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