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/* Copyright (C) 2007, 2009 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); }