add an implemetation of asin

Fixes #7

Additonally adds inline functions for macros dealing with low and high words of f64s to the root module.

Also, the muslc code used a hexdecimal float. This shouldn't be needed because Rust implements
floating point parsing well.

src/math/asin.rs

@@ -0,0 +1,113 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_asin.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.
+ * ====================================================
+ */
+/* asin(x)
+ * Method :
+ *      Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
+ *      we approximate asin(x) on [0,0.5] by
+ *              asin(x) = x + x*x^2*R(x^2)
+ *      where
+ *              R(x^2) is a rational approximation of (asin(x)-x)/x^3
+ *      and its remez error is bounded by
+ *              |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
+ *
+ *      For x in [0.5,1]
+ *              asin(x) = pi/2-2*asin(sqrt((1-x)/2))
+ *      Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
+ *      then for x>0.98
+ *              asin(x) = pi/2 - 2*(s+s*z*R(z))
+ *                      = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
+ *      For x<=0.98, let pio4_hi = pio2_hi/2, then
+ *              f = hi part of s;
+ *              c = sqrt(z) - f = (z-f*f)/(s+f)         ...f+c=sqrt(z)
+ *      and
+ *              asin(x) = pi/2 - 2*(s+s*z*R(z))
+ *                      = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
+ *                      = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
+ *
+ * Special cases:
+ *      if x is NaN, return x itself;
+ *      if |x|>1, return NaN with invalid signal.
+ *
+ */
+
+use super::{fabs, get_high_word, get_low_word, sqrt, with_set_low_word};
+
+const PIO2_HI: f64 = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
+const PIO2_LO: f64 = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
+/* coefficients for R(x^2) */
+const P_S0: f64 = 1.66666666666666657415e-01; /* 0x3FC55555, 0x55555555 */
+const P_S1: f64 = -3.25565818622400915405e-01; /* 0xBFD4D612, 0x03EB6F7D */
+const P_S2: f64 = 2.01212532134862925881e-01; /* 0x3FC9C155, 0x0E884455 */
+const P_S3: f64 = -4.00555345006794114027e-02; /* 0xBFA48228, 0xB5688F3B */
+const P_S4: f64 = 7.91534994289814532176e-04; /* 0x3F49EFE0, 0x7501B288 */
+const P_S5: f64 = 3.47933107596021167570e-05; /* 0x3F023DE1, 0x0DFDF709 */
+const Q_S1: f64 = -2.40339491173441421878e+00; /* 0xC0033A27, 0x1C8A2D4B */
+const Q_S2: f64 = 2.02094576023350569471e+00; /* 0x40002AE5, 0x9C598AC8 */
+const Q_S3: f64 = -6.88283971605453293030e-01; /* 0xBFE6066C, 0x1B8D0159 */
+const Q_S4: f64 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+fn comp_r(z: f64) -> f64 {
+    let p = z * (P_S0 + z * (P_S1 + z * (P_S2 + z * (P_S3 + z * (P_S4 + z * P_S5)))));
+    let q = 1.0 + z * (Q_S1 + z * (Q_S2 + z * (Q_S3 + z * Q_S4)));
+    return p / q;
+}
+
+pub fn asin(mut x: f64) -> f64 {
+    let z: f64;
+    let r: f64;
+    let s: f64;
+    let hx: u32;
+    let ix: u32;
+
+    hx = get_high_word(x);
+    ix = hx & 0x7fffffff;
+    /* |x| >= 1 or nan */
+    if ix >= 0x3ff00000 {
+        let lx: u32;
+        lx = get_low_word(x);
+        if (ix - 0x3ff00000 | lx) == 0 {
+            /* asin(1) = +-pi/2 with inexact */
+            return x * PIO2_HI + f64::from_bits(0x3870000000000000);
+        } else {
+            return 0.0 / (x - x);
+        }
+    }
+    /* |x| < 0.5 */
+    if ix < 0x3fe00000 {
+        /* if 0x1p-1022 <= |x| < 0x1p-26, avoid raising underflow */
+        if ix < 0x3e500000 && ix >= 0x00100000 {
+            return x;
+        } else {
+            return x + x * comp_r(x * x);
+        }
+    }
+    /* 1 > |x| >= 0.5 */
+    z = (1.0 - fabs(x)) * 0.5;
+    s = sqrt(z);
+    r = comp_r(z);
+    if ix >= 0x3fef3333 {
+        /* if |x| > 0.975 */
+        x = PIO2_HI - (2. * (s + s * r) - PIO2_LO);
+    } else {
+        let f: f64;
+        let c: f64;
+        /* f+c = sqrt(z) */
+        f = with_set_low_word(s, 0);
+        c = (z - f * f) / (s + f);
+        x = 0.5 * PIO2_HI - (2.0 * s * r - (PIO2_LO - 2.0 * c) - (0.5 * PIO2_HI - 2.0 * f));
+    }
+    if hx >> 31 != 0 {
+        return -x;
+    } else {
+        return x;
+    }
+}

src/math/mod.rs

@@ -8,6 +8,7 @@ macro_rules! force_eval {
 
 mod acos;
 mod acosf;
+mod asin;
 mod asinf;
 mod atanf;
 mod cbrt;
@@ -55,6 +56,7 @@ mod truncf;
 // Use separated imports instead of {}-grouped imports for easier merging.
 pub use self::acos::acos;
 pub use self::acosf::acosf;
+pub use self::asin::asin;
 pub use self::asinf::asinf;
 pub use self::atanf::atanf;
 pub use self::cbrt::cbrt;
@@ -109,3 +111,29 @@ use self::{
     k_cosf::k_cosf, k_sinf::k_sinf, k_tanf::k_tanf, rem_pio2_large::rem_pio2_large,
     rem_pio2f::rem_pio2f,
 };
+
+#[inline]
+pub fn get_high_word(x: f64) -> u32 {
+    (x.to_bits() >> 32) as u32
+}
+
+#[inline]
+pub fn get_low_word(x: f64) -> u32 {
+    x.to_bits() as u32
+}
+
+#[inline]
+pub fn with_set_high_word(f: f64, hi: u32) -> f64 {
+    let mut tmp = f.to_bits();
+    tmp &= 0x00000000_ffffffff;
+    tmp |= (hi as u64) << 32;
+    f64::from_bits(tmp)
+}
+
+#[inline]
+pub fn with_set_low_word(f: f64, lo: u32) -> f64 {
+    let mut tmp = f.to_bits();
+    tmp &= 0xffffffff_00000000;
+    tmp |= lo as u64;
+    f64::from_bits(tmp)
+}

test-generator/src/main.rs

@@ -698,7 +698,7 @@ f32i32_f32! {
 // With signature `fn(f64) -> f64`
 f64_f64! {
     acos,
-    // asin,
+    asin,
     // atan,
     cbrt,
     ceil,