/* Copyright (C) 2007 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 2, or (at your option) any later version. In addition to the permissions in the GNU General Public License, the Free Software Foundation gives you unlimited permission to link the compiled version of this file into combinations with other programs, and to distribute those combinations without any restriction coming from the use of this file. (The General Public License restrictions do apply in other respects; for example, they cover modification of the file, and distribution when not linked into a combine executable.) 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. You should have received a copy of the GNU General Public License along with GCC; see the file COPYING. If not, write to the Free Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */ /***************************************************************************** * BID64 divide ***************************************************************************** * * Algorithm description: * * if(coefficient_x=B, 1 otherwise * Q = 0 * else * get Q=(int)(coefficient_x/coefficient_y) * (based on double precision divide) * check for exact divide case * Let R = coefficient_x - Q*coefficient_y * Let m=16-number_digits(Q) * CA=R*10^m, Q=Q*10^m * B = coefficient_y * endif * if (CA<2^64) * Q += CA/B (64-bit unsigned divide) * else * get final Q using double precision divide, followed by 3 integer * iterations * if exact result, eliminate trailing zeros * check for underflow * round coefficient to nearest * ****************************************************************************/ #include "bid_internal.h" #include "bid_div_macros.h" #ifdef UNCHANGED_BINARY_STATUS_FLAGS #include #define FE_ALL_FLAGS FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT #endif extern UINT32 convert_table[5][128][2]; extern SINT8 factors[][2]; extern UINT8 packed_10000_zeros[]; #if DECIMAL_CALL_BY_REFERENCE void bid64_div (UINT64 * pres, UINT64 * px, UINT64 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x, y; #else UINT64 bid64_div (UINT64 x, UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 CA, CT; UINT64 sign_x, sign_y, coefficient_x, coefficient_y, A, B, QX, PD; UINT64 A2, Q, Q2, B2, B4, B5, R, T, DU, res; UINT64 valid_x, valid_y; SINT64 D; int_double t_scale, tempq, temp_b; int_float tempx, tempy; double da, db, dq, da_h, da_l; int exponent_x, exponent_y, bin_expon_cx; int diff_expon, ed1, ed2, bin_index; int rmode, amount; int nzeros, i, j, k, d5; UINT32 QX32, tdigit[3], digit, digit_h, digit_low; #ifdef UNCHANGED_BINARY_STATUS_FLAGS fexcept_t binaryflags = 0; #endif #if DECIMAL_CALL_BY_REFERENCE #if !DECIMAL_GLOBAL_ROUNDING _IDEC_round rnd_mode = *prnd_mode; #endif x = *px; y = *py; #endif valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x); valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y); // unpack arguments, check for NaN or Infinity if (!valid_x) { // x is Inf. or NaN #ifdef SET_STATUS_FLAGS if ((y & SNAN_MASK64) == SNAN_MASK64) // y is sNaN __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif // test if x is NaN if ((x & NAN_MASK64) == NAN_MASK64) { #ifdef SET_STATUS_FLAGS if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif BID_RETURN (coefficient_x & QUIET_MASK64); } // x is Infinity? if ((x & INFINITY_MASK64) == INFINITY_MASK64) { // check if y is Inf or NaN if ((y & INFINITY_MASK64) == INFINITY_MASK64) { // y==Inf, return NaN if ((y & NAN_MASK64) == INFINITY_MASK64) { // Inf/Inf #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif BID_RETURN (NAN_MASK64); } } else { // otherwise return +/-Inf BID_RETURN (((x ^ y) & 0x8000000000000000ull) | INFINITY_MASK64); } } // x==0 if (((y & INFINITY_MASK64) != INFINITY_MASK64) && !(coefficient_y)) { // y==0 , return NaN #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif BID_RETURN (NAN_MASK64); } if (((y & INFINITY_MASK64) != INFINITY_MASK64)) { if ((y & SPECIAL_ENCODING_MASK64) == SPECIAL_ENCODING_MASK64) exponent_y = ((UINT32) (y >> 51)) & 0x3ff; else exponent_y = ((UINT32) (y >> 53)) & 0x3ff; sign_y = y & 0x8000000000000000ull; exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; if (exponent_x > DECIMAL_MAX_EXPON_64) exponent_x = DECIMAL_MAX_EXPON_64; else if (exponent_x < 0) exponent_x = 0; BID_RETURN ((sign_x ^ sign_y) | (((UINT64) exponent_x) << 53)); } } if (!valid_y) { // y is Inf. or NaN // test if y is NaN if ((y & NAN_MASK64) == NAN_MASK64) { #ifdef SET_STATUS_FLAGS if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif BID_RETURN (coefficient_y & QUIET_MASK64); } // y is Infinity? if ((y & INFINITY_MASK64) == INFINITY_MASK64) { // return +/-0 BID_RETURN (((x ^ y) & 0x8000000000000000ull)); } // y is 0 #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); #endif BID_RETURN ((sign_x ^ sign_y) | INFINITY_MASK64); } #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; if (coefficient_x < coefficient_y) { // get number of decimal digits for c_x, c_y //--- get number of bits in the coefficients of x and y --- tempx.d = (float) coefficient_x; tempy.d = (float) coefficient_y; bin_index = (tempy.i - tempx.i) >> 23; A = coefficient_x * power10_index_binexp[bin_index]; B = coefficient_y; temp_b.d = (double) B; // compare A, B DU = (A - B) >> 63; ed1 = 15 + (int) DU; ed2 = estimate_decimal_digits[bin_index] + ed1; T = power10_table_128[ed1].w[0]; __mul_64x64_to_128 (CA, A, T); Q = 0; diff_expon = diff_expon - ed2; // adjust double precision db, to ensure that later A/B - (int)(da/db) > -1 if (coefficient_y < 0x0020000000000000ull) { temp_b.i += 1; db = temp_b.d; } else db = (double) (B + 2 + (B & 1)); } else { // get c_x/c_y // set last bit before conversion to DP A2 = coefficient_x | 1; da = (double) A2; db = (double) coefficient_y; tempq.d = da / db; Q = (UINT64) tempq.d; R = coefficient_x - coefficient_y * Q; // will use to get number of dec. digits of Q bin_expon_cx = (tempq.i >> 52) - 0x3ff; // R<0 ? D = ((SINT64) R) >> 63; Q += D; R += (coefficient_y & D); // exact result ? if (((SINT64) R) <= 0) { // can have R==-1 for coeff_y==1 res = get_BID64 (sign_x ^ sign_y, diff_expon, (Q + R), rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } // get decimal digits of Q DU = power10_index_binexp[bin_expon_cx] - Q - 1; DU >>= 63; ed2 = 16 - estimate_decimal_digits[bin_expon_cx] - (int) DU; T = power10_table_128[ed2].w[0]; __mul_64x64_to_128 (CA, R, T); B = coefficient_y; Q *= power10_table_128[ed2].w[0]; diff_expon -= ed2; } if (!CA.w[1]) { Q2 = CA.w[0] / B; B2 = B + B; B4 = B2 + B2; R = CA.w[0] - Q2 * B; Q += Q2; } else { // 2^64 t_scale.i = 0x43f0000000000000ull; // convert CA to DP da_h = CA.w[1]; da_l = CA.w[0]; da = da_h * t_scale.d + da_l; // quotient dq = da / db; Q2 = (UINT64) dq; // get w[0] remainder R = CA.w[0] - Q2 * B; // R<0 ? D = ((SINT64) R) >> 63; Q2 += D; R += (B & D); // now R<6*B // quick divide // 4*B B2 = B + B; B4 = B2 + B2; R = R - B4; // R<0 ? D = ((SINT64) R) >> 63; // restore R if negative R += (B4 & D); Q2 += ((~D) & 4); R = R - B2; // R<0 ? D = ((SINT64) R) >> 63; // restore R if negative R += (B2 & D); Q2 += ((~D) & 2); R = R - B; // R<0 ? D = ((SINT64) R) >> 63; // restore R if negative R += (B & D); Q2 += ((~D) & 1); Q += Q2; } #ifdef SET_STATUS_FLAGS if (R) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #ifndef LEAVE_TRAILING_ZEROS else #endif #else #ifndef LEAVE_TRAILING_ZEROS if (!R) #endif #endif #ifndef LEAVE_TRAILING_ZEROS { // eliminate trailing zeros // check whether CX, CY are short if ((coefficient_x <= 1024) && (coefficient_y <= 1024)) { i = (int) coefficient_y - 1; j = (int) coefficient_x - 1; // difference in powers of 2 factors for Y and X nzeros = ed2 - factors[i][0] + factors[j][0]; // difference in powers of 5 factors d5 = ed2 - factors[i][1] + factors[j][1]; if (d5 < nzeros) nzeros = d5; __mul_64x64_to_128 (CT, Q, reciprocals10_64[nzeros]); // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 amount = short_recip_scale[nzeros]; Q = CT.w[1] >> amount; diff_expon += nzeros; } else { tdigit[0] = Q & 0x3ffffff; tdigit[1] = 0; QX = Q >> 26; QX32 = QX; nzeros = 0; for (j = 0; QX32; j++, QX32 >>= 7) { k = (QX32 & 127); tdigit[0] += convert_table[j][k][0]; tdigit[1] += convert_table[j][k][1]; if (tdigit[0] >= 100000000) { tdigit[0] -= 100000000; tdigit[1]++; } } digit = tdigit[0]; if (!digit && !tdigit[1]) nzeros += 16; else { if (!digit) { nzeros += 8; digit = tdigit[1]; } // decompose digit PD = (UINT64) digit *0x068DB8BBull; digit_h = (UINT32) (PD >> 40); digit_low = digit - digit_h * 10000; if (!digit_low) nzeros += 4; else digit_h = digit_low; if (!(digit_h & 1)) nzeros += 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> (digit_h & 7)); } if (nzeros) { __mul_64x64_to_128 (CT, Q, reciprocals10_64[nzeros]); // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 amount = short_recip_scale[nzeros]; Q = CT.w[1] >> amount; } diff_expon += nzeros; } if (diff_expon >= 0) { res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, Q, rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } } #endif if (diff_expon >= 0) { #ifdef IEEE_ROUND_NEAREST // round to nearest code // R*10 R += R; R = (R << 2) + R; B5 = B4 + B; // compare 10*R to 5*B R = B5 - R; // correction for (R==0 && (Q&1)) R -= (Q & 1); // R<0 ? D = ((UINT64) R) >> 63; Q += D; #else #ifdef IEEE_ROUND_NEAREST_TIES_AWAY // round to nearest code // R*10 R += R; R = (R << 2) + R; B5 = B4 + B; // compare 10*R to 5*B R = B5 - R; // correction for (R==0 && (Q&1)) R -= (Q & 1); // R<0 ? D = ((UINT64) R) >> 63; Q += D; #else rmode = rnd_mode; if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; switch (rmode) { case 0: // round to nearest code case ROUNDING_TIES_AWAY: // R*10 R += R; R = (R << 2) + R; B5 = B4 + B; // compare 10*R to 5*B R = B5 - R; // correction for (R==0 && (Q&1)) R -= ((Q | (rmode >> 2)) & 1); // R<0 ? D = ((UINT64) R) >> 63; Q += D; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: break; default: // rounding up Q++; break; } #endif #endif res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, Q, rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } else { // UF occurs #ifdef SET_STATUS_FLAGS if ((diff_expon + 16 < 0)) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #endif rmode = rnd_mode; res = get_BID64_UF (sign_x ^ sign_y, diff_expon, Q, R, rmode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } } TYPE0_FUNCTION_ARGTYPE1_ARG128 (UINT64, bid64dq_div, UINT64, x, y) UINT256 CA4 = { {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256; UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp; UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, valid_y, PD, res; int_float fx, fy, f64; UINT32 QX32, tdigit[3], digit, digit_h, digit_low; int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, digits_q, amount; int nzeros, i, j, k, d5, done = 0; unsigned rmode; #ifdef UNCHANGED_BINARY_STATUS_FLAGS fexcept_t binaryflags = 0; #endif valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y); // unpack arguments, check for NaN or Infinity CX.w[1] = 0; if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], (x))) { #ifdef SET_STATUS_FLAGS if (((y.w[1] & SNAN_MASK64) == SNAN_MASK64) || // y is sNaN ((x & SNAN_MASK64) == SNAN_MASK64)) __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif // test if x is NaN if (((x) & 0x7c00000000000000ull) == 0x7c00000000000000ull) { res = CX.w[0]; BID_RETURN (res & QUIET_MASK64); } // x is Infinity? if (((x) & 0x7800000000000000ull) == 0x7800000000000000ull) { // check if y is Inf. if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull)) // return NaN { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res = 0x7c00000000000000ull; BID_RETURN (res); } if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { // otherwise return +/-Inf res = (((x) ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; BID_RETURN (res); } } // x is 0 if ((y.w[1] & INFINITY_MASK64) != INFINITY_MASK64) { if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif // x=y=0, return NaN res = 0x7c00000000000000ull; BID_RETURN (res); } // return 0 res = ((x) ^ y.w[1]) & 0x8000000000000000ull; exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128; if (exponent_x > DECIMAL_MAX_EXPON_64) exponent_x = DECIMAL_MAX_EXPON_64; else if (exponent_x < 0) exponent_x = 0; res |= (((UINT64) exponent_x) << 53); BID_RETURN (res); } } exponent_x += (DECIMAL_EXPONENT_BIAS_128 - DECIMAL_EXPONENT_BIAS); if (!valid_y) { // y is Inf. or NaN // test if y is NaN if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { #ifdef SET_STATUS_FLAGS if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif Tmp.w[1] = (CY.w[1] & 0x00003fffffffffffull); Tmp.w[0] = CY.w[0]; TP128 = reciprocals10_128[18]; __mul_128x128_full (Qh, Ql, Tmp, TP128); amount = recip_scale[18]; __shr_128 (Tmp, Qh, amount); res = (CY.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; BID_RETURN (res); } // y is Infinity? if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { // return +/-0 res = sign_x ^ sign_y; BID_RETURN (res); } // y is 0, return +/-Inf res = (((x) ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); #endif BID_RETURN (res); } #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; if (__unsigned_compare_gt_128 (CY, CX)) { // CX < CY // 2^64 f64.i = 0x5f800000; // fx ~ CX, fy ~ CY fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; // expon_cy - expon_cx bin_index = (fy.i - fx.i) >> 23; if (CX.w[1]) { T = power10_index_binexp_128[bin_index].w[0]; __mul_64x128_short (CA, T, CX); } else { T128 = power10_index_binexp_128[bin_index]; __mul_64x128_short (CA, CX.w[0], T128); } ed2 = 15; if (__unsigned_compare_gt_128 (CY, CA)) ed2++; T128 = power10_table_128[ed2]; __mul_128x128_to_256 (CA4, CA, T128); ed2 += estimate_decimal_digits[bin_index]; CQ.w[0] = CQ.w[1] = 0; diff_expon = diff_expon - ed2; } else { // get CQ = CX/CY __div_128_by_128 (&CQ, &CR, CX, CY); // get number of decimal digits in CQ // 2^64 f64.i = 0x5f800000; fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; // binary expon. of CQ bin_expon = (fx.i - 0x3f800000) >> 23; digits_q = estimate_decimal_digits[bin_expon]; TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; if (__unsigned_compare_ge_128 (CQ, TP128)) digits_q++; if (digits_q <= 16) { if (!CR.w[1] && !CR.w[0]) { res = get_BID64 (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } ed2 = 16 - digits_q; T128.w[0] = power10_table_128[ed2].w[0]; __mul_64x128_to_192 (CA4, (T128.w[0]), CR); diff_expon = diff_expon - ed2; CQ.w[0] *= T128.w[0]; } else { ed2 = digits_q - 16; diff_expon += ed2; T128 = reciprocals10_128[ed2]; __mul_128x128_to_256 (P256, CQ, T128); amount = recip_scale[ed2]; CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount)); CQ.w[1] = 0; __mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0])); __mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]); QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0]; CA4.w[1] = CX.w[1] - QB256.w[1]; CA4.w[0] = CX.w[0] - QB256.w[0]; if (CX.w[0] < QB256.w[0]) CA4.w[1]--; if (CR.w[0] || CR.w[1]) CA4.w[0] |= 1; done = 1; } } if (!done) { __div_256_by_128 (&CQ, &CA4, CY); } #ifdef SET_STATUS_FLAGS if (CA4.w[0] || CA4.w[1]) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #ifndef LEAVE_TRAILING_ZEROS else #endif #else #ifndef LEAVE_TRAILING_ZEROS if (!CA4.w[0] && !CA4.w[1]) #endif #endif #ifndef LEAVE_TRAILING_ZEROS // check whether result is exact { // check whether CX, CY are short if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { i = (int) CY.w[0] - 1; j = (int) CX.w[0] - 1; // difference in powers of 2 factors for Y and X nzeros = ed2 - factors[i][0] + factors[j][0]; // difference in powers of 5 factors d5 = ed2 - factors[i][1] + factors[j][1]; if (d5 < nzeros) nzeros = d5; // get P*(2^M[extra_digits])/10^extra_digits __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[nzeros]; __shr_128_long (CQ, Qh, amount); diff_expon += nzeros; } else { // decompose Q as Qh*10^17 + Ql Q_low = CQ.w[0]; { tdigit[0] = Q_low & 0x3ffffff; tdigit[1] = 0; QX = Q_low >> 26; QX32 = QX; nzeros = 0; for (j = 0; QX32; j++, QX32 >>= 7) { k = (QX32 & 127); tdigit[0] += convert_table[j][k][0]; tdigit[1] += convert_table[j][k][1]; if (tdigit[0] >= 100000000) { tdigit[0] -= 100000000; tdigit[1]++; } } if (tdigit[1] >= 100000000) { tdigit[1] -= 100000000; if (tdigit[1] >= 100000000) tdigit[1] -= 100000000; } digit = tdigit[0]; if (!digit && !tdigit[1]) nzeros += 16; else { if (!digit) { nzeros += 8; digit = tdigit[1]; } // decompose digit PD = (UINT64) digit *0x068DB8BBull; digit_h = (UINT32) (PD >> 40); digit_low = digit - digit_h * 10000; if (!digit_low) nzeros += 4; else digit_h = digit_low; if (!(digit_h & 1)) nzeros += 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> (digit_h & 7)); } if (nzeros) { // get P*(2^M[extra_digits])/10^extra_digits __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[nzeros]; __shr_128 (CQ, Qh, amount); } diff_expon += nzeros; } } if(diff_expon>=0){ res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } } #endif if (diff_expon >= 0) { #ifdef IEEE_ROUND_NEAREST // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); CQ.w[0] += carry64; #else #ifdef IEEE_ROUND_NEAREST_TIES_AWAY // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; #else rmode = rnd_mode; if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; switch (rmode) { case ROUNDING_TO_NEAREST: // round to nearest code // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; break; case ROUNDING_TIES_AWAY: // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: break; default: // rounding up CQ.w[0]++; if (!CQ.w[0]) CQ.w[1]++; break; } #endif #endif res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } else { // UF occurs #ifdef SET_STATUS_FLAGS if ((diff_expon + 16 < 0)) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #endif rmode = rnd_mode; res = get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } } //#define LEAVE_TRAILING_ZEROS TYPE0_FUNCTION_ARG128_ARGTYPE2 (UINT64, bid64qd_div, x, UINT64, y) UINT256 CA4 = { {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256; UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp; UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, PD, res, valid_y; int_float fx, fy, f64; UINT32 QX32, tdigit[3], digit, digit_h, digit_low; int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, digits_q, amount; int nzeros, i, j, k, d5, done = 0; unsigned rmode; #ifdef UNCHANGED_BINARY_STATUS_FLAGS fexcept_t binaryflags = 0; #endif valid_y = unpack_BID64 (&sign_y, &exponent_y, &CY.w[0], (y)); // unpack arguments, check for NaN or Infinity if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { // test if x is NaN if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { #ifdef SET_STATUS_FLAGS if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN (y & 0x7e00000000000000ull) == 0x7e00000000000000ull) __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull); Tmp.w[0] = CX.w[0]; TP128 = reciprocals10_128[18]; __mul_128x128_full (Qh, Ql, Tmp, TP128); amount = recip_scale[18]; __shr_128 (Tmp, Qh, amount); res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; BID_RETURN (res); } // x is Infinity? if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { // check if y is Inf. if (((y & 0x7c00000000000000ull) == 0x7800000000000000ull)) // return NaN { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res = 0x7c00000000000000ull; BID_RETURN (res); } if (((y & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { // otherwise return +/-Inf res = ((x.w[1] ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull; BID_RETURN (res); } } // x is 0 if (((y & INFINITY_MASK64) != INFINITY_MASK64) && !(CY.w[0])) { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif // x=y=0, return NaN res = 0x7c00000000000000ull; BID_RETURN (res); } // return 0 if (((y & 0x7800000000000000ull) != 0x7800000000000000ull)) { if (!CY.w[0]) { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res = 0x7c00000000000000ull; BID_RETURN (res); } exponent_x = exponent_x - exponent_y - DECIMAL_EXPONENT_BIAS_128 + (DECIMAL_EXPONENT_BIAS << 1); if (exponent_x > DECIMAL_MAX_EXPON_64) exponent_x = DECIMAL_MAX_EXPON_64; else if (exponent_x < 0) exponent_x = 0; res = (sign_x ^ sign_y) | (((UINT64) exponent_x) << 53); BID_RETURN (res); } } CY.w[1] = 0; if (!valid_y) { // y is Inf. or NaN // test if y is NaN if ((y & NAN_MASK64) == NAN_MASK64) { #ifdef SET_STATUS_FLAGS if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif BID_RETURN (CY.w[0] & QUIET_MASK64); } // y is Infinity? if (((y) & 0x7800000000000000ull) == 0x7800000000000000ull) { // return +/-0 res = sign_x ^ sign_y; BID_RETURN (res); } // y is 0, return +/-Inf res = ((x.w[1] ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull; #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); #endif BID_RETURN (res); } #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif diff_expon = exponent_x - exponent_y - DECIMAL_EXPONENT_BIAS_128 + (DECIMAL_EXPONENT_BIAS << 1); if (__unsigned_compare_gt_128 (CY, CX)) { // CX < CY // 2^64 f64.i = 0x5f800000; // fx ~ CX, fy ~ CY fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; // expon_cy - expon_cx bin_index = (fy.i - fx.i) >> 23; if (CX.w[1]) { T = power10_index_binexp_128[bin_index].w[0]; __mul_64x128_short (CA, T, CX); } else { T128 = power10_index_binexp_128[bin_index]; __mul_64x128_short (CA, CX.w[0], T128); } ed2 = 15; if (__unsigned_compare_gt_128 (CY, CA)) ed2++; T128 = power10_table_128[ed2]; __mul_128x128_to_256 (CA4, CA, T128); ed2 += estimate_decimal_digits[bin_index]; CQ.w[0] = CQ.w[1] = 0; diff_expon = diff_expon - ed2; } else { // get CQ = CX/CY __div_128_by_128 (&CQ, &CR, CX, CY); // get number of decimal digits in CQ // 2^64 f64.i = 0x5f800000; fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; // binary expon. of CQ bin_expon = (fx.i - 0x3f800000) >> 23; digits_q = estimate_decimal_digits[bin_expon]; TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; if (__unsigned_compare_ge_128 (CQ, TP128)) digits_q++; if (digits_q <= 16) { if (!CR.w[1] && !CR.w[0]) { res = get_BID64 (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } ed2 = 16 - digits_q; T128.w[0] = power10_table_128[ed2].w[0]; __mul_64x128_to_192 (CA4, (T128.w[0]), CR); diff_expon = diff_expon - ed2; CQ.w[0] *= T128.w[0]; } else { ed2 = digits_q - 16; diff_expon += ed2; T128 = reciprocals10_128[ed2]; __mul_128x128_to_256 (P256, CQ, T128); amount = recip_scale[ed2]; CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount)); CQ.w[1] = 0; __mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0])); __mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]); QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0]; CA4.w[1] = CX.w[1] - QB256.w[1]; CA4.w[0] = CX.w[0] - QB256.w[0]; if (CX.w[0] < QB256.w[0]) CA4.w[1]--; if (CR.w[0] || CR.w[1]) CA4.w[0] |= 1; done = 1; if(CA4.w[1]|CA4.w[0]) { __mul_64x128_low(CY, (power10_table_128[ed2].w[0]),CY); } } } if (!done) { __div_256_by_128 (&CQ, &CA4, CY); } #ifdef SET_STATUS_FLAGS if (CA4.w[0] || CA4.w[1]) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #ifndef LEAVE_TRAILING_ZEROS else #endif #else #ifndef LEAVE_TRAILING_ZEROS if (!CA4.w[0] && !CA4.w[1]) #endif #endif #ifndef LEAVE_TRAILING_ZEROS // check whether result is exact { if(!done) { // check whether CX, CY are short if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { i = (int) CY.w[0] - 1; j = (int) CX.w[0] - 1; // difference in powers of 2 factors for Y and X nzeros = ed2 - factors[i][0] + factors[j][0]; // difference in powers of 5 factors d5 = ed2 - factors[i][1] + factors[j][1]; if (d5 < nzeros) nzeros = d5; // get P*(2^M[extra_digits])/10^extra_digits __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); //__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2]; // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[nzeros]; __shr_128_long (CQ, Qh, amount); diff_expon += nzeros; } else { // decompose Q as Qh*10^17 + Ql //T128 = reciprocals10_128[17]; Q_low = CQ.w[0]; { tdigit[0] = Q_low & 0x3ffffff; tdigit[1] = 0; QX = Q_low >> 26; QX32 = QX; nzeros = 0; for (j = 0; QX32; j++, QX32 >>= 7) { k = (QX32 & 127); tdigit[0] += convert_table[j][k][0]; tdigit[1] += convert_table[j][k][1]; if (tdigit[0] >= 100000000) { tdigit[0] -= 100000000; tdigit[1]++; } } if (tdigit[1] >= 100000000) { tdigit[1] -= 100000000; if (tdigit[1] >= 100000000) tdigit[1] -= 100000000; } digit = tdigit[0]; if (!digit && !tdigit[1]) nzeros += 16; else { if (!digit) { nzeros += 8; digit = tdigit[1]; } // decompose digit PD = (UINT64) digit *0x068DB8BBull; digit_h = (UINT32) (PD >> 40); digit_low = digit - digit_h * 10000; if (!digit_low) nzeros += 4; else digit_h = digit_low; if (!(digit_h & 1)) nzeros += 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> (digit_h & 7)); } if (nzeros) { // get P*(2^M[extra_digits])/10^extra_digits __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[nzeros]; __shr_128 (CQ, Qh, amount); } diff_expon += nzeros; } } } if(diff_expon>=0){ res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } } #endif if (diff_expon >= 0) { #ifdef IEEE_ROUND_NEAREST // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); CQ.w[0] += carry64; //if(CQ.w[0]> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; #else rmode = rnd_mode; if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; switch (rmode) { case ROUNDING_TO_NEAREST: // round to nearest code // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; break; case ROUNDING_TIES_AWAY: // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: break; default: // rounding up CQ.w[0]++; if (!CQ.w[0]) CQ.w[1]++; break; } #endif #endif res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } else { // UF occurs #ifdef SET_STATUS_FLAGS if ((diff_expon + 16 < 0)) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #endif rmode = rnd_mode; res = get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } } //#define LEAVE_TRAILING_ZEROS extern UINT32 convert_table[5][128][2]; extern SINT8 factors[][2]; extern UINT8 packed_10000_zeros[]; //UINT64* bid64_div128x128(UINT64 res, UINT128 *px, UINT128 *py, unsigned rnd_mode, unsigned *pfpsf) TYPE0_FUNCTION_ARG128_ARG128 (UINT64, bid64qq_div, x, y) UINT256 CA4 = { {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256; UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp; UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, valid_y, PD, res; int_float fx, fy, f64; UINT32 QX32, tdigit[3], digit, digit_h, digit_low; int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, digits_q, amount; int nzeros, i, j, k, d5, done = 0; unsigned rmode; #ifdef UNCHANGED_BINARY_STATUS_FLAGS fexcept_t binaryflags = 0; #endif valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y); // unpack arguments, check for NaN or Infinity if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { // test if x is NaN if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { #ifdef SET_STATUS_FLAGS if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN (y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull); Tmp.w[0] = CX.w[0]; TP128 = reciprocals10_128[18]; __mul_128x128_full (Qh, Ql, Tmp, TP128); amount = recip_scale[18]; __shr_128 (Tmp, Qh, amount); res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; BID_RETURN (res); } // x is Infinity? if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { // check if y is Inf. if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull)) // return NaN { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res = 0x7c00000000000000ull; BID_RETURN (res); } if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { // otherwise return +/-Inf res = ((x.w[1] ^ y. w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; BID_RETURN (res); } } // x is 0 if (((y.w[1] & 0x7800000000000000ull) != 0x7800000000000000ull)) { if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif // x=y=0, return NaN res = 0x7c00000000000000ull; BID_RETURN (res); } // return 0 res = (x.w[1] ^ y.w[1]) & 0x8000000000000000ull; exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; if (exponent_x > DECIMAL_MAX_EXPON_64) exponent_x = DECIMAL_MAX_EXPON_64; else if (exponent_x < 0) exponent_x = 0; res |= (((UINT64) exponent_x) << 53); BID_RETURN (res); } } if (!valid_y) { // y is Inf. or NaN // test if y is NaN if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { #ifdef SET_STATUS_FLAGS if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif Tmp.w[1] = (CY.w[1] & 0x00003fffffffffffull); Tmp.w[0] = CY.w[0]; TP128 = reciprocals10_128[18]; __mul_128x128_full (Qh, Ql, Tmp, TP128); amount = recip_scale[18]; __shr_128 (Tmp, Qh, amount); res = (CY.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; BID_RETURN (res); } // y is Infinity? if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { // return +/-0 res = sign_x ^ sign_y; BID_RETURN (res); } // y is 0, return +/-Inf res = ((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); #endif BID_RETURN (res); } #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; if (__unsigned_compare_gt_128 (CY, CX)) { // CX < CY // 2^64 f64.i = 0x5f800000; // fx ~ CX, fy ~ CY fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; // expon_cy - expon_cx bin_index = (fy.i - fx.i) >> 23; if (CX.w[1]) { T = power10_index_binexp_128[bin_index].w[0]; __mul_64x128_short (CA, T, CX); } else { T128 = power10_index_binexp_128[bin_index]; __mul_64x128_short (CA, CX.w[0], T128); } ed2 = 15; if (__unsigned_compare_gt_128 (CY, CA)) ed2++; T128 = power10_table_128[ed2]; __mul_128x128_to_256 (CA4, CA, T128); ed2 += estimate_decimal_digits[bin_index]; CQ.w[0] = CQ.w[1] = 0; diff_expon = diff_expon - ed2; } else { // get CQ = CX/CY __div_128_by_128 (&CQ, &CR, CX, CY); // get number of decimal digits in CQ // 2^64 f64.i = 0x5f800000; fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; // binary expon. of CQ bin_expon = (fx.i - 0x3f800000) >> 23; digits_q = estimate_decimal_digits[bin_expon]; TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; if (__unsigned_compare_ge_128 (CQ, TP128)) digits_q++; if (digits_q <= 16) { if (!CR.w[1] && !CR.w[0]) { res = get_BID64 (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } ed2 = 16 - digits_q; T128.w[0] = power10_table_128[ed2].w[0]; __mul_64x128_to_192 (CA4, (T128.w[0]), CR); diff_expon = diff_expon - ed2; CQ.w[0] *= T128.w[0]; } else { ed2 = digits_q - 16; diff_expon += ed2; T128 = reciprocals10_128[ed2]; __mul_128x128_to_256 (P256, CQ, T128); amount = recip_scale[ed2]; CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount)); CQ.w[1] = 0; __mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0])); __mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]); QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0]; CA4.w[1] = CX.w[1] - QB256.w[1]; CA4.w[0] = CX.w[0] - QB256.w[0]; if (CX.w[0] < QB256.w[0]) CA4.w[1]--; if (CR.w[0] || CR.w[1]) CA4.w[0] |= 1; done = 1; if(CA4.w[1]|CA4.w[0]) { __mul_64x128_low(CY, (power10_table_128[ed2].w[0]),CY); } } } if (!done) { __div_256_by_128 (&CQ, &CA4, CY); } #ifdef SET_STATUS_FLAGS if (CA4.w[0] || CA4.w[1]) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #ifndef LEAVE_TRAILING_ZEROS else #endif #else #ifndef LEAVE_TRAILING_ZEROS if (!CA4.w[0] && !CA4.w[1]) #endif #endif #ifndef LEAVE_TRAILING_ZEROS // check whether result is exact { if(!done) { // check whether CX, CY are short if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { i = (int) CY.w[0] - 1; j = (int) CX.w[0] - 1; // difference in powers of 2 factors for Y and X nzeros = ed2 - factors[i][0] + factors[j][0]; // difference in powers of 5 factors d5 = ed2 - factors[i][1] + factors[j][1]; if (d5 < nzeros) nzeros = d5; // get P*(2^M[extra_digits])/10^extra_digits __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); //__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2]; // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[nzeros]; __shr_128_long (CQ, Qh, amount); diff_expon += nzeros; } else { // decompose Q as Qh*10^17 + Ql //T128 = reciprocals10_128[17]; Q_low = CQ.w[0]; { tdigit[0] = Q_low & 0x3ffffff; tdigit[1] = 0; QX = Q_low >> 26; QX32 = QX; nzeros = 0; for (j = 0; QX32; j++, QX32 >>= 7) { k = (QX32 & 127); tdigit[0] += convert_table[j][k][0]; tdigit[1] += convert_table[j][k][1]; if (tdigit[0] >= 100000000) { tdigit[0] -= 100000000; tdigit[1]++; } } if (tdigit[1] >= 100000000) { tdigit[1] -= 100000000; if (tdigit[1] >= 100000000) tdigit[1] -= 100000000; } digit = tdigit[0]; if (!digit && !tdigit[1]) nzeros += 16; else { if (!digit) { nzeros += 8; digit = tdigit[1]; } // decompose digit PD = (UINT64) digit *0x068DB8BBull; digit_h = (UINT32) (PD >> 40); digit_low = digit - digit_h * 10000; if (!digit_low) nzeros += 4; else digit_h = digit_low; if (!(digit_h & 1)) nzeros += 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> (digit_h & 7)); } if (nzeros) { // get P*(2^M[extra_digits])/10^extra_digits __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[nzeros]; __shr_128 (CQ, Qh, amount); } diff_expon += nzeros; } } } if(diff_expon>=0){ res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } } #endif if(diff_expon>=0) { #ifdef IEEE_ROUND_NEAREST // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); CQ.w[0] += carry64; //if(CQ.w[0]> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; #else rmode = rnd_mode; if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; switch (rmode) { case ROUNDING_TO_NEAREST: // round to nearest code // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; break; case ROUNDING_TIES_AWAY: // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: break; default: // rounding up CQ.w[0]++; if (!CQ.w[0]) CQ.w[1]++; break; } #endif #endif res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } else { // UF occurs #ifdef SET_STATUS_FLAGS if ((diff_expon + 16 < 0)) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #endif rmode = rnd_mode; res = get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } }