float32 float32_rem( float32 a, float32 b STATUS_PARAM )
{
- flag aSign, bSign, zSign;
+ flag aSign, zSign;
int16 aExp, bExp, expDiff;
bits32 aSig, bSig;
bits32 q;
aSign = extractFloat32Sign( a );
bSig = extractFloat32Frac( b );
bExp = extractFloat32Exp( b );
- bSign = extractFloat32Sign( b );
if ( aExp == 0xFF ) {
if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
return propagateFloat32NaN( a, b STATUS_VAR );
}
+/*----------------------------------------------------------------------------
+| Returns the binary exponential of the single-precision floating-point value
+| `a'. The operation is performed according to the IEC/IEEE Standard for
+| Binary Floating-Point Arithmetic.
+|
+| Uses the following identities:
+|
+| 1. -------------------------------------------------------------------------
+| x x*ln(2)
+| 2 = e
+|
+| 2. -------------------------------------------------------------------------
+| 2 3 4 5 n
+| x x x x x x x
+| e = 1 + --- + --- + --- + --- + --- + ... + --- + ...
+| 1! 2! 3! 4! 5! n!
+*----------------------------------------------------------------------------*/
+
+static const float64 float32_exp2_coefficients[15] =
+{
+ make_float64( 0x3ff0000000000000ll ), /* 1 */
+ make_float64( 0x3fe0000000000000ll ), /* 2 */
+ make_float64( 0x3fc5555555555555ll ), /* 3 */
+ make_float64( 0x3fa5555555555555ll ), /* 4 */
+ make_float64( 0x3f81111111111111ll ), /* 5 */
+ make_float64( 0x3f56c16c16c16c17ll ), /* 6 */
+ make_float64( 0x3f2a01a01a01a01all ), /* 7 */
+ make_float64( 0x3efa01a01a01a01all ), /* 8 */
+ make_float64( 0x3ec71de3a556c734ll ), /* 9 */
+ make_float64( 0x3e927e4fb7789f5cll ), /* 10 */
+ make_float64( 0x3e5ae64567f544e4ll ), /* 11 */
+ make_float64( 0x3e21eed8eff8d898ll ), /* 12 */
+ make_float64( 0x3de6124613a86d09ll ), /* 13 */
+ make_float64( 0x3da93974a8c07c9dll ), /* 14 */
+ make_float64( 0x3d6ae7f3e733b81fll ), /* 15 */
+};
+
+float32 float32_exp2( float32 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp;
+ bits32 aSig;
+ float64 r, x, xn;
+ int i;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+
+ if ( aExp == 0xFF) {
+ if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR );
+ return (aSign) ? float32_zero : a;
+ }
+ if (aExp == 0) {
+ if (aSig == 0) return float32_one;
+ }
+
+ float_raise( float_flag_inexact STATUS_VAR);
+
+ /* ******************************* */
+ /* using float64 for approximation */
+ /* ******************************* */
+ x = float32_to_float64(a STATUS_VAR);
+ x = float64_mul(x, float64_ln2 STATUS_VAR);
+
+ xn = x;
+ r = float64_one;
+ for (i = 0 ; i < 15 ; i++) {
+ float64 f;
+
+ f = float64_mul(xn, float32_exp2_coefficients[i] STATUS_VAR);
+ r = float64_add(r, f STATUS_VAR);
+
+ xn = float64_mul(xn, x STATUS_VAR);
+ }
+
+ return float64_to_float32(r, status);
+}
+
/*----------------------------------------------------------------------------
| Returns the binary log of the single-precision floating-point value `a'.
| The operation is performed according to the IEC/IEEE Standard for Binary
}
+
+/*----------------------------------------------------------------------------
+| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
+| half-precision floating-point value, returning the result. After being
+| shifted into the proper positions, the three fields are simply added
+| together to form the result. This means that any integer portion of `zSig'
+| will be added into the exponent. Since a properly normalized significand
+| will have an integer portion equal to 1, the `zExp' input should be 1 less
+| than the desired result exponent whenever `zSig' is a complete, normalized
+| significand.
+*----------------------------------------------------------------------------*/
+static bits16 packFloat16(flag zSign, int16 zExp, bits16 zSig)
+{
+ return (((bits32)zSign) << 15) + (((bits32)zExp) << 10) + zSig;
+}
+
+/* Half precision floats come in two formats: standard IEEE and "ARM" format.
+ The latter gains extra exponent range by omitting the NaN/Inf encodings. */
+
+float32 float16_to_float32( bits16 a, flag ieee STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp;
+ bits32 aSig;
+
+ aSign = a >> 15;
+ aExp = (a >> 10) & 0x1f;
+ aSig = a & 0x3ff;
+
+ if (aExp == 0x1f && ieee) {
+ if (aSig) {
+ /* Make sure correct exceptions are raised. */
+ float32ToCommonNaN(a STATUS_VAR);
+ aSig |= 0x200;
+ }
+ return packFloat32(aSign, 0xff, aSig << 13);
+ }
+ if (aExp == 0) {
+ int8 shiftCount;
+
+ if (aSig == 0) {
+ return packFloat32(aSign, 0, 0);
+ }
+
+ shiftCount = countLeadingZeros32( aSig ) - 21;
+ aSig = aSig << shiftCount;
+ aExp = -shiftCount;
+ }
+ return packFloat32( aSign, aExp + 0x70, aSig << 13);
+}
+
+bits16 float32_to_float16( float32 a, flag ieee STATUS_PARAM)
+{
+ flag aSign;
+ int16 aExp;
+ bits32 aSig;
+ bits32 mask;
+ bits32 increment;
+ int8 roundingMode;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ if ( aExp == 0xFF ) {
+ if (aSig) {
+ /* Make sure correct exceptions are raised. */
+ float32ToCommonNaN(a STATUS_VAR);
+ aSig |= 0x00400000;
+ }
+ return packFloat16(aSign, 0x1f, aSig >> 13);
+ }
+ if (aExp == 0 && aSign == 0) {
+ return packFloat16(aSign, 0, 0);
+ }
+ /* Decimal point between bits 22 and 23. */
+ aSig |= 0x00800000;
+ aExp -= 0x7f;
+ if (aExp < -14) {
+ mask = 0x007fffff;
+ if (aExp < -24) {
+ aExp = -25;
+ } else {
+ mask >>= 24 + aExp;
+ }
+ } else {
+ mask = 0x00001fff;
+ }
+ if (aSig & mask) {
+ float_raise( float_flag_underflow STATUS_VAR );
+ roundingMode = STATUS(float_rounding_mode);
+ switch (roundingMode) {
+ case float_round_nearest_even:
+ increment = (mask + 1) >> 1;
+ if ((aSig & mask) == increment) {
+ increment = aSig & (increment << 1);
+ }
+ break;
+ case float_round_up:
+ increment = aSign ? 0 : mask;
+ break;
+ case float_round_down:
+ increment = aSign ? mask : 0;
+ break;
+ default: /* round_to_zero */
+ increment = 0;
+ break;
+ }
+ aSig += increment;
+ if (aSig >= 0x01000000) {
+ aSig >>= 1;
+ aExp++;
+ }
+ } else if (aExp < -14
+ && STATUS(float_detect_tininess) == float_tininess_before_rounding) {
+ float_raise( float_flag_underflow STATUS_VAR);
+ }
+
+ if (ieee) {
+ if (aExp > 15) {
+ float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
+ return packFloat16(aSign, 0x1f, 0);
+ }
+ } else {
+ if (aExp > 16) {
+ float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
+ return packFloat16(aSign, 0x1f, 0x3ff);
+ }
+ }
+ if (aExp < -24) {
+ return packFloat16(aSign, 0, 0);
+ }
+ if (aExp < -14) {
+ aSig >>= -14 - aExp;
+ aExp = -14;
+ }
+ return packFloat16(aSign, aExp + 14, aSig >> 13);
+}
+
#ifdef FLOATX80
/*----------------------------------------------------------------------------
float64 float64_rem( float64 a, float64 b STATUS_PARAM )
{
- flag aSign, bSign, zSign;
+ flag aSign, zSign;
int16 aExp, bExp, expDiff;
bits64 aSig, bSig;
bits64 q, alternateASig;
aSign = extractFloat64Sign( a );
bSig = extractFloat64Frac( b );
bExp = extractFloat64Exp( b );
- bSign = extractFloat64Sign( b );
if ( aExp == 0x7FF ) {
if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) {
return propagateFloat64NaN( a, b STATUS_VAR );
floatx80 floatx80_rem( floatx80 a, floatx80 b STATUS_PARAM )
{
- flag aSign, bSign, zSign;
+ flag aSign, zSign;
int32 aExp, bExp, expDiff;
bits64 aSig0, aSig1, bSig;
bits64 q, term0, term1, alternateASig0, alternateASig1;
aSign = extractFloatx80Sign( a );
bSig = extractFloatx80Frac( b );
bExp = extractFloatx80Exp( b );
- bSign = extractFloatx80Sign( b );
if ( aExp == 0x7FFF ) {
if ( (bits64) ( aSig0<<1 )
|| ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) {
float128 float128_rem( float128 a, float128 b STATUS_PARAM )
{
- flag aSign, bSign, zSign;
+ flag aSign, zSign;
int32 aExp, bExp, expDiff;
bits64 aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2;
bits64 allZero, alternateASig0, alternateASig1, sigMean1;
bSig1 = extractFloat128Frac1( b );
bSig0 = extractFloat128Frac0( b );
bExp = extractFloat128Exp( b );
- bSign = extractFloat128Sign( b );
if ( aExp == 0x7FFF ) {
if ( ( aSig0 | aSig1 )
|| ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
projects / qemu.git / blobdiff