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</pre><pre class="rust"><code><span class="comment">/* 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.
*
*/
</span><span class="kw">use super</span>::{fabs, get_high_word, get_low_word, sqrt, with_set_low_word};
<span class="kw">const </span>PIO2_HI: f64 = <span class="number">1.57079632679489655800e+00</span>; <span class="comment">/* 0x3FF921FB, 0x54442D18 */
</span><span class="kw">const </span>PIO2_LO: f64 = <span class="number">6.12323399573676603587e-17</span>; <span class="comment">/* 0x3C91A626, 0x33145C07 */
/* coefficients for R(x^2) */
</span><span class="kw">const </span>P_S0: f64 = <span class="number">1.66666666666666657415e-01</span>; <span class="comment">/* 0x3FC55555, 0x55555555 */
</span><span class="kw">const </span>P_S1: f64 = -<span class="number">3.25565818622400915405e-01</span>; <span class="comment">/* 0xBFD4D612, 0x03EB6F7D */
</span><span class="kw">const </span>P_S2: f64 = <span class="number">2.01212532134862925881e-01</span>; <span class="comment">/* 0x3FC9C155, 0x0E884455 */
</span><span class="kw">const </span>P_S3: f64 = -<span class="number">4.00555345006794114027e-02</span>; <span class="comment">/* 0xBFA48228, 0xB5688F3B */
</span><span class="kw">const </span>P_S4: f64 = <span class="number">7.91534994289814532176e-04</span>; <span class="comment">/* 0x3F49EFE0, 0x7501B288 */
</span><span class="kw">const </span>P_S5: f64 = <span class="number">3.47933107596021167570e-05</span>; <span class="comment">/* 0x3F023DE1, 0x0DFDF709 */
</span><span class="kw">const </span>Q_S1: f64 = -<span class="number">2.40339491173441421878e+00</span>; <span class="comment">/* 0xC0033A27, 0x1C8A2D4B */
</span><span class="kw">const </span>Q_S2: f64 = <span class="number">2.02094576023350569471e+00</span>; <span class="comment">/* 0x40002AE5, 0x9C598AC8 */
</span><span class="kw">const </span>Q_S3: f64 = -<span class="number">6.88283971605453293030e-01</span>; <span class="comment">/* 0xBFE6066C, 0x1B8D0159 */
</span><span class="kw">const </span>Q_S4: f64 = <span class="number">7.70381505559019352791e-02</span>; <span class="comment">/* 0x3FB3B8C5, 0xB12E9282 */
</span><span class="kw">fn </span>comp_r(z: f64) -> f64 {
<span class="kw">let </span>p = z * (P_S0 + z * (P_S1 + z * (P_S2 + z * (P_S3 + z * (P_S4 + z * P_S5)))));
<span class="kw">let </span>q = <span class="number">1.0 </span>+ z * (Q_S1 + z * (Q_S2 + z * (Q_S3 + z * Q_S4)));
p / q
}
<span class="doccomment">/// Arcsine (f64)
///
/// Computes the inverse sine (arc sine) of the argument `x`.
/// Arguments to asin must be in the range -1 to 1.
/// Returns values in radians, in the range of -pi/2 to pi/2.
</span><span class="attr">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
</span><span class="kw">pub fn </span>asin(<span class="kw-2">mut </span>x: f64) -> f64 {
<span class="kw">let </span>z: f64;
<span class="kw">let </span>r: f64;
<span class="kw">let </span>s: f64;
<span class="kw">let </span>hx: u32;
<span class="kw">let </span>ix: u32;
hx = get_high_word(x);
ix = hx & <span class="number">0x7fffffff</span>;
<span class="comment">/* |x| >= 1 or nan */
</span><span class="kw">if </span>ix >= <span class="number">0x3ff00000 </span>{
<span class="kw">let </span>lx: u32;
lx = get_low_word(x);
<span class="kw">if </span>((ix - <span class="number">0x3ff00000</span>) | lx) == <span class="number">0 </span>{
<span class="comment">/* asin(1) = +-pi/2 with inexact */
</span><span class="kw">return </span>x * PIO2_HI + f64::from_bits(<span class="number">0x3870000000000000</span>);
} <span class="kw">else </span>{
<span class="kw">return </span><span class="number">0.0 </span>/ (x - x);
}
}
<span class="comment">/* |x| < 0.5 */
</span><span class="kw">if </span>ix < <span class="number">0x3fe00000 </span>{
<span class="comment">/* if 0x1p-1022 <= |x| < 0x1p-26, avoid raising underflow */
</span><span class="kw">if </span>ix < <span class="number">0x3e500000 </span>&& ix >= <span class="number">0x00100000 </span>{
<span class="kw">return </span>x;
} <span class="kw">else </span>{
<span class="kw">return </span>x + x * comp_r(x * x);
}
}
<span class="comment">/* 1 > |x| >= 0.5 */
</span>z = (<span class="number">1.0 </span>- fabs(x)) * <span class="number">0.5</span>;
s = sqrt(z);
r = comp_r(z);
<span class="kw">if </span>ix >= <span class="number">0x3fef3333 </span>{
<span class="comment">/* if |x| > 0.975 */
</span>x = PIO2_HI - (<span class="number">2. </span>* (s + s * r) - PIO2_LO);
} <span class="kw">else </span>{
<span class="kw">let </span>f: f64;
<span class="kw">let </span>c: f64;
<span class="comment">/* f+c = sqrt(z) */
</span>f = with_set_low_word(s, <span class="number">0</span>);
c = (z - f * f) / (s + f);
x = <span class="number">0.5 </span>* PIO2_HI - (<span class="number">2.0 </span>* s * r - (PIO2_LO - <span class="number">2.0 </span>* c) - (<span class="number">0.5 </span>* PIO2_HI - <span class="number">2.0 </span>* f));
}
<span class="kw">if </span>hx >> <span class="number">31 </span>!= <span class="number">0 </span>{
-x
} <span class="kw">else </span>{
x
}
}
</code></pre></div>
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