Merge rust-lang/libm#89

89: Adding acos implementation r=japaric a=leesdolphin

Fixes rust-lang/libm#6



Co-authored-by: Opal <leesdolphin@gmail.com>
Co-authored-by: Jorge Aparicio <jorge@japaric.io>

library/compiler-builtins/libm/src/lib.rs

@@ -414,7 +414,6 @@ pub trait F64Ext: private::Sealed {
     #[cfg(todo)]
     fn asin(self) -> Self;
 
-    #[cfg(todo)]
     fn acos(self) -> Self;
 
     #[cfg(todo)]
@@ -592,7 +591,6 @@ impl F64Ext for f64 {
         asin(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn acos(self) -> Self {
         acos(self)

library/compiler-builtins/libm/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);
+}

library/compiler-builtins/libm/src/math/mod.rs

@@ -6,6 +6,7 @@ macro_rules! force_eval {
     };
 }
 
+mod acos;
 mod cbrt;
 mod cbrtf;
 mod ceil;
@@ -42,6 +43,7 @@ mod trunc;
 mod truncf;
 
 // Use separated imports instead of {}-grouped imports for easier merging.
+pub use self::acos::acos;
 pub use self::cbrt::cbrt;
 pub use self::cbrtf::cbrtf;
 pub use self::ceil::ceil;

library/compiler-builtins/libm/test-generator/src/main.rs

@@ -696,7 +696,7 @@ f32i32_f32! {
 
 // With signature `fn(f64) -> f64`
 f64_f64! {
-    // acos,
+    acos,
     // asin,
     // atan,
     cbrt,