| /* origin: FreeBSD /usr/src/lib/msun/src/e_expf.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::scalbnf; |
| |
| const HALF: [f32; 2] = [0.5, -0.5]; |
| const LN2_HI: f32 = 6.9314575195e-01; /* 0x3f317200 */ |
| const LN2_LO: f32 = 1.4286067653e-06; /* 0x35bfbe8e */ |
| const INV_LN2: f32 = 1.4426950216e+00; /* 0x3fb8aa3b */ |
| /* |
| * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]: |
| * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74 |
| */ |
| const P1: f32 = 1.6666625440e-1; /* 0xaaaa8f.0p-26 */ |
| const P2: f32 = -2.7667332906e-3; /* -0xb55215.0p-32 */ |
| |
| /// Exponential, base *e* (f32) |
| /// |
| /// Calculate the exponential of `x`, that is, *e* raised to the power `x` |
| /// (where *e* is the base of the natural system of logarithms, approximately 2.71828). |
| #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
| pub fn expf(mut x: f32) -> f32 { |
| let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127 |
| let x1p_126 = f32::from_bits(0x800000); // 0x1p-126f === 2 ^ -126 /*original 0x1p-149f ??????????? */ |
| let mut hx = x.to_bits(); |
| let sign = (hx >> 31) as i32; /* sign bit of x */ |
| let signb: bool = sign != 0; |
| hx &= 0x7fffffff; /* high word of |x| */ |
| |
| /* special cases */ |
| if hx >= 0x42aeac50 { |
| /* if |x| >= -87.33655f or NaN */ |
| if hx > 0x7f800000 { |
| /* NaN */ |
| return x; |
| } |
| if (hx >= 0x42b17218) && (!signb) { |
| /* x >= 88.722839f */ |
| /* overflow */ |
| x *= x1p127; |
| return x; |
| } |
| if signb { |
| /* underflow */ |
| force_eval!(-x1p_126 / x); |
| if hx >= 0x42cff1b5 { |
| /* x <= -103.972084f */ |
| return 0.; |
| } |
| } |
| } |
| |
| /* argument reduction */ |
| let k: i32; |
| let hi: f32; |
| let lo: f32; |
| if hx > 0x3eb17218 { |
| /* if |x| > 0.5 ln2 */ |
| if hx > 0x3f851592 { |
| /* if |x| > 1.5 ln2 */ |
| k = (INV_LN2 * x + i!(HALF, sign as usize)) as i32; |
| } else { |
| k = 1 - sign - sign; |
| } |
| let kf = k as f32; |
| hi = x - kf * LN2_HI; /* k*ln2hi is exact here */ |
| lo = kf * LN2_LO; |
| x = hi - lo; |
| } else if hx > 0x39000000 { |
| /* |x| > 2**-14 */ |
| k = 0; |
| hi = x; |
| lo = 0.; |
| } else { |
| /* raise inexact */ |
| force_eval!(x1p127 + x); |
| return 1. + x; |
| } |
| |
| /* x is now in primary range */ |
| let xx = x * x; |
| let c = x - xx * (P1 + xx * P2); |
| let y = 1. + (x * c / (2. - c) - lo + hi); |
| if k == 0 { |
| y |
| } else { |
| scalbnf(y, k) |
| } |
| } |
