,7 +80,6 @@ pub trait F32Ext: private::Sealed {
 
     fn log10(self) -> Self;
 
-    #[cfg(todo)]
     fn cbrt(self) -> Self;
 
     fn hypot(self, other: Self) -> Self;
@@ -215,7 +213,6 @@ impl F32Ext for f32 {
         expf(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn exp2(self) -> Self {
         exp2f(self)
@@ -241,7 +238,6 @@ impl F32Ext for f32 {
         log10f(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn cbrt(self) -> Self {
         cbrtf(self)
@@ -389,7 +385,6 @@ pub trait F64Ext: private::Sealed {
 
     fn exp(self) -> Self;
 
-    #[cfg(todo)]
     fn exp2(self) -> Self;
 
     fn ln(self) -> Self;
@@ -400,7 +395,6 @@ pub trait F64Ext: private::Sealed {
 
     fn log10(self) -> Self;
 
-    #[cfg(todo)]
     fn cbrt(self) -> Self;
 
     fn hypot(self, other: Self) -> Self;
@@ -417,7 +411,6 @@ pub trait F64Ext: private::Sealed {
     #[cfg(todo)]
     fn asin(self) -> Self;
 
-    #[cfg(todo)]
     fn acos(self) -> Self;
 
     #[cfg(todo)]
@@ -534,7 +527,6 @@ impl F64Ext for f64 {
         exp(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn exp2(self) -> Self {
         exp2(self)
@@ -560,7 +552,6 @@ impl F64Ext for f64 {
         log10(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn cbrt(self) -> Self {
         cbrt(self)
@@ -595,7 +586,6 @@ impl F64Ext for f64 {
         asin(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn acos(self) -> Self {
         acos(self)

src/math/acos.rs

@@ -0,0 +1,108 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* acos(x)
+ * Method :
+ *      acos(x)  = pi/2 - asin(x)
+ *      acos(-x) = pi/2 + asin(x)
+ * For |x|<=0.5
+ *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
+ * For x>0.5
+ *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
+ *              = 2asin(sqrt((1-x)/2))
+ *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
+ *              = 2f + (2c + 2s*z*R(z))
+ *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
+ *     for f so that f+c ~ sqrt(z).
+ * For x<-0.5
+ *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
+ *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
+ *
+ * Special cases:
+ *      if x is NaN, return x itself;
+ *      if |x|>1, return NaN with invalid signal.
+ *
+ * Function needed: sqrt
+ */
+
+use super::sqrt;
+
+const PIO2_HI: f64 = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
+const PIO2_LO: f64 = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
+const PS0: f64 = 1.66666666666666657415e-01; /* 0x3FC55555, 0x55555555 */
+const PS1: f64 = -3.25565818622400915405e-01; /* 0xBFD4D612, 0x03EB6F7D */
+const PS2: f64 = 2.01212532134862925881e-01; /* 0x3FC9C155, 0x0E884455 */
+const PS3: f64 = -4.00555345006794114027e-02; /* 0xBFA48228, 0xB5688F3B */
+const PS4: f64 = 7.91534994289814532176e-04; /* 0x3F49EFE0, 0x7501B288 */
+const PS5: f64 = 3.47933107596021167570e-05; /* 0x3F023DE1, 0x0DFDF709 */
+const QS1: f64 = -2.40339491173441421878e+00; /* 0xC0033A27, 0x1C8A2D4B */
+const QS2: f64 = 2.02094576023350569471e+00; /* 0x40002AE5, 0x9C598AC8 */
+const QS3: f64 = -6.88283971605453293030e-01; /* 0xBFE6066C, 0x1B8D0159 */
+const QS4: f64 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+#[inline]
+fn r(z: f64) -> f64 {
+    let p: f64 = z * (PS0 + z * (PS1 + z * (PS2 + z * (PS3 + z * (PS4 + z * PS5)))));
+    let q: f64 = 1.0 + z * (QS1 + z * (QS2 + z * (QS3 + z * QS4)));
+    return p / q;
+}
+
+#[inline]
+pub fn acos(x: f64) -> f64 {
+    let x1p_120f = f64::from_bits(0x3870000000000000); // 0x1p-120 === 2 ^ -120
+    let z: f64;
+    let w: f64;
+    let s: f64;
+    let c: f64;
+    let df: f64;
+    let hx: u32;
+    let ix: u32;
+
+    hx = (x.to_bits() >> 32) as u32;
+    ix = hx & 0x7fffffff;
+    /* |x| >= 1 or nan */
+    if ix >= 0x3ff00000 {
+        let lx: u32 = x.to_bits() as u32;
+
+        if (ix - 0x3ff00000 | lx) == 0 {
+            /* acos(1)=0, acos(-1)=pi */
+            if (hx >> 31) != 0 {
+                return 2. * PIO2_HI + x1p_120f;
+            }
+            return 0.;
+        }
+        return 0. / (x - x);
+    }
+    /* |x| < 0.5 */
+    if ix < 0x3fe00000 {
+        if ix <= 0x3c600000 {
+            /* |x| < 2**-57 */
+            return PIO2_HI + x1p_120f;
+        }
+        return PIO2_HI - (x - (PIO2_LO - x * r(x * x)));
+    }
+    /* x < -0.5 */
+    if (hx >> 31) != 0 {
+        z = (1.0 + x) * 0.5;
+        s = sqrt(z);
+        w = r(z) * s - PIO2_LO;
+        return 2. * (PIO2_HI - (s + w));
+    }
+    /* x > 0.5 */
+    z = (1.0 - x) * 0.5;
+    s = sqrt(z);
+    // Set the low 4 bytes to zero
+    df = f64::from_bits(s.to_bits() & 0xff_ff_ff_ff_00_00_00_00);
+
+    c = (z - df * df) / (s + df);
+    w = r(z) * s + c;
+    return 2. * (df + w);
+}

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
+}