text: /*
   * Double-precision e^x function.
   *
   * Copyright (c) 2018, Arm Limited.
   * SPDX-License-Identifier: MIT
   */
  
  #include <math.h>
  #include <stdint.h>
  #include "libm.h"
  #include "exp_data.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]
  
  /* 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 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.  */
  		fp_force_eval(fp_barrier(0x1p-1022) * 0x1p-1022);
  	}
  	y = 0x1p-1022 * y;
  	return 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;
  }
  
  double exp(double x)
  {
  	uint32_t abstop;
  	uint64_t ki, idx, top, sbits;
  	double_t kd, z, r, r2, scale, tail, tmp;
  
  	abstop = top12(x) & 0x7ff;
  	if (predict_false(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;
  	/* 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.  */
  	tmp = tail + r + r2 * (C2 + r * C3) + r2 * r2 * (C4 + r * C5);
  	if (predict_false(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);
  }
  