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Diffstat (limited to 'pl/math/v_log1pf_2u1.c')
-rw-r--r-- | pl/math/v_log1pf_2u1.c | 160 |
1 files changed, 160 insertions, 0 deletions
diff --git a/pl/math/v_log1pf_2u1.c b/pl/math/v_log1pf_2u1.c new file mode 100644 index 0000000..4a7732b --- /dev/null +++ b/pl/math/v_log1pf_2u1.c @@ -0,0 +1,160 @@ +/* + * Single-precision vector log(1+x) function. + * + * Copyright (c) 2022-2023, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "v_math.h" +#include "pl_sig.h" +#include "pl_test.h" + +#if V_SUPPORTED + +#define AbsMask 0x7fffffff +#define TinyBound 0x340 /* asuint32(0x1p-23). ulp=0.5 at 0x1p-23. */ +#define MinusOne 0xbf800000 +#define Ln2 (0x1.62e43p-1f) +#define Four 0x40800000 +#define ThreeQuarters v_u32 (0x3f400000) + +#define C(i) v_f32 (__log1pf_data.coeffs[i]) + +static inline v_f32_t +eval_poly (v_f32_t m) +{ +#ifdef V_LOG1PF_1U3 + + /* Approximate log(1+m) on [-0.25, 0.5] using Horner scheme. */ + v_f32_t p = v_fma_f32 (C (8), m, C (7)); + p = v_fma_f32 (p, m, C (6)); + p = v_fma_f32 (p, m, C (5)); + p = v_fma_f32 (p, m, C (4)); + p = v_fma_f32 (p, m, C (3)); + p = v_fma_f32 (p, m, C (2)); + p = v_fma_f32 (p, m, C (1)); + p = v_fma_f32 (p, m, C (0)); + return v_fma_f32 (m, m * p, m); + +#elif defined(V_LOG1PF_2U5) + + /* Approximate log(1+m) on [-0.25, 0.5] using Estrin scheme. */ + v_f32_t p_12 = v_fma_f32 (m, C (1), C (0)); + v_f32_t p_34 = v_fma_f32 (m, C (3), C (2)); + v_f32_t p_56 = v_fma_f32 (m, C (5), C (4)); + v_f32_t p_78 = v_fma_f32 (m, C (7), C (6)); + + v_f32_t m2 = m * m; + v_f32_t p_02 = v_fma_f32 (m2, p_12, m); + v_f32_t p_36 = v_fma_f32 (m2, p_56, p_34); + v_f32_t p_79 = v_fma_f32 (m2, C (8), p_78); + + v_f32_t m4 = m2 * m2; + v_f32_t p_06 = v_fma_f32 (m4, p_36, p_02); + + return v_fma_f32 (m4, m4 * p_79, p_06); + +#else +#error No precision specified for v_log1pf +#endif +} + +static inline float +handle_special (float x) +{ + uint32_t ix = asuint (x); + uint32_t ia = ix & AbsMask; + if (ix == 0xff800000 || ia > 0x7f800000 || ix > 0xbf800000) + { + /* x == -Inf => log1pf(x) = NaN. + x < -1.0 => log1pf(x) = NaN. + x == +/-NaN => log1pf(x) = NaN. */ +#if WANT_SIMD_EXCEPT + return __math_invalidf (asfloat (ia)); +#else + return NAN; +#endif + } + if (ix == 0xbf800000) + { + /* x == -1.0 => log1pf(x) = -Inf. */ +#if WANT_SIMD_EXCEPT + return __math_divzerof (ix); +#else + return -INFINITY; +#endif + } + /* |x| < TinyBound => log1p(x) = x. */ + return x; +} + +/* Vector log1pf approximation using polynomial on reduced interval. Accuracy is + the same as for the scalar algorithm, i.e. worst-case error when using Estrin + is roughly 2.02 ULP: + log1pf(0x1.21e13ap-2) got 0x1.fe8028p-3 want 0x1.fe802cp-3. */ +VPCS_ATTR v_f32_t V_NAME (log1pf) (v_f32_t x) +{ + v_u32_t ix = v_as_u32_f32 (x); + v_u32_t ia12 = (ix >> 20) & v_u32 (0x7f8); + v_u32_t special_cases + = v_cond_u32 (ia12 - v_u32 (TinyBound) >= (0x7f8 - TinyBound)) + | v_cond_u32 (ix >= MinusOne); + v_f32_t special_arg = x; + +#if WANT_SIMD_EXCEPT + if (unlikely (v_any_u32 (special_cases))) + /* Side-step special lanes so fenv exceptions are not triggered + inadvertently. */ + x = v_sel_f32 (special_cases, v_f32 (1), x); +#endif + + /* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m + is in [-0.25, 0.5]): + log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2). + + We approximate log1p(m) with a polynomial, then scale by + k*log(2). Instead of doing this directly, we use an intermediate + scale factor s = 4*k*log(2) to ensure the scale is representable + as a normalised fp32 number. */ + + v_f32_t m = x + v_f32 (1.0f); + + /* Choose k to scale x to the range [-1/4, 1/2]. */ + v_s32_t k = (v_as_s32_f32 (m) - ThreeQuarters) & v_u32 (0xff800000); + + /* Scale x by exponent manipulation. */ + v_f32_t m_scale = v_as_f32_u32 (v_as_u32_f32 (x) - v_as_u32_s32 (k)); + + /* Scale up to ensure that the scale factor is representable as normalised + fp32 number, and scale m down accordingly. */ + v_f32_t s = v_as_f32_u32 (v_u32 (Four) - k); + m_scale = m_scale + v_fma_f32 (v_f32 (0.25f), s, v_f32 (-1.0f)); + + /* Evaluate polynomial on the reduced interval. */ + v_f32_t p = eval_poly (m_scale); + + /* The scale factor to be applied back at the end - by multiplying float(k) + by 2^-23 we get the unbiased exponent of k. */ + v_f32_t scale_back = v_to_f32_s32 (k) * v_f32 (0x1p-23f); + + /* Apply the scaling back. */ + v_f32_t y = v_fma_f32 (scale_back, v_f32 (Ln2), p); + + if (unlikely (v_any_u32 (special_cases))) + return v_call_f32 (handle_special, special_arg, y, special_cases); + return y; +} +VPCS_ALIAS + +PL_SIG (V, F, 1, log1p, -0.9, 10.0) +PL_TEST_ULP (V_NAME (log1pf), 1.53) +PL_TEST_EXPECT_FENV (V_NAME (log1pf), WANT_SIMD_EXCEPT) +PL_TEST_INTERVAL (V_NAME (log1pf), -10.0, 10.0, 10000) +PL_TEST_INTERVAL (V_NAME (log1pf), 0.0, 0x1p-23, 30000) +PL_TEST_INTERVAL (V_NAME (log1pf), 0x1p-23, 0.001, 50000) +PL_TEST_INTERVAL (V_NAME (log1pf), 0.001, 1.0, 50000) +PL_TEST_INTERVAL (V_NAME (log1pf), 0.0, -0x1p-23, 30000) +PL_TEST_INTERVAL (V_NAME (log1pf), -0x1p-23, -0.001, 30000) +PL_TEST_INTERVAL (V_NAME (log1pf), -0.001, -1.0, 50000) +PL_TEST_INTERVAL (V_NAME (log1pf), -1.0, inf, 1000) +#endif |