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+/*
+r128.h: 128-bit (64.64) signed fixed-point arithmetic. Version 1.4.3
+
+COMPILATION
+-----------
+Drop this header file somewhere in your project and include it wherever it is
+needed. There is no separate .c file for this library. To get the code, in ONE
+file in your project, put:
+
+#define R128_IMPLEMENTATION
+
+before you include this file. You may also provide a definition for R128_ASSERT
+to force the library to use a custom assert macro.
+
+COMPILER/LIBRARY SUPPORT
+------------------------
+This library requires a C89 compiler with support for 64-bit integers. If your
+compiler does not support the long long data type, the R128_U64, etc. macros
+must be set appropriately. On x86 and x64 targets, Intel intrinsics are used
+for speed. If your compiler does not support these intrinsics, you can add
+#define R128_STDC_ONLY
+in your implementation file before including r128.h.
+
+The only C runtime library functionality used by this library is <assert.h>.
+This can be avoided by defining an R128_ASSERT macro in your implementation
+file. Since this library uses 64-bit arithmetic, this may implicitly add a
+runtime library dependency on 32-bit platforms.
+
+C++ SUPPORT
+-----------
+Operator overloads are supplied for C++ files that include this file. Since all
+C++ functions are declared inline (or static inline), the R128_IMPLEMENTATION
+file can be either C++ or C.
+
+LICENSE
+-------
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+*/
+
+#ifndef H_R128_H
+#define H_R128_H
+
+#include <stddef.h>
+
+// 64-bit integer support
+// If your compiler does not have stdint.h, add appropriate defines for these macros.
+#if defined(_MSC_VER) && (_MSC_VER < 1600)
+# define R128_S32 __int32
+# define R128_U32 unsigned __int32
+# define R128_S64 __int64
+# define R128_U64 unsigned __int64
+# define R128_LIT_S64(x) x##i64
+# define R128_LIT_U64(x) x##ui64
+#else
+# include <stdint.h>
+# define R128_S32 int32_t
+# define R128_U32 uint32_t
+# define R128_S64 int64_t
+# define R128_U64 long long unsigned int
+# define R128_LIT_S64(x) x##ll
+# define R128_LIT_U64(x) x##ull
+#endif
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+typedef struct R128 {
+ R128_U64 lo;
+ R128_U64 hi;
+
+#ifdef __cplusplus
+ R128();
+ R128(double);
+ R128(int);
+ R128(R128_S64);
+ R128(R128_U64 low, R128_U64 high);
+
+ operator double() const;
+ operator R128_S64() const;
+ operator int() const;
+ operator bool() const;
+
+ bool operator!() const;
+ R128 operator~() const;
+ R128 operator-() const;
+ R128 &operator|=(const R128 &rhs);
+ R128 &operator&=(const R128 &rhs);
+ R128 &operator^=(const R128 &rhs);
+ R128 &operator+=(const R128 &rhs);
+ R128 &operator-=(const R128 &rhs);
+ R128 &operator*=(const R128 &rhs);
+ R128 &operator/=(const R128 &rhs);
+ R128 &operator%=(const R128 &rhs);
+ R128 &operator<<=(int amount);
+ R128 &operator>>=(int amount);
+#endif //__cplusplus
+} R128;
+
+// Type conversion
+extern void r128FromInt(R128 *dst, R128_S64 v);
+extern void r128FromFloat(R128 *dst, double v);
+extern R128_S64 r128ToInt(const R128 *v);
+extern double r128ToFloat(const R128 *v);
+
+// Copy
+extern void r128Copy(R128 *dst, const R128 *src);
+
+// Negate
+extern void r128Neg(R128 *dst, const R128 *src);
+
+// Bitwise operations
+extern void r128Not(R128 *dst, const R128 *src); // ~a
+extern void r128Or(R128 *dst, const R128 *a, const R128 *b); // a | b
+extern void r128And(R128 *dst, const R128 *a, const R128 *b); // a & b
+extern void r128Xor(R128 *dst, const R128 *a, const R128 *b); // a ^ b
+extern void r128Shl(R128 *dst, const R128 *src, int amount); // shift left by amount mod 128
+extern void r128Shr(R128 *dst, const R128 *src, int amount); // shift right logical by amount mod 128
+extern void r128Sar(R128 *dst, const R128 *src, int amount); // shift right arithmetic by amount mod 128
+
+// Arithmetic
+extern void r128Add(R128 *dst, const R128 *a, const R128 *b); // a + b
+extern void r128Sub(R128 *dst, const R128 *a, const R128 *b); // a - b
+extern void r128Mul(R128 *dst, const R128 *a, const R128 *b); // a * b
+extern void r128Div(R128 *dst, const R128 *a, const R128 *b); // a / b
+extern void r128Mod(R128 *dst, const R128 *a, const R128 *b); // a - toInt(a / b) * b
+
+extern void r128Sqrt(R128 *dst, const R128 *v); // sqrt(v)
+extern void r128Rsqrt(R128 *dst, const R128 *v); // 1 / sqrt(v)
+
+// Comparison
+extern int r128Cmp(const R128 *a, const R128 *b); // sign of a-b
+extern void r128Min(R128 *dst, const R128 *a, const R128 *b);
+extern void r128Max(R128 *dst, const R128 *a, const R128 *b);
+extern void r128Floor(R128 *dst, const R128 *v);
+extern void r128Ceil(R128 *dst, const R128 *v);
+extern int r128IsNeg(const R128 *v); // quick check for < 0
+
+// String conversion
+//
+typedef enum R128ToStringSign {
+ R128ToStringSign_Default, // no sign character for positive values
+ R128ToStringSign_Space, // leading space for positive values
+ R128ToStringSign_Plus, // leading '+' for positive values
+} R128ToStringSign;
+
+// Formatting options for use with r128ToStringOpt. The "defaults" correspond
+// to a format string of "%f".
+//
+typedef struct R128ToStringFormat {
+ // sign character for positive values. Default is R128ToStringSign_Default.
+ R128ToStringSign sign;
+
+ // minimum number of characters to write. Default is 0.
+ int width;
+
+ // place to the right of the decimal at which rounding is performed. If negative,
+ // a maximum of 20 decimal places will be written, with no trailing zeroes.
+ // (20 places is sufficient to ensure that r128FromString will convert back to the
+ // original value.) Default is -1. NOTE: This is not the same default that the C
+ // standard library uses for %f.
+ int precision;
+
+ // If non-zero, pads the output string with leading zeroes if the final result is
+ // fewer than width characters. Otherwise, leading spaces are used. Default is 0.
+ int zeroPad;
+
+ // Always print a decimal point, even if the value is an integer. Default is 0.
+ int decimal;
+
+ // Left-align output if width specifier requires padding.
+ // Default is 0 (right align).
+ int leftAlign;
+} R128ToStringFormat;
+
+// r128ToStringOpt: convert R128 to a decimal string, with formatting.
+//
+// dst and dstSize: specify the buffer to write into. At most dstSize bytes will be written
+// (including null terminator). No additional rounding is performed if dstSize is not large
+// enough to hold the entire string.
+//
+// opt: an R128ToStringFormat struct (q.v.) with formatting options.
+//
+// Uses the R128_decimal global as the decimal point character.
+// Always writes a null terminator, even if the destination buffer is not large enough.
+//
+// Number of bytes that will be written (i.e. how big does dst need to be?):
+// If width is specified: width + 1 bytes.
+// If precision is specified: at most precision + 22 bytes.
+// If neither is specified: at most 42 bytes.
+//
+// Returns the number of bytes that would have been written if dst was sufficiently large,
+// not including the final null terminator.
+//
+extern int r128ToStringOpt(char *dst, size_t dstSize, const R128 *v, const R128ToStringFormat *opt);
+
+// r128ToStringf: convert R128 to a decimal string, with formatting.
+//
+// dst and dstSize: specify the buffer to write into. At most dstSize bytes will be written
+// (including null terminator).
+//
+// format: a printf-style format specifier, as one would use with floating point types.
+// e.g. "%+5.2f". (The leading % and trailing f are optional.)
+// NOTE: This is NOT a full replacement for sprintf. Any characters in the format string
+// that do not correspond to a format placeholder are ignored.
+//
+// Uses the R128_decimal global as the decimal point character.
+// Always writes a null terminator, even if the destination buffer is not large enough.
+//
+// Number of bytes that will be written (i.e. how big does dst need to be?):
+// If the precision field is specified: at most max(width, precision + 21) + 1 bytes
+// Otherwise: at most max(width, 41) + 1 bytes.
+//
+// Returns the number of bytes that would have been written if dst was sufficiently large,
+// not including the final null terminator.
+//
+extern int r128ToStringf(char *dst, size_t dstSize, const char *format, const R128 *v);
+
+// r128ToString: convert R128 to a decimal string, with default formatting.
+// Equivalent to r128ToStringf(dst, dstSize, "%f", v).
+//
+// Uses the R128_decimal global as the decimal point character.
+// Always writes a null terminator, even if the destination buffer is not large enough.
+//
+// Will write at most 42 bytes (including NUL) to dst.
+//
+// Returns the number of bytes that would have been written if dst was sufficiently large,
+// not including the final null terminator.
+//
+extern int r128ToString(char *dst, size_t dstSize, const R128 *v);
+
+// r128FromString: Convert string to R128.
+//
+// The string can be formatted either as a decimal number with optional sign
+// or as hexadecimal with a prefix of 0x or 0X.
+//
+// endptr, if not NULL, is set to the character following the last character
+// used in the conversion.
+//
+extern void r128FromString(R128 *dst, const char *s, char **endptr);
+
+// Constants
+extern const R128 R128_min; // minimum (most negative) value
+extern const R128 R128_max; // maximum (most positive) value
+extern const R128 R128_smallest; // smallest positive value
+extern const R128 R128_zero; // zero
+extern const R128 R128_one; // 1.0
+
+extern char R128_decimal; // decimal point character used by r128From/ToString. defaults to '.'
+
+#ifdef __cplusplus
+}
+
+#include <limits>
+namespace std {
+template<>
+struct numeric_limits<R128>
+{
+ static const bool is_specialized = true;
+
+ static R128 min() throw() { return R128_min; }
+ static R128 max() throw() { return R128_max; }
+
+ static const int digits = 127;
+ static const int digits10 = 38;
+ static const bool is_signed = true;
+ static const bool is_integer = false;
+ static const bool is_exact = false;
+ static const int radix = 2;
+ static R128 epsilon() throw() { return R128_smallest; }
+ static R128 round_error() throw() { return R128_one; }
+
+ static const int min_exponent = 0;
+ static const int min_exponent10 = 0;
+ static const int max_exponent = 0;
+ static const int max_exponent10 = 0;
+
+ static const bool has_infinity = false;
+ static const bool has_quiet_NaN = false;
+ static const bool has_signaling_NaN = false;
+ static const float_denorm_style has_denorm = denorm_absent;
+ static const bool has_denorm_loss = false;
+
+ static R128 infinity() throw() { return R128_zero; }
+ static R128 quiet_NaN() throw() { return R128_zero; }
+ static R128 signaling_NaN() throw() { return R128_zero; }
+ static R128 denorm_min() throw() { return R128_zero; }
+
+ static const bool is_iec559 = false;
+ static const bool is_bounded = true;
+ static const bool is_modulo = true;
+
+ static const bool traps = numeric_limits<R128_U64>::traps;
+ static const bool tinyness_before = false;
+ static const float_round_style round_style = round_toward_zero;
+};
+} //namespace std
+
+inline R128::R128() {}
+
+inline R128::R128(double v)
+{
+ r128FromFloat(this, v);
+}
+
+inline R128::R128(int v)
+{
+ r128FromInt(this, v);
+}
+
+inline R128::R128(R128_S64 v)
+{
+ r128FromInt(this, v);
+}
+
+inline R128::R128(R128_U64 low, R128_U64 high)
+{
+ lo = low;
+ hi = high;
+}
+
+inline R128::operator double() const
+{
+ return r128ToFloat(this);
+}
+
+inline R128::operator R128_S64() const
+{
+ return r128ToInt(this);
+}
+
+inline R128::operator int() const
+{
+ return (int) r128ToInt(this);
+}
+
+inline R128::operator bool() const
+{
+ return lo || hi;
+}
+
+inline bool R128::operator!() const
+{
+ return !lo && !hi;
+}
+
+inline R128 R128::operator~() const
+{
+ R128 r;
+ r128Not(&r, this);
+ return r;
+}
+
+inline R128 R128::operator-() const
+{
+ R128 r;
+ r128Neg(&r, this);
+ return r;
+}
+
+inline R128 &R128::operator|=(const R128 &rhs)
+{
+ r128Or(this, this, &rhs);
+ return *this;
+}
+
+inline R128 &R128::operator&=(const R128 &rhs)
+{
+ r128And(this, this, &rhs);
+ return *this;
+}
+
+inline R128 &R128::operator^=(const R128 &rhs)
+{
+ r128Xor(this, this, &rhs);
+ return *this;
+}
+
+inline R128 &R128::operator+=(const R128 &rhs)
+{
+ r128Add(this, this, &rhs);
+ return *this;
+}
+
+inline R128 &R128::operator-=(const R128 &rhs)
+{
+ r128Sub(this, this, &rhs);
+ return *this;
+}
+
+inline R128 &R128::operator*=(const R128 &rhs)
+{
+ r128Mul(this, this, &rhs);
+ return *this;
+}
+
+inline R128 &R128::operator/=(const R128 &rhs)
+{
+ r128Div(this, this, &rhs);
+ return *this;
+}
+
+inline R128 &R128::operator%=(const R128 &rhs)
+{
+ r128Mod(this, this, &rhs);
+ return *this;
+}
+
+inline R128 &R128::operator<<=(int amount)
+{
+ r128Shl(this, this, amount);
+ return *this;
+}
+
+inline R128 &R128::operator>>=(int amount)
+{
+ r128Sar(this, this, amount);
+ return *this;
+}
+
+static inline R128 operator|(const R128 &lhs, const R128 &rhs)
+{
+ R128 r(lhs);
+ return r |= rhs;
+}
+
+static inline R128 operator&(const R128 &lhs, const R128 &rhs)
+{
+ R128 r(lhs);
+ return r &= rhs;
+}
+
+static inline R128 operator^(const R128 &lhs, const R128 &rhs)
+{
+ R128 r(lhs);
+ return r ^= rhs;
+}
+
+static inline R128 operator+(const R128 &lhs, const R128 &rhs)
+{
+ R128 r(lhs);
+ return r += rhs;
+}
+
+static inline R128 operator-(const R128 &lhs, const R128 &rhs)
+{
+ R128 r(lhs);
+ return r -= rhs;
+}
+
+static inline R128 operator*(const R128 &lhs, const R128 &rhs)
+{
+ R128 r(lhs);
+ return r *= rhs;
+}
+
+static inline R128 operator/(const R128 &lhs, const R128 &rhs)
+{
+ R128 r(lhs);
+ return r /= rhs;
+}
+
+static inline R128 operator%(const R128 &lhs, const R128 &rhs)
+{
+ R128 r(lhs);
+ return r %= rhs;
+}
+
+static inline R128 operator<<(const R128 &lhs, int amount)
+{
+ R128 r(lhs);
+ return r <<= amount;
+}
+
+static inline R128 operator>>(const R128 &lhs, int amount)
+{
+ R128 r(lhs);
+ return r >>= amount;
+}
+
+static inline bool operator<(const R128 &lhs, const R128 &rhs)
+{
+ return r128Cmp(&lhs, &rhs) < 0;
+}
+
+static inline bool operator>(const R128 &lhs, const R128 &rhs)
+{
+ return r128Cmp(&lhs, &rhs) > 0;
+}
+
+static inline bool operator<=(const R128 &lhs, const R128 &rhs)
+{
+ return r128Cmp(&lhs, &rhs) <= 0;
+}
+
+static inline bool operator>=(const R128 &lhs, const R128 &rhs)
+{
+ return r128Cmp(&lhs, &rhs) >= 0;
+}
+
+static inline bool operator==(const R128 &lhs, const R128 &rhs)
+{
+ return lhs.lo == rhs.lo && lhs.hi == rhs.hi;
+}
+
+static inline bool operator!=(const R128 &lhs, const R128 &rhs)
+{
+ return lhs.lo != rhs.lo || lhs.hi != rhs.hi;
+}
+
+#endif //__cplusplus
+#endif //H_R128_H
+
+#ifdef R128_IMPLEMENTATION
+
+#ifdef R128_DEBUG_VIS
+# define R128_DEBUG_SET(x) r128ToString(R128_last, sizeof(R128_last), x)
+#else
+# define R128_DEBUG_SET(x)
+#endif
+
+#define R128_SET2(x, l, h) do { (x)->lo = (R128_U64)(l); (x)->hi = (R128_U64)(h); } while(0)
+#define R128_R0(x) ((R128_U32)(x)->lo)
+#define R128_R2(x) ((R128_U32)(x)->hi)
+#if defined(_M_IX86)
+// workaround: MSVC x86's handling of 64-bit values is not great
+# define R128_SET4(x, r0, r1, r2, r3) do { \
+ ((R128_U32*)&(x)->lo)[0] = (R128_U32)(r0); \
+ ((R128_U32*)&(x)->lo)[1] = (R128_U32)(r1); \
+ ((R128_U32*)&(x)->hi)[0] = (R128_U32)(r2); \
+ ((R128_U32*)&(x)->hi)[1] = (R128_U32)(r3); \
+ } while(0)
+# define R128_R1(x) (((R128_U32*)&(x)->lo)[1])
+# define R128_R3(x) (((R128_U32*)&(x)->hi)[1])
+#else
+# define R128_SET4(x, r0, r1, r2, r3) do { (x)->lo = (R128_U64)(r0) | ((R128_U64)(r1) << 32); \
+ (x)->hi = (R128_U64)(r2) | ((R128_U64)(r3) << 32); } while(0)
+# define R128_R1(x) ((R128_U32)((x)->lo >> 32))
+# define R128_R3(x) ((R128_U32)((x)->hi >> 32))
+#endif
+
+#if defined(_M_X64)
+# define R128_INTEL 1
+# define R128_64BIT 1
+# ifndef R128_STDC_ONLY
+# include <intrin.h>
+# endif
+#elif defined(__x86_64__)
+# define R128_INTEL 1
+# define R128_64BIT 1
+# ifndef R128_STDC_ONLY
+# include <x86intrin.h>
+# endif
+#elif defined(_M_IX86)
+# define R128_INTEL 1
+# ifndef R128_STDC_ONLY
+# include <intrin.h>
+# endif
+#elif defined(__i386__)
+# define R128_INTEL 1
+# ifndef R128_STDC_ONLY
+# include <x86intrin.h>
+# endif
+#elif defined(_M_ARM)
+# ifndef R128_STDC_ONLY
+# include <intrin.h>
+# endif
+#elif defined(_M_ARM64)
+# define R128_64BIT 1
+# ifndef R128_STDC_ONLY
+# include <intrin.h>
+# endif
+#elif defined(__aarch64__)
+# define R128_64BIT 1
+#endif
+
+#ifndef R128_INTEL
+# define R128_INTEL 0
+#endif
+
+#ifndef R128_64BIT
+# define R128_64BIT 0
+#endif
+
+#ifndef R128_ASSERT
+# include <assert.h>
+# define R128_ASSERT(x) assert(x)
+#endif
+
+#include <stdlib.h> // for NULL
+
+static const R128ToStringFormat R128__defaultFormat = {
+ R128ToStringSign_Default,
+ 0,
+ -1,
+ 0,
+ 0,
+ 0
+};
+
+const R128 R128_min = { 0, R128_LIT_U64(0x8000000000000000) };
+const R128 R128_max = { R128_LIT_U64(0xffffffffffffffff), R128_LIT_U64(0x7fffffffffffffff) };
+const R128 R128_smallest = { 1, 0 };
+const R128 R128_zero = { 0, 0 };
+const R128 R128_one = { 0, 1 };
+char R128_decimal = '.';
+#ifdef R128_DEBUG_VIS
+char R128_last[42];
+#endif
+
+static int r128__clz64(R128_U64 x)
+{
+#if defined(R128_STDC_ONLY)
+ R128_U64 n = 64, y;
+ y = x >> 32; if (y) { n -= 32; x = y; }
+ y = x >> 16; if (y) { n -= 16; x = y; }
+ y = x >> 8; if (y) { n -= 8; x = y; }
+ y = x >> 4; if (y) { n -= 4; x = y; }
+ y = x >> 2; if (y) { n -= 2; x = y; }
+ y = x >> 1; if (y) { n -= 1; x = y; }
+ return (int)(n - x);
+#elif defined(_M_X64) || defined(_M_ARM64)
+ unsigned long idx;
+ if (_BitScanReverse64(&idx, x)) {
+ return 63 - (int)idx;
+ } else {
+ return 64;
+ }
+#elif defined(_MSC_VER)
+ unsigned long idx;
+ if (_BitScanReverse(&idx, (R128_U32)(x >> 32))) {
+ return 31 - (int)idx;
+ } else if (_BitScanReverse(&idx, (R128_U32)x)) {
+ return 63 - (int)idx;
+ } else {
+ return 64;
+ }
+#else
+ return x ? __builtin_clzll(x) : 64;
+#endif
+}
+
+#if !R128_64BIT
+// 32*32->64
+static R128_U64 r128__umul64(R128_U32 a, R128_U32 b)
+{
+# if defined(_M_IX86) && !defined(R128_STDC_ONLY)
+ return __emulu(a, b);
+# elif defined(_M_ARM) && !defined(R128_STDC_ONLY)
+ return _arm_umull(a, b);
+# else
+ return a * (R128_U64)b;
+# endif
+}
+
+// 64/32->32
+static R128_U32 r128__udiv64(R128_U32 nlo, R128_U32 nhi, R128_U32 d, R128_U32 *rem)
+{
+# if defined(_M_IX86) && (_MSC_VER >= 1920) && !defined(R128_STDC_ONLY)
+ unsigned __int64 n = ((unsigned __int64)nhi << 32) | nlo;
+ return _udiv64(n, d, rem);
+# elif defined(_M_IX86) && !defined(R128_STDC_ONLY)
+ __asm {
+ mov eax, nlo
+ mov edx, nhi
+ div d
+ mov ecx, rem
+ mov dword ptr [ecx], edx
+ }
+# elif defined(__i386__) && !defined(R128_STDC_ONLY)
+ R128_U32 q, r;
+ __asm("divl %4"
+ : "=a"(q), "=d"(r)
+ : "a"(nlo), "d"(nhi), "X"(d));
+ *rem = r;
+ return q;
+# else
+ R128_U64 n64 = ((R128_U64)nhi << 32) | nlo;
+ *rem = (R128_U32)(n64 % d);
+ return (R128_U32)(n64 / d);
+# endif
+}
+#elif !defined(_M_X64) || defined(R128_STDC_ONLY)
+#define r128__umul64(a, b) ((a) * (R128_U64)(b))
+/*static R128_U32 r128__udiv64(R128_U32 nlo, R128_U32 nhi, R128_U32 d, R128_U32 *rem)
+{
+ R128_U64 n64 = ((R128_U64)nhi << 32) | nlo;
+ *rem = (R128_U32)(n64 % d);
+ return (R128_U32)(n64 / d);
+}*/
+#endif //!R128_64BIT
+
+static void r128__neg(R128 *dst, const R128 *src)
+{
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(src != NULL);
+
+#if R128_INTEL && !defined(R128_STDC_ONLY)
+ {
+ unsigned char carry = 0;
+# if R128_64BIT
+ carry = _addcarry_u64(carry, ~src->lo, 1, &dst->lo);
+ carry = _addcarry_u64(carry, ~src->hi, 0, &dst->hi);
+# else
+ R128_U32 r0, r1, r2, r3;
+ carry = _addcarry_u32(carry, ~R128_R0(src), 1, &r0);
+ carry = _addcarry_u32(carry, ~R128_R1(src), 0, &r1);
+ carry = _addcarry_u32(carry, ~R128_R2(src), 0, &r2);
+ carry = _addcarry_u32(carry, ~R128_R3(src), 0, &r3);
+ R128_SET4(dst, r0, r1, r2, r3);
+# endif //R128_64BIT
+ }
+#else
+ if (src->lo) {
+ dst->lo = ~src->lo + 1;
+ dst->hi = ~src->hi;
+ } else {
+ dst->lo = 0;
+ dst->hi = ~src->hi + 1;
+ }
+#endif //R128_INTEL
+}
+
+// 64*64->128
+static void r128__umul128(R128 *dst, R128_U64 a, R128_U64 b)
+{
+#if defined(_M_X64) && !defined(R128_STDC_ONLY)
+ dst->lo = _umul128(a, b, &dst->hi);
+#elif R128_64BIT && !defined(_MSC_VER) && !defined(R128_STDC_ONLY)
+ unsigned __int128 p0 = a * (unsigned __int128)b;
+ dst->hi = (R128_U64)(p0 >> 64);
+ dst->lo = (R128_U64)p0;
+#else
+ R128_U32 alo = (R128_U32)a;
+ R128_U32 ahi = (R128_U32)(a >> 32);
+ R128_U32 blo = (R128_U32)b;
+ R128_U32 bhi = (R128_U32)(b >> 32);
+ R128_U64 p0, p1, p2, p3;
+
+ p0 = r128__umul64(alo, blo);
+ p1 = r128__umul64(alo, bhi);
+ p2 = r128__umul64(ahi, blo);
+ p3 = r128__umul64(ahi, bhi);
+
+ {
+#if R128_INTEL && !defined(R128_STDC_ONLY)
+ R128_U32 r0, r1, r2, r3;
+ unsigned char carry;
+
+ r0 = (R128_U32)(p0);
+ r1 = (R128_U32)(p0 >> 32);
+ r2 = (R128_U32)(p1 >> 32);
+ r3 = (R128_U32)(p3 >> 32);
+
+ carry = _addcarry_u32(0, r1, (R128_U32)p1, &r1);
+ carry = _addcarry_u32(carry, r2, (R128_U32)(p2 >> 32), &r2);
+ _addcarry_u32(carry, r3, 0, &r3);
+ carry = _addcarry_u32(0, r1, (R128_U32)p2, &r1);
+ carry = _addcarry_u32(carry, r2, (R128_U32)p3, &r2);
+ _addcarry_u32(carry, r3, 0, &r3);
+
+ R128_SET4(dst, r0, r1, r2, r3);
+#else
+ R128_U64 carry, lo, hi;
+ carry = ((R128_U64)(R128_U32)p1 + (R128_U64)(R128_U32)p2 + (p0 >> 32)) >> 32;
+
+ lo = p0 + ((p1 + p2) << 32);
+ hi = p3 + ((R128_U32)(p1 >> 32) + (R128_U32)(p2 >> 32)) + carry;
+
+ R128_SET2(dst, lo, hi);
+#endif
+ }
+#endif
+}
+
+// 128/64->64
+#if defined(_M_X64) && (_MSC_VER < 1920) && !defined(R128_STDC_ONLY)
+// MSVC x64 provides neither inline assembly nor (pre-2019) a div intrinsic, so we do fake
+// "inline assembly" to avoid long division or outline assembly.
+#pragma code_seg(".text")
+__declspec(allocate(".text")) static const unsigned char r128__udiv128Code[] = {
+ 0x48, 0x8B, 0xC1, //mov rax, rcx
+ 0x49, 0xF7, 0xF0, //div rax, r8
+ 0x49, 0x89, 0x11, //mov qword ptr [r9], rdx
+ 0xC3 //ret
+};
+typedef R128_U64 (*r128__udiv128Proc)(R128_U64 nlo, R128_U64 nhi, R128_U64 d, R128_U64 *rem);
+static const r128__udiv128Proc r128__udiv128 = (r128__udiv128Proc)(void*)r128__udiv128Code;
+#else
+static R128_U64 r128__udiv128(R128_U64 nlo, R128_U64 nhi, R128_U64 d, R128_U64 *rem)
+{
+#if defined(_M_X64) && !defined(R128_STDC_ONLY)
+ return _udiv128(nhi, nlo, d, rem);
+#elif defined(__x86_64__) && !defined(R128_STDC_ONLY)
+ R128_U64 q, r;
+ __asm("divq %4"
+ : "=a"(q), "=d"(r)
+ : "a"(nlo), "d"(nhi), "X"(d));
+ *rem = r;
+ return q;
+#else
+ R128_U64 tmp;
+ R128_U32 d0, d1;
+ R128_U32 n3, n2, n1, n0;
+ R128_U32 q0, q1;
+ R128_U32 r;
+ int shift;
+
+ R128_ASSERT(d != 0); //division by zero
+ R128_ASSERT(nhi < d); //overflow
+
+ // normalize
+ shift = r128__clz64(d);
+
+ if (shift) {
+ R128 tmp128;
+ R128_SET2(&tmp128, nlo, nhi);
+ r128Shl(&tmp128, &tmp128, shift);
+ n3 = R128_R3(&tmp128);
+ n2 = R128_R2(&tmp128);
+ n1 = R128_R1(&tmp128);
+ n0 = R128_R0(&tmp128);
+ d <<= shift;
+ } else {
+ n3 = (R128_U32)(nhi >> 32);
+ n2 = (R128_U32)nhi;
+ n1 = (R128_U32)(nlo >> 32);
+ n0 = (R128_U32)nlo;
+ }
+
+ d1 = (R128_U32)(d >> 32);
+ d0 = (R128_U32)d;
+
+ // first digit
+ R128_ASSERT(n3 <= d1);
+ if (n3 < d1) {
+ q1 = r128__udiv64(n2, n3, d1, &r);
+ } else {
+ q1 = 0xffffffffu;
+ r = n2 + d1;
+ }
+refine1:
+ if (r128__umul64(q1, d0) > ((R128_U64)r << 32) + n1) {
+ --q1;
+ if (r < ~d1 + 1) {
+ r += d1;
+ goto refine1;
+ }
+ }
+
+ tmp = ((R128_U64)n2 << 32) + n1 - (r128__umul64(q1, d0) + (r128__umul64(q1, d1) << 32));
+ n2 = (R128_U32)(tmp >> 32);
+ n1 = (R128_U32)tmp;
+
+ // second digit
+ R128_ASSERT(n2 <= d1);
+ if (n2 < d1) {
+ q0 = r128__udiv64(n1, n2, d1, &r);
+ } else {
+ q0 = 0xffffffffu;
+ r = n1 + d1;
+ }
+refine0:
+ if (r128__umul64(q0, d0) > ((R128_U64)r << 32) + n0) {
+ --q0;
+ if (r < ~d1 + 1) {
+ r += d1;
+ goto refine0;
+ }
+ }
+
+ tmp = ((R128_U64)n1 << 32) + n0 - (r128__umul64(q0, d0) + (r128__umul64(q0, d1) << 32));
+ n1 = (R128_U32)(tmp >> 32);
+ n0 = (R128_U32)tmp;
+
+ *rem = (((R128_U64)n1 << 32) + n0) >> shift;
+ return ((R128_U64)q1 << 32) + q0;
+#endif
+}
+#endif
+
+static int r128__ucmp(const R128 *a, const R128 *b)
+{
+ if (a->hi != b->hi) {
+ if (a->hi > b->hi) {
+ return 1;
+ } else {
+ return -1;
+ }
+ } else {
+ if (a->lo == b->lo) {
+ return 0;
+ } else if (a->lo > b->lo) {
+ return 1;
+ } else {
+ return -1;
+ }
+ }
+}
+
+static void r128__umul(R128 *dst, const R128 *a, const R128 *b)
+{
+#if defined(_M_X64) && !defined(R128_STDC_ONLY)
+ R128_U64 t0, t1;
+ R128_U64 lo, hi = 0;
+ unsigned char carry;
+
+ t0 = _umul128(a->lo, b->lo, &t1);
+ carry = _addcarry_u64(0, t1, t0 >> 63, &lo);
+ _addcarry_u64(carry, hi, hi, &hi);
+
+ t0 = _umul128(a->lo, b->hi, &t1);
+ carry = _addcarry_u64(0, lo, t0, &lo);
+ _addcarry_u64(carry, hi, t1, &hi);
+
+ t0 = _umul128(a->hi, b->lo, &t1);
+ carry = _addcarry_u64(0, lo, t0, &lo);
+ _addcarry_u64(carry, hi, t1, &hi);
+
+ t0 = _umul128(a->hi, b->hi, &t1);
+ hi += t0;
+
+ R128_SET2(dst, lo, hi);
+#elif defined(__x86_64__) && !defined(R128_STDC_ONLY)
+ unsigned __int128 p0, p1, p2, p3;
+ p0 = a->lo * (unsigned __int128)b->lo;
+ p1 = a->lo * (unsigned __int128)b->hi;
+ p2 = a->hi * (unsigned __int128)b->lo;
+ p3 = a->hi * (unsigned __int128)b->hi;
+
+ p0 = (p3 << 64) + p2 + p1 + (p0 >> 64) + ((R128_U64)p0 >> 63);
+ dst->lo = (R128_U64)p0;
+ dst->hi = (R128_U64)(p0 >> 64);
+#else
+ R128 p0, p1, p2, p3, round;
+
+ r128__umul128(&p0, a->lo, b->lo);
+ round.hi = 0; round.lo = p0.lo >> 63;
+ p0.lo = p0.hi; p0.hi = 0; //r128Shr(&p0, &p0, 64);
+ r128Add(&p0, &p0, &round);
+
+ r128__umul128(&p1, a->hi, b->lo);
+ r128Add(&p0, &p0, &p1);
+
+ r128__umul128(&p2, a->lo, b->hi);
+ r128Add(&p0, &p0, &p2);
+
+ r128__umul128(&p3, a->hi, b->hi);
+ p3.hi = p3.lo; p3.lo = 0; //r128Shl(&p3, &p3, 64);
+ r128Add(&p0, &p0, &p3);
+
+ R128_SET2(dst, p0.lo, p0.hi);
+#endif
+}
+
+// Shift d left until the high bit is set, and shift n left by the same amount.
+// returns non-zero on overflow.
+static int r128__norm(R128 *n, R128 *d, R128_U64 *n2)
+{
+ R128_U64 d0, d1;
+ R128_U64 n0, n1;
+ int shift;
+
+ d1 = d->hi;
+ d0 = d->lo;
+ n1 = n->hi;
+ n0 = n->lo;
+
+ if (d1) {
+ shift = r128__clz64(d1);
+ if (shift) {
+ d1 = (d1 << shift) | (d0 >> (64 - shift));
+ d0 = d0 << shift;
+ *n2 = n1 >> (64 - shift);
+ n1 = (n1 << shift) | (n0 >> (64 - shift));
+ n0 = n0 << shift;
+ } else {
+ *n2 = 0;
+ }
+ } else {
+ shift = r128__clz64(d0);
+ if (r128__clz64(n1) <= shift) {
+ return 1; // overflow
+ }
+
+ if (shift) {
+ d1 = d0 << shift;
+ d0 = 0;
+ *n2 = (n1 << shift) | (n0 >> (64 - shift));
+ n1 = n0 << shift;
+ n0 = 0;
+ } else {
+ d1 = d0;
+ d0 = 0;
+ *n2 = n1;
+ n1 = n0;
+ n0 = 0;
+ }
+ }
+
+ R128_SET2(n, n0, n1);
+ R128_SET2(d, d0, d1);
+ return 0;
+}
+
+static void r128__udiv(R128 *quotient, const R128 *dividend, const R128 *divisor)
+{
+ R128 tmp;
+ R128_U64 d0, d1;
+ R128_U64 n1, n2, n3;
+ R128 q;
+
+ R128_ASSERT(dividend != NULL);
+ R128_ASSERT(divisor != NULL);
+ R128_ASSERT(quotient != NULL);
+ R128_ASSERT(divisor->hi != 0 || divisor->lo != 0); // divide by zero
+
+ // scale dividend and normalize
+ {
+ R128 n, d;
+ R128_SET2(&n, dividend->lo, dividend->hi);
+ R128_SET2(&d, divisor->lo, divisor->hi);
+ if (r128__norm(&n, &d, &n3)) {
+ R128_SET2(quotient, R128_max.lo, R128_max.hi);
+ return;
+ }
+
+ d1 = d.hi;
+ d0 = d.lo;
+ n2 = n.hi;
+ n1 = n.lo;
+ }
+
+ // first digit
+ R128_ASSERT(n3 <= d1);
+ {
+ R128 t0, t1;
+ t0.lo = n1;
+ if (n3 < d1) {
+ q.hi = r128__udiv128(n2, n3, d1, &t0.hi);
+ } else {
+ q.hi = R128_LIT_U64(0xffffffffffffffff);
+ t0.hi = n2 + d1;
+ }
+
+refine1:
+ r128__umul128(&t1, q.hi, d0);
+ if (r128__ucmp(&t1, &t0) > 0) {
+ --q.hi;
+ if (t0.hi < ~d1 + 1) {
+ t0.hi += d1;
+ goto refine1;
+ }
+ }
+ }
+
+ {
+ R128 t0, t1, t2;
+ t0.hi = n2;
+ t0.lo = n1;
+
+ r128__umul128(&t1, q.hi, d0);
+ r128__umul128(&t2, q.hi, d1);
+
+ t2.hi = t2.lo; t2.lo = 0; //r128Shl(&t2, &t2, 64);
+ r128Add(&tmp, &t1, &t2);
+ r128Sub(&tmp, &t0, &tmp);
+ }
+ n2 = tmp.hi;
+ n1 = tmp.lo;
+
+ // second digit
+ R128_ASSERT(n2 <= d1);
+ {
+ R128 t0, t1;
+ t0.lo = 0;
+ if (n2 < d1) {
+ q.lo = r128__udiv128(n1, n2, d1, &t0.hi);
+ } else {
+ q.lo = R128_LIT_U64(0xffffffffffffffff);
+ t0.hi = n1 + d1;
+ }
+
+ refine0:
+ r128__umul128(&t1, q.lo, d0);
+ if (r128__ucmp(&t1, &t0) > 0) {
+ --q.lo;
+ if (t0.hi < ~d1 + 1) {
+ t0.hi += d1;
+ goto refine0;
+ }
+ }
+ }
+
+ R128_SET2(quotient, q.lo, q.hi);
+}
+
+static R128_U64 r128__umod(R128 *n, R128 *d)
+{
+ R128_U64 d0, d1;
+ R128_U64 n3, n2, n1;
+ R128_U64 q;
+
+ R128_ASSERT(d != NULL);
+ R128_ASSERT(n != NULL);
+ R128_ASSERT(d->hi != 0 || d->lo != 0); // divide by zero
+
+ if (r128__norm(n, d, &n3)) {
+ return R128_LIT_U64(0xffffffffffffffff);
+ }
+
+ d1 = d->hi;
+ d0 = d->lo;
+ n2 = n->hi;
+ n1 = n->lo;
+
+ R128_ASSERT(n3 < d1);
+ {
+ R128 t0, t1;
+ t0.lo = n1;
+ q = r128__udiv128(n2, n3, d1, &t0.hi);
+
+ refine1:
+ r128__umul128(&t1, q, d0);
+ if (r128__ucmp(&t1, &t0) > 0) {
+ --q;
+ if (t0.hi < ~d1 + 1) {
+ t0.hi += d1;
+ goto refine1;
+ }
+ }
+ }
+
+ return q;
+}
+
+static int r128__format(char *dst, size_t dstSize, const R128 *v, const R128ToStringFormat *format)
+{
+ char buf[128];
+ R128 tmp;
+ R128_U64 whole;
+ char *cursor, *decimal, *dstp = dst;
+ int sign = 0;
+ int fullPrecision = 1;
+ int width, precision;
+ int padCnt, trail = 0;
+
+ R128_ASSERT(dst != NULL && dstSize > 0);
+ R128_ASSERT(v != NULL);
+ R128_ASSERT(format != NULL);
+
+ --dstSize;
+
+ R128_SET2(&tmp, v->lo, v->hi);
+ if (r128IsNeg(&tmp)) {
+ r128__neg(&tmp, &tmp);
+ sign = 1;
+ }
+
+ width = format->width;
+ if (width < 0) {
+ width = 0;
+ }
+
+ precision = format->precision;
+ if (precision < 0) {
+ // print a maximum of 20 digits
+ fullPrecision = 0;
+ precision = 20;
+ } else if (precision > (int)sizeof(buf) - 21) {
+ trail = precision - (sizeof(buf) - 21);
+ precision -= trail;
+ }
+
+ whole = tmp.hi;
+ decimal = cursor = buf;
+
+ // fractional part first in case a carry into the whole part is required
+ if (tmp.lo || format->decimal) {
+ while (tmp.lo || (fullPrecision && precision)) {
+ if ((int)(cursor - buf) == precision) {
+ if ((R128_S64)tmp.lo < 0) {
+ // round up, propagate carry backwards
+ char *c;
+ for (c = cursor - 1; c >= buf; --c) {
+ char d = ++*c;
+ if (d <= '9') {
+ goto endfrac;
+ } else {
+ *c = '0';
+ }
+ }
+
+ // carry out into the whole part
+ whole++;
+ }
+
+ break;
+ }
+
+ r128__umul128(&tmp, tmp.lo, 10);
+ *cursor++ = (char)tmp.hi + '0';
+ }
+
+ endfrac:
+ if (format->decimal || precision) {
+ decimal = cursor;
+ *cursor++ = R128_decimal;
+ }
+ }
+
+ // whole part
+ do {
+ char digit = (char)(whole % 10);
+ whole /= 10;
+ *cursor++ = digit + '0';
+ } while (whole);
+
+#define R128__WRITE(c) do { if (dstp < dst + dstSize) *dstp = c; ++dstp; } while(0)
+
+ padCnt = width - (int)(cursor - buf) - 1;
+
+ // left padding
+ if (!format->leftAlign) {
+ char padChar = format->zeroPad ? '0' : ' ';
+ if (format->zeroPad) {
+ if (sign) {
+ R128__WRITE('-');
+ } else if (format->sign == R128ToStringSign_Plus) {
+ R128__WRITE('+');
+ } else if (format->sign == R128ToStringSign_Space) {
+ R128__WRITE(' ');
+ } else {
+ ++padCnt;
+ }
+ }
+
+ for (; padCnt > 0; --padCnt) {
+ R128__WRITE(padChar);
+ }
+ }
+
+ if (format->leftAlign || !format->zeroPad) {
+ if (sign) {
+ R128__WRITE('-');
+ } else if (format->sign == R128ToStringSign_Plus) {
+ R128__WRITE('+');
+ } else if (format->sign == R128ToStringSign_Space) {
+ R128__WRITE(' ');
+ } else {
+ ++padCnt;
+ }
+ }
+
+ {
+ char *i;
+
+ // reverse the whole part
+ for (i = cursor - 1; i >= decimal; --i) {
+ R128__WRITE(*i);
+ }
+
+ // copy the fractional part
+ for (i = buf; i < decimal; ++i) {
+ R128__WRITE(*i);
+ }
+ }
+
+ // right padding
+ if (format->leftAlign) {
+ char padChar = format->zeroPad ? '0' : ' ';
+ for (; padCnt > 0; --padCnt) {
+ R128__WRITE(padChar);
+ }
+ }
+
+ // trailing zeroes for very large precision
+ while (trail--) {
+ R128__WRITE('0');
+ }
+
+#undef R128__WRITE
+
+ if (dstp <= dst + dstSize) {
+ *dstp = '\0';
+ } else {
+ dst[dstSize] = '\0';
+ }
+ return (int)(dstp - dst);
+}
+
+void r128FromInt(R128 *dst, R128_S64 v)
+{
+ R128_ASSERT(dst != NULL);
+ dst->lo = 0;
+ dst->hi = (R128_U64)v;
+ R128_DEBUG_SET(dst);
+}
+
+void r128FromFloat(R128 *dst, double v)
+{
+ R128_ASSERT(dst != NULL);
+
+ if (v < -9223372036854775808.0) {
+ r128Copy(dst, &R128_min);
+ } else if (v >= 9223372036854775808.0) {
+ r128Copy(dst, &R128_max);
+ } else {
+ R128 r;
+ int sign = 0;
+
+ if (v < 0) {
+ v = -v;
+ sign = 1;
+ }
+
+ r.hi = (R128_U64)(R128_S64)v;
+ v -= (R128_S64)v;
+ r.lo = (R128_U64)(v * 18446744073709551616.0);
+
+ if (sign) {
+ r128__neg(&r, &r);
+ }
+
+ r128Copy(dst, &r);
+ }
+}
+
+void r128FromString(R128 *dst, const char *s, char **endptr)
+{
+ R128_U64 lo = 0, hi = 0;
+ R128_U64 base = 10;
+
+ int sign = 0;
+
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(s != NULL);
+
+ R128_SET2(dst, 0, 0);
+
+ // consume whitespace
+ for (;;) {
+ if (*s == ' ' || *s == '\t' || *s == '\r' || *s == '\n' || *s == '\v') {
+ ++s;
+ } else {
+ break;
+ }
+ }
+
+ // sign
+ if (*s == '-') {
+ sign = 1;
+ ++s;
+ } else if (*s == '+') {
+ ++s;
+ }
+
+ // parse base prefix
+ if (s[0] == '0' && (s[1] == 'x' || s[1] == 'X')) {
+ base = 16;
+ s += 2;
+ }
+
+ // whole part
+ for (;; ++s) {
+ R128_U64 digit;
+
+ if ('0' <= *s && *s <= '9') {
+ digit = *s - '0';
+ } else if (base == 16 && 'a' <= *s && *s <= 'f') {
+ digit = *s - 'a' + 10;
+ } else if (base == 16 && 'A' <= *s && *s <= 'F') {
+ digit = *s - 'A' + 10;
+ } else {
+ break;
+ }
+
+ hi = hi * base + digit;
+ }
+
+ // fractional part
+ if (*s == R128_decimal) {
+ const char *exp = ++s;
+
+ // find the last digit and work backwards
+ for (;; ++s) {
+ if ('0' <= *s && *s <= '9') {
+ } else if (base == 16 && ('a' <= *s && *s <= 'f')) {
+ } else if (base == 16 && ('A' <= *s && *s <= 'F')) {
+ } else {
+ break;
+ }
+ }
+
+ for (--s; s >= exp; --s) {
+ R128_U64 digit, unused;
+
+ if ('0' <= *s && *s <= '9') {
+ digit = *s - '0';
+ } else if ('a' <= *s && *s <= 'f') {
+ digit = *s - 'a' + 10;
+ } else {
+ digit = *s - 'A' + 10;
+ }
+
+ lo = r128__udiv128(lo, digit, base, &unused);
+ }
+ }
+
+ R128_SET2(dst, lo, hi);
+ if (sign) {
+ r128__neg(dst, dst);
+ }
+
+ if (endptr) {
+ *endptr = (char *) s;
+ }
+}
+
+R128_S64 r128ToInt(const R128 *v)
+{
+ R128_ASSERT(v != NULL);
+ return (R128_S64)v->hi;
+}
+
+double r128ToFloat(const R128 *v)
+{
+ R128 tmp;
+ int sign = 0;
+ double d;
+
+ R128_ASSERT(v != NULL);
+
+ R128_SET2(&tmp, v->lo, v->hi);
+ if (r128IsNeg(&tmp)) {
+ r128__neg(&tmp, &tmp);
+ sign = 1;
+ }
+
+ d = tmp.hi + tmp.lo * (1 / 18446744073709551616.0);
+ if (sign) {
+ d = -d;
+ }
+
+ return d;
+}
+
+int r128ToStringOpt(char *dst, size_t dstSize, const R128 *v, const R128ToStringFormat *opt)
+{
+ return r128__format(dst, dstSize, v, opt);
+}
+
+int r128ToStringf(char *dst, size_t dstSize, const char *format, const R128 *v)
+{
+ R128ToStringFormat opts;
+
+ R128_ASSERT(dst != NULL && dstSize);
+ R128_ASSERT(format != NULL);
+ R128_ASSERT(v != NULL);
+
+ opts.sign = R128__defaultFormat.sign;
+ opts.precision = R128__defaultFormat.precision;
+ opts.zeroPad = R128__defaultFormat.zeroPad;
+ opts.decimal = R128__defaultFormat.decimal;
+ opts.leftAlign = R128__defaultFormat.leftAlign;
+
+ if (*format == '%') {
+ ++format;
+ }
+
+ // flags field
+ for (;; ++format) {
+ if (*format == ' ' && opts.sign != R128ToStringSign_Plus) {
+ opts.sign = R128ToStringSign_Space;
+ } else if (*format == '+') {
+ opts.sign = R128ToStringSign_Plus;
+ } else if (*format == '0') {
+ opts.zeroPad = 1;
+ } else if (*format == '-') {
+ opts.leftAlign = 1;
+ } else if (*format == '#') {
+ opts.decimal = 1;
+ } else {
+ break;
+ }
+ }
+
+ // width field
+ opts.width = 0;
+ for (;;) {
+ if ('0' <= *format && *format <= '9') {
+ opts.width = opts.width * 10 + *format++ - '0';
+ } else {
+ break;
+ }
+ }
+
+ // precision field
+ if (*format == '.') {
+ opts.precision = 0;
+ ++format;
+ for (;;) {
+ if ('0' <= *format && *format <= '9') {
+ opts.precision = opts.precision * 10 + *format++ - '0';
+ } else {
+ break;
+ }
+ }
+ }
+
+ return r128__format(dst, dstSize, v, &opts);
+}
+
+int r128ToString(char *dst, size_t dstSize, const R128 *v)
+{
+ return r128__format(dst, dstSize, v, &R128__defaultFormat);
+}
+
+void r128Copy(R128 *dst, const R128 *src)
+{
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(src != NULL);
+ dst->lo = src->lo;
+ dst->hi = src->hi;
+ R128_DEBUG_SET(dst);
+}
+
+void r128Neg(R128 *dst, const R128 *src)
+{
+ r128__neg(dst, src);
+ R128_DEBUG_SET(dst);
+}
+
+void r128Not(R128 *dst, const R128 *src)
+{
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(src != NULL);
+
+ dst->lo = ~src->lo;
+ dst->hi = ~src->hi;
+ R128_DEBUG_SET(dst);
+}
+
+void r128Or(R128 *dst, const R128 *a, const R128 *b)
+{
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(a != NULL);
+ R128_ASSERT(b != NULL);
+
+ dst->lo = a->lo | b->lo;
+ dst->hi = a->hi | b->hi;
+ R128_DEBUG_SET(dst);
+}
+
+void r128And(R128 *dst, const R128 *a, const R128 *b)
+{
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(a != NULL);
+ R128_ASSERT(b != NULL);
+
+ dst->lo = a->lo & b->lo;
+ dst->hi = a->hi & b->hi;
+ R128_DEBUG_SET(dst);
+}
+
+void r128Xor(R128 *dst, const R128 *a, const R128 *b)
+{
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(a != NULL);
+ R128_ASSERT(b != NULL);
+
+ dst->lo = a->lo ^ b->lo;
+ dst->hi = a->hi ^ b->hi;
+ R128_DEBUG_SET(dst);
+}
+
+void r128Shl(R128 *dst, const R128 *src, int amount)
+{
+ R128_U64 r[4];
+
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(src != NULL);
+
+#if defined(_M_IX86) && !defined(R128_STDC_ONLY)
+ __asm {
+ // load src
+ mov edx, dword ptr[src]
+ mov ecx, amount
+
+ mov edi, dword ptr[edx]
+ mov esi, dword ptr[edx + 4]
+ mov ebx, dword ptr[edx + 8]
+ mov eax, dword ptr[edx + 12]
+
+ // shift mod 32
+ shld eax, ebx, cl
+ shld ebx, esi, cl
+ shld esi, edi, cl
+ shl edi, cl
+
+ // clear out low 12 bytes of stack
+ xor edx, edx
+ mov dword ptr[r], edx
+ mov dword ptr[r + 4], edx
+ mov dword ptr[r + 8], edx
+
+ // store shifted amount offset by count/32 bits
+ shr ecx, 5
+ and ecx, 3
+ mov dword ptr[r + ecx * 4 + 0], edi
+ mov dword ptr[r + ecx * 4 + 4], esi
+ mov dword ptr[r + ecx * 4 + 8], ebx
+ mov dword ptr[r + ecx * 4 + 12], eax
+ }
+#else
+
+ r[0] = src->lo;
+ r[1] = src->hi;
+
+ amount &= 127;
+ if (amount >= 64) {
+ r[1] = r[0] << (amount - 64);
+ r[0] = 0;
+ } else if (amount) {
+# ifdef _M_X64
+ r[1] = __shiftleft128(r[0], r[1], (char) amount);
+# else
+ r[1] = (r[1] << amount) | (r[0] >> (64 - amount));
+# endif
+ r[0] = r[0] << amount;
+ }
+#endif //_M_IX86
+
+ dst->lo = r[0];
+ dst->hi = r[1];
+ R128_DEBUG_SET(dst);
+}
+
+void r128Shr(R128 *dst, const R128 *src, int amount)
+{
+ R128_U64 r[4];
+
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(src != NULL);
+
+#if defined(_M_IX86) && !defined(R128_STDC_ONLY)
+ __asm {
+ // load src
+ mov edx, dword ptr[src]
+ mov ecx, amount
+
+ mov edi, dword ptr[edx]
+ mov esi, dword ptr[edx + 4]
+ mov ebx, dword ptr[edx + 8]
+ mov eax, dword ptr[edx + 12]
+
+ // shift mod 32
+ shrd edi, esi, cl
+ shrd esi, ebx, cl
+ shrd ebx, eax, cl
+ shr eax, cl
+
+ // clear out high 12 bytes of stack
+ xor edx, edx
+ mov dword ptr[r + 20], edx
+ mov dword ptr[r + 24], edx
+ mov dword ptr[r + 28], edx
+
+ // store shifted amount offset by -count/32 bits
+ shr ecx, 5
+ and ecx, 3
+ neg ecx
+ mov dword ptr[r + ecx * 4 + 16], edi
+ mov dword ptr[r + ecx * 4 + 20], esi
+ mov dword ptr[r + ecx * 4 + 24], ebx
+ mov dword ptr[r + ecx * 4 + 28], eax
+ }
+#else
+ r[2] = src->lo;
+ r[3] = src->hi;
+
+ amount &= 127;
+ if (amount >= 64) {
+ r[2] = r[3] >> (amount - 64);
+ r[3] = 0;
+ } else if (amount) {
+#ifdef _M_X64
+ r[2] = __shiftright128(r[2], r[3], (char) amount);
+#else
+ r[2] = (r[2] >> amount) | (r[3] << (64 - amount));
+#endif
+ r[3] = r[3] >> amount;
+ }
+#endif
+
+ dst->lo = r[2];
+ dst->hi = r[3];
+ R128_DEBUG_SET(dst);
+}
+
+void r128Sar(R128 *dst, const R128 *src, int amount)
+{
+ R128_U64 r[4];
+
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(src != NULL);
+
+#if defined(_M_IX86) && !defined(R128_STDC_ONLY)
+ __asm {
+ // load src
+ mov edx, dword ptr[src]
+ mov ecx, amount
+
+ mov edi, dword ptr[edx]
+ mov esi, dword ptr[edx + 4]
+ mov ebx, dword ptr[edx + 8]
+ mov eax, dword ptr[edx + 12]
+
+ // shift mod 32
+ shrd edi, esi, cl
+ shrd esi, ebx, cl
+ shrd ebx, eax, cl
+ sar eax, cl
+
+ // copy sign to high 12 bytes of stack
+ cdq
+ mov dword ptr[r + 20], edx
+ mov dword ptr[r + 24], edx
+ mov dword ptr[r + 28], edx
+
+ // store shifted amount offset by -count/32 bits
+ shr ecx, 5
+ and ecx, 3
+ neg ecx
+ mov dword ptr[r + ecx * 4 + 16], edi
+ mov dword ptr[r + ecx * 4 + 20], esi
+ mov dword ptr[r + ecx * 4 + 24], ebx
+ mov dword ptr[r + ecx * 4 + 28], eax
+ }
+#else
+ r[2] = src->lo;
+ r[3] = src->hi;
+
+ amount &= 127;
+ if (amount >= 64) {
+ r[2] = (R128_U64)((R128_S64)r[3] >> (amount - 64));
+ r[3] = (R128_U64)((R128_S64)r[3] >> 63);
+ } else if (amount) {
+ r[2] = (r[2] >> amount) | (R128_U64)((R128_S64)r[3] << (64 - amount));
+ r[3] = (R128_U64)((R128_S64)r[3] >> amount);
+ }
+#endif
+
+ dst->lo = r[2];
+ dst->hi = r[3];
+ R128_DEBUG_SET(dst);
+}
+
+void r128Add(R128 *dst, const R128 *a, const R128 *b)
+{
+ unsigned char carry = 0;
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(a != NULL);
+ R128_ASSERT(b != NULL);
+
+#if R128_INTEL && !defined(R128_STDC_ONLY)
+# if R128_64BIT
+ carry = _addcarry_u64(carry, a->lo, b->lo, &dst->lo);
+ carry = _addcarry_u64(carry, a->hi, b->hi, &dst->hi);
+# else
+ R128_U32 r0, r1, r2, r3;
+ carry = _addcarry_u32(carry, R128_R0(a), R128_R0(b), &r0);
+ carry = _addcarry_u32(carry, R128_R1(a), R128_R1(b), &r1);
+ carry = _addcarry_u32(carry, R128_R2(a), R128_R2(b), &r2);
+ carry = _addcarry_u32(carry, R128_R3(a), R128_R3(b), &r3);
+ R128_SET4(dst, r0, r1, r2, r3);
+# endif //R128_64BIT
+#else
+ {
+ R128_U64 r = a->lo + b->lo;
+ carry = r < a->lo;
+ dst->lo = r;
+ dst->hi = a->hi + b->hi + carry;
+ }
+#endif //R128_INTEL
+
+ R128_DEBUG_SET(dst);
+}
+
+void r128Sub(R128 *dst, const R128 *a, const R128 *b)
+{
+ unsigned char borrow = 0;
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(a != NULL);
+ R128_ASSERT(b != NULL);
+
+#if R128_INTEL && !defined(R128_STDC_ONLY)
+# if R128_64BIT
+ borrow = _subborrow_u64(borrow, a->lo, b->lo, &dst->lo);
+ borrow = _subborrow_u64(borrow, a->hi, b->hi, &dst->hi);
+# else
+ R128_U32 r0, r1, r2, r3;
+ borrow = _subborrow_u32(borrow, R128_R0(a), R128_R0(b), &r0);
+ borrow = _subborrow_u32(borrow, R128_R1(a), R128_R1(b), &r1);
+ borrow = _subborrow_u32(borrow, R128_R2(a), R128_R2(b), &r2);
+ borrow = _subborrow_u32(borrow, R128_R3(a), R128_R3(b), &r3);
+ R128_SET4(dst, r0, r1, r2, r3);
+# endif //R128_64BIT
+#else
+ {
+ R128_U64 r = a->lo - b->lo;
+ borrow = r > a->lo;
+ dst->lo = r;
+ dst->hi = a->hi - b->hi - borrow;
+ }
+#endif //R128_INTEL
+
+ R128_DEBUG_SET(dst);
+}
+
+void r128Mul(R128 *dst, const R128 *a, const R128 *b)
+{
+ int sign = 0;
+ R128 ta, tb, tc;
+
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(a != NULL);
+ R128_ASSERT(b != NULL);
+
+ R128_SET2(&ta, a->lo, a->hi);
+ R128_SET2(&tb, b->lo, b->hi);
+
+ if (r128IsNeg(&ta)) {
+ r128__neg(&ta, &ta);
+ sign = !sign;
+ }
+ if (r128IsNeg(&tb)) {
+ r128__neg(&tb, &tb);
+ sign = !sign;
+ }
+
+ r128__umul(&tc, &ta, &tb);
+ if (sign) {
+ r128__neg(&tc, &tc);
+ }
+
+ r128Copy(dst, &tc);
+}
+
+void r128Div(R128 *dst, const R128 *a, const R128 *b)
+{
+ int sign = 0;
+ R128 tn, td, tq;
+
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(a != NULL);
+ R128_ASSERT(b != NULL);
+
+ R128_SET2(&tn, a->lo, a->hi);
+ R128_SET2(&td, b->lo, b->hi);
+
+ if (r128IsNeg(&tn)) {
+ r128__neg(&tn, &tn);
+ sign = !sign;
+ }
+
+ if (td.lo == 0 && td.hi == 0) {
+ // divide by zero
+ if (sign) {
+ r128Copy(dst, &R128_min);
+ } else {
+ r128Copy(dst, &R128_max);
+ }
+ return;
+ } else if (r128IsNeg(&td)) {
+ r128__neg(&td, &td);
+ sign = !sign;
+ }
+
+ r128__udiv(&tq, &tn, &td);
+
+ if (sign) {
+ r128__neg(&tq, &tq);
+ }
+
+ r128Copy(dst, &tq);
+}
+
+void r128Mod(R128 *dst, const R128 *a, const R128 *b)
+{
+ int sign = 0;
+ R128 tn, td, tq;
+
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(a != NULL);
+ R128_ASSERT(b != NULL);
+
+ R128_SET2(&tn, a->lo, a->hi);
+ R128_SET2(&td, b->lo, b->hi);
+
+ if (r128IsNeg(&tn)) {
+ r128__neg(&tn, &tn);
+ sign = !sign;
+ }
+
+ if (td.lo == 0 && td.hi == 0) {
+ // divide by zero
+ if (sign) {
+ r128Copy(dst, &R128_min);
+ } else {
+ r128Copy(dst, &R128_max);
+ }
+ return;
+ } else if (r128IsNeg(&td)) {
+ r128__neg(&td, &td);
+ sign = !sign;
+ }
+
+ tq.hi = r128__umod(&tn, &td);
+ tq.lo = 0;
+
+ if (sign) {
+ tq.hi = ~tq.hi + 1;
+ }
+
+ r128Mul(&tq, &tq, b);
+ r128Sub(dst, a, &tq);
+}
+
+void r128Rsqrt(R128 *dst, const R128 *v)
+{
+ static const R128 threeHalves = { R128_LIT_U64(0x8000000000000000), 1 };
+ R128 x, est;
+ int i;
+
+ if ((R128_S64)v->hi < 0) {
+ r128Copy(dst, &R128_min);
+ return;
+ }
+
+ R128_SET2(&x, v->lo, v->hi);
+
+ // get initial estimate
+ if (x.hi) {
+ int shift = (64 + r128__clz64(x.hi)) >> 1;
+ est.lo = R128_LIT_U64(1) << shift;
+ est.hi = 0;
+ } else if (x.lo) {
+ int shift = r128__clz64(x.lo) >> 1;
+ est.hi = R128_LIT_U64(1) << shift;
+ est.lo = 0;
+ } else {
+ R128_SET2(dst, 0, 0);
+ return;
+ }
+
+ // x /= 2
+ r128Shr(&x, &x, 1);
+
+ // Newton-Raphson iterate
+ for (i = 0; i < 7; ++i) {
+ R128 newEst;
+
+ // newEst = est * (threeHalves - (x / 2) * est * est);
+ r128__umul(&newEst, &est, &est);
+ r128__umul(&newEst, &newEst, &x);
+ r128Sub(&newEst, &threeHalves, &newEst);
+ r128__umul(&newEst, &est, &newEst);
+
+ if (newEst.lo == est.lo && newEst.hi == est.hi) {
+ break;
+ }
+ R128_SET2(&est, newEst.lo, newEst.hi);
+ }
+
+ r128Copy(dst, &est);
+}
+
+void r128Sqrt(R128 *dst, const R128 *v)
+{
+ R128 x, est;
+ int i;
+
+ if ((R128_S64)v->hi < 0) {
+ r128Copy(dst, &R128_min);
+ return;
+ }
+
+ R128_SET2(&x, v->lo, v->hi);
+
+ // get initial estimate
+ if (x.hi) {
+ int shift = (63 - r128__clz64(x.hi)) >> 1;
+ r128Shr(&est, &x, shift);
+ } else if (x.lo) {
+ int shift = (1 + r128__clz64(x.lo)) >> 1;
+ r128Shl(&est, &x, shift);
+ } else {
+ R128_SET2(dst, 0, 0);
+ return;
+ }
+
+ // Newton-Raphson iterate
+ for (i = 0; i < 7; ++i) {
+ R128 newEst;
+
+ // newEst = (est + x / est) / 2
+ r128__udiv(&newEst, &x, &est);
+ r128Add(&newEst, &newEst, &est);
+ r128Shr(&newEst, &newEst, 1);
+
+ if (newEst.lo == est.lo && newEst.hi == est.hi) {
+ break;
+ }
+ R128_SET2(&est, newEst.lo, newEst.hi);
+ }
+
+ r128Copy(dst, &est);
+}
+
+int r128Cmp(const R128 *a, const R128 *b)
+{
+ R128_ASSERT(a != NULL);
+ R128_ASSERT(b != NULL);
+
+ if (a->hi == b->hi) {
+ if (a->lo == b->lo) {
+ return 0;
+ } else if (a->lo > b->lo) {
+ return 1;
+ } else {
+ return -1;
+ }
+ } else if ((R128_S64)a->hi > (R128_S64)b->hi) {
+ return 1;
+ } else {
+ return -1;
+ }
+}
+
+int r128IsNeg(const R128 *v)
+{
+ R128_ASSERT(v != NULL);
+
+ return (R128_S64)v->hi < 0;
+}
+
+void r128Min(R128 *dst, const R128 *a, const R128 *b)
+{
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(a != NULL);
+ R128_ASSERT(b != NULL);
+
+ if (r128Cmp(a, b) < 0) {
+ r128Copy(dst, a);
+ } else {
+ r128Copy(dst, b);
+ }
+}
+
+void r128Max(R128 *dst, const R128 *a, const R128 *b)
+{
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(a != NULL);
+ R128_ASSERT(b != NULL);
+
+ if (r128Cmp(a, b) > 0) {
+ r128Copy(dst, a);
+ } else {
+ r128Copy(dst, b);
+ }
+}
+
+void r128Floor(R128 *dst, const R128 *v)
+{
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(v != NULL);
+
+ if ((R128_S64)v->hi < 0) {
+ dst->hi = v->hi - (v->lo != 0);
+ } else {
+ dst->hi = v->hi;
+ }
+ dst->lo = 0;
+ R128_DEBUG_SET(dst);
+}
+
+void r128Ceil(R128 *dst, const R128 *v)
+{
+ R128_ASSERT(dst != NULL);
+ R128_ASSERT(v != NULL);
+
+ if ((R128_S64)v->hi > 0) {
+ dst->hi = v->hi + (v->lo != 0);
+ } else {
+ dst->hi = v->hi;
+ }
+ dst->lo = 0;
+ R128_DEBUG_SET(dst);
+}
+
+#endif //R128_IMPLEMENTATION
+
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-22 03:28:19 +0000