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| // origin: FreeBSD /usr/src/lib/msun/src/s_exp2f.c | ||
| //- | ||
| // Copyright (c) 2005 David Schultz <[email protected]> | ||
| // 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. | ||
| // | ||
| // THIS SOFTWARE IS PROVIDED BY THE AUTHOR 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 AUTHOR 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. | ||
|
|
||
| const TBLSIZE: usize = 16; | ||
|
|
||
| static EXP2FT: [u64; TBLSIZE] = [ | ||
| 0x3fe6a09e667f3bcd, | ||
| 0x3fe7a11473eb0187, | ||
| 0x3fe8ace5422aa0db, | ||
| 0x3fe9c49182a3f090, | ||
| 0x3feae89f995ad3ad, | ||
| 0x3fec199bdd85529c, | ||
| 0x3fed5818dcfba487, | ||
| 0x3feea4afa2a490da, | ||
| 0x3ff0000000000000, | ||
| 0x3ff0b5586cf9890f, | ||
| 0x3ff172b83c7d517b, | ||
| 0x3ff2387a6e756238, | ||
| 0x3ff306fe0a31b715, | ||
| 0x3ff3dea64c123422, | ||
| 0x3ff4bfdad5362a27, | ||
| 0x3ff5ab07dd485429, | ||
| ]; | ||
|
|
||
| // exp2f(x): compute the base 2 exponential of x | ||
| // | ||
| // Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927. | ||
| // | ||
| // Method: (equally-spaced tables) | ||
| // | ||
| // Reduce x: | ||
| // x = k + y, for integer k and |y| <= 1/2. | ||
| // Thus we have exp2f(x) = 2**k * exp2(y). | ||
| // | ||
| // Reduce y: | ||
| // y = i/TBLSIZE + z for integer i near y * TBLSIZE. | ||
| // Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z), | ||
| // with |z| <= 2**-(TBLSIZE+1). | ||
| // | ||
| // We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a | ||
| // degree-4 minimax polynomial with maximum error under 1.4 * 2**-33. | ||
| // Using double precision for everything except the reduction makes | ||
| // roundoff error insignificant and simplifies the scaling step. | ||
| // | ||
| // This method is due to Tang, but I do not use his suggested parameters: | ||
| // | ||
| // Tang, P. Table-driven Implementation of the Exponential Function | ||
| // in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989). | ||
| /* wf_exp2.c -- float version of w_exp2.c. | ||
| * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected]. | ||
| */ | ||
|
|
||
| /* | ||
| * ==================================================== | ||
| * 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. | ||
| * ==================================================== | ||
| */ | ||
|
|
||
| use super::powf; | ||
|
|
||
| /// Exponential, base 2 (f32) | ||
| /// | ||
| /// Calculate `2^x`, that is, 2 raised to the power `x`. | ||
| #[inline] | ||
| #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] | ||
| pub fn exp2f(mut x: f32) -> f32 { | ||
| let redux = f32::from_bits(0x4b400000) / TBLSIZE as f32; | ||
| let p1 = f32::from_bits(0x3f317218); | ||
| let p2 = f32::from_bits(0x3e75fdf0); | ||
| let p3 = f32::from_bits(0x3d6359a4); | ||
| let p4 = f32::from_bits(0x3c1d964e); | ||
|
|
||
| // double_t t, r, z; | ||
| // uint32_t ix, i0, k; | ||
|
|
||
| let x1p127 = f32::from_bits(0x7f000000); | ||
| pub fn exp2f(x: f32) -> f32 { | ||
| powf(2f32, x) | ||
| } | ||
|
|
||
| /* Filter out exceptional cases. */ | ||
| let ui = f32::to_bits(x); | ||
| let ix = ui & 0x7fffffff; | ||
| if ix > 0x42fc0000 { | ||
| /* |x| > 126 */ | ||
| if ix > 0x7f800000 { | ||
| /* NaN */ | ||
| return x; | ||
| } | ||
| if ui >= 0x43000000 && ui < 0x80000000 { | ||
| /* x >= 128 */ | ||
| x *= x1p127; | ||
| return x; | ||
| } | ||
| if ui >= 0x80000000 { | ||
| /* x < -126 */ | ||
| if ui >= 0xc3160000 || (ui & 0x0000ffff != 0) { | ||
| force_eval!(f32::from_bits(0x80000001) / x); | ||
| } | ||
| if ui >= 0xc3160000 { | ||
| /* x <= -150 */ | ||
| return 0.0; | ||
| } | ||
| } | ||
| } else if ix <= 0x33000000 { | ||
| /* |x| <= 0x1p-25 */ | ||
| return 1.0 + x; | ||
| #[cfg(test)] | ||
| mod tests { | ||
| #[test] | ||
| fn sanity_check() { | ||
| assert_eq!(super::exp2f(1.1), 2.143547); | ||
| } | ||
| } | ||
|
|
||
| /* Reduce x, computing z, i0, and k. */ | ||
| let ui = f32::to_bits(x + redux); | ||
| let mut i0 = ui; | ||
| i0 += TBLSIZE as u32 / 2; | ||
| let k = i0 / TBLSIZE as u32; | ||
| let ukf = f64::from_bits(((0x3ff + k) as u64) << 52); | ||
| i0 &= TBLSIZE as u32 - 1; | ||
| let mut uf = f32::from_bits(ui); | ||
| uf -= redux; | ||
| let z: f64 = (x - uf) as f64; | ||
| /* Compute r = exp2(y) = exp2ft[i0] * p(z). */ | ||
| let r: f64 = f64::from_bits(EXP2FT[i0 as usize]); | ||
| let t: f64 = r as f64 * z; | ||
| let r: f64 = r + t * (p1 as f64 + z * p2 as f64) + t * (z * z) * (p3 as f64 + z * p4 as f64); | ||
|
|
||
| /* Scale by 2**k */ | ||
| (r * ukf) as f32 | ||
| } |