| /* |
| * Single-precision tanh(x) function. |
| * |
| * Copyright (c) 2022-2023, Arm Limited. |
| * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception |
| */ |
| #include "math_config.h" |
| #include "pl_sig.h" |
| #include "pl_test.h" |
| |
| #define BoringBound \ |
| 0x41102cb3 /* 0x1.205966p+3, above which tanhf rounds to 1 (or -1 for \ |
| negative). */ |
| #define AbsMask 0x7fffffff |
| #define One 0x3f800000 |
| |
| #define Shift (0x1.8p23f) |
| #define InvLn2 (0x1.715476p+0f) |
| #define Ln2hi (0x1.62e4p-1f) |
| #define Ln2lo (0x1.7f7d1cp-20f) |
| |
| #define C(i) __expm1f_poly[i] |
| |
| static inline float |
| expm1f_inline (float x) |
| { |
| /* Helper routine for calculating exp(x) - 1. |
| Copied from expm1f_1u6.c, with several simplifications: |
| - No special-case handling for tiny or special values, instead return early |
| from the main routine. |
| - No special handling for large values: |
| - No early return for infinity. |
| - Simpler combination of p and t in final stage of algorithm. |
| - |i| < 27, so can calculate t by simpler shift-and-add, instead of |
| ldexpf (same as vector algorithm). */ |
| |
| /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */ |
| float j = fmaf (InvLn2, x, Shift) - Shift; |
| int32_t i = j; |
| float f = fmaf (j, -Ln2hi, x); |
| f = fmaf (j, -Ln2lo, f); |
| |
| /* Approximate expm1(f) with polynomial P, expm1(f) ~= f + f^2 * P(f). |
| Uses Estrin scheme, where the main expm1f routine uses Horner. */ |
| float f2 = f * f; |
| float p_01 = fmaf (f, C (1), C (0)); |
| float p_23 = fmaf (f, C (3), C (2)); |
| float p = fmaf (f2, p_23, p_01); |
| p = fmaf (f2 * f2, C (4), p); |
| p = fmaf (f2, p, f); |
| |
| /* t = 2^i. */ |
| float t = asfloat ((uint32_t) (i + 127) << 23); |
| /* expm1(x) ~= p * t + (t - 1). */ |
| return fmaf (p, t, t - 1); |
| } |
| |
| /* Approximation for single-precision tanh(x), using a simplified version of |
| expm1f. The maximum error is 2.58 ULP: |
| tanhf(0x1.fa5eep-5) got 0x1.f9ba02p-5 |
| want 0x1.f9ba08p-5. */ |
| float |
| tanhf (float x) |
| { |
| uint32_t ix = asuint (x); |
| uint32_t iax = ix & AbsMask; |
| uint32_t sign = ix & ~AbsMask; |
| |
| if (unlikely (iax > BoringBound)) |
| { |
| if (iax > 0x7f800000) |
| return __math_invalidf (x); |
| return asfloat (One | sign); |
| } |
| |
| if (unlikely (iax < 0x34000000)) |
| return x; |
| |
| /* tanh(x) = (e^2x - 1) / (e^2x + 1). */ |
| float q = expm1f_inline (2 * x); |
| return q / (q + 2); |
| } |
| |
| PL_SIG (S, F, 1, tanh, -10.0, 10.0) |
| PL_TEST_ULP (tanhf, 2.09) |
| PL_TEST_INTERVAL (tanhf, 0, 0x1p-23, 1000) |
| PL_TEST_INTERVAL (tanhf, -0, -0x1p-23, 1000) |
| PL_TEST_INTERVAL (tanhf, 0x1p-23, 0x1.205966p+3, 100000) |
| PL_TEST_INTERVAL (tanhf, -0x1p-23, -0x1.205966p+3, 100000) |
| PL_TEST_INTERVAL (tanhf, 0x1.205966p+3, inf, 100) |
| PL_TEST_INTERVAL (tanhf, -0x1.205966p+3, -inf, 100) |