return target;
}
-/* To evaluate powi(x,n), the floating point value x raised to the
- constant integer exponent n, we use a hybrid algorithm that
- combines the "window method" with look-up tables. For an
- introduction to exponentiation algorithms and "addition chains",
- see section 4.6.3, "Evaluation of Powers" of Donald E. Knuth,
- "Seminumerical Algorithms", Vol. 2, "The Art of Computer Programming",
- 3rd Edition, 1998, and Daniel M. Gordon, "A Survey of Fast Exponentiation
- Methods", Journal of Algorithms, Vol. 27, pp. 129-146, 1998. */
-
-/* Provide a default value for POWI_MAX_MULTS, the maximum number of
- multiplications to inline before calling the system library's pow
- function. powi(x,n) requires at worst 2*bits(n)-2 multiplications,
- so this default never requires calling pow, powf or powl. */
-
-#ifndef POWI_MAX_MULTS
-#define POWI_MAX_MULTS (2*HOST_BITS_PER_WIDE_INT-2)
-#endif
-
-/* The size of the "optimal power tree" lookup table. All
- exponents less than this value are simply looked up in the
- powi_table below. This threshold is also used to size the
- cache of pseudo registers that hold intermediate results. */
-#define POWI_TABLE_SIZE 256
-
-/* The size, in bits of the window, used in the "window method"
- exponentiation algorithm. This is equivalent to a radix of
- (1<<POWI_WINDOW_SIZE) in the corresponding "m-ary method". */
-#define POWI_WINDOW_SIZE 3
-
-/* The following table is an efficient representation of an
- "optimal power tree". For each value, i, the corresponding
- value, j, in the table states than an optimal evaluation
- sequence for calculating pow(x,i) can be found by evaluating
- pow(x,j)*pow(x,i-j). An optimal power tree for the first
- 100 integers is given in Knuth's "Seminumerical algorithms". */
-
-static const unsigned char powi_table[POWI_TABLE_SIZE] =
- {
- 0, 1, 1, 2, 2, 3, 3, 4, /* 0 - 7 */
- 4, 6, 5, 6, 6, 10, 7, 9, /* 8 - 15 */
- 8, 16, 9, 16, 10, 12, 11, 13, /* 16 - 23 */
- 12, 17, 13, 18, 14, 24, 15, 26, /* 24 - 31 */
- 16, 17, 17, 19, 18, 33, 19, 26, /* 32 - 39 */
- 20, 25, 21, 40, 22, 27, 23, 44, /* 40 - 47 */
- 24, 32, 25, 34, 26, 29, 27, 44, /* 48 - 55 */
- 28, 31, 29, 34, 30, 60, 31, 36, /* 56 - 63 */
- 32, 64, 33, 34, 34, 46, 35, 37, /* 64 - 71 */
- 36, 65, 37, 50, 38, 48, 39, 69, /* 72 - 79 */
- 40, 49, 41, 43, 42, 51, 43, 58, /* 80 - 87 */
- 44, 64, 45, 47, 46, 59, 47, 76, /* 88 - 95 */
- 48, 65, 49, 66, 50, 67, 51, 66, /* 96 - 103 */
- 52, 70, 53, 74, 54, 104, 55, 74, /* 104 - 111 */
- 56, 64, 57, 69, 58, 78, 59, 68, /* 112 - 119 */
- 60, 61, 61, 80, 62, 75, 63, 68, /* 120 - 127 */
- 64, 65, 65, 128, 66, 129, 67, 90, /* 128 - 135 */
- 68, 73, 69, 131, 70, 94, 71, 88, /* 136 - 143 */
- 72, 128, 73, 98, 74, 132, 75, 121, /* 144 - 151 */
- 76, 102, 77, 124, 78, 132, 79, 106, /* 152 - 159 */
- 80, 97, 81, 160, 82, 99, 83, 134, /* 160 - 167 */
- 84, 86, 85, 95, 86, 160, 87, 100, /* 168 - 175 */
- 88, 113, 89, 98, 90, 107, 91, 122, /* 176 - 183 */
- 92, 111, 93, 102, 94, 126, 95, 150, /* 184 - 191 */
- 96, 128, 97, 130, 98, 133, 99, 195, /* 192 - 199 */
- 100, 128, 101, 123, 102, 164, 103, 138, /* 200 - 207 */
- 104, 145, 105, 146, 106, 109, 107, 149, /* 208 - 215 */
- 108, 200, 109, 146, 110, 170, 111, 157, /* 216 - 223 */
- 112, 128, 113, 130, 114, 182, 115, 132, /* 224 - 231 */
- 116, 200, 117, 132, 118, 158, 119, 206, /* 232 - 239 */
- 120, 240, 121, 162, 122, 147, 123, 152, /* 240 - 247 */
- 124, 166, 125, 214, 126, 138, 127, 153, /* 248 - 255 */
- };
-
-
-/* Return the number of multiplications required to calculate
- powi(x,n) where n is less than POWI_TABLE_SIZE. This is a
- subroutine of powi_cost. CACHE is an array indicating
- which exponents have already been calculated. */
-
-static int
-powi_lookup_cost (unsigned HOST_WIDE_INT n, bool *cache)
-{
- /* If we've already calculated this exponent, then this evaluation
- doesn't require any additional multiplications. */
- if (cache[n])
- return 0;
-
- cache[n] = true;
- return powi_lookup_cost (n - powi_table[n], cache)
- + powi_lookup_cost (powi_table[n], cache) + 1;
-}
-
-/* Return the number of multiplications required to calculate
- powi(x,n) for an arbitrary x, given the exponent N. This
- function needs to be kept in sync with expand_powi below. */
-
-static int
-powi_cost (HOST_WIDE_INT n)
-{
- bool cache[POWI_TABLE_SIZE];
- unsigned HOST_WIDE_INT digit;
- unsigned HOST_WIDE_INT val;
- int result;
-
- if (n == 0)
- return 0;
-
- /* Ignore the reciprocal when calculating the cost. */
- val = (n < 0) ? -n : n;
-
- /* Initialize the exponent cache. */
- memset (cache, 0, POWI_TABLE_SIZE * sizeof (bool));
- cache[1] = true;
-
- result = 0;
-
- while (val >= POWI_TABLE_SIZE)
- {
- if (val & 1)
- {
- digit = val & ((1 << POWI_WINDOW_SIZE) - 1);
- result += powi_lookup_cost (digit, cache)
- + POWI_WINDOW_SIZE + 1;
- val >>= POWI_WINDOW_SIZE;
- }
- else
- {
- val >>= 1;
- result++;
- }
- }
-
- return result + powi_lookup_cost (val, cache);
-}
-
-/* Recursive subroutine of expand_powi. This function takes the array,
- CACHE, of already calculated exponents and an exponent N and returns
- an RTX that corresponds to CACHE[1]**N, as calculated in mode MODE. */
-
-static rtx
-expand_powi_1 (enum machine_mode mode, unsigned HOST_WIDE_INT n, rtx *cache)
-{
- unsigned HOST_WIDE_INT digit;
- rtx target, result;
- rtx op0, op1;
-
- if (n < POWI_TABLE_SIZE)
- {
- if (cache[n])
- return cache[n];
-
- target = gen_reg_rtx (mode);
- cache[n] = target;
-
- op0 = expand_powi_1 (mode, n - powi_table[n], cache);
- op1 = expand_powi_1 (mode, powi_table[n], cache);
- }
- else if (n & 1)
- {
- target = gen_reg_rtx (mode);
- digit = n & ((1 << POWI_WINDOW_SIZE) - 1);
- op0 = expand_powi_1 (mode, n - digit, cache);
- op1 = expand_powi_1 (mode, digit, cache);
- }
- else
- {
- target = gen_reg_rtx (mode);
- op0 = expand_powi_1 (mode, n >> 1, cache);
- op1 = op0;
- }
-
- result = expand_mult (mode, op0, op1, target, 0);
- if (result != target)
- emit_move_insn (target, result);
- return target;
-}
-
-/* Expand the RTL to evaluate powi(x,n) in mode MODE. X is the
- floating point operand in mode MODE, and N is the exponent. This
- function needs to be kept in sync with powi_cost above. */
-
-static rtx
-expand_powi (rtx x, enum machine_mode mode, HOST_WIDE_INT n)
-{
- rtx cache[POWI_TABLE_SIZE];
- rtx result;
-
- if (n == 0)
- return CONST1_RTX (mode);
-
- memset (cache, 0, sizeof (cache));
- cache[1] = x;
-
- result = expand_powi_1 (mode, (n < 0) ? -n : n, cache);
-
- /* If the original exponent was negative, reciprocate the result. */
- if (n < 0)
- result = expand_binop (mode, sdiv_optab, CONST1_RTX (mode),
- result, NULL_RTX, 0, OPTAB_LIB_WIDEN);
-
- return result;
-}
-
-/* Fold a builtin function call to pow, powf, or powl into a series of sqrts or
- cbrts. Return NULL_RTX if no simplification can be made or expand the tree
- if we can simplify it. */
-static rtx
-expand_builtin_pow_root (location_t loc, tree arg0, tree arg1, tree type,
- rtx subtarget)
-{
- if (TREE_CODE (arg1) == REAL_CST
- && !TREE_OVERFLOW (arg1)
- && flag_unsafe_math_optimizations)
- {
- enum machine_mode mode = TYPE_MODE (type);
- tree sqrtfn = mathfn_built_in (type, BUILT_IN_SQRT);
- tree cbrtfn = mathfn_built_in (type, BUILT_IN_CBRT);
- REAL_VALUE_TYPE c = TREE_REAL_CST (arg1);
- tree op = NULL_TREE;
-
- if (sqrtfn)
- {
- /* Optimize pow (x, 0.5) into sqrt. */
- if (REAL_VALUES_EQUAL (c, dconsthalf))
- op = build_call_nofold_loc (loc, sqrtfn, 1, arg0);
-
- /* Don't do this optimization if we don't have a sqrt insn. */
- else if (optab_handler (sqrt_optab, mode) != CODE_FOR_nothing)
- {
- REAL_VALUE_TYPE dconst1_4 = dconst1;
- REAL_VALUE_TYPE dconst3_4;
- SET_REAL_EXP (&dconst1_4, REAL_EXP (&dconst1_4) - 2);
-
- real_from_integer (&dconst3_4, VOIDmode, 3, 0, 0);
- SET_REAL_EXP (&dconst3_4, REAL_EXP (&dconst3_4) - 2);
-
- /* Optimize pow (x, 0.25) into sqrt (sqrt (x)). Assume on most
- machines that a builtin sqrt instruction is smaller than a
- call to pow with 0.25, so do this optimization even if
- -Os. */
- if (REAL_VALUES_EQUAL (c, dconst1_4))
- {
- op = build_call_nofold_loc (loc, sqrtfn, 1, arg0);
- op = build_call_nofold_loc (loc, sqrtfn, 1, op);
- }
-
- /* Optimize pow (x, 0.75) = sqrt (x) * sqrt (sqrt (x)) unless we
- are optimizing for space. */
- else if (optimize_insn_for_speed_p ()
- && !TREE_SIDE_EFFECTS (arg0)
- && REAL_VALUES_EQUAL (c, dconst3_4))
- {
- tree sqrt1 = build_call_expr_loc (loc, sqrtfn, 1, arg0);
- tree sqrt2 = builtin_save_expr (sqrt1);
- tree sqrt3 = build_call_expr_loc (loc, sqrtfn, 1, sqrt1);
- op = fold_build2_loc (loc, MULT_EXPR, type, sqrt2, sqrt3);
- }
- }
- }
-
- /* Check whether we can do cbrt insstead of pow (x, 1./3.) and
- cbrt/sqrts instead of pow (x, 1./6.). */
- if (cbrtfn && ! op
- && (tree_expr_nonnegative_p (arg0) || !HONOR_NANS (mode)))
- {
- /* First try 1/3. */
- REAL_VALUE_TYPE dconst1_3
- = real_value_truncate (mode, dconst_third ());
-
- if (REAL_VALUES_EQUAL (c, dconst1_3))
- op = build_call_nofold_loc (loc, cbrtfn, 1, arg0);
-
- /* Now try 1/6. */
- else if (optimize_insn_for_speed_p ()
- && optab_handler (sqrt_optab, mode) != CODE_FOR_nothing)
- {
- REAL_VALUE_TYPE dconst1_6 = dconst1_3;
- SET_REAL_EXP (&dconst1_6, REAL_EXP (&dconst1_6) - 1);
-
- if (REAL_VALUES_EQUAL (c, dconst1_6))
- {
- op = build_call_nofold_loc (loc, sqrtfn, 1, arg0);
- op = build_call_nofold_loc (loc, cbrtfn, 1, op);
- }
- }
- }
-
- if (op)
- return expand_expr (op, subtarget, mode, EXPAND_NORMAL);
- }
-
- return NULL_RTX;
-}
-
-/* Expand a call to the pow built-in mathematical function. Return NULL_RTX if
- a normal call should be emitted rather than expanding the function
- in-line. EXP is the expression that is a call to the builtin
- function; if convenient, the result should be placed in TARGET. */
-
-static rtx
-expand_builtin_pow (tree exp, rtx target, rtx subtarget)
-{
- tree arg0, arg1;
- tree fn, narg0;
- tree type = TREE_TYPE (exp);
- REAL_VALUE_TYPE cint, c, c2;
- HOST_WIDE_INT n;
- rtx op, op2;
- enum machine_mode mode = TYPE_MODE (type);
-
- if (! validate_arglist (exp, REAL_TYPE, REAL_TYPE, VOID_TYPE))
- return NULL_RTX;
-
- arg0 = CALL_EXPR_ARG (exp, 0);
- arg1 = CALL_EXPR_ARG (exp, 1);
-
- if (TREE_CODE (arg1) != REAL_CST
- || TREE_OVERFLOW (arg1))
- return expand_builtin_mathfn_2 (exp, target, subtarget);
-
- /* Handle constant exponents. */
-
- /* For integer valued exponents we can expand to an optimal multiplication
- sequence using expand_powi. */
- c = TREE_REAL_CST (arg1);
- n = real_to_integer (&c);
- real_from_integer (&cint, VOIDmode, n, n < 0 ? -1 : 0, 0);
- if (real_identical (&c, &cint)
- && ((n >= -1 && n <= 2)
- || (flag_unsafe_math_optimizations
- && optimize_insn_for_speed_p ()
- && powi_cost (n) <= POWI_MAX_MULTS)))
- {
- op = expand_expr (arg0, subtarget, VOIDmode, EXPAND_NORMAL);
- if (n != 1)
- {
- op = force_reg (mode, op);
- op = expand_powi (op, mode, n);
- }
- return op;
- }
-
- narg0 = builtin_save_expr (arg0);
-
- /* If the exponent is not integer valued, check if it is half of an integer.
- In this case we can expand to sqrt (x) * x**(n/2). */
- fn = mathfn_built_in (type, BUILT_IN_SQRT);
- if (fn != NULL_TREE)
- {
- real_arithmetic (&c2, MULT_EXPR, &c, &dconst2);
- n = real_to_integer (&c2);
- real_from_integer (&cint, VOIDmode, n, n < 0 ? -1 : 0, 0);
- if (real_identical (&c2, &cint)
- && ((flag_unsafe_math_optimizations
- && optimize_insn_for_speed_p ()
- && powi_cost (n/2) <= POWI_MAX_MULTS)
- /* Even the c == 0.5 case cannot be done unconditionally
- when we need to preserve signed zeros, as
- pow (-0, 0.5) is +0, while sqrt(-0) is -0. */
- || (!HONOR_SIGNED_ZEROS (mode) && n == 1)
- /* For c == 1.5 we can assume that x * sqrt (x) is always
- smaller than pow (x, 1.5) if sqrt will not be expanded
- as a call. */
- || (n == 3
- && optab_handler (sqrt_optab, mode) != CODE_FOR_nothing)))
- {
- tree call_expr = build_call_nofold_loc (EXPR_LOCATION (exp), fn, 1,
- narg0);
- /* Use expand_expr in case the newly built call expression
- was folded to a non-call. */
- op = expand_expr (call_expr, subtarget, mode, EXPAND_NORMAL);
- if (n != 1)
- {
- op2 = expand_expr (narg0, subtarget, VOIDmode, EXPAND_NORMAL);
- op2 = force_reg (mode, op2);
- op2 = expand_powi (op2, mode, abs (n / 2));
- op = expand_simple_binop (mode, MULT, op, op2, NULL_RTX,
- 0, OPTAB_LIB_WIDEN);
- /* If the original exponent was negative, reciprocate the
- result. */
- if (n < 0)
- op = expand_binop (mode, sdiv_optab, CONST1_RTX (mode),
- op, NULL_RTX, 0, OPTAB_LIB_WIDEN);
- }
- return op;
- }
- }
-
- /* Check whether we can do a series of sqrt or cbrt's instead of the pow
- call. */
- op = expand_builtin_pow_root (EXPR_LOCATION (exp), arg0, arg1, type,
- subtarget);
- if (op)
- return op;
-
- /* Try if the exponent is a third of an integer. In this case
- we can expand to x**(n/3) * cbrt(x)**(n%3). As cbrt (x) is
- different from pow (x, 1./3.) due to rounding and behavior
- with negative x we need to constrain this transformation to
- unsafe math and positive x or finite math. */
- fn = mathfn_built_in (type, BUILT_IN_CBRT);
- if (fn != NULL_TREE
- && flag_unsafe_math_optimizations
- && (tree_expr_nonnegative_p (arg0)
- || !HONOR_NANS (mode)))
- {
- REAL_VALUE_TYPE dconst3;
- real_from_integer (&dconst3, VOIDmode, 3, 0, 0);
- real_arithmetic (&c2, MULT_EXPR, &c, &dconst3);
- real_round (&c2, mode, &c2);
- n = real_to_integer (&c2);
- real_from_integer (&cint, VOIDmode, n, n < 0 ? -1 : 0, 0);
- real_arithmetic (&c2, RDIV_EXPR, &cint, &dconst3);
- real_convert (&c2, mode, &c2);
- if (real_identical (&c2, &c)
- && ((optimize_insn_for_speed_p ()
- && powi_cost (n/3) <= POWI_MAX_MULTS)
- || n == 1))
- {
- tree call_expr = build_call_nofold_loc (EXPR_LOCATION (exp), fn, 1,
- narg0);
- op = expand_builtin (call_expr, NULL_RTX, subtarget, mode, 0);
- if (abs (n) % 3 == 2)
- op = expand_simple_binop (mode, MULT, op, op, op,
- 0, OPTAB_LIB_WIDEN);
- if (n != 1)
- {
- op2 = expand_expr (narg0, subtarget, VOIDmode, EXPAND_NORMAL);
- op2 = force_reg (mode, op2);
- op2 = expand_powi (op2, mode, abs (n / 3));
- op = expand_simple_binop (mode, MULT, op, op2, NULL_RTX,
- 0, OPTAB_LIB_WIDEN);
- /* If the original exponent was negative, reciprocate the
- result. */
- if (n < 0)
- op = expand_binop (mode, sdiv_optab, CONST1_RTX (mode),
- op, NULL_RTX, 0, OPTAB_LIB_WIDEN);
- }
- return op;
- }
- }
-
- /* Fall back to optab expansion. */
- return expand_builtin_mathfn_2 (exp, target, subtarget);
-}
-
/* Expand a call to the powi built-in mathematical function. Return NULL_RTX if
a normal call should be emitted rather than expanding the function
in-line. EXP is the expression that is a call to the builtin
arg1 = CALL_EXPR_ARG (exp, 1);
mode = TYPE_MODE (TREE_TYPE (exp));
- /* Handle constant power. */
-
- if (TREE_CODE (arg1) == INTEGER_CST
- && !TREE_OVERFLOW (arg1))
- {
- HOST_WIDE_INT n = TREE_INT_CST_LOW (arg1);
-
- /* If the exponent is -1, 0, 1 or 2, then expand_powi is exact.
- Otherwise, check the number of multiplications required. */
- if ((TREE_INT_CST_HIGH (arg1) == 0
- || TREE_INT_CST_HIGH (arg1) == -1)
- && ((n >= -1 && n <= 2)
- || (optimize_insn_for_speed_p ()
- && powi_cost (n) <= POWI_MAX_MULTS)))
- {
- op0 = expand_expr (arg0, NULL_RTX, VOIDmode, EXPAND_NORMAL);
- op0 = force_reg (mode, op0);
- return expand_powi (op0, mode, n);
- }
- }
-
/* Emit a libcall to libgcc. */
/* Mode of the 2nd argument must match that of an int. */
return target;
break;
- CASE_FLT_FN (BUILT_IN_POW):
- target = expand_builtin_pow (exp, target, subtarget);
- if (target)
- return target;
- break;
-
CASE_FLT_FN (BUILT_IN_POWI):
target = expand_builtin_powi (exp, target);
if (target)
CASE_FLT_FN (BUILT_IN_FMOD):
CASE_FLT_FN (BUILT_IN_REMAINDER):
CASE_FLT_FN (BUILT_IN_DREM):
+ CASE_FLT_FN (BUILT_IN_POW):
target = expand_builtin_mathfn_2 (exp, target, subtarget);
if (target)
return target;
projects / gcc.git / commitdiff