| 1 | /* $Id: IEMGenFpuConstants.c 106061 2024-09-16 14:03:52Z vboxsync $ */
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| 2 | /** @file
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| 3 | * IEMGenFpuConstants - Generates FPU constants for IEMAllAImplC.cpp.
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| 4 | *
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| 5 | * Compile on linux: gcc -I../../../../include -DIN_RING3 IEMGenFpuConstants.c -lmpfr -g -o IEMGenFpuConstants
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| 6 | */
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| 7 |
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| 8 | /*
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| 9 | * Copyright (C) 2022-2024 Oracle and/or its affiliates.
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| 10 | *
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| 11 | * This file is part of VirtualBox base platform packages, as
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| 12 | * available from https://www.virtualbox.org.
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| 13 | *
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| 14 | * This program is free software; you can redistribute it and/or
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| 15 | * modify it under the terms of the GNU General Public License
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| 16 | * as published by the Free Software Foundation, in version 3 of the
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| 17 | * License.
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| 18 | *
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| 19 | * This program is distributed in the hope that it will be useful, but
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| 20 | * WITHOUT ANY WARRANTY; without even the implied warranty of
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| 21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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| 22 | * General Public License for more details.
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| 23 | *
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| 24 | * You should have received a copy of the GNU General Public License
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| 25 | * along with this program; if not, see <https://www.gnu.org/licenses>.
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| 26 | *
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| 27 | * SPDX-License-Identifier: GPL-3.0-only
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| 28 | */
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| 29 |
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| 30 |
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| 31 | /*********************************************************************************************************************************
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| 32 | * Header Files *
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| 33 | *********************************************************************************************************************************/
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| 34 | #include <iprt/types.h>
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| 35 | #include <iprt/assertcompile.h>
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| 36 | #include <stdio.h>
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| 37 | #define MPFR_WANT_FLOAT128
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| 38 | #include <gmp.h>
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| 39 | #include <mpfr.h>
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| 40 |
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| 41 |
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| 42 | void PrintComment(const char *pszComment, va_list va, mpfr_srcptr pVal, bool fList)
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| 43 | {
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| 44 | const char * const pszIndent = fList ? " " : "";
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| 45 | printf(fList ? " /* " : "/** ");
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| 46 | vprintf(pszComment, va);
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| 47 | printf("\n%s * base-10: ", pszIndent);
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| 48 | mpfr_out_str(stdout, 10, 0, pVal, MPFR_RNDD);
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| 49 | printf("\n%s * base-16: ", pszIndent);
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| 50 | mpfr_out_str(stdout, 16, 0, pVal, MPFR_RNDD);
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| 51 | printf("\n%s * base-2 : ", pszIndent);
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| 52 | mpfr_out_str(stdout, 2, 0, pVal, MPFR_RNDD);
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| 53 | printf(" */\n");
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| 54 | }
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| 55 |
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| 56 |
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| 57 | uint64_t BinStrToU64(const char *psz, size_t cch)
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| 58 | {
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| 59 | uint64_t u = 0;
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| 60 | while (cch-- > 0)
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| 61 | {
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| 62 | u <<= 1;
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| 63 | u |= *psz++ == '1';
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| 64 | }
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| 65 | return u;
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| 66 | }
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| 67 |
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| 68 |
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| 69 | void PrintU128(mpfr_srcptr pVal, const char *pszVariable, const char *pszComment, ...)
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| 70 | {
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| 71 | va_list va;
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| 72 | va_start(va, pszComment);
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| 73 | PrintComment(pszComment, va, pVal, !pszVariable);
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| 74 | va_end(va);
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| 75 | if (pszVariable)
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| 76 | printf("const RTUINT128U %s = ", pszVariable);
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| 77 | else
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| 78 | printf(" ");
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| 79 | mpfr_exp_t iExpBinary;
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| 80 | char *pszBinary = mpfr_get_str(NULL, &iExpBinary, 2, 0, pVal, MPFR_RNDD);
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| 81 | printf("RTUINT128_INIT_C(%#llx, %#llx)%s\n",
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| 82 | BinStrToU64(pszBinary, 64), BinStrToU64(&pszBinary[64], 64), pszVariable ? ";" : ",");
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| 83 | mpfr_free_str(pszBinary);
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| 84 | }
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| 85 |
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| 86 |
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| 87 | void PrintF128(mpfr_srcptr pVal, const char *pszVariable, const char *pszComment, ...)
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| 88 | {
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| 89 | RTFLOAT128U r128;
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| 90 | *(_Float128 *)&r128 = mpfr_get_float128(pVal, MPFR_RNDD);
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| 91 |
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| 92 | va_list va;
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| 93 | va_start(va, pszComment);
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| 94 | PrintComment(pszComment, va, pVal, !pszVariable);
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| 95 | va_end(va);
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| 96 | if (pszVariable)
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| 97 | printf("const RTFLOAT128U %s = ", pszVariable);
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| 98 | else
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| 99 | printf(" ");
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| 100 | printf("RTFLOAT128U_INIT_C(%d, 0x%012llx, 0x%016llx, 0x%04x)%s\n",
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| 101 | r128.s.fSign, r128.s64.uFractionHi, r128.s64.uFractionLo, r128.s64.uExponent, pszVariable ? ";" : ",");
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| 102 | }
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| 103 |
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| 104 |
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| 105 | int main(void)
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| 106 | {
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| 107 | mpfr_t Val;
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| 108 |
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| 109 | mpfr_init2(Val, 112 + 1);
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| 110 | mpfr_const_log2(Val, MPFR_RNDN);
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| 111 | PrintF128(Val, "g_r128Ln2", "The ln2 constant as 128-bit floating point value.");
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| 112 |
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| 113 | mpfr_init2(Val, 128);
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| 114 | mpfr_const_log2(Val, MPFR_RNDN);
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| 115 | PrintU128(Val, "g_u128Ln2Mantissa", "High precision ln2 value.");
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| 116 |
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| 117 | mpfr_t Val2;
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| 118 | mpfr_init2(Val2, 67);
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| 119 | mpfr_const_log2(Val2, MPFR_RNDN);
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| 120 | mpfr_set(Val, Val2, MPFR_RNDN);
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| 121 | PrintU128(Val, "g_u128Ln2MantissaIntel", "High precision ln2 value, compatible with f2xm1 results on intel 10980XE.");
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| 122 |
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| 123 | /** @todo emit constants with 68-bit precision (1+67 bits), as that's what we
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| 124 | * use for intel now. */
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| 125 | printf("\n"
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| 126 | "/** Horner constants for f2xm1 */\n"
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| 127 | "const RTFLOAT128U g_ar128F2xm1HornerConsts[] =\n"
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| 128 | "{\n");
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| 129 | mpfr_t One;
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| 130 | mpfr_init2(One, 112 + 1);
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| 131 | mpfr_set_ui(One, 1, MPFR_RNDD);
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| 132 | PrintF128(One, NULL, "a0");
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| 133 |
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| 134 | mpfr_init2(Val, 112 + 1);
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| 135 | mpfr_set_ui(Val, 1, MPFR_RNDD);
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| 136 | for (unsigned a = 1; a < 22; a++)
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| 137 | {
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| 138 | mpfr_div_ui(Val, Val, a + 1, MPFR_RNDD);
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| 139 | PrintF128(Val, NULL, "a%u", a);
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| 140 | }
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| 141 |
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| 142 | printf("};\n");
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| 143 |
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| 144 | mpfr_init2(Val, 112 + 1);
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| 145 | mpfr_const_pi(Val, MPFR_RNDN);
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| 146 | PrintF128(Val, "g_r128pi", "The pi constant as 128-bit floating point value.");
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| 147 | mpfr_div_ui(Val, Val, 2, MPFR_RNDD);
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| 148 | PrintF128(Val, "g_r128pi2", "The pi/2 constant as 128-bit floating point value.");
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| 149 |
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| 150 | printf("\n"
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| 151 | "/** CORDIC constants for fsin and fcos, defined by c(i)=atan(2^(-i)) */\n"
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| 152 | "const RTFLOAT128U g_ar128FsincosCORDICConsts[] =\n"
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| 153 | "{\n");
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| 154 | mpfr_init2(Val, 112 + 1);
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| 155 | signed kmax = 68;
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| 156 |
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| 157 | for (signed k = 0; k < kmax; k++)
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| 158 | {
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| 159 | // mpfr_mul_2si ?
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| 160 | mpfr_set_si_2exp(Val, 1, -k, MPFR_RNDD);
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| 161 | mpfr_atan(Val, Val, MPFR_RNDD);
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| 162 | PrintF128(Val, NULL, "c%u", k);
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| 163 | }
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| 164 |
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| 165 | printf("};\n");
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| 166 |
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| 167 | printf("\n"
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| 168 | "/** CORDIC multipliers for fsin and fcos, defined by K(i)=1/sqrt(1+2^(-2i)) */\n"
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| 169 | "const RTFLOAT128U g_ar128FsincosCORDICConsts2[] =\n"
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| 170 | "{\n");
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| 171 |
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| 172 | mpfr_init2(Val, 112 + 1);
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| 173 | mpfr_init2(Val2, 112 + 1);
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| 174 |
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| 175 | mpfr_set_ui(Val, 2, MPFR_RNDD);
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| 176 | mpfr_sqrt(Val, Val, MPFR_RNDD);
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| 177 | mpfr_ui_div(Val2, 1, Val, MPFR_RNDD);
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| 178 | PrintF128(Val2, NULL, "K_%u", 0);
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| 179 |
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| 180 | for (signed k = 1; k < kmax; k++)
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| 181 | {
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| 182 | mpfr_set_si_2exp(Val, 1, -2 * k, MPFR_RNDD);
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| 183 | mpfr_add_ui(Val, Val, 1, MPFR_RNDD);
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| 184 | mpfr_sqrt(Val, Val, MPFR_RNDD);
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| 185 | mpfr_div(Val2, Val2, Val, MPFR_RNDD);
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| 186 | PrintF128(Val2, NULL, "K_%u", k);
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| 187 | }
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| 188 |
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| 189 | printf("};\n");
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| 190 |
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| 191 | printf("\n"
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| 192 | "/** Chebyshev coeffs for log2 function in [1, 2] interval */\n"
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| 193 | "const RTFLOAT128U g_ar128ChebLog2Consts[] =\n"
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| 194 | "{\n");
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| 195 | signed j, d, dmax = 22;
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| 196 | mpfr_t ValX, ValXX, ValA, ValB, ValBmA, ValCos, ValSum;
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| 197 | mpfr_init2(Val, 112 + 1);
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| 198 | mpfr_init2(Val2, 112 + 1);
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| 199 | mpfr_init2(ValX, 112 + 1);
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| 200 | mpfr_init2(ValXX, 112 + 1);
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| 201 | mpfr_init2(ValA, 112 + 1);
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| 202 | mpfr_init2(ValB, 112 + 1);
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| 203 | mpfr_init2(ValBmA, 112 + 1);
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| 204 | mpfr_init2(ValCos, 112 + 1);
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| 205 | mpfr_init2(ValSum, 112 + 1);
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| 206 |
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| 207 | /* Setting the desired interpolation range [1.0, 2.0] */
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| 208 | mpfr_set_d(ValA, 1.0, MPFR_RNDD);
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| 209 | mpfr_set_d(ValB, 2.0, MPFR_RNDD);
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| 210 | mpfr_sub(ValBmA, ValB, ValA, MPFR_RNDD);
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| 211 |
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| 212 | for (signed d = 0; d < dmax; d++)
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| 213 | {
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| 214 | mpfr_set_si(ValSum, 0, MPFR_RNDD);
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| 215 |
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| 216 | for(j = 0; j < dmax; j++)
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| 217 | {
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| 218 | mpfr_set_si_2exp(Val, 1, -1, MPFR_RNDD);
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| 219 | mpfr_add_ui(Val, Val, j, MPFR_RNDD);
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| 220 | mpfr_const_pi(Val2, MPFR_RNDN);
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| 221 | mpfr_mul(Val, Val2, Val, MPFR_RNDN);
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| 222 | mpfr_div_si(Val, Val, dmax, MPFR_RNDN);
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| 223 | /* Val = M_PIq * (j + 0.5Q) / N */
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| 224 |
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| 225 | mpfr_cos(ValX, Val, MPFR_RNDN);
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| 226 | /* ValX = cos(M_PIq * (j + 0.5Q) / N) */
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| 227 |
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| 228 | mpfr_mul_si(Val, Val, d, MPFR_RNDN);
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| 229 | mpfr_cos(ValCos, Val, MPFR_RNDN);
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| 230 | /* ValCos = cos(M_PIq * d * (j + 0.5Q) / N) */
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| 231 |
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| 232 | mpfr_add_si(Val, ValX, 1, MPFR_RNDN);
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| 233 | mpfr_div_si(Val, Val, 2, MPFR_RNDN);
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| 234 | mpfr_mul(Val, ValBmA, Val, MPFR_RNDN);
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| 235 | mpfr_add(ValXX, ValA, Val, MPFR_RNDN);
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| 236 | /* ValXX = a + (b - a) * (x + 1.0Q) / 2.0Q */
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| 237 |
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| 238 | mpfr_sub_si(Val, ValXX, 1, MPFR_RNDN);
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| 239 | mpfr_log2(Val2, ValXX, MPFR_RNDN);
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| 240 | mpfr_div(Val, Val2, Val, MPFR_RNDN);
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| 241 | mpfr_mul(Val, Val, ValCos, MPFR_RNDN);
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| 242 | mpfr_add(ValSum, ValSum, Val, MPFR_RNDN);
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| 243 | }
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| 244 |
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| 245 | mpfr_div_si(ValSum, ValSum, dmax, MPFR_RNDN);
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| 246 |
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| 247 | if (d != 0)
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| 248 | mpfr_mul_si(ValSum, ValSum, 2, MPFR_RNDN);
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| 249 |
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| 250 | PrintF128(ValSum, NULL, "c%u", d);
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| 251 | }
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| 252 |
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| 253 | printf("};\n");
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| 254 |
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| 255 | mpfr_init2(One, 112 + 1);
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| 256 | mpfr_set_ui(One, 1, MPFR_RNDD);
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| 257 |
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| 258 | mpfr_init2(Val, 112 + 1);
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| 259 | mpfr_exp(Val, One, MPFR_RNDD);
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| 260 | mpfr_log2(Val, Val, MPFR_RNDD);
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| 261 |
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| 262 | PrintF128(Val, "g_r128Log2e", "The log2e constant as 128-bit floating point value.");
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| 263 |
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| 264 | mpfr_clear(ValXX);
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| 265 | mpfr_clear(ValX);
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| 266 | mpfr_clear(Val);
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| 267 | mpfr_clear(Val2);
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| 268 | mpfr_clear(One);
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| 269 | mpfr_free_cache();
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| 270 | return 0;
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| 271 | }
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| 272 |
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