/rust/registry/src/index.crates.io-1949cf8c6b5b557f/pxfm-0.1.25/src/asinpif.rs

Source
/*
 * // Copyright (c) Radzivon Bartoshyk 6/2025. All rights reserved.
 * //
 * // Redistribution and use in source and binary forms, with or without modification,
 * // are permitted provided that the following conditions are met:
 * //
 * // 1.  Redistributions of source code must retain the above copyright notice, this
 * // list of conditions and the following disclaimer.
 * //
 * // 2.  Redistributions in binary form must reproduce the above copyright notice,
 * // this list of conditions and the following disclaimer in the documentation
 * // and/or other materials provided with the distribution.
 * //
 * // 3.  Neither the name of the copyright holder nor the names of its
 * // contributors may be used to endorse or promote products derived from
 * // this software without specific prior written permission.
 * //
 * // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
 * // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
 * // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
 * // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
 * // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
use crate::common::f_fmla;

pub(crate) static ASINCOSF_PI_TABLE: [[u64; 8]; 16] = [
    [
        0x3fd45f306dc9c882,
        0x3fab2995e7b7dc2f,
        0x3f98723a1cf50c7e,
        0x3f8d1a4591d16a29,
        0x3f83ce3aa68ddaee,
        0x3f7d3182ab0cc1bf,
        0x3f762b379a8b88e3,
        0x3f76811411fcfec2,
    ],
    [
        0x3fdffffffffd3cda,
        0xbfb17cc1b3355fdd,
        0x3f9d067a1e8d5a99,
        0xbf908e16fb09314a,
        0x3f85eed43d42dcb2,
        0xbf7f58baca7acc71,
        0x3f75dab64e2dcf15,
        0xbf659270e30797ac,
    ],
    [
        0x3fdfffffff7c4617,
        0xbfb17cc149ded3a2,
        0x3f9d0654d4cb2c1a,
        0xbf908c3ba713d33a,
        0x3f85d2053481079c,
        0xbf7e485ebc545e7e,
        0x3f7303baca167ddd,
        0xbf5dee8d16d06b38,
    ],
    [
        0x3fdffffffa749848,
        0xbfb17cbe71559350,
        0x3f9d05a312269adf,
        0xbf90862b3ee617d7,
        0x3f85920708db2a73,
        0xbf7cb0463b3862c3,
        0x3f702b82478f95d7,
        0xbf552a7b8579e729,
    ],
    [
        0x3fdfffffe1f92bb5,
        0xbfb17cb3e74c64e3,
        0x3f9d03af67311cbf,
        0xbf9079441cbfc7a0,
        0x3f852b4287805a61,
        0xbf7ac3286d604a98,
        0x3f6b2f1210d9701b,
        0xbf4e740ddc25afd6,
    ],
    [
        0x3fdfffff92beb6e2,
        0xbfb17c986fe9518b,
        0x3f9cff98167c9a5e,
        0xbf90638b591eae52,
        0x3f84a0803828959e,
        0xbf78adeca229f11d,
        0x3f66b9a7ba05dfce,
        0xbf4640521a43b2d0,
    ],
    [
        0x3fdffffeccee5bfc,
        0xbfb17c5f1753f5ea,
        0x3f9cf874e4fe258f,
        0xbf9043e6cf77b256,
        0x3f83f7db42227d92,
        0xbf7691a6fa2a2882,
        0x3f62f6543162bc61,
        0xbf407d5da05822b6,
    ],
    [
        0x3fdffffd2f64431d,
        0xbfb17bf8208c10c1,
        0x3f9ced7487cdb124,
        0xbf901a0d30932905,
        0x3f83388f99b254da,
        0xbf74844e245c65bd,
        0x3f5fa777150197c6,
        0xbf38c1ecf16a05c8,
    ],
    [
        0x3fdffffa36d1712e,
        0xbfb17b523971bd4e,
        0x3f9cddee26de2dee,
        0xbf8fccb00abaaabc,
        0x3f8269afc3622342,
        0xbf72933152686752,
        0x3f5a76d4956cc9a3,
        0xbf32ce7d6dc651ce,
    ],
    [
        0x3fdffff5402ab3a1,
        0xbfb17a5ba85da77a,
        0x3f9cc96894e05c02,
        0xbf8f532143cb832e,
        0x3f819180b660ff09,
        0xbf70c57417a78b3c,
        0x3f562e26cbd7bb1e,
        0xbf2ce28d33fe1df3,
    ],
    [
        0x3fdfffed8d639751,
        0xbfb1790349f3ae76,
        0x3f9caf9a4fd1b398,
        0xbf8ec986b111342e,
        0x3f80b53c3ad4baa4,
        0xbf6e3c2282eeace4,
        0x3f52a55369f55bbe,
        0xbf2667fe48c396e8,
    ],
    [
        0x3fdfffe24b714161,
        0xbfb177394fbcb719,
        0x3f9c90652d920ebd,
        0xbf8e3239197bddf1,
        0x3f7fb2188525b025,
        0xbf6b3aadd451afc7,
        0x3f4f74020f31fdab,
        0xbf218b0cb246768d,
    ],
    [
        0x3fdfffd298bec9e2,
        0xbfb174efbfd34648,
        0x3f9c6bcfe48ea92b,
        0xbf8d8f9f2a16157c,
        0x3f7e0044f56c8864,
        0xbf6883e2347fe76c,
        0x3f4a9f0e3c1b7af5,
        0xbf1bb5acc0e60825,
    ],
    [
        0x3fdfffbd8b784c4d,
        0xbfb1721abdd3722e,
        0x3f9c41fee756d4b0,
        0xbf8ce40bccf8065f,
        0x3f7c59b684b70ef9,
        0xbf66133d027996b3,
        0x3f469cad01106397,
        0xbf160f8e45494156,
    ],
    [
        0x3fdfffa23749cf88,
        0xbfb16eb0a8285c06,
        0x3f9c132d762e1b0d,
        0xbf8c31a959398f4e,
        0x3f7ac1c5b46bc8a0,
        0xbf63e34f1abe51dc,
        0x3f4346738737c0b9,
        0xbf11b227a3f5c750,
    ],
    [
        0x3fdfff7fb25bb407,
        0xbfb16aaa14d75640,
        0x3f9bdfa75fca5ff2,
        0xbf8b7a6e260d079c,
        0x3f793ab06911033c,
        0xbf61ee5560967fd5,
        0x3f407d31060838bf,
        0xbf0c96f33a283115,
    ],
];

/// Computes asin(x)/PI
///
/// Max ULP 0.5
#[inline]
pub fn f_asinpif(x: f32) -> f32 {
    let ax = x.abs();
    let az = ax as f64;
    let z = x as f64;
    let t = x.to_bits();
    let e: i32 = ((t >> 23) & 0xff) as i32;
    if e >= 127 {
        // |x| >= 1 or nan
        if ax == 1.0 {
            return f32::copysign(0.5, x);
        } // |x| = 1
        if e == 0xff && (t.wrapping_shl(9)) != 0 {
            return x + x;
        } // x = nan
        return f32::NAN; // |x| > 1
    }
    let s: i32 = 146i32.wrapping_sub(e);
    let mut i = 0i32;
    // s<32 corresponds to |x| >= 2^-12
    if s < 32 {
        i = (((t & 0x007fffff) | 1 << 23) >> s) as i32;
    }
    let z2 = z * z;
    let z4 = z2 * z2;
    let c = ASINCOSF_PI_TABLE[i as usize & 15];
    if i == 0 {
        // |x| < 2^-4
        let mut c0 = f_fmla(z2, f64::from_bits(c[1]), f64::from_bits(c[0]));
        let c2 = f_fmla(z2, f64::from_bits(c[3]), f64::from_bits(c[2]));
        let mut c4 = f_fmla(z2, f64::from_bits(c[5]), f64::from_bits(c[4]));
        let c6 = f_fmla(z2, f64::from_bits(c[7]), f64::from_bits(c[6]));
        c0 = f_fmla(c2, z4, c0);
        c4 = f_fmla(c6, z4, c4);
        c0 += c4 * (z4 * z4);
        (z * c0) as f32
    } else {
        // |x| >= 2^-4
        let f = (1. - az).sqrt();
        let mut c0 = f_fmla(az, f64::from_bits(c[1]), f64::from_bits(c[0]));
        let c2 = f_fmla(az, f64::from_bits(c[3]), f64::from_bits(c[2]));
        let mut c4 = f_fmla(az, f64::from_bits(c[5]), f64::from_bits(c[4]));
        let c6 = f_fmla(az, f64::from_bits(c[7]), f64::from_bits(c[6]));
        c0 = f_fmla(c2, z2, c0);
        c4 = f_fmla(c6, z2, c4);
        c0 += c4 * z4;
        let r = f_fmla(
            -c0,
            f64::copysign(f, x as f64),
            f64::copysign(0.5, x as f64),
        );
        r as f32
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_asinpif() {
        assert_eq!(f_asinpif(0.0), 0.);
        assert_eq!(f_asinpif(0.5), 0.16666667);
        assert!(f_asinpif(1.5).is_nan());
    }
}

Coverage Report

Created: 2025-11-24 07:30

Line	Count	Source
1		/*
2		* // Copyright (c) Radzivon Bartoshyk 6/2025. All rights reserved.
3		* //
4		* // Redistribution and use in source and binary forms, with or without modification,
5		* // are permitted provided that the following conditions are met:
6		* //
7		* // 1. Redistributions of source code must retain the above copyright notice, this
8		* // list of conditions and the following disclaimer.
9		* //
10		* // 2. Redistributions in binary form must reproduce the above copyright notice,
11		* // this list of conditions and the following disclaimer in the documentation
12		* // and/or other materials provided with the distribution.
13		* //
14		* // 3. Neither the name of the copyright holder nor the names of its
15		* // contributors may be used to endorse or promote products derived from
16		* // this software without specific prior written permission.
17		* //
18		* // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
19		* // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20		* // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
21		* // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
22		* // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23		* // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
24		* // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
25		* // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
26		* // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
27		* // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
28		*/
29		use crate::common::f_fmla;
30
31		pub(crate) static ASINCOSF_PI_TABLE: [[u64; 8]; 16] = [
32		[
33		0x3fd45f306dc9c882,
34		0x3fab2995e7b7dc2f,
35		0x3f98723a1cf50c7e,
36		0x3f8d1a4591d16a29,
37		0x3f83ce3aa68ddaee,
38		0x3f7d3182ab0cc1bf,
39		0x3f762b379a8b88e3,
40		0x3f76811411fcfec2,
41		],
42		[
43		0x3fdffffffffd3cda,
44		0xbfb17cc1b3355fdd,
45		0x3f9d067a1e8d5a99,
46		0xbf908e16fb09314a,
47		0x3f85eed43d42dcb2,
48		0xbf7f58baca7acc71,
49		0x3f75dab64e2dcf15,
50		0xbf659270e30797ac,
51		],
52		[
53		0x3fdfffffff7c4617,
54		0xbfb17cc149ded3a2,
55		0x3f9d0654d4cb2c1a,
56		0xbf908c3ba713d33a,
57		0x3f85d2053481079c,
58		0xbf7e485ebc545e7e,
59		0x3f7303baca167ddd,
60		0xbf5dee8d16d06b38,
61		],
62		[
63		0x3fdffffffa749848,
64		0xbfb17cbe71559350,
65		0x3f9d05a312269adf,
66		0xbf90862b3ee617d7,
67		0x3f85920708db2a73,
68		0xbf7cb0463b3862c3,
69		0x3f702b82478f95d7,
70		0xbf552a7b8579e729,
71		],
72		[
73		0x3fdfffffe1f92bb5,
74		0xbfb17cb3e74c64e3,
75		0x3f9d03af67311cbf,
76		0xbf9079441cbfc7a0,
77		0x3f852b4287805a61,
78		0xbf7ac3286d604a98,
79		0x3f6b2f1210d9701b,
80		0xbf4e740ddc25afd6,
81		],
82		[
83		0x3fdfffff92beb6e2,
84		0xbfb17c986fe9518b,
85		0x3f9cff98167c9a5e,
86		0xbf90638b591eae52,
87		0x3f84a0803828959e,
88		0xbf78adeca229f11d,
89		0x3f66b9a7ba05dfce,
90		0xbf4640521a43b2d0,
91		],
92		[
93		0x3fdffffeccee5bfc,
94		0xbfb17c5f1753f5ea,
95		0x3f9cf874e4fe258f,
96		0xbf9043e6cf77b256,
97		0x3f83f7db42227d92,
98		0xbf7691a6fa2a2882,
99		0x3f62f6543162bc61,
100		0xbf407d5da05822b6,
101		],
102		[
103		0x3fdffffd2f64431d,
104		0xbfb17bf8208c10c1,
105		0x3f9ced7487cdb124,
106		0xbf901a0d30932905,
107		0x3f83388f99b254da,
108		0xbf74844e245c65bd,
109		0x3f5fa777150197c6,
110		0xbf38c1ecf16a05c8,
111		],
112		[
113		0x3fdffffa36d1712e,
114		0xbfb17b523971bd4e,
115		0x3f9cddee26de2dee,
116		0xbf8fccb00abaaabc,
117		0x3f8269afc3622342,
118		0xbf72933152686752,
119		0x3f5a76d4956cc9a3,
120		0xbf32ce7d6dc651ce,
121		],
122		[
123		0x3fdffff5402ab3a1,
124		0xbfb17a5ba85da77a,
125		0x3f9cc96894e05c02,
126		0xbf8f532143cb832e,
127		0x3f819180b660ff09,
128		0xbf70c57417a78b3c,
129		0x3f562e26cbd7bb1e,
130		0xbf2ce28d33fe1df3,
131		],
132		[
133		0x3fdfffed8d639751,
134		0xbfb1790349f3ae76,
135		0x3f9caf9a4fd1b398,
136		0xbf8ec986b111342e,
137		0x3f80b53c3ad4baa4,
138		0xbf6e3c2282eeace4,
139		0x3f52a55369f55bbe,
140		0xbf2667fe48c396e8,
141		],
142		[
143		0x3fdfffe24b714161,
144		0xbfb177394fbcb719,
145		0x3f9c90652d920ebd,
146		0xbf8e3239197bddf1,
147		0x3f7fb2188525b025,
148		0xbf6b3aadd451afc7,
149		0x3f4f74020f31fdab,
150		0xbf218b0cb246768d,
151		],
152		[
153		0x3fdfffd298bec9e2,
154		0xbfb174efbfd34648,
155		0x3f9c6bcfe48ea92b,
156		0xbf8d8f9f2a16157c,
157		0x3f7e0044f56c8864,
158		0xbf6883e2347fe76c,
159		0x3f4a9f0e3c1b7af5,
160		0xbf1bb5acc0e60825,
161		],
162		[
163		0x3fdfffbd8b784c4d,
164		0xbfb1721abdd3722e,
165		0x3f9c41fee756d4b0,
166		0xbf8ce40bccf8065f,
167		0x3f7c59b684b70ef9,
168		0xbf66133d027996b3,
169		0x3f469cad01106397,
170		0xbf160f8e45494156,
171		],
172		[
173		0x3fdfffa23749cf88,
174		0xbfb16eb0a8285c06,
175		0x3f9c132d762e1b0d,
176		0xbf8c31a959398f4e,
177		0x3f7ac1c5b46bc8a0,
178		0xbf63e34f1abe51dc,
179		0x3f4346738737c0b9,
180		0xbf11b227a3f5c750,
181		],
182		[
183		0x3fdfff7fb25bb407,
184		0xbfb16aaa14d75640,
185		0x3f9bdfa75fca5ff2,
186		0xbf8b7a6e260d079c,
187		0x3f793ab06911033c,
188		0xbf61ee5560967fd5,
189		0x3f407d31060838bf,
190		0xbf0c96f33a283115,
191		],
192		];
193
194		/// Computes asin(x)/PI
195		///
196		/// Max ULP 0.5
197		#[inline]
198	0	pub fn f_asinpif(x: f32) -> f32 {
199	0	let ax = x.abs();
200	0	let az = ax as f64;
201	0	let z = x as f64;
202	0	let t = x.to_bits();
203	0	let e: i32 = ((t >> 23) & 0xff) as i32;
204	0	if e >= 127 {
205		// \|x\| >= 1 or nan
206	0	if ax == 1.0 {
207	0	return f32::copysign(0.5, x);
208	0	} // \|x\| = 1
209	0	if e == 0xff && (t.wrapping_shl(9)) != 0 {
210	0	return x + x;
211	0	} // x = nan
212	0	return f32::NAN; // \|x\| > 1
213	0	}
214	0	let s: i32 = 146i32.wrapping_sub(e);
215	0	let mut i = 0i32;
216		// s<32 corresponds to \|x\| >= 2^-12
217	0	if s < 32 {
218	0	i = (((t & 0x007fffff) \| 1 << 23) >> s) as i32;
219	0	}
220	0	let z2 = z * z;
221	0	let z4 = z2 * z2;
222	0	let c = ASINCOSF_PI_TABLE[i as usize & 15];
223	0	if i == 0 {
224		// \|x\| < 2^-4
225	0	let mut c0 = f_fmla(z2, f64::from_bits(c[1]), f64::from_bits(c[0]));
226	0	let c2 = f_fmla(z2, f64::from_bits(c[3]), f64::from_bits(c[2]));
227	0	let mut c4 = f_fmla(z2, f64::from_bits(c[5]), f64::from_bits(c[4]));
228	0	let c6 = f_fmla(z2, f64::from_bits(c[7]), f64::from_bits(c[6]));
229	0	c0 = f_fmla(c2, z4, c0);
230	0	c4 = f_fmla(c6, z4, c4);
231	0	c0 += c4 * (z4 * z4);
232	0	(z * c0) as f32
233		} else {
234		// \|x\| >= 2^-4
235	0	let f = (1. - az).sqrt();
236	0	let mut c0 = f_fmla(az, f64::from_bits(c[1]), f64::from_bits(c[0]));
237	0	let c2 = f_fmla(az, f64::from_bits(c[3]), f64::from_bits(c[2]));
238	0	let mut c4 = f_fmla(az, f64::from_bits(c[5]), f64::from_bits(c[4]));
239	0	let c6 = f_fmla(az, f64::from_bits(c[7]), f64::from_bits(c[6]));
240	0	c0 = f_fmla(c2, z2, c0);
241	0	c4 = f_fmla(c6, z2, c4);
242	0	c0 += c4 * z4;
243	0	let r = f_fmla(
244	0	-c0,
245	0	f64::copysign(f, x as f64),
246	0	f64::copysign(0.5, x as f64),
247		);
248	0	r as f32
249		}
250	0	}
251
252		#[cfg(test)]
253		mod tests {
254		use super::*;
255
256		#[test]
257		fn test_asinpif() {
258		assert_eq!(f_asinpif(0.0), 0.);
259		assert_eq!(f_asinpif(0.5), 0.16666667);
260		assert!(f_asinpif(1.5).is_nan());
261		}
262		}