@@ -625,6 +625,54 @@ static uint64_t estimateDiv128To64( uint64_t a0, uint64_t a1, uint64_t b )
}
+/* From the GNU Multi Precision Library - longlong.h __udiv_qrnnd
+ * (https://gmplib.org/repo/gmp/file/tip/longlong.h)
+ *
+ * Licensed under the GPLv2/LGPLv3
+ */
+static uint64_t div128To64(uint64_t n0, uint64_t n1, uint64_t d)
+{
+ uint64_t d0, d1, q0, q1, r1, r0, m;
+
+ d0 = (uint32_t)d;
+ d1 = d >> 32;
+
+ r1 = n1 % d1;
+ q1 = n1 / d1;
+ m = q1 * d0;
+ r1 = (r1 << 32) | (n0 >> 32);
+ if (r1 < m) {
+ q1 -= 1;
+ r1 += d;
+ if (r1 >= d) {
+ if (r1 < m) {
+ q1 -= 1;
+ r1 += d;
+ }
+ }
+ }
+ r1 -= m;
+
+ r0 = r1 % d1;
+ q0 = r1 / d1;
+ m = q0 * d0;
+ r0 = (r0 << 32) | (uint32_t)n0;
+ if (r0 < m) {
+ q0 -= 1;
+ r0 += d;
+ if (r0 >= d) {
+ if (r0 < m) {
+ q0 -= 1;
+ r0 += d;
+ }
+ }
+ }
+ r0 -= m;
+
+ /* Return remainder in LSB */
+ return (q1 << 32) | q0 | (r0 != 0);
+}
+
/*----------------------------------------------------------------------------
| Returns an approximation to the square root of the 32-bit significand given
| by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of
@@ -816,6 +816,94 @@ float64 __attribute__((flatten)) float64_mul(float64 a, float64 b,
return float64_round_pack_canonical(pr, status);
}
+/*
+ * Returns the result of dividing the floating-point value `a' by the
+ * corresponding value `b'. The operation is performed according to
+ * the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+ */
+
+static FloatParts div_floats(FloatParts a, FloatParts b, float_status *s)
+{
+ bool sign = a.sign ^ b.sign;
+
+ if (a.cls == float_class_normal && b.cls == float_class_normal) {
+ uint64_t temp_lo, temp_hi;
+ int exp = a.exp - b.exp;
+ if (a.frac < b.frac) {
+ exp -= 1;
+ shortShift128Left(0, a.frac, DECOMPOSED_BINARY_POINT + 1,
+ &temp_hi, &temp_lo);
+ } else {
+ shortShift128Left(0, a.frac, DECOMPOSED_BINARY_POINT,
+ &temp_hi, &temp_lo);
+ }
+ /* LSB of quot is set if inexact which roundandpack will use
+ * to set flags. Yet again we re-use a for the result */
+ a.frac = div128To64(temp_lo, temp_hi, b.frac);
+ a.sign = sign;
+ a.exp = exp;
+ return a;
+ }
+ /* handle all the NaN cases */
+ if (is_nan(a.cls) || is_nan(b.cls)) {
+ return pick_nan(a, b, s);
+ }
+ /* 0/0 or Inf/Inf */
+ if (a.cls == b.cls
+ &&
+ (a.cls == float_class_inf || a.cls == float_class_zero)) {
+ s->float_exception_flags |= float_flag_invalid;
+ a.cls = float_class_dnan;
+ return a;
+ }
+ /* Div 0 => Inf */
+ if (b.cls == float_class_zero) {
+ s->float_exception_flags |= float_flag_divbyzero;
+ a.cls = float_class_inf;
+ a.sign = sign;
+ return a;
+ }
+ /* Inf / x or 0 / x */
+ if (a.cls == float_class_inf || a.cls == float_class_zero) {
+ a.sign = sign;
+ return a;
+ }
+ /* Div by Inf */
+ if (b.cls == float_class_inf) {
+ a.cls = float_class_zero;
+ a.sign = sign;
+ return a;
+ }
+ g_assert_not_reached();
+}
+
+float16 float16_div(float16 a, float16 b, float_status *status)
+{
+ FloatParts pa = float16_unpack_canonical(a, status);
+ FloatParts pb = float16_unpack_canonical(b, status);
+ FloatParts pr = div_floats(pa, pb, status);
+
+ return float16_round_pack_canonical(pr, status);
+}
+
+float32 float32_div(float32 a, float32 b, float_status *status)
+{
+ FloatParts pa = float32_unpack_canonical(a, status);
+ FloatParts pb = float32_unpack_canonical(b, status);
+ FloatParts pr = div_floats(pa, pb, status);
+
+ return float32_round_pack_canonical(pr, status);
+}
+
+float64 float64_div(float64 a, float64 b, float_status *status)
+{
+ FloatParts pa = float64_unpack_canonical(a, status);
+ FloatParts pb = float64_unpack_canonical(b, status);
+ FloatParts pr = div_floats(pa, pb, status);
+
+ return float64_round_pack_canonical(pr, status);
+}
+
/*----------------------------------------------------------------------------
| Takes a 64-bit fixed-point value `absZ' with binary point between bits 6
| and 7, and returns the properly rounded 32-bit integer corresponding to the
@@ -2627,77 +2715,6 @@ float32 float32_round_to_int(float32 a, float_status *status)
}
-
-/*----------------------------------------------------------------------------
-| Returns the result of dividing the single-precision floating-point value `a'
-| by the corresponding value `b'. The operation is performed according to the
-| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-float32 float32_div(float32 a, float32 b, float_status *status)
-{
- flag aSign, bSign, zSign;
- int aExp, bExp, zExp;
- uint32_t aSig, bSig, zSig;
- a = float32_squash_input_denormal(a, status);
- b = float32_squash_input_denormal(b, status);
-
- aSig = extractFloat32Frac( a );
- aExp = extractFloat32Exp( a );
- aSign = extractFloat32Sign( a );
- bSig = extractFloat32Frac( b );
- bExp = extractFloat32Exp( b );
- bSign = extractFloat32Sign( b );
- zSign = aSign ^ bSign;
- if ( aExp == 0xFF ) {
- if (aSig) {
- return propagateFloat32NaN(a, b, status);
- }
- if ( bExp == 0xFF ) {
- if (bSig) {
- return propagateFloat32NaN(a, b, status);
- }
- float_raise(float_flag_invalid, status);
- return float32_default_nan(status);
- }
- return packFloat32( zSign, 0xFF, 0 );
- }
- if ( bExp == 0xFF ) {
- if (bSig) {
- return propagateFloat32NaN(a, b, status);
- }
- return packFloat32( zSign, 0, 0 );
- }
- if ( bExp == 0 ) {
- if ( bSig == 0 ) {
- if ( ( aExp | aSig ) == 0 ) {
- float_raise(float_flag_invalid, status);
- return float32_default_nan(status);
- }
- float_raise(float_flag_divbyzero, status);
- return packFloat32( zSign, 0xFF, 0 );
- }
- normalizeFloat32Subnormal( bSig, &bExp, &bSig );
- }
- if ( aExp == 0 ) {
- if ( aSig == 0 ) return packFloat32( zSign, 0, 0 );
- normalizeFloat32Subnormal( aSig, &aExp, &aSig );
- }
- zExp = aExp - bExp + 0x7D;
- aSig = ( aSig | 0x00800000 )<<7;
- bSig = ( bSig | 0x00800000 )<<8;
- if ( bSig <= ( aSig + aSig ) ) {
- aSig >>= 1;
- ++zExp;
- }
- zSig = ( ( (uint64_t) aSig )<<32 ) / bSig;
- if ( ( zSig & 0x3F ) == 0 ) {
- zSig |= ( (uint64_t) bSig * zSig != ( (uint64_t) aSig )<<32 );
- }
- return roundAndPackFloat32(zSign, zExp, zSig, status);
-
-}
-
/*----------------------------------------------------------------------------
| Returns the remainder of the single-precision floating-point value `a'
| with respect to the corresponding value `b'. The operation is performed
@@ -4159,83 +4176,6 @@ float64 float64_trunc_to_int(float64 a, float_status *status)
return res;
}
-/*----------------------------------------------------------------------------
-| Returns the result of dividing the double-precision floating-point value `a'
-| by the corresponding value `b'. The operation is performed according to
-| the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-float64 float64_div(float64 a, float64 b, float_status *status)
-{
- flag aSign, bSign, zSign;
- int aExp, bExp, zExp;
- uint64_t aSig, bSig, zSig;
- uint64_t rem0, rem1;
- uint64_t term0, term1;
- a = float64_squash_input_denormal(a, status);
- b = float64_squash_input_denormal(b, status);
-
- aSig = extractFloat64Frac( a );
- aExp = extractFloat64Exp( a );
- aSign = extractFloat64Sign( a );
- bSig = extractFloat64Frac( b );
- bExp = extractFloat64Exp( b );
- bSign = extractFloat64Sign( b );
- zSign = aSign ^ bSign;
- if ( aExp == 0x7FF ) {
- if (aSig) {
- return propagateFloat64NaN(a, b, status);
- }
- if ( bExp == 0x7FF ) {
- if (bSig) {
- return propagateFloat64NaN(a, b, status);
- }
- float_raise(float_flag_invalid, status);
- return float64_default_nan(status);
- }
- return packFloat64( zSign, 0x7FF, 0 );
- }
- if ( bExp == 0x7FF ) {
- if (bSig) {
- return propagateFloat64NaN(a, b, status);
- }
- return packFloat64( zSign, 0, 0 );
- }
- if ( bExp == 0 ) {
- if ( bSig == 0 ) {
- if ( ( aExp | aSig ) == 0 ) {
- float_raise(float_flag_invalid, status);
- return float64_default_nan(status);
- }
- float_raise(float_flag_divbyzero, status);
- return packFloat64( zSign, 0x7FF, 0 );
- }
- normalizeFloat64Subnormal( bSig, &bExp, &bSig );
- }
- if ( aExp == 0 ) {
- if ( aSig == 0 ) return packFloat64( zSign, 0, 0 );
- normalizeFloat64Subnormal( aSig, &aExp, &aSig );
- }
- zExp = aExp - bExp + 0x3FD;
- aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10;
- bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
- if ( bSig <= ( aSig + aSig ) ) {
- aSig >>= 1;
- ++zExp;
- }
- zSig = estimateDiv128To64( aSig, 0, bSig );
- if ( ( zSig & 0x1FF ) <= 2 ) {
- mul64To128( bSig, zSig, &term0, &term1 );
- sub128( aSig, 0, term0, term1, &rem0, &rem1 );
- while ( (int64_t) rem0 < 0 ) {
- --zSig;
- add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
- }
- zSig |= ( rem1 != 0 );
- }
- return roundAndPackFloat64(zSign, zExp, zSig, status);
-
-}
/*----------------------------------------------------------------------------
| Returns the remainder of the double-precision floating-point value `a'
@@ -240,6 +240,7 @@ float64 float16_to_float64(float16 a, flag ieee, float_status *status);
float16 float16_add(float16, float16, float_status *status);
float16 float16_sub(float16, float16, float_status *status);
float16 float16_mul(float16, float16, float_status *status);
+float16 float16_div(float16, float16, float_status *status);
int float16_is_quiet_nan(float16, float_status *status);
int float16_is_signaling_nan(float16, float_status *status);