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view libgcc/config/libbid/bid128_div.c @ 158:494b0b89df80 default tip
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| author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
|---|---|
| date | Mon, 25 May 2020 18:13:55 +0900 |
| parents | 1830386684a0 |
| children |
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/* Copyright (C) 2007-2020 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_div_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 extern UINT32 convert_table[5][128][2]; extern SINT8 factors[][2]; extern UINT8 packed_10000_zeros[]; BID128_FUNCTION_ARG2 (bid128_div, x, y) UINT256 CA4, CA4r, P256; UINT128 CX, CY, T128, CQ, CR, CA, TP128, Qh, res; UINT64 sign_x, sign_y, T, carry64, D, Q_high, Q_low, QX, PD, 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; 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 res.w[1] = (CX.w[1]) & QUIET_MASK64; res.w[0] = CX.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.w[1] = 0x7c00000000000000ull; res.w[0] = 0; BID_RETURN (res); } // y is NaN? if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) // return NaN { // return +/-Inf res.w[1] = ((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; res.w[0] = 0; 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.w[1] = 0x7c00000000000000ull; res.w[0] = 0; BID_RETURN (res); } // return 0 res.w[1] = (x.w[1] ^ y.w[1]) & 0x8000000000000000ull; exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128; if (exponent_x > DECIMAL_MAX_EXPON_128) exponent_x = DECIMAL_MAX_EXPON_128; else if (exponent_x < 0) exponent_x = 0; res.w[1] |= (((UINT64) exponent_x) << 49); res.w[0] = 0; 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 res.w[1] = CY.w[1] & QUIET_MASK64; res.w[0] = CY.w[0]; BID_RETURN (res); } // y is Infinity? if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { // return +/-0 res.w[1] = sign_x ^ sign_y; res.w[0] = 0; BID_RETURN (res); } // y is 0, return +/-Inf #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); #endif res.w[1] = ((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; res.w[0] = 0; 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; 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 = 33; 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); if (!CR.w[1] && !CR.w[0]) { get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } // 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++; ed2 = 34 - digits_q; T128.w[0] = power10_table_128[ed2].w[0]; T128.w[1] = power10_table_128[ed2].w[1]; __mul_128x128_to_256 (CA4, CR, T128); diff_expon = diff_expon - ed2; __mul_128x128_low (CQ, CQ, T128); } __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_high (Qh, 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 //T128 = reciprocals10_128[17]; T128.w[0] = 0x44909befeb9fad49ull; T128.w[1] = 0x000b877aa3236a4bull; __mul_128x128_to_256 (P256, CQ, T128); //amount = recip_scale[17]; Q_high = (P256.w[2] >> 44) | (P256.w[3] << (64 - 44)); Q_low = CQ.w[0] - Q_high * 100000000000000000ull; if (!Q_low) { diff_expon += 17; tdigit[0] = Q_high & 0x3ffffff; tdigit[1] = 0; QX = Q_high >> 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) { __mul_64x64_to_128 (CQ, Q_high, reciprocals10_64[nzeros]); // now get P/10^extra_digits: shift C64 right by M[extra_digits]-64 amount = short_recip_scale[nzeros]; CQ.w[0] = CQ.w[1] >> amount; } else CQ.w[0] = Q_high; CQ.w[1] = 0; diff_expon += nzeros; } else { 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_high (Qh, 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; } } get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &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] < carry64) CQ.w[1]++; #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 } else { #ifdef SET_STATUS_FLAGS if (CA4.w[0] || CA4.w[1]) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #endif handle_UF_128_rem (&res, sign_x ^ sign_y, diff_expon, CQ, CA4.w[1] | CA4.w[0], &rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } //#define LEAVE_TRAILING_ZEROS TYPE0_FUNCTION_ARGTYPE1_ARGTYPE2 (UINT128, bid128dd_div, UINT64, x, UINT64, y) UINT256 CA4, CA4r, P256; UINT128 CX, CY, T128, CQ, CR, CA, TP128, Qh, res; UINT64 sign_x, sign_y, T, carry64, D, Q_high, Q_low, QX, PD, 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; 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 CX.w[1] = 0; if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], (x))) { #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 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) { // check if y is Inf. if ((((y) & 0x7c00000000000000ull) == 0x7800000000000000ull)) // return NaN { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res.w[1] = 0x7c00000000000000ull; res.w[0] = 0; BID_RETURN (res); } if ((((y) & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { // otherwise return +/-Inf res.w[1] = (((x) ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull; res.w[0] = 0; BID_RETURN (res); } } // x is 0 if ((((y) & 0x7800000000000000ull) != 0x7800000000000000ull)) { if(!CY.w[0]) { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif // x=y=0, return NaN res.w[1] = 0x7c00000000000000ull; res.w[0] = 0; BID_RETURN (res); } // return 0 res.w[1] = ((x) ^ (y)) & 0x8000000000000000ull; if (((y) & 0x6000000000000000ull) == 0x6000000000000000ull) exponent_y = ((UINT32) ((y) >> 51)) & 0x3ff; else exponent_y = ((UINT32) ((y) >> 53)) & 0x3ff; exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128; if (exponent_x > DECIMAL_MAX_EXPON_128) exponent_x = DECIMAL_MAX_EXPON_128; else if (exponent_x < 0) exponent_x = 0; res.w[1] |= (((UINT64) exponent_x) << 49); res.w[0] = 0; 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 res.w[0] = (CY.w[0] & 0x0003ffffffffffffull); __mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]); res.w[1] |= ((CY.w[0]) & 0xfc00000000000000ull); BID_RETURN (res); } // y is Infinity? if (((y) & 0x7800000000000000ull) == 0x7800000000000000ull) { // return +/-0 res.w[1] = sign_x ^ sign_y; res.w[0] = 0; BID_RETURN (res); } // y is 0, return +/-Inf res.w[1] = (((x) ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull; res.w[0] = 0; #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; 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 = 33; 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); if (!CR.w[1] && !CR.w[0]) { get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } // 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++; ed2 = 34 - digits_q; T128.w[0] = power10_table_128[ed2].w[0]; T128.w[1] = power10_table_128[ed2].w[1]; __mul_128x128_to_256 (CA4, CR, T128); diff_expon = diff_expon - ed2; __mul_128x128_low (CQ, CQ, T128); } __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_high (Qh, 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]; T128.w[0] = 0x44909befeb9fad49ull; T128.w[1] = 0x000b877aa3236a4bull; __mul_128x128_to_256 (P256, CQ, T128); //amount = recip_scale[17]; Q_high = (P256.w[2] >> 44) | (P256.w[3] << (64 - 44)); Q_low = CQ.w[0] - Q_high * 100000000000000000ull; if (!Q_low) { diff_expon += 17; tdigit[0] = Q_high & 0x3ffffff; tdigit[1] = 0; QX = Q_high >> 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) { __mul_64x64_to_128 (CQ, Q_high, reciprocals10_64[nzeros]); // now get P/10^extra_digits: shift C64 right by M[extra_digits]-64 amount = short_recip_scale[nzeros]; CQ.w[0] = CQ.w[1] >> amount; } else CQ.w[0] = Q_high; CQ.w[1] = 0; diff_expon += nzeros; } else { 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_high (Qh, 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; } } get_BID128(&res, sign_x ^ sign_y, diff_expon, CQ, &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] < carry64) CQ.w[1]++; #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 } else { #ifdef SET_STATUS_FLAGS if (CA4.w[0] || CA4.w[1]) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #endif handle_UF_128_rem (&res, sign_x ^ sign_y, diff_expon, CQ, CA4.w[1] | CA4.w[0], &rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } BID128_FUNCTION_ARGTYPE1_ARG128 (bid128dq_div, UINT64, x, y) UINT256 CA4, CA4r, P256; UINT128 CX, CY, T128, CQ, CR, CA, TP128, Qh, res; UINT64 sign_x, sign_y, T, carry64, D, Q_high, Q_low, QX, valid_y, PD; 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; 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 __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 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) { // 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.w[1] = 0x7c00000000000000ull; res.w[0] = 0; BID_RETURN (res); } if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { // otherwise return +/-Inf res.w[1] = ((x ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; res.w[0] = 0; 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.w[1] = 0x7c00000000000000ull; res.w[0] = 0; BID_RETURN (res); } // return 0 res.w[1] = (x ^ y.w[1]) & 0x8000000000000000ull; exponent_x = exponent_x - exponent_y + (DECIMAL_EXPONENT_BIAS_128<<1) - DECIMAL_EXPONENT_BIAS; if (exponent_x > DECIMAL_MAX_EXPON_128) exponent_x = DECIMAL_MAX_EXPON_128; else if (exponent_x < 0) exponent_x = 0; res.w[1] |= (((UINT64) exponent_x) << 49); res.w[0] = 0; 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 res.w[1] = CY.w[1] & QUIET_MASK64; res.w[0] = CY.w[0]; BID_RETURN (res); } // y is Infinity? if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { // return +/-0 res.w[1] = sign_x ^ sign_y; res.w[0] = 0; BID_RETURN (res); } // y is 0, return +/-Inf res.w[1] = ((x ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; res.w[0] = 0; #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; 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 = 33; 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); if (!CR.w[1] && !CR.w[0]) { get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } // 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++; ed2 = 34 - digits_q; T128.w[0] = power10_table_128[ed2].w[0]; T128.w[1] = power10_table_128[ed2].w[1]; __mul_128x128_to_256 (CA4, CR, T128); diff_expon = diff_expon - ed2; __mul_128x128_low (CQ, CQ, T128); } __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 { //printf("ed2=%d,nz=%d,a=%d,CQ="LX16","LX16", RH="LX16", RL="LX16"\n",ed2,nzeros,amount,CQ.w[1],CQ.w[0],reciprocals10_128[nzeros].w[1],reciprocals10_128[nzeros].w[0]);fflush(stdout); // 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_high (Qh, 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]; T128.w[0] = 0x44909befeb9fad49ull; T128.w[1] = 0x000b877aa3236a4bull; __mul_128x128_to_256 (P256, CQ, T128); //amount = recip_scale[17]; Q_high = (P256.w[2] >> 44) | (P256.w[3] << (64 - 44)); Q_low = CQ.w[0] - Q_high * 100000000000000000ull; if (!Q_low) { diff_expon += 17; tdigit[0] = Q_high & 0x3ffffff; tdigit[1] = 0; QX = Q_high >> 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); //printf("i=%d, nz=%d, digit=%d (%d, %016I64x %016I64x)\n",i,nzeros,digit_h,digit,PD,digit_h);fflush(stdout); 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 (CQ, Q_high, reciprocals10_64[nzeros]); // now get P/10^extra_digits: shift C64 right by M[extra_digits]-64 amount = short_recip_scale[nzeros]; CQ.w[0] = CQ.w[1] >> amount; } else CQ.w[0] = Q_high; CQ.w[1] = 0; diff_expon += nzeros; } else { 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); //printf("i=%d, nz=%d, digit=%d (%d, %016I64x %016I64x)\n",i,nzeros,digit_h,digit,PD,digit_h);fflush(stdout); 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_high (Qh, 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; } } get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &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] < carry64) CQ.w[1]++; #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 } else { #ifdef SET_STATUS_FLAGS if (CA4.w[0] || CA4.w[1]) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #endif handle_UF_128_rem (&res, sign_x ^ sign_y, diff_expon, CQ, CA4.w[1] | CA4.w[0], &rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } BID128_FUNCTION_ARG128_ARGTYPE2 (bid128qd_div, x, UINT64, y) UINT256 CA4, CA4r, P256; UINT128 CX, CY, T128, CQ, CR, CA, TP128, Qh, res; UINT64 sign_x, sign_y, T, carry64, D, Q_high, Q_low, QX, PD, 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, 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 res.w[1] = (CX.w[1]) & QUIET_MASK64; res.w[0] = CX.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.w[1] = 0x7c00000000000000ull; res.w[0] = 0; BID_RETURN (res); } // y is NaN? if (((y & 0x7c00000000000000ull) != 0x7c00000000000000ull)) // return NaN { // return +/-Inf res.w[1] = ((x.w[1] ^ y) & 0x8000000000000000ull) | 0x7800000000000000ull; res.w[0] = 0; BID_RETURN (res); } } // x is 0 if ((y & 0x7800000000000000ull) < 0x7800000000000000ull) { if (!CY.w[0]) { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif // x=y=0, return NaN res.w[1] = 0x7c00000000000000ull; res.w[0] = 0; BID_RETURN (res); } // return 0 res.w[1] = (x.w[1] ^ y) & 0x8000000000000000ull; exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; if (exponent_x > DECIMAL_MAX_EXPON_128) exponent_x = DECIMAL_MAX_EXPON_128; else if (exponent_x < 0) exponent_x = 0; res.w[1] |= (((UINT64) exponent_x) << 49); res.w[0] = 0; 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 res.w[0] = (CY.w[0] & 0x0003ffffffffffffull); __mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]); res.w[1] |= ((CY.w[0]) & 0xfc00000000000000ull); BID_RETURN (res); } // y is Infinity? if ((y & INFINITY_MASK64) == INFINITY_MASK64) { // return +/-0 res.w[1] = ((x.w[1] ^ y) & 0x8000000000000000ull); res.w[0] = 0; BID_RETURN (res); } // y is 0 #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); #endif res.w[1] = (sign_x ^ sign_y) | INFINITY_MASK64; res.w[0] = 0; 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 = 33; 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); if (!CR.w[1] && !CR.w[0]) { get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } // 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++; ed2 = 34 - digits_q; T128.w[0] = power10_table_128[ed2].w[0]; T128.w[1] = power10_table_128[ed2].w[1]; __mul_128x128_to_256 (CA4, CR, T128); diff_expon = diff_expon - ed2; __mul_128x128_low (CQ, CQ, T128); } __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_high (Qh, 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]; T128.w[0] = 0x44909befeb9fad49ull; T128.w[1] = 0x000b877aa3236a4bull; __mul_128x128_to_256 (P256, CQ, T128); //amount = recip_scale[17]; Q_high = (P256.w[2] >> 44) | (P256.w[3] << (64 - 44)); Q_low = CQ.w[0] - Q_high * 100000000000000000ull; if (!Q_low) { diff_expon += 17; tdigit[0] = Q_high & 0x3ffffff; tdigit[1] = 0; QX = Q_high >> 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) { __mul_64x64_to_128 (CQ, Q_high, reciprocals10_64[nzeros]); // now get P/10^extra_digits: shift C64 right by M[extra_digits]-64 amount = short_recip_scale[nzeros]; CQ.w[0] = CQ.w[1] >> amount; } else CQ.w[0] = Q_high; CQ.w[1] = 0; diff_expon += nzeros; } else { 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_high (Qh, 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; } } get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &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] < carry64) CQ.w[1]++; #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 } else { #ifdef SET_STATUS_FLAGS if (CA4.w[0] || CA4.w[1]) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #endif handle_UF_128_rem (&res, sign_x ^ sign_y, diff_expon, CQ, CA4.w[1] | CA4.w[0], &rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); }