/*
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* e_expf.c - single-precision exp function
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*
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* Copyright (c) 2009-2018, Arm Limited.
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* SPDX-License-Identifier: MIT
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*/
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/*
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* Algorithm was once taken from Cody & Waite, but has been munged
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* out of all recognition by SGT.
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*/
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#include <math.h>
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#include <errno.h>
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#include "math_private.h"
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float
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expf(float X)
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{
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int N; float XN, g, Rg, Result;
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unsigned ix = fai(X), edgecaseflag = 0;
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/*
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* Handle infinities, NaNs and big numbers.
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*/
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if (__builtin_expect((ix << 1) - 0x67000000 > 0x85500000 - 0x67000000, 0)) {
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if (!(0x7f800000 & ~ix)) {
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if (ix == 0xff800000)
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return 0.0f;
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else
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return FLOAT_INFNAN(X);/* do the right thing with both kinds of NaN and with +inf */
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} else if ((ix << 1) < 0x67000000) {
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return 1.0f; /* magnitude so small the answer can't be distinguished from 1 */
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} else if ((ix << 1) > 0x85a00000) {
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__set_errno(ERANGE);
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if (ix & 0x80000000) {
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return FLOAT_UNDERFLOW;
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} else {
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return FLOAT_OVERFLOW;
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}
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} else {
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edgecaseflag = 1;
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}
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}
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/*
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* Split the input into an integer multiple of log(2)/4, and a
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* fractional part.
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*/
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XN = X * (4.0f*1.4426950408889634074f);
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#ifdef __TARGET_FPU_SOFTVFP
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XN = _frnd(XN);
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N = (int)XN;
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#else
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N = (int)(XN + (ix & 0x80000000 ? -0.5f : 0.5f));
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XN = N;
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#endif
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g = (X - XN * 0x1.62ep-3F) - XN * 0x1.0bfbe8p-17F; /* prec-and-a-half representation of log(2)/4 */
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/*
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* Now we compute exp(X) in, conceptually, three parts:
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* - a pure power of two which we get from N>>2
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* - exp(g) for g in [-log(2)/8,+log(2)/8], which we compute
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* using a Remez-generated polynomial approximation
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* - exp(k*log(2)/4) (aka 2^(k/4)) for k in [0..3], which we
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* get from a lookup table in precision-and-a-half and
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* multiply by g.
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*
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* We gain a bit of extra precision by the fact that actually
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* our polynomial approximation gives us exp(g)-1, and we add
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* the 1 back on by tweaking the prec-and-a-half multiplication
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* step.
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*
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* Coefficients generated by the command
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./auxiliary/remez.jl --variable=g --suffix=f -- '-log(BigFloat(2))/8' '+log(BigFloat(2))/8' 3 0 '(expm1(x))/x'
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*/
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Rg = g * (
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9.999999412829185331953781321128516523408059996430919985217971370689774264850229e-01f+g*(4.999999608551332693833317084753864837160947932961832943901913087652889900683833e-01f+g*(1.667292360203016574303631953046104769969440903672618034272397630620346717392378e-01f+g*(4.168230895653321517750133783431970715648192153539929404872173693978116154823859e-02f)))
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);
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/*
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* Do the table lookup and combine it with Rg, to get our final
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* answer apart from the exponent.
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*/
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{
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static const float twotokover4top[4] = { 0x1p+0F, 0x1.306p+0F, 0x1.6ap+0F, 0x1.ae8p+0F };
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static const float twotokover4bot[4] = { 0x0p+0F, 0x1.fc1464p-13F, 0x1.3cccfep-13F, 0x1.3f32b6p-13F };
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static const float twotokover4all[4] = { 0x1p+0F, 0x1.306fep+0F, 0x1.6a09e6p+0F, 0x1.ae89fap+0F };
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int index = (N & 3);
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Rg = twotokover4top[index] + (twotokover4bot[index] + twotokover4all[index]*Rg);
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N >>= 2;
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}
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/*
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* Combine the output exponent and mantissa, and return.
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*/
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if (__builtin_expect(edgecaseflag, 0)) {
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Result = fhex(((N/2) << 23) + 0x3f800000);
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Result *= Rg;
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Result *= fhex(((N-N/2) << 23) + 0x3f800000);
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/*
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* Step not mentioned in C&W: set errno reliably.
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*/
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if (fai(Result) == 0)
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return MATHERR_EXPF_UFL(Result);
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if (fai(Result) == 0x7f800000)
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return MATHERR_EXPF_OFL(Result);
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return FLOAT_CHECKDENORM(Result);
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} else {
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Result = fhex(N * 8388608.0f + (float)0x3f800000);
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Result *= Rg;
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}
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return Result;
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}
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