| 1 | /* |
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| 2 | * Single-precision 2^x function. |
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| 3 | * |
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| 4 | * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
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| 5 | * See https://llvm.org/LICENSE.txt for license information. |
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| 6 | * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
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| 7 | */ |
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| 8 | |
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| 9 | #include <math.h> |
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| 10 | #include <stdint.h> |
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| 11 | #include "math_config.h" |
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| 12 | |
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| 13 | /* |
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| 14 | EXP2F_TABLE_BITS = 5 |
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| 15 | EXP2F_POLY_ORDER = 3 |
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| 16 | |
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| 17 | ULP error: 0.502 (nearest rounding.) |
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| 18 | Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.) |
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| 19 | Wrong count: 168353 (all nearest rounding wrong results with fma.) |
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| 20 | Non-nearest ULP error: 1 (rounded ULP error) |
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| 21 | */ |
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| 22 | |
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| 23 | #define N (1 << EXP2F_TABLE_BITS) |
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| 24 | #define T __exp2f_data.tab |
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| 25 | #define C __exp2f_data.poly |
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| 26 | #define SHIFT __exp2f_data.shift_scaled |
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| 27 | |
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| 28 | static inline uint32_t |
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| 29 | top12 (float x) |
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| 30 | { |
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| 31 | return asuint (f: x) >> 20; |
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| 32 | } |
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| 33 | |
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| 34 | float |
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| 35 | exp2f (float x) |
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| 36 | { |
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| 37 | uint32_t abstop; |
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| 38 | uint64_t ki, t; |
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| 39 | /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ |
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| 40 | double_t kd, xd, z, r, r2, y, s; |
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| 41 | |
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| 42 | xd = (double_t) x; |
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| 43 | abstop = top12 (x) & 0x7ff; |
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| 44 | if (unlikely (abstop >= top12 (128.0f))) |
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| 45 | { |
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| 46 | /* |x| >= 128 or x is nan. */ |
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| 47 | if (asuint (f: x) == asuint (f: -INFINITY)) |
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| 48 | return 0.0f; |
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| 49 | if (abstop >= top12 (INFINITY)) |
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| 50 | return x + x; |
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| 51 | if (x > 0.0f) |
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| 52 | return __math_oflowf (0); |
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| 53 | if (x <= -150.0f) |
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| 54 | return __math_uflowf (0); |
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| 55 | #if WANT_ERRNO_UFLOW |
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| 56 | if (x < -149.0f) |
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| 57 | return __math_may_uflowf (0); |
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| 58 | #endif |
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| 59 | } |
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| 60 | |
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| 61 | /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */ |
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| 62 | kd = eval_as_double (x: xd + SHIFT); |
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| 63 | ki = asuint64 (f: kd); |
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| 64 | kd -= SHIFT; /* k/N for int k. */ |
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| 65 | r = xd - kd; |
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| 66 | |
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| 67 | /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ |
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| 68 | t = T[ki % N]; |
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| 69 | t += ki << (52 - EXP2F_TABLE_BITS); |
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| 70 | s = asdouble (i: t); |
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| 71 | z = C[0] * r + C[1]; |
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| 72 | r2 = r * r; |
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| 73 | y = C[2] * r + 1; |
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| 74 | y = z * r2 + y; |
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| 75 | y = y * s; |
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| 76 | return eval_as_float (x: y); |
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| 77 | } |
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| 78 | #if USE_GLIBC_ABI |
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| 79 | strong_alias (exp2f, __exp2f_finite) |
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| 80 | hidden_alias (exp2f, __ieee754_exp2f) |
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| 81 | #endif |
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| 82 | |
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