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| <span id="513">513</span> |
| <span id="514">514</span> |
| <span id="515">515</span> |
| <span id="516">516</span> |
| <span id="517">517</span> |
| <span id="518">518</span> |
| <span id="519">519</span> |
| <span id="520">520</span> |
| <span id="521">521</span> |
| <span id="522">522</span> |
| <span id="523">523</span> |
| <span id="524">524</span> |
| <span id="525">525</span> |
| <span id="526">526</span> |
| <span id="527">527</span> |
| <span id="528">528</span> |
| <span id="529">529</span> |
| <span id="530">530</span> |
| <span id="531">531</span> |
| <span id="532">532</span> |
| <span id="533">533</span> |
| <span id="534">534</span> |
| <span id="535">535</span> |
| <span id="536">536</span> |
| <span id="537">537</span> |
| <span id="538">538</span> |
| <span id="539">539</span> |
| <span id="540">540</span> |
| <span id="541">541</span> |
| <span id="542">542</span> |
| <span id="543">543</span> |
| <span id="544">544</span> |
| <span id="545">545</span> |
| <span id="546">546</span> |
| <span id="547">547</span> |
| <span id="548">548</span> |
| <span id="549">549</span> |
| <span id="550">550</span> |
| <span id="551">551</span> |
| <span id="552">552</span> |
| <span id="553">553</span> |
| <span id="554">554</span> |
| <span id="555">555</span> |
| <span id="556">556</span> |
| <span id="557">557</span> |
| <span id="558">558</span> |
| <span id="559">559</span> |
| <span id="560">560</span> |
| <span id="561">561</span> |
| <span id="562">562</span> |
| <span id="563">563</span> |
| <span id="564">564</span> |
| <span id="565">565</span> |
| <span id="566">566</span> |
| <span id="567">567</span> |
| <span id="568">568</span> |
| <span id="569">569</span> |
| <span id="570">570</span> |
| <span id="571">571</span> |
| <span id="572">572</span> |
| <span id="573">573</span> |
| <span id="574">574</span> |
| <span id="575">575</span> |
| <span id="576">576</span> |
| <span id="577">577</span> |
| <span id="578">578</span> |
| <span id="579">579</span> |
| <span id="580">580</span> |
| <span id="581">581</span> |
| <span id="582">582</span> |
| <span id="583">583</span> |
| <span id="584">584</span> |
| <span id="585">585</span> |
| <span id="586">586</span> |
| <span id="587">587</span> |
| <span id="588">588</span> |
| <span id="589">589</span> |
| <span id="590">590</span> |
| <span id="591">591</span> |
| <span id="592">592</span> |
| <span id="593">593</span> |
| <span id="594">594</span> |
| <span id="595">595</span> |
| <span id="596">596</span> |
| <span id="597">597</span> |
| <span id="598">598</span> |
| <span id="599">599</span> |
| <span id="600">600</span> |
| <span id="601">601</span> |
| <span id="602">602</span> |
| <span id="603">603</span> |
| <span id="604">604</span> |
| <span id="605">605</span> |
| <span id="606">606</span> |
| <span id="607">607</span> |
| <span id="608">608</span> |
| <span id="609">609</span> |
| <span id="610">610</span> |
| <span id="611">611</span> |
| <span id="612">612</span> |
| <span id="613">613</span> |
| <span id="614">614</span> |
| <span id="615">615</span> |
| <span id="616">616</span> |
| <span id="617">617</span> |
| <span id="618">618</span> |
| <span id="619">619</span> |
| <span id="620">620</span> |
| <span id="621">621</span> |
| <span id="622">622</span> |
| <span id="623">623</span> |
| <span id="624">624</span> |
| <span id="625">625</span> |
| <span id="626">626</span> |
| <span id="627">627</span> |
| <span id="628">628</span> |
| <span id="629">629</span> |
| <span id="630">630</span> |
| <span id="631">631</span> |
| <span id="632">632</span> |
| <span id="633">633</span> |
| </pre><pre class="rust"><code><span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/e_pow.c */</span> |
| <span class="comment">/* |
| * ==================================================== |
| * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */</span> |
| |
| <span class="comment">// pow(x,y) return x**y</span> |
| <span class="comment">//</span> |
| <span class="comment">// n</span> |
| <span class="comment">// Method: Let x = 2 * (1+f)</span> |
| <span class="comment">// 1. Compute and return log2(x) in two pieces:</span> |
| <span class="comment">// log2(x) = w1 + w2,</span> |
| <span class="comment">// where w1 has 53-24 = 29 bit trailing zeros.</span> |
| <span class="comment">// 2. Perform y*log2(x) = n+y' by simulating muti-precision</span> |
| <span class="comment">// arithmetic, where |y'|<=0.5.</span> |
| <span class="comment">// 3. Return x**y = 2**n*exp(y'*log2)</span> |
| <span class="comment">//</span> |
| <span class="comment">// Special cases:</span> |
| <span class="comment">// 1. (anything) ** 0 is 1</span> |
| <span class="comment">// 2. 1 ** (anything) is 1</span> |
| <span class="comment">// 3. (anything except 1) ** NAN is NAN</span> |
| <span class="comment">// 4. NAN ** (anything except 0) is NAN</span> |
| <span class="comment">// 5. +-(|x| > 1) ** +INF is +INF</span> |
| <span class="comment">// 6. +-(|x| > 1) ** -INF is +0</span> |
| <span class="comment">// 7. +-(|x| < 1) ** +INF is +0</span> |
| <span class="comment">// 8. +-(|x| < 1) ** -INF is +INF</span> |
| <span class="comment">// 9. -1 ** +-INF is 1</span> |
| <span class="comment">// 10. +0 ** (+anything except 0, NAN) is +0</span> |
| <span class="comment">// 11. -0 ** (+anything except 0, NAN, odd integer) is +0</span> |
| <span class="comment">// 12. +0 ** (-anything except 0, NAN) is +INF, raise divbyzero</span> |
| <span class="comment">// 13. -0 ** (-anything except 0, NAN, odd integer) is +INF, raise divbyzero</span> |
| <span class="comment">// 14. -0 ** (+odd integer) is -0</span> |
| <span class="comment">// 15. -0 ** (-odd integer) is -INF, raise divbyzero</span> |
| <span class="comment">// 16. +INF ** (+anything except 0,NAN) is +INF</span> |
| <span class="comment">// 17. +INF ** (-anything except 0,NAN) is +0</span> |
| <span class="comment">// 18. -INF ** (+odd integer) is -INF</span> |
| <span class="comment">// 19. -INF ** (anything) = -0 ** (-anything), (anything except odd integer)</span> |
| <span class="comment">// 20. (anything) ** 1 is (anything)</span> |
| <span class="comment">// 21. (anything) ** -1 is 1/(anything)</span> |
| <span class="comment">// 22. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)</span> |
| <span class="comment">// 23. (-anything except 0 and inf) ** (non-integer) is NAN</span> |
| <span class="comment">//</span> |
| <span class="comment">// Accuracy:</span> |
| <span class="comment">// pow(x,y) returns x**y nearly rounded. In particular</span> |
| <span class="comment">// pow(integer,integer)</span> |
| <span class="comment">// always returns the correct integer provided it is</span> |
| <span class="comment">// representable.</span> |
| <span class="comment">//</span> |
| <span class="comment">// Constants :</span> |
| <span class="comment">// The hexadecimal values are the intended ones for the following</span> |
| <span class="comment">// constants. The decimal values may be used, provided that the</span> |
| <span class="comment">// compiler will convert from decimal to binary accurately enough</span> |
| <span class="comment">// to produce the hexadecimal values shown.</span> |
| <span class="comment">//</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">scalbn</span>, <span class="ident">sqrt</span>, <span class="ident">with_set_high_word</span>, <span class="ident">with_set_low_word</span>}; |
| |
| <span class="kw">const</span> <span class="ident">BP</span>: [<span class="ident">f64</span>; <span class="number">2</span>] <span class="op">=</span> [<span class="number">1.0</span>, <span class="number">1.5</span>]; |
| <span class="kw">const</span> <span class="ident">DP_H</span>: [<span class="ident">f64</span>; <span class="number">2</span>] <span class="op">=</span> [<span class="number">0.0</span>, <span class="number">5.84962487220764160156e-01</span>]; <span class="comment">/* 0x3fe2b803_40000000 */</span> |
| <span class="kw">const</span> <span class="ident">DP_L</span>: [<span class="ident">f64</span>; <span class="number">2</span>] <span class="op">=</span> [<span class="number">0.0</span>, <span class="number">1.35003920212974897128e-08</span>]; <span class="comment">/* 0x3E4CFDEB, 0x43CFD006 */</span> |
| <span class="kw">const</span> <span class="ident">TWO53</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">9007199254740992.0</span>; <span class="comment">/* 0x43400000_00000000 */</span> |
| <span class="kw">const</span> <span class="ident">HUGE</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.0e300</span>; |
| <span class="kw">const</span> <span class="ident">TINY</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.0e-300</span>; |
| |
| <span class="comment">// poly coefs for (3/2)*(log(x)-2s-2/3*s**3:</span> |
| <span class="kw">const</span> <span class="ident">L1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">5.99999999999994648725e-01</span>; <span class="comment">/* 0x3fe33333_33333303 */</span> |
| <span class="kw">const</span> <span class="ident">L2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">4.28571428578550184252e-01</span>; <span class="comment">/* 0x3fdb6db6_db6fabff */</span> |
| <span class="kw">const</span> <span class="ident">L3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.33333329818377432918e-01</span>; <span class="comment">/* 0x3fd55555_518f264d */</span> |
| <span class="kw">const</span> <span class="ident">L4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.72728123808534006489e-01</span>; <span class="comment">/* 0x3fd17460_a91d4101 */</span> |
| <span class="kw">const</span> <span class="ident">L5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.30660745775561754067e-01</span>; <span class="comment">/* 0x3fcd864a_93c9db65 */</span> |
| <span class="kw">const</span> <span class="ident">L6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.06975017800338417784e-01</span>; <span class="comment">/* 0x3fca7e28_4a454eef */</span> |
| <span class="kw">const</span> <span class="ident">P1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.66666666666666019037e-01</span>; <span class="comment">/* 0x3fc55555_5555553e */</span> |
| <span class="kw">const</span> <span class="ident">P2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">2.77777777770155933842e-03</span>; <span class="comment">/* 0xbf66c16c_16bebd93 */</span> |
| <span class="kw">const</span> <span class="ident">P3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.61375632143793436117e-05</span>; <span class="comment">/* 0x3f11566a_af25de2c */</span> |
| <span class="kw">const</span> <span class="ident">P4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.65339022054652515390e-06</span>; <span class="comment">/* 0xbebbbd41_c5d26bf1 */</span> |
| <span class="kw">const</span> <span class="ident">P5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">4.13813679705723846039e-08</span>; <span class="comment">/* 0x3e663769_72bea4d0 */</span> |
| <span class="kw">const</span> <span class="ident">LG2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.93147180559945286227e-01</span>; <span class="comment">/* 0x3fe62e42_fefa39ef */</span> |
| <span class="kw">const</span> <span class="ident">LG2_H</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.93147182464599609375e-01</span>; <span class="comment">/* 0x3fe62e43_00000000 */</span> |
| <span class="kw">const</span> <span class="ident">LG2_L</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.90465429995776804525e-09</span>; <span class="comment">/* 0xbe205c61_0ca86c39 */</span> |
| <span class="kw">const</span> <span class="ident">OVT</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">8.0085662595372944372e-017</span>; <span class="comment">/* -(1024-log2(ovfl+.5ulp)) */</span> |
| <span class="kw">const</span> <span class="ident">CP</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">9.61796693925975554329e-01</span>; <span class="comment">/* 0x3feec709_dc3a03fd =2/(3ln2) */</span> |
| <span class="kw">const</span> <span class="ident">CP_H</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">9.61796700954437255859e-01</span>; <span class="comment">/* 0x3feec709_e0000000 =(float)cp */</span> |
| <span class="kw">const</span> <span class="ident">CP_L</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">7.02846165095275826516e-09</span>; <span class="comment">/* 0xbe3e2fe0_145b01f5 =tail of cp_h*/</span> |
| <span class="kw">const</span> <span class="ident">IVLN2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.44269504088896338700e+00</span>; <span class="comment">/* 0x3ff71547_652b82fe =1/ln2 */</span> |
| <span class="kw">const</span> <span class="ident">IVLN2_H</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.44269502162933349609e+00</span>; <span class="comment">/* 0x3ff71547_60000000 =24b 1/ln2*/</span> |
| <span class="kw">const</span> <span class="ident">IVLN2_L</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.92596299112661746887e-08</span>; <span class="comment">/* 0x3e54ae0b_f85ddf44 =1/ln2 tail*/</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">pow</span>(<span class="ident">x</span>: <span class="ident">f64</span>, <span class="ident">y</span>: <span class="ident">f64</span>) -> <span class="ident">f64</span> { |
| <span class="kw">let</span> <span class="ident">t1</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">t2</span>: <span class="ident">f64</span>; |
| |
| <span class="kw">let</span> (<span class="ident">hx</span>, <span class="ident">lx</span>): (<span class="ident">i32</span>, <span class="ident">u32</span>) <span class="op">=</span> ((<span class="ident">x</span>.<span class="ident">to_bits</span>() <span class="op">></span><span class="op">></span> <span class="number">32</span>) <span class="kw">as</span> <span class="ident">i32</span>, <span class="ident">x</span>.<span class="ident">to_bits</span>() <span class="kw">as</span> <span class="ident">u32</span>); |
| <span class="kw">let</span> (<span class="ident">hy</span>, <span class="ident">ly</span>): (<span class="ident">i32</span>, <span class="ident">u32</span>) <span class="op">=</span> ((<span class="ident">y</span>.<span class="ident">to_bits</span>() <span class="op">></span><span class="op">></span> <span class="number">32</span>) <span class="kw">as</span> <span class="ident">i32</span>, <span class="ident">y</span>.<span class="ident">to_bits</span>() <span class="kw">as</span> <span class="ident">u32</span>); |
| |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ix</span>: <span class="ident">i32</span> <span class="op">=</span> (<span class="ident">hx</span> <span class="op">&</span> <span class="number">0x7fffffff</span>) <span class="kw">as</span> <span class="ident">i32</span>; |
| <span class="kw">let</span> <span class="ident">iy</span>: <span class="ident">i32</span> <span class="op">=</span> (<span class="ident">hy</span> <span class="op">&</span> <span class="number">0x7fffffff</span>) <span class="kw">as</span> <span class="ident">i32</span>; |
| |
| <span class="comment">/* x**0 = 1, even if x is NaN */</span> |
| <span class="kw">if</span> ((<span class="ident">iy</span> <span class="kw">as</span> <span class="ident">u32</span>) <span class="op">|</span> <span class="ident">ly</span>) <span class="op">==</span> <span class="number">0</span> { |
| <span class="kw">return</span> <span class="number">1.0</span>; |
| } |
| |
| <span class="comment">/* 1**y = 1, even if y is NaN */</span> |
| <span class="kw">if</span> <span class="ident">hx</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="kw">return</span> <span class="number">1.0</span>; |
| } |
| |
| <span class="comment">/* NaN if either arg is NaN */</span> |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span> <span class="number">0x7ff00000</span> |
| <span class="op">|</span><span class="op">|</span> (<span class="ident">ix</span> <span class="op">==</span> <span class="number">0x7ff00000</span> <span class="op">&&</span> <span class="ident">lx</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span>) |
| <span class="op">|</span><span class="op">|</span> <span class="ident">iy</span> <span class="op">></span> <span class="number">0x7ff00000</span> |
| <span class="op">|</span><span class="op">|</span> (<span class="ident">iy</span> <span class="op">==</span> <span class="number">0x7ff00000</span> <span class="op">&&</span> <span class="ident">ly</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span>) |
| { |
| <span class="kw">return</span> <span class="ident">x</span> <span class="op">+</span> <span class="ident">y</span>; |
| } |
| |
| <span class="comment">/* determine if y is an odd int when x < 0 |
| * yisint = 0 ... y is not an integer |
| * yisint = 1 ... y is an odd int |
| * yisint = 2 ... y is an even int |
| */</span> |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">yisint</span>: <span class="ident">i32</span> <span class="op">=</span> <span class="number">0</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">k</span>: <span class="ident">i32</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">j</span>: <span class="ident">i32</span>; |
| <span class="kw">if</span> <span class="ident">hx</span> <span class="op"><</span> <span class="number">0</span> { |
| <span class="kw">if</span> <span class="ident">iy</span> <span class="op">></span><span class="op">=</span> <span class="number">0x43400000</span> { |
| <span class="ident">yisint</span> <span class="op">=</span> <span class="number">2</span>; <span class="comment">/* even integer y */</span> |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">iy</span> <span class="op">></span><span class="op">=</span> <span class="number">0x3ff00000</span> { |
| <span class="ident">k</span> <span class="op">=</span> (<span class="ident">iy</span> <span class="op">></span><span class="op">></span> <span class="number">20</span>) <span class="op">-</span> <span class="number">0x3ff</span>; <span class="comment">/* exponent */</span> |
| |
| <span class="kw">if</span> <span class="ident">k</span> <span class="op">></span> <span class="number">20</span> { |
| <span class="ident">j</span> <span class="op">=</span> (<span class="ident">ly</span> <span class="op">></span><span class="op">></span> (<span class="number">52</span> <span class="op">-</span> <span class="ident">k</span>)) <span class="kw">as</span> <span class="ident">i32</span>; |
| |
| <span class="kw">if</span> (<span class="ident">j</span> <span class="op"><</span><span class="op"><</span> (<span class="number">52</span> <span class="op">-</span> <span class="ident">k</span>)) <span class="op">==</span> (<span class="ident">ly</span> <span class="kw">as</span> <span class="ident">i32</span>) { |
| <span class="ident">yisint</span> <span class="op">=</span> <span class="number">2</span> <span class="op">-</span> (<span class="ident">j</span> <span class="op">&</span> <span class="number">1</span>); |
| } |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ly</span> <span class="op">==</span> <span class="number">0</span> { |
| <span class="ident">j</span> <span class="op">=</span> <span class="ident">iy</span> <span class="op">></span><span class="op">></span> (<span class="number">20</span> <span class="op">-</span> <span class="ident">k</span>); |
| |
| <span class="kw">if</span> (<span class="ident">j</span> <span class="op"><</span><span class="op"><</span> (<span class="number">20</span> <span class="op">-</span> <span class="ident">k</span>)) <span class="op">==</span> <span class="ident">iy</span> { |
| <span class="ident">yisint</span> <span class="op">=</span> <span class="number">2</span> <span class="op">-</span> (<span class="ident">j</span> <span class="op">&</span> <span class="number">1</span>); |
| } |
| } |
| } |
| } |
| |
| <span class="kw">if</span> <span class="ident">ly</span> <span class="op">==</span> <span class="number">0</span> { |
| <span class="comment">/* special value of y */</span> |
| <span class="kw">if</span> <span class="ident">iy</span> <span class="op">==</span> <span class="number">0x7ff00000</span> { |
| <span class="comment">/* y is +-inf */</span> |
| |
| <span class="kw">return</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="kw">as</span> <span class="ident">i32</span>)) <span class="op">==</span> <span class="number">0</span> { |
| <span class="comment">/* (-1)**+-inf is 1 */</span> |
| <span class="number">1.0</span> |
| } <span class="kw">else</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="comment">/* (|x|>1)**+-inf = inf,0 */</span> |
| <span class="kw">if</span> <span class="ident">hy</span> <span class="op">></span><span class="op">=</span> <span class="number">0</span> { |
| <span class="ident">y</span> |
| } <span class="kw">else</span> { |
| <span class="number">0.0</span> |
| } |
| } <span class="kw">else</span> { |
| <span class="comment">/* (|x|<1)**+-inf = 0,inf */</span> |
| <span class="kw">if</span> <span class="ident">hy</span> <span class="op">></span><span class="op">=</span> <span class="number">0</span> { |
| <span class="number">0.0</span> |
| } <span class="kw">else</span> { |
| <span class="op">-</span><span class="ident">y</span> |
| } |
| }; |
| } |
| |
| <span class="kw">if</span> <span class="ident">iy</span> <span class="op">==</span> <span class="number">0x3ff00000</span> { |
| <span class="comment">/* y is +-1 */</span> |
| <span class="kw">return</span> <span class="kw">if</span> <span class="ident">hy</span> <span class="op">></span><span class="op">=</span> <span class="number">0</span> { <span class="ident">x</span> } <span class="kw">else</span> { <span class="number">1.0</span> <span class="op">/</span> <span class="ident">x</span> }; |
| } |
| |
| <span class="kw">if</span> <span class="ident">hy</span> <span class="op">==</span> <span class="number">0x40000000</span> { |
| <span class="comment">/* y is 2 */</span> |
| <span class="kw">return</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>; |
| } |
| |
| <span class="kw">if</span> <span class="ident">hy</span> <span class="op">==</span> <span class="number">0x3fe00000</span> { |
| <span class="comment">/* y is 0.5 */</span> |
| <span class="kw">if</span> <span class="ident">hx</span> <span class="op">></span><span class="op">=</span> <span class="number">0</span> { |
| <span class="comment">/* x >= +0 */</span> |
| <span class="kw">return</span> <span class="ident">sqrt</span>(<span class="ident">x</span>); |
| } |
| } |
| } |
| |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ax</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">fabs</span>(<span class="ident">x</span>); |
| <span class="kw">if</span> <span class="ident">lx</span> <span class="op">==</span> <span class="number">0</span> { |
| <span class="comment">/* special value of x */</span> |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">==</span> <span class="number">0x7ff00000</span> <span class="op">|</span><span class="op">|</span> <span class="ident">ix</span> <span class="op">==</span> <span class="number">0</span> <span class="op">|</span><span class="op">|</span> <span class="ident">ix</span> <span class="op">==</span> <span class="number">0x3ff00000</span> { |
| <span class="comment">/* x is +-0,+-inf,+-1 */</span> |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">z</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">ax</span>; |
| |
| <span class="kw">if</span> <span class="ident">hy</span> <span class="op"><</span> <span class="number">0</span> { |
| <span class="comment">/* z = (1/|x|) */</span> |
| <span class="ident">z</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">/</span> <span class="ident">z</span>; |
| } |
| |
| <span class="kw">if</span> <span class="ident">hx</span> <span class="op"><</span> <span class="number">0</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">yisint</span>) <span class="op">==</span> <span class="number">0</span> { |
| <span class="ident">z</span> <span class="op">=</span> (<span class="ident">z</span> <span class="op">-</span> <span class="ident">z</span>) <span class="op">/</span> (<span class="ident">z</span> <span class="op">-</span> <span class="ident">z</span>); <span class="comment">/* (-1)**non-int is NaN */</span> |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">yisint</span> <span class="op">==</span> <span class="number">1</span> { |
| <span class="ident">z</span> <span class="op">=</span> <span class="op">-</span><span class="ident">z</span>; <span class="comment">/* (x<0)**odd = -(|x|**odd) */</span> |
| } |
| } |
| |
| <span class="kw">return</span> <span class="ident">z</span>; |
| } |
| } |
| |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">s</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.0</span>; <span class="comment">/* sign of result */</span> |
| <span class="kw">if</span> <span class="ident">hx</span> <span class="op"><</span> <span class="number">0</span> { |
| <span class="kw">if</span> <span class="ident">yisint</span> <span class="op">==</span> <span class="number">0</span> { |
| <span class="comment">/* (x<0)**(non-int) is NaN */</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">x</span> <span class="op">-</span> <span class="ident">x</span>); |
| } |
| |
| <span class="kw">if</span> <span class="ident">yisint</span> <span class="op">==</span> <span class="number">1</span> { |
| <span class="comment">/* (x<0)**(odd int) */</span> |
| <span class="ident">s</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.0</span>; |
| } |
| } |
| |
| <span class="comment">/* |y| is HUGE */</span> |
| <span class="kw">if</span> <span class="ident">iy</span> <span class="op">></span> <span class="number">0x41e00000</span> { |
| <span class="comment">/* if |y| > 2**31 */</span> |
| <span class="kw">if</span> <span class="ident">iy</span> <span class="op">></span> <span class="number">0x43f00000</span> { |
| <span class="comment">/* if |y| > 2**64, must o/uflow */</span> |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span><span class="op">=</span> <span class="number">0x3fefffff</span> { |
| <span class="kw">return</span> <span class="kw">if</span> <span class="ident">hy</span> <span class="op"><</span> <span class="number">0</span> { <span class="ident">HUGE</span> <span class="op">*</span> <span class="ident">HUGE</span> } <span class="kw">else</span> { <span class="ident">TINY</span> <span class="op">*</span> <span class="ident">TINY</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">return</span> <span class="kw">if</span> <span class="ident">hy</span> <span class="op">></span> <span class="number">0</span> { <span class="ident">HUGE</span> <span class="op">*</span> <span class="ident">HUGE</span> } <span class="kw">else</span> { <span class="ident">TINY</span> <span class="op">*</span> <span class="ident">TINY</span> }; |
| } |
| } |
| |
| <span class="comment">/* over/underflow if x is not close to one */</span> |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x3fefffff</span> { |
| <span class="kw">return</span> <span class="kw">if</span> <span class="ident">hy</span> <span class="op"><</span> <span class="number">0</span> { |
| <span class="ident">s</span> <span class="op">*</span> <span class="ident">HUGE</span> <span class="op">*</span> <span class="ident">HUGE</span> |
| } <span class="kw">else</span> { |
| <span class="ident">s</span> <span class="op">*</span> <span class="ident">TINY</span> <span class="op">*</span> <span class="ident">TINY</span> |
| }; |
| } |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span> <span class="number">0x3ff00000</span> { |
| <span class="kw">return</span> <span class="kw">if</span> <span class="ident">hy</span> <span class="op">></span> <span class="number">0</span> { |
| <span class="ident">s</span> <span class="op">*</span> <span class="ident">HUGE</span> <span class="op">*</span> <span class="ident">HUGE</span> |
| } <span class="kw">else</span> { |
| <span class="ident">s</span> <span class="op">*</span> <span class="ident">TINY</span> <span class="op">*</span> <span class="ident">TINY</span> |
| }; |
| } |
| |
| <span class="comment">/* now |1-x| is TINY <= 2**-20, suffice to compute |
| log(x) by x-x^2/2+x^3/3-x^4/4 */</span> |
| <span class="kw">let</span> <span class="ident">t</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">ax</span> <span class="op">-</span> <span class="number">1.0</span>; <span class="comment">/* t has 20 trailing zeros */</span> |
| <span class="kw">let</span> <span class="ident">w</span>: <span class="ident">f64</span> <span class="op">=</span> (<span class="ident">t</span> <span class="op">*</span> <span class="ident">t</span>) <span class="op">*</span> (<span class="number">0.5</span> <span class="op">-</span> <span class="ident">t</span> <span class="op">*</span> (<span class="number">0.3333333333333333333333</span> <span class="op">-</span> <span class="ident">t</span> <span class="op">*</span> <span class="number">0.25</span>)); |
| <span class="kw">let</span> <span class="ident">u</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">IVLN2_H</span> <span class="op">*</span> <span class="ident">t</span>; <span class="comment">/* ivln2_h has 21 sig. bits */</span> |
| <span class="kw">let</span> <span class="ident">v</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">t</span> <span class="op">*</span> <span class="ident">IVLN2_L</span> <span class="op">-</span> <span class="ident">w</span> <span class="op">*</span> <span class="ident">IVLN2</span>; |
| <span class="ident">t1</span> <span class="op">=</span> <span class="ident">with_set_low_word</span>(<span class="ident">u</span> <span class="op">+</span> <span class="ident">v</span>, <span class="number">0</span>); |
| <span class="ident">t2</span> <span class="op">=</span> <span class="ident">v</span> <span class="op">-</span> (<span class="ident">t1</span> <span class="op">-</span> <span class="ident">u</span>); |
| } <span class="kw">else</span> { |
| <span class="comment">// double ss,s2,s_h,s_l,t_h,t_l;</span> |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">n</span>: <span class="ident">i32</span> <span class="op">=</span> <span class="number">0</span>; |
| |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x00100000</span> { |
| <span class="comment">/* take care subnormal number */</span> |
| <span class="ident">ax</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">TWO53</span>; |
| <span class="ident">n</span> <span class="op">-</span><span class="op">=</span> <span class="number">53</span>; |
| <span class="ident">ix</span> <span class="op">=</span> <span class="ident">get_high_word</span>(<span class="ident">ax</span>) <span class="kw">as</span> <span class="ident">i32</span>; |
| } |
| |
| <span class="ident">n</span> <span class="op">+</span><span class="op">=</span> (<span class="ident">ix</span> <span class="op">></span><span class="op">></span> <span class="number">20</span>) <span class="op">-</span> <span class="number">0x3ff</span>; |
| <span class="ident">j</span> <span class="op">=</span> <span class="ident">ix</span> <span class="op">&</span> <span class="number">0x000fffff</span>; |
| |
| <span class="comment">/* determine interval */</span> |
| <span class="kw">let</span> <span class="ident">k</span>: <span class="ident">i32</span>; |
| <span class="ident">ix</span> <span class="op">=</span> <span class="ident">j</span> <span class="op">|</span> <span class="number">0x3ff00000</span>; <span class="comment">/* normalize ix */</span> |
| <span class="kw">if</span> <span class="ident">j</span> <span class="op"><</span><span class="op">=</span> <span class="number">0x3988E</span> { |
| <span class="comment">/* |x|<sqrt(3/2) */</span> |
| <span class="ident">k</span> <span class="op">=</span> <span class="number">0</span>; |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">j</span> <span class="op"><</span> <span class="number">0xBB67A</span> { |
| <span class="comment">/* |x|<sqrt(3) */</span> |
| <span class="ident">k</span> <span class="op">=</span> <span class="number">1</span>; |
| } <span class="kw">else</span> { |
| <span class="ident">k</span> <span class="op">=</span> <span class="number">0</span>; |
| <span class="ident">n</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>; |
| <span class="ident">ix</span> <span class="op">-</span><span class="op">=</span> <span class="number">0x00100000</span>; |
| } |
| <span class="ident">ax</span> <span class="op">=</span> <span class="ident">with_set_high_word</span>(<span class="ident">ax</span>, <span class="ident">ix</span> <span class="kw">as</span> <span class="ident">u32</span>); |
| |
| <span class="comment">/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */</span> |
| <span class="kw">let</span> <span class="ident">u</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">ax</span> <span class="op">-</span> <span class="ident">BP</span>[<span class="ident">k</span> <span class="kw">as</span> <span class="ident">usize</span>]; <span class="comment">/* bp[0]=1.0, bp[1]=1.5 */</span> |
| <span class="kw">let</span> <span class="ident">v</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">/</span> (<span class="ident">ax</span> <span class="op">+</span> <span class="ident">BP</span>[<span class="ident">k</span> <span class="kw">as</span> <span class="ident">usize</span>]); |
| <span class="kw">let</span> <span class="ident">ss</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">u</span> <span class="op">*</span> <span class="ident">v</span>; |
| <span class="kw">let</span> <span class="ident">s_h</span> <span class="op">=</span> <span class="ident">with_set_low_word</span>(<span class="ident">ss</span>, <span class="number">0</span>); |
| |
| <span class="comment">/* t_h=ax+bp[k] High */</span> |
| <span class="kw">let</span> <span class="ident">t_h</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">with_set_high_word</span>( |
| <span class="number">0.0</span>, |
| ((<span class="ident">ix</span> <span class="kw">as</span> <span class="ident">u32</span> <span class="op">></span><span class="op">></span> <span class="number">1</span>) <span class="op">|</span> <span class="number">0x20000000</span>) <span class="op">+</span> <span class="number">0x00080000</span> <span class="op">+</span> ((<span class="ident">k</span> <span class="kw">as</span> <span class="ident">u32</span>) <span class="op"><</span><span class="op"><</span> <span class="number">18</span>), |
| ); |
| <span class="kw">let</span> <span class="ident">t_l</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">ax</span> <span class="op">-</span> (<span class="ident">t_h</span> <span class="op">-</span> <span class="ident">BP</span>[<span class="ident">k</span> <span class="kw">as</span> <span class="ident">usize</span>]); |
| <span class="kw">let</span> <span class="ident">s_l</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">v</span> <span class="op">*</span> ((<span class="ident">u</span> <span class="op">-</span> <span class="ident">s_h</span> <span class="op">*</span> <span class="ident">t_h</span>) <span class="op">-</span> <span class="ident">s_h</span> <span class="op">*</span> <span class="ident">t_l</span>); |
| |
| <span class="comment">/* compute log(ax) */</span> |
| <span class="kw">let</span> <span class="ident">s2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">ss</span> <span class="op">*</span> <span class="ident">ss</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">r</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">s2</span> <span class="op">*</span> <span class="ident">s2</span> <span class="op">*</span> (<span class="ident">L1</span> <span class="op">+</span> <span class="ident">s2</span> <span class="op">*</span> (<span class="ident">L2</span> <span class="op">+</span> <span class="ident">s2</span> <span class="op">*</span> (<span class="ident">L3</span> <span class="op">+</span> <span class="ident">s2</span> <span class="op">*</span> (<span class="ident">L4</span> <span class="op">+</span> <span class="ident">s2</span> <span class="op">*</span> (<span class="ident">L5</span> <span class="op">+</span> <span class="ident">s2</span> <span class="op">*</span> <span class="ident">L6</span>))))); |
| <span class="ident">r</span> <span class="op">+</span><span class="op">=</span> <span class="ident">s_l</span> <span class="op">*</span> (<span class="ident">s_h</span> <span class="op">+</span> <span class="ident">ss</span>); |
| <span class="kw">let</span> <span class="ident">s2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">s_h</span> <span class="op">*</span> <span class="ident">s_h</span>; |
| <span class="kw">let</span> <span class="ident">t_h</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">with_set_low_word</span>(<span class="number">3.0</span> <span class="op">+</span> <span class="ident">s2</span> <span class="op">+</span> <span class="ident">r</span>, <span class="number">0</span>); |
| <span class="kw">let</span> <span class="ident">t_l</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">r</span> <span class="op">-</span> ((<span class="ident">t_h</span> <span class="op">-</span> <span class="number">3.0</span>) <span class="op">-</span> <span class="ident">s2</span>); |
| |
| <span class="comment">/* u+v = ss*(1+...) */</span> |
| <span class="kw">let</span> <span class="ident">u</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">s_h</span> <span class="op">*</span> <span class="ident">t_h</span>; |
| <span class="kw">let</span> <span class="ident">v</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">s_l</span> <span class="op">*</span> <span class="ident">t_h</span> <span class="op">+</span> <span class="ident">t_l</span> <span class="op">*</span> <span class="ident">ss</span>; |
| |
| <span class="comment">/* 2/(3log2)*(ss+...) */</span> |
| <span class="kw">let</span> <span class="ident">p_h</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">with_set_low_word</span>(<span class="ident">u</span> <span class="op">+</span> <span class="ident">v</span>, <span class="number">0</span>); |
| <span class="kw">let</span> <span class="ident">p_l</span> <span class="op">=</span> <span class="ident">v</span> <span class="op">-</span> (<span class="ident">p_h</span> <span class="op">-</span> <span class="ident">u</span>); |
| <span class="kw">let</span> <span class="ident">z_h</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">CP_H</span> <span class="op">*</span> <span class="ident">p_h</span>; <span class="comment">/* cp_h+cp_l = 2/(3*log2) */</span> |
| <span class="kw">let</span> <span class="ident">z_l</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">CP_L</span> <span class="op">*</span> <span class="ident">p_h</span> <span class="op">+</span> <span class="ident">p_l</span> <span class="op">*</span> <span class="ident">CP</span> <span class="op">+</span> <span class="ident">DP_L</span>[<span class="ident">k</span> <span class="kw">as</span> <span class="ident">usize</span>]; |
| |
| <span class="comment">/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */</span> |
| <span class="kw">let</span> <span class="ident">t</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">n</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="ident">t1</span> <span class="op">=</span> <span class="ident">with_set_low_word</span>(((<span class="ident">z_h</span> <span class="op">+</span> <span class="ident">z_l</span>) <span class="op">+</span> <span class="ident">DP_H</span>[<span class="ident">k</span> <span class="kw">as</span> <span class="ident">usize</span>]) <span class="op">+</span> <span class="ident">t</span>, <span class="number">0</span>); |
| <span class="ident">t2</span> <span class="op">=</span> <span class="ident">z_l</span> <span class="op">-</span> (((<span class="ident">t1</span> <span class="op">-</span> <span class="ident">t</span>) <span class="op">-</span> <span class="ident">DP_H</span>[<span class="ident">k</span> <span class="kw">as</span> <span class="ident">usize</span>]) <span class="op">-</span> <span class="ident">z_h</span>); |
| } |
| |
| <span class="comment">/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */</span> |
| <span class="kw">let</span> <span class="ident">y1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">with_set_low_word</span>(<span class="ident">y</span>, <span class="number">0</span>); |
| <span class="kw">let</span> <span class="ident">p_l</span>: <span class="ident">f64</span> <span class="op">=</span> (<span class="ident">y</span> <span class="op">-</span> <span class="ident">y1</span>) <span class="op">*</span> <span class="ident">t1</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> <span class="ident">t2</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">p_h</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">y1</span> <span class="op">*</span> <span class="ident">t1</span>; |
| <span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">p_l</span> <span class="op">+</span> <span class="ident">p_h</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">j</span>: <span class="ident">i32</span> <span class="op">=</span> (<span class="ident">z</span>.<span class="ident">to_bits</span>() <span class="op">></span><span class="op">></span> <span class="number">32</span>) <span class="kw">as</span> <span class="ident">i32</span>; |
| <span class="kw">let</span> <span class="ident">i</span>: <span class="ident">i32</span> <span class="op">=</span> <span class="ident">z</span>.<span class="ident">to_bits</span>() <span class="kw">as</span> <span class="ident">i32</span>; |
| <span class="comment">// let (j, i): (i32, i32) = ((z.to_bits() >> 32) as i32, z.to_bits() as i32);</span> |
| |
| <span class="kw">if</span> <span class="ident">j</span> <span class="op">></span><span class="op">=</span> <span class="number">0x40900000</span> { |
| <span class="comment">/* z >= 1024 */</span> |
| <span class="kw">if</span> (<span class="ident">j</span> <span class="op">-</span> <span class="number">0x40900000</span>) <span class="op">|</span> <span class="ident">i</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { |
| <span class="comment">/* if z > 1024 */</span> |
| <span class="kw">return</span> <span class="ident">s</span> <span class="op">*</span> <span class="ident">HUGE</span> <span class="op">*</span> <span class="ident">HUGE</span>; <span class="comment">/* overflow */</span> |
| } |
| |
| <span class="kw">if</span> <span class="ident">p_l</span> <span class="op">+</span> <span class="ident">OVT</span> <span class="op">></span> <span class="ident">z</span> <span class="op">-</span> <span class="ident">p_h</span> { |
| <span class="kw">return</span> <span class="ident">s</span> <span class="op">*</span> <span class="ident">HUGE</span> <span class="op">*</span> <span class="ident">HUGE</span>; <span class="comment">/* overflow */</span> |
| } |
| } <span class="kw">else</span> <span class="kw">if</span> (<span class="ident">j</span> <span class="op">&</span> <span class="number">0x7fffffff</span>) <span class="op">></span><span class="op">=</span> <span class="number">0x4090cc00</span> { |
| <span class="comment">/* z <= -1075 */</span> |
| <span class="comment">// FIXME: instead of abs(j) use unsigned j</span> |
| |
| <span class="kw">if</span> (((<span class="ident">j</span> <span class="kw">as</span> <span class="ident">u32</span>) <span class="op">-</span> <span class="number">0xc090cc00</span>) <span class="op">|</span> (<span class="ident">i</span> <span class="kw">as</span> <span class="ident">u32</span>)) <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { |
| <span class="comment">/* z < -1075 */</span> |
| <span class="kw">return</span> <span class="ident">s</span> <span class="op">*</span> <span class="ident">TINY</span> <span class="op">*</span> <span class="ident">TINY</span>; <span class="comment">/* underflow */</span> |
| } |
| |
| <span class="kw">if</span> <span class="ident">p_l</span> <span class="op"><</span><span class="op">=</span> <span class="ident">z</span> <span class="op">-</span> <span class="ident">p_h</span> { |
| <span class="kw">return</span> <span class="ident">s</span> <span class="op">*</span> <span class="ident">TINY</span> <span class="op">*</span> <span class="ident">TINY</span>; <span class="comment">/* underflow */</span> |
| } |
| } |
| |
| <span class="comment">/* compute 2**(p_h+p_l) */</span> |
| <span class="kw">let</span> <span class="ident">i</span>: <span class="ident">i32</span> <span class="op">=</span> <span class="ident">j</span> <span class="op">&</span> (<span class="number">0x7fffffff</span> <span class="kw">as</span> <span class="ident">i32</span>); |
| <span class="ident">k</span> <span class="op">=</span> (<span class="ident">i</span> <span class="op">></span><span class="op">></span> <span class="number">20</span>) <span class="op">-</span> <span class="number">0x3ff</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">n</span>: <span class="ident">i32</span> <span class="op">=</span> <span class="number">0</span>; |
| |
| <span class="kw">if</span> <span class="ident">i</span> <span class="op">></span> <span class="number">0x3fe00000</span> { |
| <span class="comment">/* if |z| > 0.5, set n = [z+0.5] */</span> |
| <span class="ident">n</span> <span class="op">=</span> <span class="ident">j</span> <span class="op">+</span> (<span class="number">0x00100000</span> <span class="op">></span><span class="op">></span> (<span class="ident">k</span> <span class="op">+</span> <span class="number">1</span>)); |
| <span class="ident">k</span> <span class="op">=</span> ((<span class="ident">n</span> <span class="op">&</span> <span class="number">0x7fffffff</span>) <span class="op">></span><span class="op">></span> <span class="number">20</span>) <span class="op">-</span> <span class="number">0x3ff</span>; <span class="comment">/* new k for n */</span> |
| <span class="kw">let</span> <span class="ident">t</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">with_set_high_word</span>(<span class="number">0.0</span>, (<span class="ident">n</span> <span class="op">&</span> <span class="op">!</span>(<span class="number">0x000fffff</span> <span class="op">></span><span class="op">></span> <span class="ident">k</span>)) <span class="kw">as</span> <span class="ident">u32</span>); |
| <span class="ident">n</span> <span class="op">=</span> ((<span class="ident">n</span> <span class="op">&</span> <span class="number">0x000fffff</span>) <span class="op">|</span> <span class="number">0x00100000</span>) <span class="op">></span><span class="op">></span> (<span class="number">20</span> <span class="op">-</span> <span class="ident">k</span>); |
| <span class="kw">if</span> <span class="ident">j</span> <span class="op"><</span> <span class="number">0</span> { |
| <span class="ident">n</span> <span class="op">=</span> <span class="op">-</span><span class="ident">n</span>; |
| } |
| <span class="ident">p_h</span> <span class="op">-</span><span class="op">=</span> <span class="ident">t</span>; |
| } |
| |
| <span class="kw">let</span> <span class="ident">t</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">with_set_low_word</span>(<span class="ident">p_l</span> <span class="op">+</span> <span class="ident">p_h</span>, <span class="number">0</span>); |
| <span class="kw">let</span> <span class="ident">u</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">t</span> <span class="op">*</span> <span class="ident">LG2_H</span>; |
| <span class="kw">let</span> <span class="ident">v</span>: <span class="ident">f64</span> <span class="op">=</span> (<span class="ident">p_l</span> <span class="op">-</span> (<span class="ident">t</span> <span class="op">-</span> <span class="ident">p_h</span>)) <span class="op">*</span> <span class="ident">LG2</span> <span class="op">+</span> <span class="ident">t</span> <span class="op">*</span> <span class="ident">LG2_L</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">z</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">u</span> <span class="op">+</span> <span class="ident">v</span>; |
| <span class="kw">let</span> <span class="ident">w</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">v</span> <span class="op">-</span> (<span class="ident">z</span> <span class="op">-</span> <span class="ident">u</span>); |
| <span class="kw">let</span> <span class="ident">t</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">z</span>; |
| <span class="kw">let</span> <span class="ident">t1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">-</span> <span class="ident">t</span> <span class="op">*</span> (<span class="ident">P1</span> <span class="op">+</span> <span class="ident">t</span> <span class="op">*</span> (<span class="ident">P2</span> <span class="op">+</span> <span class="ident">t</span> <span class="op">*</span> (<span class="ident">P3</span> <span class="op">+</span> <span class="ident">t</span> <span class="op">*</span> (<span class="ident">P4</span> <span class="op">+</span> <span class="ident">t</span> <span class="op">*</span> <span class="ident">P5</span>)))); |
| <span class="kw">let</span> <span class="ident">r</span>: <span class="ident">f64</span> <span class="op">=</span> (<span class="ident">z</span> <span class="op">*</span> <span class="ident">t1</span>) <span class="op">/</span> (<span class="ident">t1</span> <span class="op">-</span> <span class="number">2.0</span>) <span class="op">-</span> (<span class="ident">w</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">w</span>); |
| <span class="ident">z</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">-</span> (<span class="ident">r</span> <span class="op">-</span> <span class="ident">z</span>); |
| <span class="ident">j</span> <span class="op">=</span> <span class="ident">get_high_word</span>(<span class="ident">z</span>) <span class="kw">as</span> <span class="ident">i32</span>; |
| <span class="ident">j</span> <span class="op">+</span><span class="op">=</span> <span class="ident">n</span> <span class="op"><</span><span class="op"><</span> <span class="number">20</span>; |
| |
| <span class="kw">if</span> (<span class="ident">j</span> <span class="op">></span><span class="op">></span> <span class="number">20</span>) <span class="op"><</span><span class="op">=</span> <span class="number">0</span> { |
| <span class="comment">/* subnormal output */</span> |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">scalbn</span>(<span class="ident">z</span>, <span class="ident">n</span>); |
| } <span class="kw">else</span> { |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">with_set_high_word</span>(<span class="ident">z</span>, <span class="ident">j</span> <span class="kw">as</span> <span class="ident">u32</span>); |
| } |
| |
| <span class="ident">s</span> <span class="op">*</span> <span class="ident">z</span> |
| } |
| |
| <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span> |
| <span class="kw">mod</span> <span class="ident">tests</span> { |
| <span class="kw">extern</span> <span class="kw">crate</span> <span class="ident">core</span>; |
| |
| <span class="kw">use</span> <span class="ident"><span class="self">self</span>::core::f64::consts</span>::{<span class="ident">E</span>, <span class="ident">PI</span>}; |
| <span class="kw">use</span> <span class="ident"><span class="self">self</span>::core::f64</span>::{<span class="ident">EPSILON</span>, <span class="ident">INFINITY</span>, <span class="ident">MAX</span>, <span class="ident">MIN</span>, <span class="ident">MIN_POSITIVE</span>, <span class="ident">NAN</span>, <span class="ident">NEG_INFINITY</span>}; |
| <span class="kw">use</span> <span class="ident"><span class="kw">super</span>::pow</span>; |
| |
| <span class="kw">const</span> <span class="ident">POS_ZERO</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[<span class="number">0.0</span>]; |
| <span class="kw">const</span> <span class="ident">NEG_ZERO</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[<span class="op">-</span><span class="number">0.0</span>]; |
| <span class="kw">const</span> <span class="ident">POS_ONE</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[<span class="number">1.0</span>]; |
| <span class="kw">const</span> <span class="ident">NEG_ONE</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[<span class="op">-</span><span class="number">1.0</span>]; |
| <span class="kw">const</span> <span class="ident">POS_FLOATS</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[<span class="number">99.0</span> <span class="op">/</span> <span class="number">70.0</span>, <span class="ident">E</span>, <span class="ident">PI</span>]; |
| <span class="kw">const</span> <span class="ident">NEG_FLOATS</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[<span class="op">-</span><span class="number">99.0</span> <span class="op">/</span> <span class="number">70.0</span>, <span class="op">-</span><span class="ident">E</span>, <span class="op">-</span><span class="ident">PI</span>]; |
| <span class="kw">const</span> <span class="ident">POS_SMALL_FLOATS</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[(<span class="number">1.0</span> <span class="op">/</span> <span class="number">2.0</span>), <span class="ident">MIN_POSITIVE</span>, <span class="ident">EPSILON</span>]; |
| <span class="kw">const</span> <span class="ident">NEG_SMALL_FLOATS</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[<span class="op">-</span>(<span class="number">1.0</span> <span class="op">/</span> <span class="number">2.0</span>), <span class="op">-</span><span class="ident">MIN_POSITIVE</span>, <span class="op">-</span><span class="ident">EPSILON</span>]; |
| <span class="kw">const</span> <span class="ident">POS_EVENS</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[<span class="number">2.0</span>, <span class="number">6.0</span>, <span class="number">8.0</span>, <span class="number">10.0</span>, <span class="number">22.0</span>, <span class="number">100.0</span>, <span class="ident">MAX</span>]; |
| <span class="kw">const</span> <span class="ident">NEG_EVENS</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[<span class="ident">MIN</span>, <span class="op">-</span><span class="number">100.0</span>, <span class="op">-</span><span class="number">22.0</span>, <span class="op">-</span><span class="number">10.0</span>, <span class="op">-</span><span class="number">8.0</span>, <span class="op">-</span><span class="number">6.0</span>, <span class="op">-</span><span class="number">2.0</span>]; |
| <span class="kw">const</span> <span class="ident">POS_ODDS</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[<span class="number">3.0</span>, <span class="number">7.0</span>]; |
| <span class="kw">const</span> <span class="ident">NEG_ODDS</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[<span class="op">-</span><span class="number">7.0</span>, <span class="op">-</span><span class="number">3.0</span>]; |
| <span class="kw">const</span> <span class="ident">NANS</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[<span class="ident">NAN</span>]; |
| <span class="kw">const</span> <span class="ident">POS_INF</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[<span class="ident">INFINITY</span>]; |
| <span class="kw">const</span> <span class="ident">NEG_INF</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>] <span class="op">=</span> <span class="kw-2">&</span>[<span class="ident">NEG_INFINITY</span>]; |
| |
| <span class="kw">const</span> <span class="ident">ALL</span>: <span class="kw-2">&</span>[<span class="kw-2">&</span>[<span class="ident">f64</span>]] <span class="op">=</span> <span class="kw-2">&</span>[ |
| <span class="ident">POS_ZERO</span>, |
| <span class="ident">NEG_ZERO</span>, |
| <span class="ident">NANS</span>, |
| <span class="ident">NEG_SMALL_FLOATS</span>, |
| <span class="ident">POS_SMALL_FLOATS</span>, |
| <span class="ident">NEG_FLOATS</span>, |
| <span class="ident">POS_FLOATS</span>, |
| <span class="ident">NEG_EVENS</span>, |
| <span class="ident">POS_EVENS</span>, |
| <span class="ident">NEG_ODDS</span>, |
| <span class="ident">POS_ODDS</span>, |
| <span class="ident">NEG_INF</span>, |
| <span class="ident">POS_INF</span>, |
| <span class="ident">NEG_ONE</span>, |
| <span class="ident">POS_ONE</span>, |
| ]; |
| <span class="kw">const</span> <span class="ident">POS</span>: <span class="kw-2">&</span>[<span class="kw-2">&</span>[<span class="ident">f64</span>]] <span class="op">=</span> <span class="kw-2">&</span>[<span class="ident">POS_ZERO</span>, <span class="ident">POS_ODDS</span>, <span class="ident">POS_ONE</span>, <span class="ident">POS_FLOATS</span>, <span class="ident">POS_EVENS</span>, <span class="ident">POS_INF</span>]; |
| <span class="kw">const</span> <span class="ident">NEG</span>: <span class="kw-2">&</span>[<span class="kw-2">&</span>[<span class="ident">f64</span>]] <span class="op">=</span> <span class="kw-2">&</span>[<span class="ident">NEG_ZERO</span>, <span class="ident">NEG_ODDS</span>, <span class="ident">NEG_ONE</span>, <span class="ident">NEG_FLOATS</span>, <span class="ident">NEG_EVENS</span>, <span class="ident">NEG_INF</span>]; |
| |
| <span class="kw">fn</span> <span class="ident">pow_test</span>(<span class="ident">base</span>: <span class="ident">f64</span>, <span class="ident">exponent</span>: <span class="ident">f64</span>, <span class="ident">expected</span>: <span class="ident">f64</span>) { |
| <span class="kw">let</span> <span class="ident">res</span> <span class="op">=</span> <span class="ident">pow</span>(<span class="ident">base</span>, <span class="ident">exponent</span>); |
| <span class="macro">assert!</span>( |
| <span class="kw">if</span> <span class="ident">expected</span>.<span class="ident">is_nan</span>() { |
| <span class="ident">res</span>.<span class="ident">is_nan</span>() |
| } <span class="kw">else</span> { |
| <span class="ident">pow</span>(<span class="ident">base</span>, <span class="ident">exponent</span>) <span class="op">==</span> <span class="ident">expected</span> |
| }, |
| <span class="string">"{} ** {} was {} instead of {}"</span>, |
| <span class="ident">base</span>, |
| <span class="ident">exponent</span>, |
| <span class="ident">res</span>, |
| <span class="ident">expected</span> |
| ); |
| } |
| |
| <span class="kw">fn</span> <span class="ident">test_sets_as_base</span>(<span class="ident">sets</span>: <span class="kw-2">&</span>[<span class="kw-2">&</span>[<span class="ident">f64</span>]], <span class="ident">exponent</span>: <span class="ident">f64</span>, <span class="ident">expected</span>: <span class="ident">f64</span>) { |
| <span class="ident">sets</span>.<span class="ident">iter</span>() |
| .<span class="ident">for_each</span>(<span class="op">|</span><span class="ident">s</span><span class="op">|</span> <span class="ident">s</span>.<span class="ident">iter</span>().<span class="ident">for_each</span>(<span class="op">|</span><span class="ident">val</span><span class="op">|</span> <span class="ident">pow_test</span>(<span class="kw-2">*</span><span class="ident">val</span>, <span class="ident">exponent</span>, <span class="ident">expected</span>))); |
| } |
| |
| <span class="kw">fn</span> <span class="ident">test_sets_as_exponent</span>(<span class="ident">base</span>: <span class="ident">f64</span>, <span class="ident">sets</span>: <span class="kw-2">&</span>[<span class="kw-2">&</span>[<span class="ident">f64</span>]], <span class="ident">expected</span>: <span class="ident">f64</span>) { |
| <span class="ident">sets</span>.<span class="ident">iter</span>() |
| .<span class="ident">for_each</span>(<span class="op">|</span><span class="ident">s</span><span class="op">|</span> <span class="ident">s</span>.<span class="ident">iter</span>().<span class="ident">for_each</span>(<span class="op">|</span><span class="ident">val</span><span class="op">|</span> <span class="ident">pow_test</span>(<span class="ident">base</span>, <span class="kw-2">*</span><span class="ident">val</span>, <span class="ident">expected</span>))); |
| } |
| |
| <span class="kw">fn</span> <span class="ident">test_sets</span>(<span class="ident">sets</span>: <span class="kw-2">&</span>[<span class="kw-2">&</span>[<span class="ident">f64</span>]], <span class="ident">computed</span>: <span class="kw-2">&</span><span class="kw">dyn</span> <span class="ident">Fn</span>(<span class="ident">f64</span>) -> <span class="ident">f64</span>, <span class="ident">expected</span>: <span class="kw-2">&</span><span class="kw">dyn</span> <span class="ident">Fn</span>(<span class="ident">f64</span>) -> <span class="ident">f64</span>) { |
| <span class="ident">sets</span>.<span class="ident">iter</span>().<span class="ident">for_each</span>(<span class="op">|</span><span class="ident">s</span><span class="op">|</span> { |
| <span class="ident">s</span>.<span class="ident">iter</span>().<span class="ident">for_each</span>(<span class="op">|</span><span class="ident">val</span><span class="op">|</span> { |
| <span class="kw">let</span> <span class="ident">exp</span> <span class="op">=</span> <span class="ident">expected</span>(<span class="kw-2">*</span><span class="ident">val</span>); |
| <span class="kw">let</span> <span class="ident">res</span> <span class="op">=</span> <span class="ident">computed</span>(<span class="kw-2">*</span><span class="ident">val</span>); |
| |
| <span class="macro">assert!</span>( |
| <span class="kw">if</span> <span class="ident">exp</span>.<span class="ident">is_nan</span>() { |
| <span class="ident">res</span>.<span class="ident">is_nan</span>() |
| } <span class="kw">else</span> { |
| <span class="ident">exp</span> <span class="op">==</span> <span class="ident">res</span> |
| }, |
| <span class="string">"test for {} was {} instead of {}"</span>, |
| <span class="ident">val</span>, |
| <span class="ident">res</span>, |
| <span class="ident">exp</span> |
| ); |
| }) |
| }); |
| } |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">zero_as_exponent</span>() { |
| <span class="ident">test_sets_as_base</span>(<span class="ident">ALL</span>, <span class="number">0.0</span>, <span class="number">1.0</span>); |
| <span class="ident">test_sets_as_base</span>(<span class="ident">ALL</span>, <span class="op">-</span><span class="number">0.0</span>, <span class="number">1.0</span>); |
| } |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">one_as_base</span>() { |
| <span class="ident">test_sets_as_exponent</span>(<span class="number">1.0</span>, <span class="ident">ALL</span>, <span class="number">1.0</span>); |
| } |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">nan_inputs</span>() { |
| <span class="comment">// NAN as the base:</span> |
| <span class="comment">// (NAN ^ anything *but 0* should be NAN)</span> |
| <span class="ident">test_sets_as_exponent</span>(<span class="ident">NAN</span>, <span class="kw-2">&</span><span class="ident">ALL</span>[<span class="number">2</span>..], <span class="ident">NAN</span>); |
| |
| <span class="comment">// NAN as the exponent:</span> |
| <span class="comment">// (anything *but 1* ^ NAN should be NAN)</span> |
| <span class="ident">test_sets_as_base</span>(<span class="kw-2">&</span><span class="ident">ALL</span>[..(<span class="ident">ALL</span>.<span class="ident">len</span>() <span class="op">-</span> <span class="number">2</span>)], <span class="ident">NAN</span>, <span class="ident">NAN</span>); |
| } |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">infinity_as_base</span>() { |
| <span class="comment">// Positive Infinity as the base:</span> |
| <span class="comment">// (+Infinity ^ positive anything but 0 and NAN should be +Infinity)</span> |
| <span class="ident">test_sets_as_exponent</span>(<span class="ident">INFINITY</span>, <span class="kw-2">&</span><span class="ident">POS</span>[<span class="number">1</span>..], <span class="ident">INFINITY</span>); |
| |
| <span class="comment">// (+Infinity ^ negative anything except 0 and NAN should be 0.0)</span> |
| <span class="ident">test_sets_as_exponent</span>(<span class="ident">INFINITY</span>, <span class="kw-2">&</span><span class="ident">NEG</span>[<span class="number">1</span>..], <span class="number">0.0</span>); |
| |
| <span class="comment">// Negative Infinity as the base:</span> |
| <span class="comment">// (-Infinity ^ positive odd ints should be -Infinity)</span> |
| <span class="ident">test_sets_as_exponent</span>(<span class="ident">NEG_INFINITY</span>, <span class="kw-2">&</span>[<span class="ident">POS_ODDS</span>], <span class="ident">NEG_INFINITY</span>); |
| |
| <span class="comment">// (-Infinity ^ anything but odd ints should be == -0 ^ (-anything))</span> |
| <span class="comment">// We can lump in pos/neg odd ints here because they don't seem to</span> |
| <span class="comment">// cause panics (div by zero) in release mode (I think).</span> |
| <span class="ident">test_sets</span>(<span class="ident">ALL</span>, <span class="kw-2">&</span><span class="op">|</span><span class="ident">v</span>: <span class="ident">f64</span><span class="op">|</span> <span class="ident">pow</span>(<span class="ident">NEG_INFINITY</span>, <span class="ident">v</span>), <span class="kw-2">&</span><span class="op">|</span><span class="ident">v</span>: <span class="ident">f64</span><span class="op">|</span> <span class="ident">pow</span>(<span class="op">-</span><span class="number">0.0</span>, <span class="op">-</span><span class="ident">v</span>)); |
| } |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">infinity_as_exponent</span>() { |
| <span class="comment">// Positive/Negative base greater than 1:</span> |
| <span class="comment">// (pos/neg > 1 ^ Infinity should be Infinity - note this excludes NAN as the base)</span> |
| <span class="ident">test_sets_as_base</span>(<span class="kw-2">&</span><span class="ident">ALL</span>[<span class="number">5</span>..(<span class="ident">ALL</span>.<span class="ident">len</span>() <span class="op">-</span> <span class="number">2</span>)], <span class="ident">INFINITY</span>, <span class="ident">INFINITY</span>); |
| |
| <span class="comment">// (pos/neg > 1 ^ -Infinity should be 0.0)</span> |
| <span class="ident">test_sets_as_base</span>(<span class="kw-2">&</span><span class="ident">ALL</span>[<span class="number">5</span>..<span class="ident">ALL</span>.<span class="ident">len</span>() <span class="op">-</span> <span class="number">2</span>], <span class="ident">NEG_INFINITY</span>, <span class="number">0.0</span>); |
| |
| <span class="comment">// Positive/Negative base less than 1:</span> |
| <span class="kw">let</span> <span class="ident">base_below_one</span> <span class="op">=</span> <span class="kw-2">&</span>[<span class="ident">POS_ZERO</span>, <span class="ident">NEG_ZERO</span>, <span class="ident">NEG_SMALL_FLOATS</span>, <span class="ident">POS_SMALL_FLOATS</span>]; |
| |
| <span class="comment">// (pos/neg < 1 ^ Infinity should be 0.0 - this also excludes NAN as the base)</span> |
| <span class="ident">test_sets_as_base</span>(<span class="ident">base_below_one</span>, <span class="ident">INFINITY</span>, <span class="number">0.0</span>); |
| |
| <span class="comment">// (pos/neg < 1 ^ -Infinity should be Infinity)</span> |
| <span class="ident">test_sets_as_base</span>(<span class="ident">base_below_one</span>, <span class="ident">NEG_INFINITY</span>, <span class="ident">INFINITY</span>); |
| |
| <span class="comment">// Positive/Negative 1 as the base:</span> |
| <span class="comment">// (pos/neg 1 ^ Infinity should be 1)</span> |
| <span class="ident">test_sets_as_base</span>(<span class="kw-2">&</span>[<span class="ident">NEG_ONE</span>, <span class="ident">POS_ONE</span>], <span class="ident">INFINITY</span>, <span class="number">1.0</span>); |
| |
| <span class="comment">// (pos/neg 1 ^ -Infinity should be 1)</span> |
| <span class="ident">test_sets_as_base</span>(<span class="kw-2">&</span>[<span class="ident">NEG_ONE</span>, <span class="ident">POS_ONE</span>], <span class="ident">NEG_INFINITY</span>, <span class="number">1.0</span>); |
| } |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">zero_as_base</span>() { |
| <span class="comment">// Positive Zero as the base:</span> |
| <span class="comment">// (+0 ^ anything positive but 0 and NAN should be +0)</span> |
| <span class="ident">test_sets_as_exponent</span>(<span class="number">0.0</span>, <span class="kw-2">&</span><span class="ident">POS</span>[<span class="number">1</span>..], <span class="number">0.0</span>); |
| |
| <span class="comment">// (+0 ^ anything negative but 0 and NAN should be Infinity)</span> |
| <span class="comment">// (this should panic because we're dividing by zero)</span> |
| <span class="ident">test_sets_as_exponent</span>(<span class="number">0.0</span>, <span class="kw-2">&</span><span class="ident">NEG</span>[<span class="number">1</span>..], <span class="ident">INFINITY</span>); |
| |
| <span class="comment">// Negative Zero as the base:</span> |
| <span class="comment">// (-0 ^ anything positive but 0, NAN, and odd ints should be +0)</span> |
| <span class="ident">test_sets_as_exponent</span>(<span class="op">-</span><span class="number">0.0</span>, <span class="kw-2">&</span><span class="ident">POS</span>[<span class="number">3</span>..], <span class="number">0.0</span>); |
| |
| <span class="comment">// (-0 ^ anything negative but 0, NAN, and odd ints should be Infinity)</span> |
| <span class="comment">// (should panic because of divide by zero)</span> |
| <span class="ident">test_sets_as_exponent</span>(<span class="op">-</span><span class="number">0.0</span>, <span class="kw-2">&</span><span class="ident">NEG</span>[<span class="number">3</span>..], <span class="ident">INFINITY</span>); |
| |
| <span class="comment">// (-0 ^ positive odd ints should be -0)</span> |
| <span class="ident">test_sets_as_exponent</span>(<span class="op">-</span><span class="number">0.0</span>, <span class="kw-2">&</span>[<span class="ident">POS_ODDS</span>], <span class="op">-</span><span class="number">0.0</span>); |
| |
| <span class="comment">// (-0 ^ negative odd ints should be -Infinity)</span> |
| <span class="comment">// (should panic because of divide by zero)</span> |
| <span class="ident">test_sets_as_exponent</span>(<span class="op">-</span><span class="number">0.0</span>, <span class="kw-2">&</span>[<span class="ident">NEG_ODDS</span>], <span class="ident">NEG_INFINITY</span>); |
| } |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">special_cases</span>() { |
| <span class="comment">// One as the exponent:</span> |
| <span class="comment">// (anything ^ 1 should be anything - i.e. the base)</span> |
| <span class="ident">test_sets</span>(<span class="ident">ALL</span>, <span class="kw-2">&</span><span class="op">|</span><span class="ident">v</span>: <span class="ident">f64</span><span class="op">|</span> <span class="ident">pow</span>(<span class="ident">v</span>, <span class="number">1.0</span>), <span class="kw-2">&</span><span class="op">|</span><span class="ident">v</span>: <span class="ident">f64</span><span class="op">|</span> <span class="ident">v</span>); |
| |
| <span class="comment">// Negative One as the exponent:</span> |
| <span class="comment">// (anything ^ -1 should be 1/anything)</span> |
| <span class="ident">test_sets</span>(<span class="ident">ALL</span>, <span class="kw-2">&</span><span class="op">|</span><span class="ident">v</span>: <span class="ident">f64</span><span class="op">|</span> <span class="ident">pow</span>(<span class="ident">v</span>, <span class="op">-</span><span class="number">1.0</span>), <span class="kw-2">&</span><span class="op">|</span><span class="ident">v</span>: <span class="ident">f64</span><span class="op">|</span> <span class="number">1.0</span> <span class="op">/</span> <span class="ident">v</span>); |
| |
| <span class="comment">// Factoring -1 out:</span> |
| <span class="comment">// (negative anything ^ integer should be (-1 ^ integer) * (positive anything ^ integer))</span> |
| <span class="kw-2">&</span>[<span class="ident">POS_ZERO</span>, <span class="ident">NEG_ZERO</span>, <span class="ident">POS_ONE</span>, <span class="ident">NEG_ONE</span>, <span class="ident">POS_EVENS</span>, <span class="ident">NEG_EVENS</span>] |
| .<span class="ident">iter</span>() |
| .<span class="ident">for_each</span>(<span class="op">|</span><span class="ident">int_set</span><span class="op">|</span> { |
| <span class="ident">int_set</span>.<span class="ident">iter</span>().<span class="ident">for_each</span>(<span class="op">|</span><span class="ident">int</span><span class="op">|</span> { |
| <span class="ident">test_sets</span>(<span class="ident">ALL</span>, <span class="kw-2">&</span><span class="op">|</span><span class="ident">v</span>: <span class="ident">f64</span><span class="op">|</span> <span class="ident">pow</span>(<span class="op">-</span><span class="ident">v</span>, <span class="kw-2">*</span><span class="ident">int</span>), <span class="kw-2">&</span><span class="op">|</span><span class="ident">v</span>: <span class="ident">f64</span><span class="op">|</span> { |
| <span class="ident">pow</span>(<span class="op">-</span><span class="number">1.0</span>, <span class="kw-2">*</span><span class="ident">int</span>) <span class="op">*</span> <span class="ident">pow</span>(<span class="ident">v</span>, <span class="kw-2">*</span><span class="ident">int</span>) |
| }); |
| }) |
| }); |
| |
| <span class="comment">// Negative base (imaginary results):</span> |
| <span class="comment">// (-anything except 0 and Infinity ^ non-integer should be NAN)</span> |
| <span class="kw-2">&</span><span class="ident">NEG</span>[<span class="number">1</span>..(<span class="ident">NEG</span>.<span class="ident">len</span>() <span class="op">-</span> <span class="number">1</span>)].<span class="ident">iter</span>().<span class="ident">for_each</span>(<span class="op">|</span><span class="ident">set</span><span class="op">|</span> { |
| <span class="ident">set</span>.<span class="ident">iter</span>().<span class="ident">for_each</span>(<span class="op">|</span><span class="ident">val</span><span class="op">|</span> { |
| <span class="ident">test_sets</span>(<span class="kw-2">&</span><span class="ident">ALL</span>[<span class="number">3</span>..<span class="number">7</span>], <span class="kw-2">&</span><span class="op">|</span><span class="ident">v</span>: <span class="ident">f64</span><span class="op">|</span> <span class="ident">pow</span>(<span class="kw-2">*</span><span class="ident">val</span>, <span class="ident">v</span>), <span class="kw-2">&</span><span class="op">|</span><span class="kw">_</span><span class="op">|</span> <span class="ident">NAN</span>); |
| }) |
| }); |
| } |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">normal_cases</span>() { |
| <span class="macro">assert_eq!</span>(<span class="ident">pow</span>(<span class="number">2.0</span>, <span class="number">20.0</span>), (<span class="number">1</span> <span class="op"><</span><span class="op"><</span> <span class="number">20</span>) <span class="kw">as</span> <span class="ident">f64</span>); |
| <span class="macro">assert_eq!</span>(<span class="ident">pow</span>(<span class="op">-</span><span class="number">1.0</span>, <span class="number">9.0</span>), <span class="op">-</span><span class="number">1.0</span>); |
| <span class="macro">assert!</span>(<span class="ident">pow</span>(<span class="op">-</span><span class="number">1.0</span>, <span class="number">2.2</span>).<span class="ident">is_nan</span>()); |
| <span class="macro">assert!</span>(<span class="ident">pow</span>(<span class="op">-</span><span class="number">1.0</span>, <span class="op">-</span><span class="number">1.14</span>).<span class="ident">is_nan</span>()); |
| } |
| } |
| </code></pre></div> |
| </section><section id="search" class="content hidden"></section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-current-crate="libm" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.60.0-nightly (1bd4fdc94 2022-01-12)" ></div> |
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