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[FAST486]
Implement FPATAN. Fix the sign of the FPTAN result. Spotted by fox_anthony. svn path=/trunk/; revision=67933
This commit is contained in:
Aleksandar Andrejevic
parent
d0860613d9
commit
391168594d
1 changed files with 206 additions and 6 deletions
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@ -221,6 +221,60 @@ static const FAST486_FPU_DATA_REG FpuInverseNumberCosine[INVERSE_NUMBERS_COUNT]
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{0xD3D56292AB7E800DULL, FPU_REAL10_BIAS - 14, FALSE}, /* 1 / 9900 */
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{0xD3D56292AB7E800DULL, FPU_REAL10_BIAS - 14, FALSE}, /* 1 / 9900 */
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};
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};
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static const FAST486_FPU_DATA_REG FpuInverseNumberAtan[INVERSE_NUMBERS_COUNT] =
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{
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{0xAAAAAAAAAAAAAAAAULL, FPU_REAL10_BIAS - 1, FALSE}, /* 2 / 3 */
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{0xCCCCCCCCCCCCCCCCULL, FPU_REAL10_BIAS - 1, FALSE}, /* 4 / 5 */
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{0xDB6DB6DB6DB6DB6DULL, FPU_REAL10_BIAS - 1, FALSE}, /* 6 / 7 */
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{0xE38E38E38E38E38EULL, FPU_REAL10_BIAS - 1, FALSE}, /* 8 / 9 */
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{0xE8BA2E8BA2E8BA2EULL, FPU_REAL10_BIAS - 1, FALSE}, /* 10 / 11 */
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{0xEC4EC4EC4EC4EC4EULL, FPU_REAL10_BIAS - 1, FALSE}, /* 12 / 13 */
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{0xEEEEEEEEEEEEEEEEULL, FPU_REAL10_BIAS - 1, FALSE}, /* 14 / 15 */
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{0xF0F0F0F0F0F0F0F0ULL, FPU_REAL10_BIAS - 1, FALSE}, /* 16 / 17 */
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{0xF286BCA1AF286BCAULL, FPU_REAL10_BIAS - 1, FALSE}, /* 18 / 19 */
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{0xF3CF3CF3CF3CF3CFULL, FPU_REAL10_BIAS - 1, FALSE}, /* 20 / 21 */
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{0xF4DE9BD37A6F4DE9ULL, FPU_REAL10_BIAS - 1, FALSE}, /* 22 / 23 */
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{0xF5C28F5C28F5C28FULL, FPU_REAL10_BIAS - 1, FALSE}, /* 24 / 25 */
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{0xF684BDA12F684BDAULL, FPU_REAL10_BIAS - 1, FALSE}, /* 26 / 27 */
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{0xF72C234F72C234F7ULL, FPU_REAL10_BIAS - 1, FALSE}, /* 28 / 29 */
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{0xF7BDEF7BDEF7BDEFULL, FPU_REAL10_BIAS - 1, FALSE}, /* 30 / 31 */
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{0xF83E0F83E0F83E0FULL, FPU_REAL10_BIAS - 1, FALSE}, /* 32 / 33 */
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{0xF8AF8AF8AF8AF8AFULL, FPU_REAL10_BIAS - 1, FALSE}, /* 34 / 35 */
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{0xF914C1BACF914C1BULL, FPU_REAL10_BIAS - 1, FALSE}, /* 36 / 37 */
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{0xF96F96F96F96F96FULL, FPU_REAL10_BIAS - 1, FALSE}, /* 38 / 39 */
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{0xF9C18F9C18F9C18FULL, FPU_REAL10_BIAS - 1, FALSE}, /* 40 / 41 */
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{0xFA0BE82FA0BE82FAULL, FPU_REAL10_BIAS - 1, FALSE}, /* 42 / 43 */
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{0xFA4FA4FA4FA4FA4FULL, FPU_REAL10_BIAS - 1, FALSE}, /* 44 / 45 */
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{0xFA8D9DF51B3BEA36ULL, FPU_REAL10_BIAS - 1, FALSE}, /* 46 / 47 */
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{0xFAC687D6343EB1A1ULL, FPU_REAL10_BIAS - 1, FALSE}, /* 48 / 49 */
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{0xFAFAFAFAFAFAFAFAULL, FPU_REAL10_BIAS - 1, FALSE}, /* 50 / 51 */
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{0xFB2B78C13521CFB2ULL, FPU_REAL10_BIAS - 1, FALSE}, /* 52 / 53 */
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{0xFB586FB586FB586FULL, FPU_REAL10_BIAS - 1, FALSE}, /* 54 / 55 */
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{0xFB823EE08FB823EEULL, FPU_REAL10_BIAS - 1, FALSE}, /* 56 / 57 */
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{0xFBA9386822B63CBEULL, FPU_REAL10_BIAS - 1, FALSE}, /* 58 / 59 */
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{0xFBCDA3AC10C9714FULL, FPU_REAL10_BIAS - 1, FALSE}, /* 60 / 61 */
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{0xFBEFBEFBEFBEFBEFULL, FPU_REAL10_BIAS - 1, FALSE}, /* 62 / 63 */
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{0xFC0FC0FC0FC0FC0FULL, FPU_REAL10_BIAS - 1, FALSE}, /* 64 / 65 */
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{0xFC2DD9CA81E9131AULL, FPU_REAL10_BIAS - 1, FALSE}, /* 66 / 67 */
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{0xFC4A33F128CFC4A3ULL, FPU_REAL10_BIAS - 1, FALSE}, /* 68 / 69 */
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{0xFC64F52EDF8C9EA5ULL, FPU_REAL10_BIAS - 1, FALSE}, /* 70 / 71 */
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{0xFC7E3F1F8FC7E3F1ULL, FPU_REAL10_BIAS - 1, FALSE}, /* 72 / 73 */
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{0xFC962FC962FC962FULL, FPU_REAL10_BIAS - 1, FALSE}, /* 74 / 75 */
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{0xFCACE213F2B3884FULL, FPU_REAL10_BIAS - 1, FALSE}, /* 76 / 77 */
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{0xFCC26E2D5DF984DCULL, FPU_REAL10_BIAS - 1, FALSE}, /* 78 / 79 */
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{0xFCD6E9E06522C3F3ULL, FPU_REAL10_BIAS - 1, FALSE}, /* 80 / 81 */
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{0xFCEA68DE12818ACBULL, FPU_REAL10_BIAS - 1, FALSE}, /* 82 / 83 */
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{0xFCFCFCFCFCFCFCFCULL, FPU_REAL10_BIAS - 1, FALSE}, /* 84 / 85 */
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{0xFD0EB66FD0EB66FDULL, FPU_REAL10_BIAS - 1, FALSE}, /* 86 / 87 */
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{0xFD1FA3F47E8FD1FAULL, FPU_REAL10_BIAS - 1, FALSE}, /* 88 / 89 */
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{0xFD2FD2FD2FD2FD2FULL, FPU_REAL10_BIAS - 1, FALSE}, /* 90 / 91 */
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{0xFD3F4FD3F4FD3F4FULL, FPU_REAL10_BIAS - 1, FALSE}, /* 92 / 93 */
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{0xFD4E25B9EFD4E25BULL, FPU_REAL10_BIAS - 1, FALSE}, /* 94 / 95 */
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{0xFD5C5F02A3A0FD5CULL, FPU_REAL10_BIAS - 1, FALSE}, /* 96 / 97 */
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{0xFD6A052BF5A814AFULL, FPU_REAL10_BIAS - 1, FALSE}, /* 98 / 99 */
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{0xFD7720F353A4C0A2ULL, FPU_REAL10_BIAS - 1, FALSE}, /* 100 / 101 */
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};
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/* PRIVATE FUNCTIONS **********************************************************/
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/* PRIVATE FUNCTIONS **********************************************************/
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#ifndef FAST486_NO_FPU
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#ifndef FAST486_NO_FPU
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@ -1313,7 +1367,7 @@ Fast486FpuRemainder(PFAST486_STATE State,
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PCFAST486_FPU_DATA_REG FirstOperand,
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PCFAST486_FPU_DATA_REG FirstOperand,
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PCFAST486_FPU_DATA_REG SecondOperand,
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PCFAST486_FPU_DATA_REG SecondOperand,
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BOOLEAN RoundToNearest,
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BOOLEAN RoundToNearest,
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PFAST486_FPU_DATA_REG Result,
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PFAST486_FPU_DATA_REG Result OPTIONAL,
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PLONGLONG Quotient OPTIONAL)
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PLONGLONG Quotient OPTIONAL)
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{
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{
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BOOLEAN Success = FALSE;
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BOOLEAN Success = FALSE;
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@ -1326,10 +1380,13 @@ Fast486FpuRemainder(PFAST486_STATE State,
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State->FpuControl.Rc = RoundToNearest ? FPU_ROUND_NEAREST : FPU_ROUND_TRUNCATE;
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State->FpuControl.Rc = RoundToNearest ? FPU_ROUND_NEAREST : FPU_ROUND_TRUNCATE;
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if (!Fast486FpuToInteger(State, &Temp, &Integer)) goto Cleanup;
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if (!Fast486FpuToInteger(State, &Temp, &Integer)) goto Cleanup;
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Fast486FpuFromInteger(State, Integer, &Temp);
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if (!Fast486FpuMultiply(State, &Temp, SecondOperand, &Temp)) goto Cleanup;
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if (Result)
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if (!Fast486FpuSubtract(State, FirstOperand, &Temp, Result)) goto Cleanup;
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{
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Fast486FpuFromInteger(State, Integer, &Temp);
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if (!Fast486FpuMultiply(State, &Temp, SecondOperand, &Temp)) goto Cleanup;
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if (!Fast486FpuSubtract(State, FirstOperand, &Temp, Result)) goto Cleanup;
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}
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if (Quotient) *Quotient = Integer;
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if (Quotient) *Quotient = Integer;
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Success = TRUE;
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Success = TRUE;
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@ -1562,6 +1619,123 @@ Fast486FpuCalculateSquareRoot(PFAST486_STATE State,
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return TRUE;
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return TRUE;
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}
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}
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/*
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* Calculates arctan using Euler's formula:
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* arctan(x) = (x / (1 + x^2)) * sum { prod { (2j * x^2)
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* / ((2j + 1) * (1 + x^2)), j >= 1, j <= i }, i >= 0 }
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*/
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static inline BOOLEAN FASTCALL
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Fast486FpuCalculateArcTangent(PFAST486_STATE State,
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PCFAST486_FPU_DATA_REG Numerator,
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PCFAST486_FPU_DATA_REG Denominator,
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PFAST486_FPU_DATA_REG Result)
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{
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INT i;
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BOOLEAN Inverted = FALSE;
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FAST486_FPU_DATA_REG TempNumerator = *Numerator;
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FAST486_FPU_DATA_REG TempDenominator = *Denominator;
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FAST486_FPU_DATA_REG Value;
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FAST486_FPU_DATA_REG TempResult;
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FAST486_FPU_DATA_REG ValDivValSqP1;
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FAST486_FPU_DATA_REG SeriesElement = FpuOne;
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TempNumerator.Sign = FALSE;
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TempDenominator.Sign = FALSE;
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/* Compare the numerator to the denominator */
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if (!Fast486FpuSubtract(State, &TempNumerator, &TempDenominator, &TempResult))
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{
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return FALSE;
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}
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if ((Inverted = !TempResult.Sign))
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{
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if (!Fast486FpuDivide(State, &TempDenominator, &TempNumerator, &Value))
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{
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return FALSE;
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}
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}
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else
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{
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if (!Fast486FpuDivide(State, &TempNumerator, &TempDenominator, &Value))
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{
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return FALSE;
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}
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}
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/* Apparently, atan2(0, 0) = +/- 0 or +/- pi for some reason... */
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if (FPU_IS_INDEFINITE(&Value)) Value = FpuZero;
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/* Calculate the value divided by the value squared plus one */
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if (!Fast486FpuMultiply(State, &Value, &Value, &ValDivValSqP1)) return FALSE;
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if (!Fast486FpuAdd(State, &ValDivValSqP1, &FpuOne, &ValDivValSqP1)) return FALSE;
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if (!Fast486FpuDivide(State, &Value, &ValDivValSqP1, &ValDivValSqP1)) return FALSE;
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TempResult = FpuOne;
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for (i = 0; i < INVERSE_NUMBERS_COUNT; i++)
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{
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if (!Fast486FpuMultiply(State, &SeriesElement, &Value, &SeriesElement))
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{
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/* An exception occurred */
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return FALSE;
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}
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if (!Fast486FpuMultiply(State, &SeriesElement, &ValDivValSqP1, &SeriesElement))
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{
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/* An exception occurred */
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return FALSE;
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}
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if (!Fast486FpuMultiply(State,
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&SeriesElement,
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&FpuInverseNumberAtan[i],
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&SeriesElement))
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{
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/* An exception occurred */
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return FALSE;
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}
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if (!Fast486FpuAdd(State, &TempResult, &SeriesElement, &TempResult))
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{
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/* An exception occurred */
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return FALSE;
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}
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}
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if (!Fast486FpuMultiply(State, &TempResult, &ValDivValSqP1, &TempResult))
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{
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/* An exception occurred */
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return FALSE;
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}
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if (Inverted)
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{
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/* Since y/x is positive, arctan(y/x) = pi/2 - arctan(x/y) */
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if (!Fast486FpuSubtract(State, &FpuHalfPi, &TempResult, &TempResult)) return FALSE;
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}
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/* Adjust the sign */
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if (!(!Numerator->Sign == !Denominator->Sign)) TempResult.Sign = !TempResult.Sign;
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if (Denominator->Sign)
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{
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if (Numerator->Sign)
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{
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/* Subtract PI */
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if (!Fast486FpuSubtract(State, &TempResult, &FpuPi, &TempResult)) return FALSE;
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}
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else
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{
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/* Add PI */
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if (!Fast486FpuAdd(State, &TempResult, &FpuPi, &TempResult)) return FALSE;
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}
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}
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*Result = TempResult;
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return TRUE;
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}
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static inline BOOLEAN FASTCALL
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static inline BOOLEAN FASTCALL
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Fast486FpuLoadEnvironment(PFAST486_STATE State,
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Fast486FpuLoadEnvironment(PFAST486_STATE State,
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INT Segment,
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INT Segment,
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@ -2138,15 +2312,33 @@ FAST486_OPCODE_HANDLER(Fast486FpuOpcodeD9)
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{
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{
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FAST486_FPU_DATA_REG Sine;
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FAST486_FPU_DATA_REG Sine;
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FAST486_FPU_DATA_REG Cosine;
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FAST486_FPU_DATA_REG Cosine;
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ULONGLONG Quadrant;
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/* Compute the sine */
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/* Compute the sine */
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if (!Fast486FpuCalculateSine(State, &FPU_ST(0), &Sine)) break;
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if (!Fast486FpuCalculateSine(State, &FPU_ST(0), &Sine)) break;
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/* Normalize the angle */
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if (!Fast486FpuRemainder(State,
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&FPU_ST(0),
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&FpuHalfPi,
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FALSE,
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NULL,
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(PLONGLONG)&Quadrant))
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{
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break;
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}
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/* Normalize the quadrant number */
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Quadrant &= 3;
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/* Find the cosine by calculating sqrt(1 - sin(x) ^ 2) */
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/* Find the cosine by calculating sqrt(1 - sin(x) ^ 2) */
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if (!Fast486FpuMultiply(State, &Sine, &Sine, &Cosine)) break;
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if (!Fast486FpuMultiply(State, &Sine, &Sine, &Cosine)) break;
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if (!Fast486FpuSubtract(State, &FpuOne, &Cosine, &Cosine)) break;
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if (!Fast486FpuSubtract(State, &FpuOne, &Cosine, &Cosine)) break;
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if (!Fast486FpuCalculateSquareRoot(State, &Cosine, &Cosine)) break;
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if (!Fast486FpuCalculateSquareRoot(State, &Cosine, &Cosine)) break;
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/* Adjust the sign of the cosine */
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if (Quadrant == 1 || Quadrant == 2) Cosine.Sign = TRUE;
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/* Divide the sine by the cosine to get the tangent */
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/* Divide the sine by the cosine to get the tangent */
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if (!Fast486FpuDivide(State, &Sine, &Cosine, &FPU_ST(0))) break;
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if (!Fast486FpuDivide(State, &Sine, &Cosine, &FPU_ST(0))) break;
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FPU_UPDATE_TAG(0);
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FPU_UPDATE_TAG(0);
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@ -2159,9 +2351,17 @@ FAST486_OPCODE_HANDLER(Fast486FpuOpcodeD9)
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/* FPATAN */
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/* FPATAN */
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case 0x33:
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case 0x33:
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{
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{
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// TODO: NOT IMPLEMENTED
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if (!Fast486FpuCalculateArcTangent(State,
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UNIMPLEMENTED;
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&FPU_ST(1),
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&FPU_ST(0),
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&FPU_ST(1)))
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{
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break;
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}
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FPU_UPDATE_TAG(1);
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Fast486FpuPop(State);
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break;
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break;
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}
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}
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