gcc/libgcc/config/libbid/bid128_sqrt.c

/* Copyright (C) 2007-2022 Free Software Foundation, Inc.

This file is part of GCC.

GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.

GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.

You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
<http://www.gnu.org/licenses/>.  */

#define BID_128RES
#include "bid_internal.h"
#include "bid_sqrt_macros.h"
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
#include <fenv.h>

#define FE_ALL_FLAGS FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT
#endif

BID128_FUNCTION_ARG1 (bid128_sqrt, x)

     UINT256 M256, C256, C4, C8;
     UINT128 CX, CX1, CX2, A10, S2, T128, TP128, CS, CSM, res;
     UINT64 sign_x, Carry;
     SINT64 D;
     int_float fx, f64;
     int exponent_x, bin_expon_cx;
     int digits, scale, exponent_q;
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
     fexcept_t binaryflags = 0;
#endif

  // unpack arguments, check for NaN or Infinity
if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) {
res.w[1] = CX.w[1];
res.w[0] = CX.w[0];
    // NaN ?
if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
#ifdef SET_STATUS_FLAGS
  if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull)	// sNaN
    __set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
  res.w[1] = CX.w[1] & QUIET_MASK64;
  BID_RETURN (res);
}
    // x is Infinity?
if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
  res.w[1] = CX.w[1];
  if (sign_x) {
    // -Inf, return NaN
    res.w[1] = 0x7c00000000000000ull;
#ifdef SET_STATUS_FLAGS
    __set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
  }
  BID_RETURN (res);
}
    // x is 0 otherwise

res.w[1] =
  sign_x |
  ((((UINT64) (exponent_x + DECIMAL_EXPONENT_BIAS_128)) >> 1) << 49);
res.w[0] = 0;
BID_RETURN (res);
}
if (sign_x) {
  res.w[1] = 0x7c00000000000000ull;
  res.w[0] = 0;
#ifdef SET_STATUS_FLAGS
  __set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
  BID_RETURN (res);
}
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
  // 2^64
f64.i = 0x5f800000;

  // fx ~ CX
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
bin_expon_cx = ((fx.i >> 23) & 0xff) - 0x7f;
digits = estimate_decimal_digits[bin_expon_cx];

A10 = CX;
if (exponent_x & 1) {
  A10.w[1] = (CX.w[1] << 3) | (CX.w[0] >> 61);
  A10.w[0] = CX.w[0] << 3;
  CX2.w[1] = (CX.w[1] << 1) | (CX.w[0] >> 63);
  CX2.w[0] = CX.w[0] << 1;
  __add_128_128 (A10, A10, CX2);
}

CS.w[0] = short_sqrt128 (A10);
CS.w[1] = 0;
  // check for exact result
if (CS.w[0] * CS.w[0] == A10.w[0]) {
  __mul_64x64_to_128_fast (S2, CS.w[0], CS.w[0]);
  if (S2.w[1] == A10.w[1])	// && S2.w[0]==A10.w[0])
  {
    get_BID128_very_fast (&res, 0,
			  (exponent_x +
			   DECIMAL_EXPONENT_BIAS_128) >> 1, CS);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
    (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
    BID_RETURN (res);
  }
}
  // get number of digits in CX
D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1];
if (D > 0
    || (!D && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0]))
  digits++;

  // if exponent is odd, scale coefficient by 10
scale = 67 - digits;
exponent_q = exponent_x - scale;
scale += (exponent_q & 1);	// exp. bias is even

if (scale > 38) {
  T128 = power10_table_128[scale - 37];
  __mul_128x128_low (CX1, CX, T128);

  TP128 = power10_table_128[37];
  __mul_128x128_to_256 (C256, CX1, TP128);
} else {
  T128 = power10_table_128[scale];
  __mul_128x128_to_256 (C256, CX, T128);
}


  // 4*C256
C4.w[3] = (C256.w[3] << 2) | (C256.w[2] >> 62);
C4.w[2] = (C256.w[2] << 2) | (C256.w[1] >> 62);
C4.w[1] = (C256.w[1] << 2) | (C256.w[0] >> 62);
C4.w[0] = C256.w[0] << 2;

long_sqrt128 (&CS, C256);

#ifndef IEEE_ROUND_NEAREST
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
if (!((rnd_mode) & 3)) {
#endif
#endif
  // compare to midpoints
  CSM.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
  CSM.w[0] = (CS.w[0] + CS.w[0]) | 1;
  // CSM^2
  //__mul_128x128_to_256(M256, CSM, CSM);
  __sqr128_to_256 (M256, CSM);

  if (C4.w[3] > M256.w[3]
      || (C4.w[3] == M256.w[3]
	  && (C4.w[2] > M256.w[2]
	      || (C4.w[2] == M256.w[2]
		  && (C4.w[1] > M256.w[1]
		      || (C4.w[1] == M256.w[1]
			  && C4.w[0] > M256.w[0])))))) {
    // round up
    CS.w[0]++;
    if (!CS.w[0])
      CS.w[1]++;
  } else {
    C8.w[1] = (CS.w[1] << 3) | (CS.w[0] >> 61);
    C8.w[0] = CS.w[0] << 3;
    // M256 - 8*CSM
    __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
    __sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
    __sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
    M256.w[3] = M256.w[3] - Carry;

    // if CSM' > C256, round up
    if (M256.w[3] > C4.w[3]
	|| (M256.w[3] == C4.w[3]
	    && (M256.w[2] > C4.w[2]
		|| (M256.w[2] == C4.w[2]
		    && (M256.w[1] > C4.w[1]
			|| (M256.w[1] == C4.w[1]
			    && M256.w[0] > C4.w[0])))))) {
      // round down
      if (!CS.w[0])
	CS.w[1]--;
      CS.w[0]--;
    }
  }
#ifndef IEEE_ROUND_NEAREST
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
} else {
  __sqr128_to_256 (M256, CS);
  C8.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
  C8.w[0] = CS.w[0] << 1;
  if (M256.w[3] > C256.w[3]
      || (M256.w[3] == C256.w[3]
	  && (M256.w[2] > C256.w[2]
	      || (M256.w[2] == C256.w[2]
		  && (M256.w[1] > C256.w[1]
		      || (M256.w[1] == C256.w[1]
			  && M256.w[0] > C256.w[0])))))) {
    __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
    __sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
    __sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
    M256.w[3] = M256.w[3] - Carry;
    M256.w[0]++;
    if (!M256.w[0]) {
      M256.w[1]++;
      if (!M256.w[1]) {
	M256.w[2]++;
	if (!M256.w[2])
	  M256.w[3]++;
      }
    }

    if (!CS.w[0])
      CS.w[1]--;
    CS.w[0]--;

    if (M256.w[3] > C256.w[3]
	|| (M256.w[3] == C256.w[3]
	    && (M256.w[2] > C256.w[2]
		|| (M256.w[2] == C256.w[2]
		    && (M256.w[1] > C256.w[1]
			|| (M256.w[1] == C256.w[1]
			    && M256.w[0] > C256.w[0])))))) {

      if (!CS.w[0])
	CS.w[1]--;
      CS.w[0]--;
    }
  }

  else {
    __add_carry_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
    __add_carry_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
    __add_carry_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
    M256.w[3] = M256.w[3] + Carry;
    M256.w[0]++;
    if (!M256.w[0]) {
      M256.w[1]++;
      if (!M256.w[1]) {
	M256.w[2]++;
	if (!M256.w[2])
	  M256.w[3]++;
      }
    }
    if (M256.w[3] < C256.w[3]
	|| (M256.w[3] == C256.w[3]
	    && (M256.w[2] < C256.w[2]
		|| (M256.w[2] == C256.w[2]
		    && (M256.w[1] < C256.w[1]
			|| (M256.w[1] == C256.w[1]
			    && M256.w[0] <= C256.w[0])))))) {

      CS.w[0]++;
      if (!CS.w[0])
	CS.w[1]++;
    }
  }
  // RU?
  if ((rnd_mode) == ROUNDING_UP) {
    CS.w[0]++;
    if (!CS.w[0])
      CS.w[1]++;
  }

}
#endif
#endif

#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
#endif
get_BID128_fast (&res, 0,
		 (exponent_q + DECIMAL_EXPONENT_BIAS_128) >> 1, CS);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}



BID128_FUNCTION_ARGTYPE1 (bid128d_sqrt, UINT64, x)

     UINT256 M256, C256, C4, C8;
     UINT128 CX, CX1, CX2, A10, S2, T128, TP128, CS, CSM, res;
     UINT64 sign_x, Carry;
     SINT64 D;
     int_float fx, f64;
     int exponent_x, bin_expon_cx;
     int digits, scale, exponent_q;
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
     fexcept_t binaryflags = 0;
#endif

	// unpack arguments, check for NaN or Infinity
   // unpack arguments, check for NaN or Infinity
CX.w[1] = 0;
if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], x)) {
res.w[1] = CX.w[0];
res.w[0] = 0;
	   // NaN ?
if ((x & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
#ifdef SET_STATUS_FLAGS
  if ((x & SNAN_MASK64) == SNAN_MASK64)	// sNaN
    __set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
  res.w[0] = (CX.w[0] & 0x0003ffffffffffffull);
  __mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]);
  res.w[1] |= ((CX.w[0]) & 0xfc00000000000000ull);
  BID_RETURN (res);
}
	   // x is Infinity?
if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) {
  if (sign_x) {
    // -Inf, return NaN
    res.w[1] = 0x7c00000000000000ull;
#ifdef SET_STATUS_FLAGS
    __set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
  }
  BID_RETURN (res);
}
	   // x is 0 otherwise

exponent_x =
  exponent_x - DECIMAL_EXPONENT_BIAS + DECIMAL_EXPONENT_BIAS_128;
res.w[1] =
  sign_x | ((((UINT64) (exponent_x + DECIMAL_EXPONENT_BIAS_128)) >> 1)
	    << 49);
res.w[0] = 0;
BID_RETURN (res);
}
if (sign_x) {
  res.w[1] = 0x7c00000000000000ull;
  res.w[0] = 0;
#ifdef SET_STATUS_FLAGS
  __set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
  BID_RETURN (res);
}
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
exponent_x =
  exponent_x - DECIMAL_EXPONENT_BIAS + DECIMAL_EXPONENT_BIAS_128;

	   // 2^64
f64.i = 0x5f800000;

	   // fx ~ CX
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
bin_expon_cx = ((fx.i >> 23) & 0xff) - 0x7f;
digits = estimate_decimal_digits[bin_expon_cx];

A10 = CX;
if (exponent_x & 1) {
  A10.w[1] = (CX.w[1] << 3) | (CX.w[0] >> 61);
  A10.w[0] = CX.w[0] << 3;
  CX2.w[1] = (CX.w[1] << 1) | (CX.w[0] >> 63);
  CX2.w[0] = CX.w[0] << 1;
  __add_128_128 (A10, A10, CX2);
}

CS.w[0] = short_sqrt128 (A10);
CS.w[1] = 0;
	   // check for exact result
if (CS.w[0] * CS.w[0] == A10.w[0]) {
  __mul_64x64_to_128_fast (S2, CS.w[0], CS.w[0]);
  if (S2.w[1] == A10.w[1]) {
    get_BID128_very_fast (&res, 0,
			  (exponent_x + DECIMAL_EXPONENT_BIAS_128) >> 1,
			  CS);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
    (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
    BID_RETURN (res);
  }
}
	   // get number of digits in CX
D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1];
if (D > 0
    || (!D && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0]))
  digits++;

		// if exponent is odd, scale coefficient by 10
scale = 67 - digits;
exponent_q = exponent_x - scale;
scale += (exponent_q & 1);	// exp. bias is even

if (scale > 38) {
  T128 = power10_table_128[scale - 37];
  __mul_128x128_low (CX1, CX, T128);

  TP128 = power10_table_128[37];
  __mul_128x128_to_256 (C256, CX1, TP128);
} else {
  T128 = power10_table_128[scale];
  __mul_128x128_to_256 (C256, CX, T128);
}


	   // 4*C256
C4.w[3] = (C256.w[3] << 2) | (C256.w[2] >> 62);
C4.w[2] = (C256.w[2] << 2) | (C256.w[1] >> 62);
C4.w[1] = (C256.w[1] << 2) | (C256.w[0] >> 62);
C4.w[0] = C256.w[0] << 2;

long_sqrt128 (&CS, C256);

#ifndef IEEE_ROUND_NEAREST
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
if (!((rnd_mode) & 3)) {
#endif
#endif
  // compare to midpoints
  CSM.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
  CSM.w[0] = (CS.w[0] + CS.w[0]) | 1;
  // CSM^2
  //__mul_128x128_to_256(M256, CSM, CSM);
  __sqr128_to_256 (M256, CSM);

  if (C4.w[3] > M256.w[3]
      || (C4.w[3] == M256.w[3]
	  && (C4.w[2] > M256.w[2]
	      || (C4.w[2] == M256.w[2]
		  && (C4.w[1] > M256.w[1]
		      || (C4.w[1] == M256.w[1]
			  && C4.w[0] > M256.w[0])))))) {
    // round up
    CS.w[0]++;
    if (!CS.w[0])
      CS.w[1]++;
  } else {
    C8.w[1] = (CS.w[1] << 3) | (CS.w[0] >> 61);
    C8.w[0] = CS.w[0] << 3;
    // M256 - 8*CSM
    __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
    __sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
    __sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
    M256.w[3] = M256.w[3] - Carry;

    // if CSM' > C256, round up
    if (M256.w[3] > C4.w[3]
	|| (M256.w[3] == C4.w[3]
	    && (M256.w[2] > C4.w[2]
		|| (M256.w[2] == C4.w[2]
		    && (M256.w[1] > C4.w[1]
			|| (M256.w[1] == C4.w[1]
			    && M256.w[0] > C4.w[0])))))) {
      // round down
      if (!CS.w[0])
	CS.w[1]--;
      CS.w[0]--;
    }
  }
#ifndef IEEE_ROUND_NEAREST
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
} else {
  __sqr128_to_256 (M256, CS);
  C8.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
  C8.w[0] = CS.w[0] << 1;
  if (M256.w[3] > C256.w[3]
      || (M256.w[3] == C256.w[3]
	  && (M256.w[2] > C256.w[2]
	      || (M256.w[2] == C256.w[2]
		  && (M256.w[1] > C256.w[1]
		      || (M256.w[1] == C256.w[1]
			  && M256.w[0] > C256.w[0])))))) {
    __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
    __sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
    __sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
    M256.w[3] = M256.w[3] - Carry;
    M256.w[0]++;
    if (!M256.w[0]) {
      M256.w[1]++;
      if (!M256.w[1]) {
	M256.w[2]++;
	if (!M256.w[2])
	  M256.w[3]++;
      }
    }

    if (!CS.w[0])
      CS.w[1]--;
    CS.w[0]--;

    if (M256.w[3] > C256.w[3]
	|| (M256.w[3] == C256.w[3]
	    && (M256.w[2] > C256.w[2]
		|| (M256.w[2] == C256.w[2]
		    && (M256.w[1] > C256.w[1]
			|| (M256.w[1] == C256.w[1]
			    && M256.w[0] > C256.w[0])))))) {

      if (!CS.w[0])
	CS.w[1]--;
      CS.w[0]--;
    }
  }

  else {
    __add_carry_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
    __add_carry_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
    __add_carry_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
    M256.w[3] = M256.w[3] + Carry;
    M256.w[0]++;
    if (!M256.w[0]) {
      M256.w[1]++;
      if (!M256.w[1]) {
	M256.w[2]++;
	if (!M256.w[2])
	  M256.w[3]++;
      }
    }
    if (M256.w[3] < C256.w[3]
	|| (M256.w[3] == C256.w[3]
	    && (M256.w[2] < C256.w[2]
		|| (M256.w[2] == C256.w[2]
		    && (M256.w[1] < C256.w[1]
			|| (M256.w[1] == C256.w[1]
			    && M256.w[0] <= C256.w[0])))))) {

      CS.w[0]++;
      if (!CS.w[0])
	CS.w[1]++;
    }
  }
  // RU?
  if ((rnd_mode) == ROUNDING_UP) {
    CS.w[0]++;
    if (!CS.w[0])
      CS.w[1]++;
  }

}
#endif
#endif

#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
#endif
get_BID128_fast (&res, 0, (exponent_q + DECIMAL_EXPONENT_BIAS_128) >> 1,
		 CS);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);


}