From 42f467eaa7de29cb33a37304bd5b812e78797a54 Mon Sep 17 00:00:00 2001 From: Benjamin Schultzer Date: Fri, 17 May 2019 09:43:16 -0700 Subject: [PATCH] Add newlib exp2f --- src/math/exp2f.rs | 151 ++++++++-------------------------------------- 1 file changed, 24 insertions(+), 127 deletions(-) diff --git a/src/math/exp2f.rs b/src/math/exp2f.rs index 12c9e76a4..c777dc654 100644 --- a/src/math/exp2f.rs +++ b/src/math/exp2f.rs @@ -1,136 +1,33 @@ -// origin: FreeBSD /usr/src/lib/msun/src/s_exp2f.c -//- -// Copyright (c) 2005 David Schultz -// 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, ian@cygnus.com. + */ + +/* + * ==================================================== + * 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 }