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367 lines
11 KiB
367 lines
11 KiB
/*++
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Copyright (c) 2000 Microsoft Corporation
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Module Name:
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dblint.h
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Abstract:
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Support primitives for bignum package.
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--*/
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/*
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File: dblint.h. Supplement to bignum.h
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This file has declarations related to
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double-precision integers,
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such as typedefs, constants, and primitive operations.
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Before #including this, one should #define
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digit_t -- typedef for single-precision integers.
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RADIX_BITS -- Number of bits per digit_t.
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and identify which compiler one is using.
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Constants defined herein include
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DBLINT_BUILTIN -- 1 if compiler directly
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supports double integers, 0 if not.
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DBLINT_HIGH_INDEX (optional) -- When DBLINT_BUILTIN == 1,
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this is 0 if compiler stores
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the most significant half of a
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dblint_t datum first, and 1
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if compiler stores the least
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significant half first. See
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HIGH_DIGIT and MAKE_DBLINT below.
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If this is not defined, then HIGH_DIGIT
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and MAKE_DBLINT are defined using
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shifts by RADIX_BITS. If the compiler
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optimizes such shifts, then
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leave DBLINT_HIGH_INDEX undefined.
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The dblint_t type is unsigned and holds
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twice as many bits as a digit_t datum.
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If (DBLINT_BUILTIN = 1),
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then use the type already in the language.
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Otherwise (DBLINT_BUILTIN = 0)
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construct one of our own,
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using a struct with two digit_t fields.
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Let u, u1, u2 have type digit_t and
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d, d1, d2 have type dblint_t.
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The following primitives are defined,
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whether we use the built-in type or our own type:
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DBLINT(u) -- Convert u from type digit_t to type dblint_t.
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DBLINT_ADD(d1, d2) -- Sum d1 + d2.
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DBLINT_EQ(d1, d2) -- Test whether d1 == d2.
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DBLINT_GE(d1, d2) -- Test whether d1 >= d2.
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DBLINT_GT(d1, d2) -- Test whether d1 > d2.
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DBLINT_LE(d1, d2) -- Test whether d1 >= d2.
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DBLINT_LT(d1, d2) -- Test whether d1 > d2.
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DBLINT_NE(d1, d2) -- Test whether d1 <> d2.
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DBLINT_SUB(d1, d2) -- Difference d1 - d2.
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DPRODUU(u1, u2) -- Product of u1 and u2, as a dblint_t.
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HPRODUU(u1, u2) -- Most significant half of product
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of u1 and u2, as a digit_t.
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HIGH_DIGIT(d) -- Most significant half of d.
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LOW_DIGIT(d) -- Least significant half of d.
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MAKE_DBLINT(u1, u2) -- Construct a dblint_t
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whose most significant half is u1 and
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whose least significant half is u2.
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*/
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#if COMPILER == COMPILER_GCC
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#define DBLINT_BUILTIN 1
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typedef unsigned long long dblint_t;
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#define DBLINT_HIGH_INDEX 0
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/* GCC on SPARC stores high half of dblint_t first */
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#endif
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#if COMPILER == COMPILER_VC && RADIX_BITS == 32
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#define DBLINT_BUILTIN 1
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typedef unsigned __int64 dblint_t;
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#if TARGET == TARGET_ALPHA
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/* If the Alpha is using RADIX_BITS == 32,
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then use the shift instruction
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for HIGH_DIGIT and MAKE_DBLINT */
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#else
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#define DBLINT_HIGH_INDEX 1
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/* Visual C++ on ix86 stores low half of dblint_t first */
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#endif
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#endif
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#ifndef DBLINT_BUILTIN
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/* No language support -- simulate using structs */
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#define DBLINT_BUILTIN 0
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typedef struct {
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digit_t high;
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digit_t low;
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} dblint_t;
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#endif
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typedef const dblint_t dblint_tc;
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#if DBLINT_BUILTIN
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/*
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If language has support for double-length integers, use it.
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Good compilers will inline these simple operations.
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*/
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#define DBLINT(u) ((dblint_t)(u))
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#define DBLINT_ADD(d1, d2) ((d1) + (d2))
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#define DBLINT_EQ( d1, d2) ((d1) == (d2))
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#define DBLINT_GE( d1, d2) ((d1) >= (d2))
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#define DBLINT_GT( d1, d2) ((d1) > (d2))
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#define DBLINT_LE( d1, d2) ((d1) <= (d2))
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#define DBLINT_LT( d1, d2) ((d1) < (d2))
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#define DBLINT_NE( d1, d2) ((d1) != (d2))
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#define DBLINT_SUB(d1, d2) ((d1) - (d2))
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#if COMPILER == COMPILER_GCC
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#define DPRODUU(u1, u2) (DBLINT(u1) * DBLINT(u2))
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#endif
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#if COMPILER == COMPILER_VC
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/*
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A problem in Visual C/C++ 4.0 (x86 version, 1995)
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prevents proper inlining of the DPRODUU function
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if we code it in a straightforward way. Specifically,
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if we have two nearby references DPRODUU(x, y)
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and DPRODUU(x, z), where one argument (here x) is
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repeated, then the compiler calls library function
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__allmul rather than emit a MUL instruction.
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The -volatile- keyword inhibits the compiler from
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recognizing the repeated subexpression DBLINT(x),
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and circumvents the problem, alas with extra memory
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references.
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x86 version of VC 4.1 adds an __emulu function
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*/
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static inline dblint_t DPRODUU(digit_tc u1, digit_tc u2)
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{
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#if TARGET == TARGET_IX86
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#if _MFC_VER < 0x0410
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volatile digit_tc u1copy = u1, u2copy = u2;
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return DBLINT(u1copy) * DBLINT(u2copy);
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#else
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#pragma intrinsic(__emulu)
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return __emulu(u1, u2);
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#endif
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#elif TARGET == TARGET_MIPS
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#pragma intrinsic(__emulu)
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return __emulu(u1, u2);
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#else
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return DBLINT(u1) * DBLINT(u2);
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#endif
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}
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#endif
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#define LOW_DIGIT(d) ((digit_t)(d))
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#ifdef DBLINT_HIGH_INDEX
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#if DBLINT_HIGH_INDEX < 0 || DBLINT_HIGH_INDEX > 1
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#error "Illegal value of DBLINT_HIGH_INDEX"
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#endif
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static inline digit_t HIGH_DIGIT(dblint_tc d)
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{
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dblint_tc dcopy = d;
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return ((digit_tc*)&dcopy)[DBLINT_HIGH_INDEX];
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}
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static inline dblint_t MAKE_DBLINT(digit_tc high, digit_tc low)
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{
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dblint_t build = low;
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((digit_t*)&build)[DBLINT_HIGH_INDEX] = high;
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return build;
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}
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#else /* DBLINT_HIGH_INDEX */
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#define HIGH_DIGIT(d) ((digit_t)((d) >> RADIX_BITS))
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#define MAKE_DBLINT(high, low) \
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( (DBLINT(high) << RADIX_BITS) | DBLINT(low) )
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#endif /* DBLINT_HIGH_INDEX */
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#else /* DBLINT_BUILTIN */
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static inline dblint_t DBLINT(digit_tc d)
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{
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dblint_t answer;
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answer.low = d;
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answer.high = 0;
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return answer;
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}
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static inline dblint_t DBLINT_ADD(dblint_tc d1, dblint_tc d2)
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{
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dblint_t answer;
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answer.low = d1.low + d2.low;
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answer.high = d1.high + d2.high + (answer.low < d1.low);
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return answer;
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}
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static inline BOOL DBLINT_EQ(dblint_tc d1, dblint_tc d2)
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{
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return (d1.high == d2.high && d1.low == d2.low);
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}
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static inline BOOL DBLINT_GE(dblint_tc d1, dblint_tc d2)
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{
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return (d1.high == d2.high ? d1.low >= d2.low
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: d1.high >= d2.high);
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}
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static inline BOOL DBLINT_GT(dblint_tc d1, dblint_tc d2)
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{
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return (d1.high == d2.high ? d1.low > d2.low
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: d1.high > d2.high);
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}
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#define DBLINT_LE(d1, d2) DBLINT_GE(d2, d1)
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#define DBLINT_LT(d1, d2) DBLINT_GT(d2, d1)
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static inline BOOL DBLINT_NE(dblint_tc d1, dblint_tc d2)
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{
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return (d1.high != d2.high || d1.low != d2.low);
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}
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static inline dblint_t DBLINT_SUB(dblint_tc d1, dblint_tc d2)
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{
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dblint_t answer;
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answer.low = d1.low - d2.low;
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answer.high = d1.high - d2.high - (d1.low < d2.low);
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return answer;
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}
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#define HIGH_DIGIT(d) ((d).high)
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#define LOW_DIGIT(d) ((d).low)
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static inline dblint_t MAKE_DBLINT(digit_tc high, digit_tc low)
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{
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dblint_t answer;
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answer.low = low;
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answer.high = high;
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return answer;
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}
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#if TARGET == TARGET_ALPHA
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#pragma intrinsic(__UMULH)
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#define HPRODUU(u1, u2) __UMULH(u1, u2)
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static inline dblint_t DPRODUU(digit_tc u1, digit_tc u2)
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{
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dblint_t answer;
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answer.high = HPRODUU(u1, u2); /* Upper product */
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answer.low = u1*u2; /* Lower product */
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return answer;
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}
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#else
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static inline dblint_t DPRODUU(digit_tc u1, digit_tc u2)
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/*
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Multiply two single-precision operands,
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return double precision product.
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This will normally be replaced by an assembly language routine.
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unless the top half of the product is available in C.
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*/
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{
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dblint_t answer;
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digit_tc u1bot = u1 & RADIX_HALFMASK_BOTTOM, u1top = u1 >> HALF_RADIX_BITS;
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digit_tc u2bot = u2 & RADIX_HALFMASK_BOTTOM, u2top = u2 >> HALF_RADIX_BITS;
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digit_tc low = u1bot * u2bot;
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digit_t mid1 = u1bot * u2top;
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digit_tc mid2 = u1top * u2bot;
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digit_tc high = u1top * u2top;
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/*
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Each half-word product is bounded by
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(SQRT(RADIX) - 1)^2 = RADIX - 2*SQRT(RADIX) + 1,
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so we can add two half-word operands
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to any product without risking integer overflow.
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*/
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mid1 += (mid2 & RADIX_HALFMASK_BOTTOM) + (low >> HALF_RADIX_BITS);
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answer.high = high + (mid1 >> HALF_RADIX_BITS)
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+ (mid2 >> HALF_RADIX_BITS);
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answer.low = (low & RADIX_HALFMASK_BOTTOM) + (mid1 << HALF_RADIX_BITS);
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return answer;
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}
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#endif /* multiplication */
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#endif /* DBLINT_BUILTIN */
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#ifndef HPRODUU
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#define HPRODUU(u1, u2) HIGH_DIGIT(DPRODUU(u1, u2))
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#endif
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/*
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The DBLINT_SUM, MULTIPLY_ADD1. MULTIPLY_ADD2
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functions take single-length (digit_t) operands and
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return double-length (dblint_t) results.
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Overflow is impossible.
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*/
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#if TARGET == TARGET_ALPHA && RADIX_BITS == 64 && !DBLINT_BUILT_IN
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static inline dblint_t DBLINT_SUM(digit_tc d1, digit_tc d2)
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{
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dblint_t answer;
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answer.low = d1 + d2;
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answer.high = (answer.low < d1);
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return answer;
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}
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static inline dblint_t MULTIPLY_ADD1(digit_tc d1, digit_tc d2, digit_tc d3)
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{
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dblint_t answer;
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digit_t ah, al;
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al = d1*d2;
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ah = __UMULH(d1, d2);
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al += d3;
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answer.high = ah + (al < d3);
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answer.low = al;
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return answer;
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}
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static inline dblint_t MULTIPLY_ADD2(digit_tc d1, digit_tc d2,
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digit_tc d3, digit_tc d4)
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{
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dblint_t answer;
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digit_t ah, al, bh, bl;
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al = d1*d2;
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ah = __UMULH(d1, d2);
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bl = d3 + d4;
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bh = (bl < d3);
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answer.low = al + bl;
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answer.high = ah + bh + (answer.low < al);
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return answer;
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}
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#else
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#define DBLINT_SUM(d1, d2) DBLINT_ADD(DBLINT(d1), DBLINT(d2))
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/* d1 + d2 */
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#define MULTIPLY_ADD1(d1, d2, d3) \
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DBLINT_ADD(DPRODUU(d1, d2), DBLINT(d3));
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/* d1*d2 + d3 */
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#define MULTIPLY_ADD2(d1, d2, d3, d4) \
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DBLINT_ADD(DBLINT_ADD(DPRODUU(d1, d2), DBLINT(d3)), \
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DBLINT(d4))
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/* d1*d2 + d3 + d4 */
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#endif
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