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Diffstat (limited to 'pl/math/sv_exp_1u5.c')
| -rw-r--r-- | pl/math/sv_exp_1u5.c | 137 |
1 files changed, 137 insertions, 0 deletions
diff --git a/pl/math/sv_exp_1u5.c b/pl/math/sv_exp_1u5.c new file mode 100644 index 000000000000..c187def9e625 --- /dev/null +++ b/pl/math/sv_exp_1u5.c @@ -0,0 +1,137 @@ +/* + * Double-precision vector e^x function. + * + * Copyright (c) 2023, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "sv_math.h" +#include "pl_sig.h" +#include "pl_test.h" + +static const struct data +{ + double poly[4]; + double ln2_hi, ln2_lo, inv_ln2, shift, thres; +} data = { + .poly = { /* ulp error: 0.53. */ + 0x1.fffffffffdbcdp-2, 0x1.555555555444cp-3, 0x1.555573c6a9f7dp-5, + 0x1.1111266d28935p-7 }, + .ln2_hi = 0x1.62e42fefa3800p-1, + .ln2_lo = 0x1.ef35793c76730p-45, + /* 1/ln2. */ + .inv_ln2 = 0x1.71547652b82fep+0, + /* 1.5*2^46+1023. This value is further explained below. */ + .shift = 0x1.800000000ffc0p+46, + .thres = 704.0, +}; + +#define C(i) sv_f64 (d->poly[i]) +#define SpecialOffset 0x6000000000000000 /* 0x1p513. */ +/* SpecialBias1 + SpecialBias1 = asuint(1.0). */ +#define SpecialBias1 0x7000000000000000 /* 0x1p769. */ +#define SpecialBias2 0x3010000000000000 /* 0x1p-254. */ + +/* Update of both special and non-special cases, if any special case is + detected. */ +static inline svfloat64_t +special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n) +{ + /* s=2^n may overflow, break it up into s=s1*s2, + such that exp = s + s*y can be computed as s1*(s2+s2*y) + and s1*s1 overflows only if n>0. */ + + /* If n<=0 then set b to 0x6, 0 otherwise. */ + svbool_t p_sign = svcmple (pg, n, 0.0); /* n <= 0. */ + svuint64_t b + = svdup_u64_z (p_sign, SpecialOffset); /* Inactive lanes set to 0. */ + + /* Set s1 to generate overflow depending on sign of exponent n. */ + svfloat64_t s1 = svreinterpret_f64 ( + svsubr_x (pg, b, SpecialBias1)); /* 0x70...0 - b. */ + /* Offset s to avoid overflow in final result if n is below threshold. */ + svfloat64_t s2 = svreinterpret_f64 ( + svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), + b)); /* as_u64 (s) - 0x3010...0 + b. */ + + /* |n| > 1280 => 2^(n) overflows. */ + svbool_t p_cmp = svacgt (pg, n, 1280.0); + + svfloat64_t r1 = svmul_x (pg, s1, s1); + svfloat64_t r2 = svmla_x (pg, s2, s2, y); + svfloat64_t r0 = svmul_x (pg, r2, s1); + + return svsel (p_cmp, r1, r0); +} + +/* SVE exp algorithm. Maximum measured error is 1.01ulps: + SV_NAME_D1 (exp)(0x1.4619d7b04da41p+6) got 0x1.885d9acc41da7p+117 + want 0x1.885d9acc41da6p+117. */ +svfloat64_t SV_NAME_D1 (exp) (svfloat64_t x, const svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + + svbool_t special = svacgt (pg, x, d->thres); + + /* Use a modifed version of the shift used for flooring, such that x/ln2 is + rounded to a multiple of 2^-6=1/64, shift = 1.5 * 2^52 * 2^-6 = 1.5 * + 2^46. + + n is not an integer but can be written as n = m + i/64, with i and m + integer, 0 <= i < 64 and m <= n. + + Bits 5:0 of z will be null every time x/ln2 reaches a new integer value + (n=m, i=0), and is incremented every time z (or n) is incremented by 1/64. + FEXPA expects i in bits 5:0 of the input so it can be used as index into + FEXPA hardwired table T[i] = 2^(i/64) for i = 0:63, that will in turn + populate the mantissa of the output. Therefore, we use u=asuint(z) as + input to FEXPA. + + We add 1023 to the modified shift value in order to set bits 16:6 of u to + 1, such that once these bits are moved to the exponent of the output of + FEXPA, we get the exponent of 2^n right, i.e. we get 2^m. */ + svfloat64_t z = svmla_x (pg, sv_f64 (d->shift), x, d->inv_ln2); + svuint64_t u = svreinterpret_u64 (z); + svfloat64_t n = svsub_x (pg, z, d->shift); + + /* r = x - n * ln2, r is in [-ln2/(2N), ln2/(2N)]. */ + svfloat64_t ln2 = svld1rq (svptrue_b64 (), &d->ln2_hi); + svfloat64_t r = svmls_lane (x, n, ln2, 0); + r = svmls_lane (r, n, ln2, 1); + + /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5. */ + svfloat64_t r2 = svmul_x (pg, r, r); + svfloat64_t p01 = svmla_x (pg, C (0), C (1), r); + svfloat64_t p23 = svmla_x (pg, C (2), C (3), r); + svfloat64_t p04 = svmla_x (pg, p01, p23, r2); + svfloat64_t y = svmla_x (pg, r, p04, r2); + + /* s = 2^n, computed using FEXPA. FEXPA does not propagate NaNs, so for + consistent NaN handling we have to manually propagate them. This comes at + significant performance cost. */ + svfloat64_t s = svexpa (u); + + /* Assemble result as exp(x) = 2^n * exp(r). If |x| > Thresh the + multiplication may overflow, so use special case routine. */ + + if (unlikely (svptest_any (pg, special))) + { + /* FEXPA zeroes the sign bit, however the sign is meaningful to the + special case function so needs to be copied. + e = sign bit of u << 46. */ + svuint64_t e = svand_x (pg, svlsl_x (pg, u, 46), 0x8000000000000000); + /* Copy sign to s. */ + s = svreinterpret_f64 (svadd_x (pg, e, svreinterpret_u64 (s))); + return special_case (pg, s, y, n); + } + + /* No special case. */ + return svmla_x (pg, s, s, y); +} + +PL_SIG (SV, D, 1, exp, -9.9, 9.9) +PL_TEST_ULP (SV_NAME_D1 (exp), 1.46) +PL_TEST_SYM_INTERVAL (SV_NAME_D1 (exp), 0, 0x1p-23, 40000) +PL_TEST_SYM_INTERVAL (SV_NAME_D1 (exp), 0x1p-23, 1, 50000) +PL_TEST_SYM_INTERVAL (SV_NAME_D1 (exp), 1, 0x1p23, 50000) +PL_TEST_SYM_INTERVAL (SV_NAME_D1 (exp), 0x1p23, inf, 50000) |