80 lines
1.9 KiB
C
80 lines
1.9 KiB
C
/*
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* Single-precision e^x function.
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*
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* Copyright (c) 2017-2018, Arm Limited.
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* SPDX-License-Identifier: MIT
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*/
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#include "libc/math/math.h"
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#include "libc/math/libm.h"
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#include "libc/math/exp2f_data.h"
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/*
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EXP2F_TABLE_BITS = 5
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EXP2F_POLY_ORDER = 3
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ULP error: 0.502 (nearest rounding.)
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Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
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Wrong count: 170635 (all nearest rounding wrong results with fma.)
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Non-nearest ULP error: 1 (rounded ULP error)
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*/
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#define N (1 << EXP2F_TABLE_BITS)
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#define InvLn2N __exp2f_data.invln2_scaled
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#define T __exp2f_data.tab
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#define C __exp2f_data.poly_scaled
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static inline uint32_t top12(float x)
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{
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return asuint(x) >> 20;
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}
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float expf(float x)
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{
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uint32_t abstop;
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uint64_t ki, t;
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double_t kd, xd, z, r, r2, y, s;
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xd = (double_t)x;
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abstop = top12(x) & 0x7ff;
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if (predict_false(abstop >= top12(88.0f))) {
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/* |x| >= 88 or x is nan. */
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if (asuint(x) == asuint(-INFINITY))
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return 0.0f;
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if (abstop >= top12(INFINITY))
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return x + x;
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if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
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return __math_oflowf(0);
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if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
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return __math_uflowf(0);
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}
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/* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */
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z = InvLn2N * xd;
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/* Round and convert z to int, the result is in [-150*N, 128*N] and
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ideally ties-to-even rule is used, otherwise the magnitude of r
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can be bigger which gives larger approximation error. */
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#if TOINT_INTRINSICS
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kd = roundtoint(z);
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ki = converttoint(z);
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#else
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# define SHIFT __exp2f_data.shift
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kd = eval_as_double(z + SHIFT);
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ki = asuint64(kd);
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kd -= SHIFT;
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#endif
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r = z - kd;
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/* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
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t = T[ki % N];
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t += ki << (52 - EXP2F_TABLE_BITS);
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s = asdouble(t);
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z = C[0] * r + C[1];
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r2 = r * r;
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y = C[2] * r + 1;
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y = z * r2 + y;
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y = y * s;
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return eval_as_float(y);
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}
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