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Diffstat (limited to 'pl/math/exp.c')
| -rw-r--r-- | pl/math/exp.c | 163 |
1 files changed, 0 insertions, 163 deletions
diff --git a/pl/math/exp.c b/pl/math/exp.c deleted file mode 100644 index 90253b68875d..000000000000 --- a/pl/math/exp.c +++ /dev/null @@ -1,163 +0,0 @@ -/* - * 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); -} - |