1 /* SPDX-License-Identifier: GPL-2.0 */ 2 #ifndef _ASM_HASH_H 3 #define _ASM_HASH_H 4 5 /* 6 * HP-PA only implements integer multiply in the FPU. However, for 7 * integer multiplies by constant, it has a number of shift-and-add 8 * (but no shift-and-subtract, sigh!) instructions that a compiler 9 * can synthesize a code sequence with. 10 * 11 * Unfortunately, GCC isn't very efficient at using them. For example 12 * it uses three instructions for "x *= 21" when only two are needed. 13 * But we can find a sequence manually. 14 */ 15 16 #define HAVE_ARCH__HASH_32 1 17 18 /* 19 * This is a multiply by GOLDEN_RATIO_32 = 0x61C88647 optimized for the 20 * PA7100 pairing rules. This is an in-order 2-way superscalar processor. 21 * Only one instruction in a pair may be a shift (by more than 3 bits), 22 * but other than that, simple ALU ops (including shift-and-add by up 23 * to 3 bits) may be paired arbitrarily. 24 * 25 * PA8xxx processors also dual-issue ALU instructions, although with 26 * fewer constraints, so this schedule is good for them, too. 27 * 28 * This 6-step sequence was found by Yevgen Voronenko's implementation 29 * of the Hcub algorithm at http://spiral.ece.cmu.edu/mcm/gen.html. 30 */ 31 static inline u32 __attribute_const__ __hash_32(u32 x) 32 { 33 u32 a, b, c; 34 35 /* 36 * Phase 1: Compute a = (x << 19) + x, 37 * b = (x << 9) + a, c = (x << 23) + b. 38 */ 39 a = x << 19; /* Two shifts can't be paired */ 40 b = x << 9; a += x; 41 c = x << 23; b += a; 42 c += b; 43 /* Phase 2: Return (b<<11) + (c<<6) + (a<<3) - c */ 44 b <<= 11; 45 a += c << 3; b -= c; 46 return (a << 3) + b; 47 } 48 49 #if BITS_PER_LONG == 64 50 51 #define HAVE_ARCH_HASH_64 1 52 53 /* 54 * Finding a good shift-and-add chain for GOLDEN_RATIO_64 is tricky, 55 * because available software for the purpose chokes on constants this 56 * large. (It's mostly designed for compiling FIR filter coefficients 57 * into FPGAs.) 58 * 59 * However, Jason Thong pointed out a work-around. The Hcub software 60 * (http://spiral.ece.cmu.edu/mcm/gen.html) is designed for *multiple* 61 * constant multiplication, and is good at finding shift-and-add chains 62 * which share common terms. 63 * 64 * Looking at 0x0x61C8864680B583EB in binary: 65 * 0110000111001000100001100100011010000000101101011000001111101011 66 * \______________/ \__________/ \_______/ \________/ 67 * \____________________________/ \____________________/ 68 * you can see the non-zero bits are divided into several well-separated 69 * blocks. Hcub can find algorithms for those terms separately, which 70 * can then be shifted and added together. 71 * 72 * Dividing the input into 2, 3 or 4 blocks, Hcub can find solutions 73 * with 10, 9 or 8 adds, respectively, making a total of 11 for the 74 * whole number. 75 * 76 * Using just two large blocks, 0xC3910C8D << 31 in the high bits, 77 * and 0xB583EB in the low bits, produces as good an algorithm as any, 78 * and with one more small shift than alternatives. 79 * 80 * The high bits are a larger number and more work to compute, as well 81 * as needing one extra cycle to shift left 31 bits before the final 82 * addition, so they are the critical path for scheduling. The low bits 83 * can fit into the scheduling slots left over. 84 */ 85 86 87 /* 88 * This _ASSIGN(dst, src) macro performs "dst = src", but prevents GCC 89 * from inferring anything about the value assigned to "dest". 90 * 91 * This prevents it from mis-optimizing certain sequences. 92 * In particular, gcc is annoyingly eager to combine consecutive shifts. 93 * Given "x <<= 19; y += x; z += x << 1;", GCC will turn this into 94 * "y += x << 19; z += x << 20;" even though the latter sequence needs 95 * an additional instruction and temporary register. 96 * 97 * Because no actual assembly code is generated, this construct is 98 * usefully portable across all GCC platforms, and so can be test-compiled 99 * on non-PA systems. 100 * 101 * In two places, additional unused input dependencies are added. This 102 * forces GCC's scheduling so it does not rearrange instructions too much. 103 * Because the PA-8xxx is out of order, I'm not sure how much this matters, 104 * but why make it more difficult for the processor than necessary? 105 */ 106 #define _ASSIGN(dst, src, ...) asm("" : "=r" (dst) : "0" (src), ##__VA_ARGS__) 107 108 /* 109 * Multiply by GOLDEN_RATIO_64 = 0x0x61C8864680B583EB using a heavily 110 * optimized shift-and-add sequence. 111 * 112 * Without the final shift, the multiply proper is 19 instructions, 113 * 10 cycles and uses only 4 temporaries. Whew! 114 * 115 * You are not expected to understand this. 116 */ 117 static __always_inline u32 __attribute_const__ 118 hash_64(u64 a, unsigned int bits) 119 { 120 u64 b, c, d; 121 122 /* 123 * Encourage GCC to move a dynamic shift to %sar early, 124 * thereby freeing up an additional temporary register. 125 */ 126 if (!__builtin_constant_p(bits)) 127 asm("" : "=q" (bits) : "0" (64 - bits)); 128 else 129 bits = 64 - bits; 130 131 _ASSIGN(b, a*5); c = a << 13; 132 b = (b << 2) + a; _ASSIGN(d, a << 17); 133 a = b + (a << 1); c += d; 134 d = a << 10; _ASSIGN(a, a << 19); 135 d = a - d; _ASSIGN(a, a << 4, "X" (d)); 136 c += b; a += b; 137 d -= c; c += a << 1; 138 a += c << 3; _ASSIGN(b, b << (7+31), "X" (c), "X" (d)); 139 a <<= 31; b += d; 140 a += b; 141 return a >> bits; 142 } 143 #undef _ASSIGN /* We're a widely-used header file, so don't litter! */ 144 145 #endif /* BITS_PER_LONG == 64 */ 146 147 #endif /* _ASM_HASH_H */ 148