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Diffstat (limited to 'contrib/arm-optimized-routines/pl/math/exp.c')
| -rw-r--r-- | contrib/arm-optimized-routines/pl/math/exp.c | 163 |
1 files changed, 163 insertions, 0 deletions
diff --git a/contrib/arm-optimized-routines/pl/math/exp.c b/contrib/arm-optimized-routines/pl/math/exp.c new file mode 100644 index 000000000000..90253b68875d --- /dev/null +++ b/contrib/arm-optimized-routines/pl/math/exp.c @@ -0,0 +1,163 @@ +/* + * Double-precision e^x function. + * + * Copyright (c) 2018-2023, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include <float.h> +#include <math.h> +#include <stdint.h> +#include "math_config.h" + +#define N (1 << EXP_TABLE_BITS) +#define InvLn2N __exp_data.invln2N +#define NegLn2hiN __exp_data.negln2hiN +#define NegLn2loN __exp_data.negln2loN +#define Shift __exp_data.shift +#define T __exp_data.tab +#define C2 __exp_data.poly[5 - EXP_POLY_ORDER] +#define C3 __exp_data.poly[6 - EXP_POLY_ORDER] +#define C4 __exp_data.poly[7 - EXP_POLY_ORDER] +#define C5 __exp_data.poly[8 - EXP_POLY_ORDER] +#define C6 __exp_data.poly[9 - EXP_POLY_ORDER] + +/* Handle cases that may overflow or underflow when computing the result that + is scale*(1+TMP) without intermediate rounding. The bit representation of + scale is in SBITS, however it has a computed exponent that may have + overflown into the sign bit so that needs to be adjusted before using it as + a double. (int32_t)KI is the k used in the argument reduction and exponent + adjustment of scale, positive k here means the result may overflow and + negative k means the result may underflow. */ +static inline double +specialcase (double_t tmp, uint64_t sbits, uint64_t ki) +{ + double_t scale, y; + + if ((ki & 0x80000000) == 0) + { + /* k > 0, the exponent of scale might have overflowed by <= 460. */ + sbits -= 1009ull << 52; + scale = asdouble (sbits); + y = 0x1p1009 * (scale + scale * tmp); + return check_oflow (eval_as_double (y)); + } + /* k < 0, need special care in the subnormal range. */ + sbits += 1022ull << 52; + scale = asdouble (sbits); + y = scale + scale * tmp; + if (y < 1.0) + { + /* Round y to the right precision before scaling it into the subnormal + range to avoid double rounding that can cause 0.5+E/2 ulp error where + E is the worst-case ulp error outside the subnormal range. So this + is only useful if the goal is better than 1 ulp worst-case error. */ + double_t hi, lo; + lo = scale - y + scale * tmp; + hi = 1.0 + y; + lo = 1.0 - hi + y + lo; + y = eval_as_double (hi + lo) - 1.0; + /* Avoid -0.0 with downward rounding. */ + if (WANT_ROUNDING && y == 0.0) + y = 0.0; + /* The underflow exception needs to be signaled explicitly. */ + force_eval_double (opt_barrier_double (0x1p-1022) * 0x1p-1022); + } + y = 0x1p-1022 * y; + return check_uflow (eval_as_double (y)); +} + +/* Top 12 bits of a double (sign and exponent bits). */ +static inline uint32_t +top12 (double x) +{ + return asuint64 (x) >> 52; +} + +/* Computes exp(x+xtail) where |xtail| < 2^-8/N and |xtail| <= |x|. + If hastail is 0 then xtail is assumed to be 0 too. */ +static inline double +exp_inline (double x, double xtail, int hastail) +{ + uint32_t abstop; + uint64_t ki, idx, top, sbits; + /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ + double_t kd, z, r, r2, scale, tail, tmp; + + abstop = top12 (x) & 0x7ff; + if (unlikely (abstop - top12 (0x1p-54) >= top12 (512.0) - top12 (0x1p-54))) + { + if (abstop - top12 (0x1p-54) >= 0x80000000) + /* Avoid spurious underflow for tiny x. */ + /* Note: 0 is common input. */ + return WANT_ROUNDING ? 1.0 + x : 1.0; + if (abstop >= top12 (1024.0)) + { + if (asuint64 (x) == asuint64 (-INFINITY)) + return 0.0; + if (abstop >= top12 (INFINITY)) + return 1.0 + x; + if (asuint64 (x) >> 63) + return __math_uflow (0); + else + return __math_oflow (0); + } + /* Large x is special cased below. */ + abstop = 0; + } + + /* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)]. */ + /* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N]. */ + z = InvLn2N * x; +#if TOINT_INTRINSICS + kd = roundtoint (z); + ki = converttoint (z); +#elif EXP_USE_TOINT_NARROW + /* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes. */ + kd = eval_as_double (z + Shift); + ki = asuint64 (kd) >> 16; + kd = (double_t) (int32_t) ki; +#else + /* z - kd is in [-1, 1] in non-nearest rounding modes. */ + kd = eval_as_double (z + Shift); + ki = asuint64 (kd); + kd -= Shift; +#endif + r = x + kd * NegLn2hiN + kd * NegLn2loN; + /* The code assumes 2^-200 < |xtail| < 2^-8/N. */ + if (hastail) + r += xtail; + /* 2^(k/N) ~= scale * (1 + tail). */ + idx = 2 * (ki % N); + top = ki << (52 - EXP_TABLE_BITS); + tail = asdouble (T[idx]); + /* This is only a valid scale when -1023*N < k < 1024*N. */ + sbits = T[idx + 1] + top; + /* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (tail + exp(r) - 1). */ + /* Evaluation is optimized assuming superscalar pipelined execution. */ + r2 = r * r; + /* Without fma the worst case error is 0.25/N ulp larger. */ + /* Worst case error is less than 0.5+1.11/N+(abs poly error * 2^53) ulp. */ +#if EXP_POLY_ORDER == 4 + tmp = tail + r + r2 * C2 + r * r2 * (C3 + r * C4); +#elif EXP_POLY_ORDER == 5 + tmp = tail + r + r2 * (C2 + r * C3) + r2 * r2 * (C4 + r * C5); +#elif EXP_POLY_ORDER == 6 + tmp = tail + r + r2 * (0.5 + r * C3) + r2 * r2 * (C4 + r * C5 + r2 * C6); +#endif + if (unlikely (abstop == 0)) + return specialcase (tmp, sbits, ki); + scale = asdouble (sbits); + /* Note: tmp == 0 or |tmp| > 2^-200 and scale > 2^-739, so there + is no spurious underflow here even without fma. */ + return eval_as_double (scale + scale * tmp); +} + +/* May be useful for implementing pow where more than double + precision input is needed. */ +double +__exp_dd (double x, double xtail) +{ + return exp_inline (x, xtail, 1); +} + |