131914882SAlex Richardson /*
231914882SAlex Richardson * Single-precision e^x function.
331914882SAlex Richardson *
4*f3087befSAndrew Turner * Copyright (c) 2017-2024, Arm Limited.
5072a4ba8SAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
631914882SAlex Richardson */
731914882SAlex Richardson
831914882SAlex Richardson #include <math.h>
931914882SAlex Richardson #include <stdint.h>
1031914882SAlex Richardson #include "math_config.h"
11*f3087befSAndrew Turner #include "test_defs.h"
12*f3087befSAndrew Turner #include "test_sig.h"
1331914882SAlex Richardson
1431914882SAlex Richardson /*
1531914882SAlex Richardson EXP2F_TABLE_BITS = 5
1631914882SAlex Richardson EXP2F_POLY_ORDER = 3
1731914882SAlex Richardson
1831914882SAlex Richardson ULP error: 0.502 (nearest rounding.)
1931914882SAlex Richardson Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
2031914882SAlex Richardson Wrong count: 170635 (all nearest rounding wrong results with fma.)
2131914882SAlex Richardson Non-nearest ULP error: 1 (rounded ULP error)
2231914882SAlex Richardson */
2331914882SAlex Richardson
2431914882SAlex Richardson #define N (1 << EXP2F_TABLE_BITS)
2531914882SAlex Richardson #define InvLn2N __exp2f_data.invln2_scaled
2631914882SAlex Richardson #define T __exp2f_data.tab
2731914882SAlex Richardson #define C __exp2f_data.poly_scaled
2831914882SAlex Richardson
2931914882SAlex Richardson static inline uint32_t
top12(float x)3031914882SAlex Richardson top12 (float x)
3131914882SAlex Richardson {
3231914882SAlex Richardson return asuint (x) >> 20;
3331914882SAlex Richardson }
3431914882SAlex Richardson
3531914882SAlex Richardson float
expf(float x)3631914882SAlex Richardson expf (float x)
3731914882SAlex Richardson {
3831914882SAlex Richardson uint32_t abstop;
3931914882SAlex Richardson uint64_t ki, t;
4031914882SAlex Richardson /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
4131914882SAlex Richardson double_t kd, xd, z, r, r2, y, s;
4231914882SAlex Richardson
4331914882SAlex Richardson xd = (double_t) x;
4431914882SAlex Richardson abstop = top12 (x) & 0x7ff;
4531914882SAlex Richardson if (unlikely (abstop >= top12 (88.0f)))
4631914882SAlex Richardson {
4731914882SAlex Richardson /* |x| >= 88 or x is nan. */
4831914882SAlex Richardson if (asuint (x) == asuint (-INFINITY))
4931914882SAlex Richardson return 0.0f;
5031914882SAlex Richardson if (abstop >= top12 (INFINITY))
5131914882SAlex Richardson return x + x;
5231914882SAlex Richardson if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
5331914882SAlex Richardson return __math_oflowf (0);
5431914882SAlex Richardson if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
5531914882SAlex Richardson return __math_uflowf (0);
5631914882SAlex Richardson #if WANT_ERRNO_UFLOW
5731914882SAlex Richardson if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */
5831914882SAlex Richardson return __math_may_uflowf (0);
5931914882SAlex Richardson #endif
6031914882SAlex Richardson }
6131914882SAlex Richardson
6231914882SAlex Richardson /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */
6331914882SAlex Richardson z = InvLn2N * xd;
6431914882SAlex Richardson
6531914882SAlex Richardson /* Round and convert z to int, the result is in [-150*N, 128*N] and
6631914882SAlex Richardson ideally nearest int is used, otherwise the magnitude of r can be
6731914882SAlex Richardson bigger which gives larger approximation error. */
6831914882SAlex Richardson #if TOINT_INTRINSICS
6931914882SAlex Richardson kd = roundtoint (z);
7031914882SAlex Richardson ki = converttoint (z);
7131914882SAlex Richardson #else
7231914882SAlex Richardson # define SHIFT __exp2f_data.shift
7331914882SAlex Richardson kd = eval_as_double (z + SHIFT);
7431914882SAlex Richardson ki = asuint64 (kd);
7531914882SAlex Richardson kd -= SHIFT;
7631914882SAlex Richardson #endif
7731914882SAlex Richardson r = z - kd;
7831914882SAlex Richardson
7931914882SAlex Richardson /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
8031914882SAlex Richardson t = T[ki % N];
8131914882SAlex Richardson t += ki << (52 - EXP2F_TABLE_BITS);
8231914882SAlex Richardson s = asdouble (t);
8331914882SAlex Richardson z = C[0] * r + C[1];
8431914882SAlex Richardson r2 = r * r;
8531914882SAlex Richardson y = C[2] * r + 1;
8631914882SAlex Richardson y = z * r2 + y;
8731914882SAlex Richardson y = y * s;
8831914882SAlex Richardson return eval_as_float (y);
8931914882SAlex Richardson }
9031914882SAlex Richardson #if USE_GLIBC_ABI
9131914882SAlex Richardson strong_alias (expf, __expf_finite)
9231914882SAlex Richardson hidden_alias (expf, __ieee754_expf)
9331914882SAlex Richardson #endif
94*f3087befSAndrew Turner
95*f3087befSAndrew Turner TEST_SIG (S, F, 1, exp, -9.9, 9.9)
96*f3087befSAndrew Turner TEST_ULP (expf, 0.01)
97*f3087befSAndrew Turner TEST_ULP_NONNEAREST (expf, 0.5)
98*f3087befSAndrew Turner TEST_INTERVAL (expf, 0, 0xffff0000, 10000)
99*f3087befSAndrew Turner TEST_SYM_INTERVAL (expf, 0x1p-14, 0x1p8, 500000)
100