llvm-project

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/*
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 * Single-precision pow function.
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 *
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 * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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 * See https://llvm.org/LICENSE.txt for license information.
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 * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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 */
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#include <math.h>
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#include <stdint.h>
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#include "math_config.h"
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/*
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POWF_LOG2_POLY_ORDER = 5
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EXP2F_TABLE_BITS = 5
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ULP error: 0.82 (~ 0.5 + relerr*2^24)
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relerr: 1.27 * 2^-26 (Relative error ~= 128*Ln2*relerr_log2 + relerr_exp2)
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relerr_log2: 1.83 * 2^-33 (Relative error of logx.)
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relerr_exp2: 1.69 * 2^-34 (Relative error of exp2(ylogx).)
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*/
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#define N (1 << POWF_LOG2_TABLE_BITS)
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#define T __powf_log2_data.tab
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#define A __powf_log2_data.poly
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#define OFF 0x3f330000
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/* Subnormal input is normalized so ix has negative biased exponent.
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   Output is multiplied by N (POWF_SCALE) if TOINT_INTRINSICS is set.  */
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static inline double_t
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log2_inline (uint32_t ix)
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{
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  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
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  double_t z, r, r2, r4, p, q, y, y0, invc, logc;
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  uint32_t iz, top, tmp;
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  int k, i;
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  /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
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     The range is split into N subintervals.
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     The ith subinterval contains z and c is near its center.  */
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  tmp = ix - OFF;
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  i = (tmp >> (23 - POWF_LOG2_TABLE_BITS)) % N;
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  top = tmp & 0xff800000;
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  iz = ix - top;
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  k = (int32_t) top >> (23 - POWF_SCALE_BITS); /* arithmetic shift */
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  invc = T[i].invc;
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  logc = T[i].logc;
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  z = (double_t) asfloat (iz);
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  /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
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  r = z * invc - 1;
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  y0 = logc + (double_t) k;
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  /* Pipelined polynomial evaluation to approximate log1p(r)/ln2.  */
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  r2 = r * r;
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  y = A[0] * r + A[1];
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  p = A[2] * r + A[3];
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  r4 = r2 * r2;
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  q = A[4] * r + y0;
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  q = p * r2 + q;
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  y = y * r4 + q;
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  return y;
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}
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#undef N
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#undef T
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#define N (1 << EXP2F_TABLE_BITS)
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#define T __exp2f_data.tab
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#define SIGN_BIAS (1 << (EXP2F_TABLE_BITS + 11))
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/* The output of log2 and thus the input of exp2 is either scaled by N
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   (in case of fast toint intrinsics) or not.  The unscaled xd must be
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   in [-1021,1023], sign_bias sets the sign of the result.  */
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static inline float
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exp2_inline (double_t xd, uint32_t sign_bias)
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{
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  uint64_t ki, ski, t;
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  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
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  double_t kd, z, r, r2, y, s;
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#if TOINT_INTRINSICS
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# define C __exp2f_data.poly_scaled
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  /* N*x = k + r with r in [-1/2, 1/2] */
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  kd = roundtoint (xd); /* k */
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  ki = converttoint (xd);
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#else
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# define C __exp2f_data.poly
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# define SHIFT __exp2f_data.shift_scaled
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  /* x = k/N + r with r in [-1/(2N), 1/(2N)] */
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  kd = eval_as_double (xd + SHIFT);
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  ki = asuint64 (kd);
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  kd -= SHIFT; /* k/N */
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#endif
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  r = xd - kd;
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  /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
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  t = T[ki % N];
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  ski = ki + sign_bias;
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  t += ski << (52 - EXP2F_TABLE_BITS);
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  s = asdouble (t);
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  z = C[0] * r + C[1];
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  r2 = r * r;
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  y = C[2] * r + 1;
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  y = z * r2 + y;
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  y = y * s;
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  return eval_as_float (y);
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}
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/* Returns 0 if not int, 1 if odd int, 2 if even int.  The argument is
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   the bit representation of a non-zero finite floating-point value.  */
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static inline int
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checkint (uint32_t iy)
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{
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  int e = iy >> 23 & 0xff;
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  if (e < 0x7f)
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    return 0;
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  if (e > 0x7f + 23)
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    return 2;
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  if (iy & ((1 << (0x7f + 23 - e)) - 1))
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    return 0;
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  if (iy & (1 << (0x7f + 23 - e)))
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    return 1;
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  return 2;
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}
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static inline int
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zeroinfnan (uint32_t ix)
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{
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  return 2 * ix - 1 >= 2u * 0x7f800000 - 1;
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}
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float
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powf (float x, float y)
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{
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  uint32_t sign_bias = 0;
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  uint32_t ix, iy;
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  ix = asuint (x);
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  iy = asuint (y);
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  if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000 || zeroinfnan (iy)))
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    {
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      /* Either (x < 0x1p-126 or inf or nan) or (y is 0 or inf or nan).  */
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      if (unlikely (zeroinfnan (iy)))
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	{
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	  if (2 * iy == 0)
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	    return issignalingf_inline (x) ? x + y : 1.0f;
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	  if (ix == 0x3f800000)
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	    return issignalingf_inline (y) ? x + y : 1.0f;
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	  if (2 * ix > 2u * 0x7f800000 || 2 * iy > 2u * 0x7f800000)
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	    return x + y;
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	  if (2 * ix == 2 * 0x3f800000)
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	    return 1.0f;
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	  if ((2 * ix < 2 * 0x3f800000) == !(iy & 0x80000000))
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	    return 0.0f; /* |x|<1 && y==inf or |x|>1 && y==-inf.  */
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	  return y * y;
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	}
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      if (unlikely (zeroinfnan (ix)))
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	{
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	  float_t x2 = x * x;
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	  if (ix & 0x80000000 && checkint (iy) == 1)
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	    {
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	      x2 = -x2;
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	      sign_bias = 1;
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	    }
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#if WANT_ERRNO
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	  if (2 * ix == 0 && iy & 0x80000000)
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	    return __math_divzerof (sign_bias);
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#endif
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	  /* Without the barrier some versions of clang hoist the 1/x2 and
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	     thus division by zero exception can be signaled spuriously.  */
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	  return iy & 0x80000000 ? opt_barrier_float (1 / x2) : x2;
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	}
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      /* x and y are non-zero finite.  */
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      if (ix & 0x80000000)
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	{
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	  /* Finite x < 0.  */
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	  int yint = checkint (iy);
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	  if (yint == 0)
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	    return __math_invalidf (x);
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	  if (yint == 1)
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	    sign_bias = SIGN_BIAS;
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	  ix &= 0x7fffffff;
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	}
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      if (ix < 0x00800000)
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	{
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	  /* Normalize subnormal x so exponent becomes negative.  */
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	  ix = asuint (x * 0x1p23f);
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	  ix &= 0x7fffffff;
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	  ix -= 23 << 23;
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	}
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    }
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  double_t logx = log2_inline (ix);
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  double_t ylogx = y * logx; /* Note: cannot overflow, y is single prec.  */
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  if (unlikely ((asuint64 (ylogx) >> 47 & 0xffff)
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		 >= asuint64 (126.0 * POWF_SCALE) >> 47))
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    {
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      /* |y*log(x)| >= 126.  */
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      if (ylogx > 0x1.fffffffd1d571p+6 * POWF_SCALE)
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	/* |x^y| > 0x1.ffffffp127.  */
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	return __math_oflowf (sign_bias);
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      if (WANT_ROUNDING && WANT_ERRNO
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	  && ylogx > 0x1.fffffffa3aae2p+6 * POWF_SCALE)
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	/* |x^y| > 0x1.fffffep127, check if we round away from 0.  */
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	if ((!sign_bias
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	     && eval_as_float (1.0f + opt_barrier_float (0x1p-25f)) != 1.0f)
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	    || (sign_bias
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		&& eval_as_float (-1.0f - opt_barrier_float (0x1p-25f))
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		     != -1.0f))
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	  return __math_oflowf (sign_bias);
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      if (ylogx <= -150.0 * POWF_SCALE)
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	return __math_uflowf (sign_bias);
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#if WANT_ERRNO_UFLOW
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      if (ylogx < -149.0 * POWF_SCALE)
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	return __math_may_uflowf (sign_bias);
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#endif
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    }
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  return exp2_inline (ylogx, sign_bias);
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}
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#if USE_GLIBC_ABI
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strong_alias (powf, __powf_finite)
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hidden_alias (powf, __ieee754_powf)
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#endif
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