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</pre><pre class="rust"><code><span class="comment">// origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c
//
// ====================================================
// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
//
// Developed at SunPro, a Sun Microsystems, Inc. business.
// Permission to use, copy, modify, and distribute this
// software is freely granted, provided that this notice
// is preserved.
// ====================================================
//
// Optimized by Bruce D. Evans. */
</span><span class="kw">use </span><span class="kw">super</span>::rem_pio2_large;
<span class="comment">// #if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
// #define EPS DBL_EPSILON
</span><span class="kw">const </span>EPS: f64 = <span class="number">2.2204460492503131e-16</span>;
<span class="comment">// #elif FLT_EVAL_METHOD==2
// #define EPS LDBL_EPSILON
// #endif
// TODO: Support FLT_EVAL_METHOD?
</span><span class="kw">const </span>TO_INT: f64 = <span class="number">1.5 </span>/ EPS;
<span class="doccomment">/// 53 bits of 2/pi
</span><span class="kw">const </span>INV_PIO2: f64 = <span class="number">6.36619772367581382433e-01</span>; <span class="comment">/* 0x3FE45F30, 0x6DC9C883 */
</span><span class="doccomment">/// first 33 bits of pi/2
</span><span class="kw">const </span>PIO2_1: f64 = <span class="number">1.57079632673412561417e+00</span>; <span class="comment">/* 0x3FF921FB, 0x54400000 */
</span><span class="doccomment">/// pi/2 - PIO2_1
</span><span class="kw">const </span>PIO2_1T: f64 = <span class="number">6.07710050650619224932e-11</span>; <span class="comment">/* 0x3DD0B461, 0x1A626331 */
</span><span class="doccomment">/// second 33 bits of pi/2
</span><span class="kw">const </span>PIO2_2: f64 = <span class="number">6.07710050630396597660e-11</span>; <span class="comment">/* 0x3DD0B461, 0x1A600000 */
</span><span class="doccomment">/// pi/2 - (PIO2_1+PIO2_2)
</span><span class="kw">const </span>PIO2_2T: f64 = <span class="number">2.02226624879595063154e-21</span>; <span class="comment">/* 0x3BA3198A, 0x2E037073 */
</span><span class="doccomment">/// third 33 bits of pi/2
</span><span class="kw">const </span>PIO2_3: f64 = <span class="number">2.02226624871116645580e-21</span>; <span class="comment">/* 0x3BA3198A, 0x2E000000 */
</span><span class="doccomment">/// pi/2 - (PIO2_1+PIO2_2+PIO2_3)
</span><span class="kw">const </span>PIO2_3T: f64 = <span class="number">8.47842766036889956997e-32</span>; <span class="comment">/* 0x397B839A, 0x252049C1 */
// return the remainder of x rem pi/2 in y[0]+y[1]
// use rem_pio2_large() for large x
//
// caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
</span><span class="attr">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
</span><span class="kw">pub</span>(<span class="kw">crate</span>) <span class="kw">fn </span>rem_pio2(x: f64) -> (i32, f64, f64) {
<span class="kw">let </span>x1p24 = f64::from_bits(<span class="number">0x4170000000000000</span>);
<span class="kw">let </span>sign = (f64::to_bits(x) >> <span class="number">63</span>) <span class="kw">as </span>i32;
<span class="kw">let </span>ix = (f64::to_bits(x) >> <span class="number">32</span>) <span class="kw">as </span>u32 & <span class="number">0x7fffffff</span>;
<span class="kw">fn </span>medium(x: f64, ix: u32) -> (i32, f64, f64) {
<span class="comment">/* rint(x/(pi/2)), Assume round-to-nearest. */
</span><span class="kw">let </span>tmp = x <span class="kw">as </span>f64 * INV_PIO2 + TO_INT;
<span class="comment">// force rounding of tmp to it's storage format on x87 to avoid
// excess precision issues.
</span><span class="attr">#[cfg(all(target_arch = <span class="string">"x86"</span>, not(target_feature = <span class="string">"sse2"</span>)))]
</span><span class="kw">let </span>tmp = <span class="macro">force_eval!</span>(tmp);
<span class="kw">let </span>f_n = tmp - TO_INT;
<span class="kw">let </span>n = f_n <span class="kw">as </span>i32;
<span class="kw">let </span><span class="kw-2">mut </span>r = x - f_n * PIO2_1;
<span class="kw">let </span><span class="kw-2">mut </span>w = f_n * PIO2_1T; <span class="comment">/* 1st round, good to 85 bits */
</span><span class="kw">let </span><span class="kw-2">mut </span>y0 = r - w;
<span class="kw">let </span>ui = f64::to_bits(y0);
<span class="kw">let </span>ey = (ui >> <span class="number">52</span>) <span class="kw">as </span>i32 & <span class="number">0x7ff</span>;
<span class="kw">let </span>ex = (ix >> <span class="number">20</span>) <span class="kw">as </span>i32;
<span class="kw">if </span>ex - ey > <span class="number">16 </span>{
<span class="comment">/* 2nd round, good to 118 bits */
</span><span class="kw">let </span>t = r;
w = f_n * PIO2_2;
r = t - w;
w = f_n * PIO2_2T - ((t - r) - w);
y0 = r - w;
<span class="kw">let </span>ey = (f64::to_bits(y0) >> <span class="number">52</span>) <span class="kw">as </span>i32 & <span class="number">0x7ff</span>;
<span class="kw">if </span>ex - ey > <span class="number">49 </span>{
<span class="comment">/* 3rd round, good to 151 bits, covers all cases */
</span><span class="kw">let </span>t = r;
w = f_n * PIO2_3;
r = t - w;
w = f_n * PIO2_3T - ((t - r) - w);
y0 = r - w;
}
}
<span class="kw">let </span>y1 = (r - y0) - w;
(n, y0, y1)
}
<span class="kw">if </span>ix <= <span class="number">0x400f6a7a </span>{
<span class="comment">/* |x| ~<= 5pi/4 */
</span><span class="kw">if </span>(ix & <span class="number">0xfffff</span>) == <span class="number">0x921fb </span>{
<span class="comment">/* |x| ~= pi/2 or 2pi/2 */
</span><span class="kw">return </span>medium(x, ix); <span class="comment">/* cancellation -- use medium case */
</span>}
<span class="kw">if </span>ix <= <span class="number">0x4002d97c </span>{
<span class="comment">/* |x| ~<= 3pi/4 */
</span><span class="kw">if </span>sign == <span class="number">0 </span>{
<span class="kw">let </span>z = x - PIO2_1; <span class="comment">/* one round good to 85 bits */
</span><span class="kw">let </span>y0 = z - PIO2_1T;
<span class="kw">let </span>y1 = (z - y0) - PIO2_1T;
<span class="kw">return </span>(<span class="number">1</span>, y0, y1);
} <span class="kw">else </span>{
<span class="kw">let </span>z = x + PIO2_1;
<span class="kw">let </span>y0 = z + PIO2_1T;
<span class="kw">let </span>y1 = (z - y0) + PIO2_1T;
<span class="kw">return </span>(-<span class="number">1</span>, y0, y1);
}
} <span class="kw">else if </span>sign == <span class="number">0 </span>{
<span class="kw">let </span>z = x - <span class="number">2.0 </span>* PIO2_1;
<span class="kw">let </span>y0 = z - <span class="number">2.0 </span>* PIO2_1T;
<span class="kw">let </span>y1 = (z - y0) - <span class="number">2.0 </span>* PIO2_1T;
<span class="kw">return </span>(<span class="number">2</span>, y0, y1);
} <span class="kw">else </span>{
<span class="kw">let </span>z = x + <span class="number">2.0 </span>* PIO2_1;
<span class="kw">let </span>y0 = z + <span class="number">2.0 </span>* PIO2_1T;
<span class="kw">let </span>y1 = (z - y0) + <span class="number">2.0 </span>* PIO2_1T;
<span class="kw">return </span>(-<span class="number">2</span>, y0, y1);
}
}
<span class="kw">if </span>ix <= <span class="number">0x401c463b </span>{
<span class="comment">/* |x| ~<= 9pi/4 */
</span><span class="kw">if </span>ix <= <span class="number">0x4015fdbc </span>{
<span class="comment">/* |x| ~<= 7pi/4 */
</span><span class="kw">if </span>ix == <span class="number">0x4012d97c </span>{
<span class="comment">/* |x| ~= 3pi/2 */
</span><span class="kw">return </span>medium(x, ix);
}
<span class="kw">if </span>sign == <span class="number">0 </span>{
<span class="kw">let </span>z = x - <span class="number">3.0 </span>* PIO2_1;
<span class="kw">let </span>y0 = z - <span class="number">3.0 </span>* PIO2_1T;
<span class="kw">let </span>y1 = (z - y0) - <span class="number">3.0 </span>* PIO2_1T;
<span class="kw">return </span>(<span class="number">3</span>, y0, y1);
} <span class="kw">else </span>{
<span class="kw">let </span>z = x + <span class="number">3.0 </span>* PIO2_1;
<span class="kw">let </span>y0 = z + <span class="number">3.0 </span>* PIO2_1T;
<span class="kw">let </span>y1 = (z - y0) + <span class="number">3.0 </span>* PIO2_1T;
<span class="kw">return </span>(-<span class="number">3</span>, y0, y1);
}
} <span class="kw">else </span>{
<span class="kw">if </span>ix == <span class="number">0x401921fb </span>{
<span class="comment">/* |x| ~= 4pi/2 */
</span><span class="kw">return </span>medium(x, ix);
}
<span class="kw">if </span>sign == <span class="number">0 </span>{
<span class="kw">let </span>z = x - <span class="number">4.0 </span>* PIO2_1;
<span class="kw">let </span>y0 = z - <span class="number">4.0 </span>* PIO2_1T;
<span class="kw">let </span>y1 = (z - y0) - <span class="number">4.0 </span>* PIO2_1T;
<span class="kw">return </span>(<span class="number">4</span>, y0, y1);
} <span class="kw">else </span>{
<span class="kw">let </span>z = x + <span class="number">4.0 </span>* PIO2_1;
<span class="kw">let </span>y0 = z + <span class="number">4.0 </span>* PIO2_1T;
<span class="kw">let </span>y1 = (z - y0) + <span class="number">4.0 </span>* PIO2_1T;
<span class="kw">return </span>(-<span class="number">4</span>, y0, y1);
}
}
}
<span class="kw">if </span>ix < <span class="number">0x413921fb </span>{
<span class="comment">/* |x| ~< 2^20*(pi/2), medium size */
</span><span class="kw">return </span>medium(x, ix);
}
<span class="comment">/*
* all other (large) arguments
*/
</span><span class="kw">if </span>ix >= <span class="number">0x7ff00000 </span>{
<span class="comment">/* x is inf or NaN */
</span><span class="kw">let </span>y0 = x - x;
<span class="kw">let </span>y1 = y0;
<span class="kw">return </span>(<span class="number">0</span>, y0, y1);
}
<span class="comment">/* set z = scalbn(|x|,-ilogb(x)+23) */
</span><span class="kw">let </span><span class="kw-2">mut </span>ui = f64::to_bits(x);
ui &= (!<span class="number">1</span>) >> <span class="number">12</span>;
ui |= (<span class="number">0x3ff </span>+ <span class="number">23</span>) << <span class="number">52</span>;
<span class="kw">let </span><span class="kw-2">mut </span>z = f64::from_bits(ui);
<span class="kw">let </span><span class="kw-2">mut </span>tx = [<span class="number">0.0</span>; <span class="number">3</span>];
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..<span class="number">2 </span>{
<span class="macro">i!</span>(tx,i, =, z <span class="kw">as </span>i32 <span class="kw">as </span>f64);
z = (z - <span class="macro">i!</span>(tx, i)) * x1p24;
}
<span class="macro">i!</span>(tx,<span class="number">2</span>, =, z);
<span class="comment">/* skip zero terms, first term is non-zero */
</span><span class="kw">let </span><span class="kw-2">mut </span>i = <span class="number">2</span>;
<span class="kw">while </span>i != <span class="number">0 </span>&& <span class="macro">i!</span>(tx, i) == <span class="number">0.0 </span>{
i -= <span class="number">1</span>;
}
<span class="kw">let </span><span class="kw-2">mut </span>ty = [<span class="number">0.0</span>; <span class="number">3</span>];
<span class="kw">let </span>n = rem_pio2_large(<span class="kw-2">&</span>tx[..=i], <span class="kw-2">&mut </span>ty, ((ix <span class="kw">as </span>i32) >> <span class="number">20</span>) - (<span class="number">0x3ff </span>+ <span class="number">23</span>), <span class="number">1</span>);
<span class="kw">if </span>sign != <span class="number">0 </span>{
<span class="kw">return </span>(-n, -<span class="macro">i!</span>(ty, <span class="number">0</span>), -<span class="macro">i!</span>(ty, <span class="number">1</span>));
}
(n, <span class="macro">i!</span>(ty, <span class="number">0</span>), <span class="macro">i!</span>(ty, <span class="number">1</span>))
}
<span class="attr">#[cfg(test)]
</span><span class="kw">mod </span>tests {
<span class="kw">use </span><span class="kw">super</span>::rem_pio2;
<span class="attr">#[test]
</span><span class="kw">fn </span>test_near_pi() {
<span class="kw">let </span>arg = <span class="number">3.141592025756836</span>;
<span class="kw">let </span>arg = <span class="macro">force_eval!</span>(arg);
<span class="macro">assert_eq!</span>(
rem_pio2(arg),
(<span class="number">2</span>, -<span class="number">6.278329573009626e-7</span>, -<span class="number">2.1125998133974653e-23</span>)
);
<span class="kw">let </span>arg = <span class="number">3.141592033207416</span>;
<span class="kw">let </span>arg = <span class="macro">force_eval!</span>(arg);
<span class="macro">assert_eq!</span>(
rem_pio2(arg),
(<span class="number">2</span>, -<span class="number">6.20382377148128e-7</span>, -<span class="number">2.1125998133974653e-23</span>)
);
<span class="kw">let </span>arg = <span class="number">3.141592144966125</span>;
<span class="kw">let </span>arg = <span class="macro">force_eval!</span>(arg);
<span class="macro">assert_eq!</span>(
rem_pio2(arg),
(<span class="number">2</span>, -<span class="number">5.086236681942706e-7</span>, -<span class="number">2.1125998133974653e-23</span>)
);
<span class="kw">let </span>arg = <span class="number">3.141592979431152</span>;
<span class="kw">let </span>arg = <span class="macro">force_eval!</span>(arg);
<span class="macro">assert_eq!</span>(
rem_pio2(arg),
(<span class="number">2</span>, <span class="number">3.2584135866119817e-7</span>, -<span class="number">2.1125998133974653e-23</span>)
);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_overflow_b9b847() {
<span class="kw">let _ </span>= rem_pio2(-<span class="number">3054214.5490637687</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_overflow_4747b9() {
<span class="kw">let _ </span>= rem_pio2(<span class="number">917340800458.2274</span>);
}
}
</code></pre></div>
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