From 353409ada712abee04099d2a640f2c6ddf1d20e6 Mon Sep 17 00:00:00 2001 From: C Jones Date: Sat, 14 Jul 2018 05:04:46 -0400 Subject: [PATCH] Add exp2f --- library/compiler-builtins/libm/src/lib.rs | 2 - .../compiler-builtins/libm/src/math/exp2f.rs | 130 ++++++++++++++++++ .../compiler-builtins/libm/src/math/mod.rs | 2 + .../libm/test-generator/src/main.rs | 2 +- 4 files changed, 133 insertions(+), 3 deletions(-) create mode 100644 library/compiler-builtins/libm/src/math/exp2f.rs diff --git a/library/compiler-builtins/libm/src/lib.rs b/library/compiler-builtins/libm/src/lib.rs index fddb8ca70fb2..c6e01df415e2 100644 --- a/library/compiler-builtins/libm/src/lib.rs +++ b/library/compiler-builtins/libm/src/lib.rs @@ -70,7 +70,6 @@ pub trait F32Ext: private::Sealed { fn exp(self) -> Self; - #[cfg(todo)] fn exp2(self) -> Self; fn ln(self) -> Self; @@ -214,7 +213,6 @@ impl F32Ext for f32 { expf(self) } - #[cfg(todo)] #[inline] fn exp2(self) -> Self { exp2f(self) 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 000000000000..947679a8389d --- /dev/null +++ b/library/compiler-builtins/libm/src/math/exp2f.rs @@ -0,0 +1,130 @@ +// 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; + +// 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). +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); + + let exp2ft: [f64; TBLSIZE] = [ + f64::from_bits(0x3fe6a09e667f3bcd), + f64::from_bits(0x3fe7a11473eb0187), + f64::from_bits(0x3fe8ace5422aa0db), + f64::from_bits(0x3fe9c49182a3f090), + f64::from_bits(0x3feae89f995ad3ad), + f64::from_bits(0x3fec199bdd85529c), + f64::from_bits(0x3fed5818dcfba487), + f64::from_bits(0x3feea4afa2a490da), + f64::from_bits(0x3ff0000000000000), + f64::from_bits(0x3ff0b5586cf9890f), + f64::from_bits(0x3ff172b83c7d517b), + f64::from_bits(0x3ff2387a6e756238), + f64::from_bits(0x3ff306fe0a31b715), + f64::from_bits(0x3ff3dea64c123422), + f64::from_bits(0x3ff4bfdad5362a27), + f64::from_bits(0x3ff5ab07dd485429), + ]; + + // 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 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; + } + + /* 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 = 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 +} diff --git a/library/compiler-builtins/libm/src/math/mod.rs b/library/compiler-builtins/libm/src/math/mod.rs index 59d669ab6a91..5540ba838257 100644 --- a/library/compiler-builtins/libm/src/math/mod.rs +++ b/library/compiler-builtins/libm/src/math/mod.rs @@ -12,6 +12,7 @@ mod ceil; mod ceilf; mod cosf; mod exp; +mod exp2f; mod expf; mod fabs; mod fabsf; @@ -48,6 +49,7 @@ pub use self::ceil::ceil; pub use self::ceilf::ceilf; pub use self::cosf::cosf; pub use self::exp::exp; +pub use self::exp2f::exp2f; pub use self::expf::expf; pub use self::fabs::fabs; pub use self::fabsf::fabsf; diff --git a/library/compiler-builtins/libm/test-generator/src/main.rs b/library/compiler-builtins/libm/test-generator/src/main.rs index bce4284b3d0e..dfe912a508b0 100644 --- a/library/compiler-builtins/libm/test-generator/src/main.rs +++ b/library/compiler-builtins/libm/test-generator/src/main.rs @@ -660,7 +660,7 @@ f32_f32! { cosf, ceilf, // coshf, - // exp2f, + exp2f, expf, log10f, log1pf,