New frsqrte implementation; verified accurate.
This is similar to the old implementation, but it uses smaller tables, and handles more edge cases correctly. (hwtest coming soon.)
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@ -6,7 +6,6 @@
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#include "Common/CPUDetect.h"
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#include "Common/MathUtil.h"
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#include "Core/PowerPC/LUT_frsqrtex.h"
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#include "Core/PowerPC/Interpreter/Interpreter.h"
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using namespace MathUtil;
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@ -333,31 +332,68 @@ inline double ApproximateReciprocal(double val)
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inline double ApproximateReciprocalSquareRoot(double val)
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{
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if (val < 0)
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return PPC_NAN;
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if (val == 0.0)
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return INFINITY;
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static const int expected_base[] = {
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0x3ffa000, 0x3c29000, 0x38aa000, 0x3572000,
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0x3279000, 0x2fb7000, 0x2d26000, 0x2ac0000,
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0x2881000, 0x2665000, 0x2468000, 0x2287000,
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0x20c1000, 0x1f12000, 0x1d79000, 0x1bf4000,
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0x1a7e800, 0x17cb800, 0x1552800, 0x130c000,
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0x10f2000, 0x0eff000, 0x0d2e000, 0x0b7c000,
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0x09e5000, 0x0867000, 0x06ff000, 0x05ab800,
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0x046a000, 0x0339800, 0x0218800, 0x0105800,
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};
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static const int expected_dec[] = {
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0x7a4, 0x700, 0x670, 0x5f2,
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0x584, 0x524, 0x4cc, 0x47e,
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0x43a, 0x3fa, 0x3c2, 0x38e,
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0x35e, 0x332, 0x30a, 0x2e6,
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0x568, 0x4f3, 0x48d, 0x435,
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0x3e7, 0x3a2, 0x365, 0x32e,
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0x2fc, 0x2d0, 0x2a8, 0x283,
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0x261, 0x243, 0x226, 0x20b,
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};
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union
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{
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union {
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double valf;
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u64 vali;
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long long vali;
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};
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valf = val;
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long long mantissa = vali & ((1LL << 52) - 1);
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long long sign = vali & (1ULL << 63);
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long long exponent = vali & (0x7FFLL << 52);
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u32 fsa = vali >> 32;
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u32 idx = (fsa >> 5) % (sizeof(frsqrtex_lut) / sizeof(frsqrtex_lut[0]));
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// Special case 0
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if (mantissa == 0 && exponent == 0)
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return sign ? -INFINITY : INFINITY;
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// Special case NaN-ish numbers
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if (exponent == (0x7FFLL << 52))
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{
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if (mantissa == 0)
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return sign ? NAN : 0.0;
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return 0.0 + valf;
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}
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// Negative numbers return NaN
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if (sign)
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return NAN;
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s32 e = fsa >> (32 - 12);
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e &= 2047;
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e -= 1023;
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s32 oe = -((e + 1) / 2);
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oe -= ((e + 1) & 1);
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if (!exponent)
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{
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// "Normalize" denormal values
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do
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{
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exponent -= 1LL << 52;
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mantissa <<= 1;
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} while (!(mantissa & (1LL << 52)));
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mantissa &= (1LL << 52) - 1;
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exponent += 1LL << 52;
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}
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u32 outb = frsqrtex_lut[idx] << 20;
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u32 outa = ((oe + 1023) & 2047) << 20;
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outa |= frsqrtex_lut[idx] >> 12;
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bool odd_exponent = !(exponent & (1LL << 52));
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exponent = ((0x3FFLL << 52) - ((exponent - (0x3FELL << 52)) / 2)) & (0x7FFLL << 52);
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vali = ((u64)outa << 32) + (u64)outb;
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int i = (int)(mantissa >> 37);
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vali = sign | exponent;
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int index = i / 2048 + (odd_exponent ? 16 : 0);
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vali |= (long long)(expected_base[index] - expected_dec[index] * (i % 2048)) << 26;
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return valf;
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}
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