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Diffstat (limited to 'library/compiler-builtins/libm/src/math/exp2f.rs')
| -rw-r--r-- | library/compiler-builtins/libm/src/math/exp2f.rs | 135 |
1 files changed, 135 insertions, 0 deletions
diff --git a/library/compiler-builtins/libm/src/math/exp2f.rs b/library/compiler-builtins/libm/src/math/exp2f.rs new file mode 100644 index 00000000000..f452b6a20f8 --- /dev/null +++ b/library/compiler-builtins/libm/src/math/exp2f.rs @@ -0,0 +1,135 @@ +// origin: FreeBSD /usr/src/lib/msun/src/s_exp2f.c +//- +// Copyright (c) 2005 David Schultz <das@FreeBSD.ORG> +// 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). + +/// Exponential, base 2 (f32) +/// +/// Calculate `2^x`, that is, 2 raised to the power `x`. +#[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); + + /* 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 (0x43000000..0x80000000).contains(&ui) { + /* 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; + } + + /* 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(i!(EXP2FT, i0 as usize)); + let t: f64 = r * 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 +} |