/*- * SPDX-License-Identifier: BSD-2-Clause-FreeBSD * * 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.
*/
/* * 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 = 2**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).
*/ float
exp2f(float x)
{ double tv, twopk, u, z; float t;
uint32_t hx, ix, i0;
int32_t k;
/* Filter out exceptional cases. */
GET_FLOAT_WORD(hx, x);
ix = hx & 0x7fffffff; /* high word of |x| */ if(ix >= 0x43000000) { /* |x| >= 128 */ if(ix >= 0x7f800000) { if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0) return (x + x); /* x is NaN or +Inf */ else return (0.0); /* x is -Inf */
} if(x >= 0x1.0p7f) return (huge * huge); /* overflow */ if(x <= -0x1.2cp7f) return (twom100 * twom100); /* underflow */
} elseif (ix <= 0x33000000) { /* |x| <= 0x1p-25 */ return (1.0f + x);
}
/* Reduce x, computing z, i0, and k. */
STRICT_ASSIGN(float, t, x + redux);
GET_FLOAT_WORD(i0, t);
i0 += TBLSIZE / 2;
k = (i0 >> TBLBITS) << 20;
i0 &= TBLSIZE - 1;
t -= redux;
z = x - t;
INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
/* Compute r = exp2(y) = exp2ft[i0] * p(z). */
tv = exp2ft[i0];
u = tv * z;
tv = tv + u * (P1 + z * P2) + u * (z * z) * (P3 + z * P4);
/* Scale by 2**(k>>20). */ return (tv * twopk);
}
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