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| 1 | +use float::Float; |
| 2 | +use int::{CastInto, Int}; |
| 3 | + |
| 4 | +fn trunc<F: Float, R: Float>(a: F) -> R |
| 5 | +where |
| 6 | + F::Int: CastInto<u64>, |
| 7 | + F::Int: CastInto<u32>, |
| 8 | + u64: CastInto<F::Int>, |
| 9 | + u32: CastInto<F::Int>, |
| 10 | + |
| 11 | + R::Int: CastInto<u32>, |
| 12 | + u32: CastInto<R::Int>, |
| 13 | + F::Int: CastInto<R::Int>, |
| 14 | +{ |
| 15 | + let src_zero = F::Int::ZERO; |
| 16 | + let src_one = F::Int::ONE; |
| 17 | + let src_bits = F::BITS; |
| 18 | + let src_exp_bias = F::EXPONENT_BIAS; |
| 19 | + |
| 20 | + let src_min_normal = F::IMPLICIT_BIT; |
| 21 | + let src_significand_mask = F::SIGNIFICAND_MASK; |
| 22 | + let src_infinity = F::EXPONENT_MASK; |
| 23 | + let src_sign_mask = F::SIGN_MASK; |
| 24 | + let src_abs_mask = src_sign_mask - src_one; |
| 25 | + let round_mask = (src_one << (F::SIGNIFICAND_BITS - R::SIGNIFICAND_BITS)) - src_one; |
| 26 | + let halfway = src_one << (F::SIGNIFICAND_BITS - R::SIGNIFICAND_BITS - 1); |
| 27 | + let src_qnan = src_one << (F::SIGNIFICAND_BITS - 1); |
| 28 | + let src_nan_code = src_qnan - src_one; |
| 29 | + |
| 30 | + let dst_zero = R::Int::ZERO; |
| 31 | + let dst_one = R::Int::ONE; |
| 32 | + let dst_bits = R::BITS; |
| 33 | + let dst_inf_exp = R::EXPONENT_MAX; |
| 34 | + let dst_exp_bias = R::EXPONENT_BIAS; |
| 35 | + |
| 36 | + let underflow_exponent: F::Int = (src_exp_bias + 1 - dst_exp_bias).cast(); |
| 37 | + let overflow_exponent: F::Int = (src_exp_bias + dst_inf_exp - dst_exp_bias).cast(); |
| 38 | + let underflow: F::Int = underflow_exponent << F::SIGNIFICAND_BITS; |
| 39 | + let overflow: F::Int = overflow_exponent << F::SIGNIFICAND_BITS; |
| 40 | + |
| 41 | + let dst_qnan = R::Int::ONE << (R::SIGNIFICAND_BITS - 1); |
| 42 | + let dst_nan_code = dst_qnan - dst_one; |
| 43 | + |
| 44 | + let sign_bits_delta = F::SIGNIFICAND_BITS - R::SIGNIFICAND_BITS; |
| 45 | + // Break a into a sign and representation of the absolute value. |
| 46 | + let a_abs = a.repr() & src_abs_mask; |
| 47 | + let sign = a.repr() & src_sign_mask; |
| 48 | + let mut abs_result: R::Int; |
| 49 | + |
| 50 | + if a_abs.wrapping_sub(underflow) < a_abs.wrapping_sub(overflow) { |
| 51 | + // The exponent of a is within the range of normal numbers in the |
| 52 | + // destination format. We can convert by simply right-shifting with |
| 53 | + // rounding and adjusting the exponent. |
| 54 | + abs_result = (a_abs >> sign_bits_delta).cast(); |
| 55 | + let tmp = src_exp_bias.wrapping_sub(dst_exp_bias) << R::SIGNIFICAND_BITS; |
| 56 | + abs_result = abs_result.wrapping_sub(tmp.cast()); |
| 57 | + |
| 58 | + let round_bits = a_abs & round_mask; |
| 59 | + if round_bits > halfway { |
| 60 | + // Round to nearest. |
| 61 | + abs_result += dst_one; |
| 62 | + } else if round_bits == halfway { |
| 63 | + // Tie to even. |
| 64 | + abs_result += abs_result & dst_one; |
| 65 | + }; |
| 66 | + } else if a_abs > src_infinity { |
| 67 | + // a is NaN. |
| 68 | + // Conjure the result by beginning with infinity, setting the qNaN |
| 69 | + // bit and inserting the (truncated) trailing NaN field. |
| 70 | + abs_result = (dst_inf_exp << R::SIGNIFICAND_BITS).cast(); |
| 71 | + abs_result |= dst_qnan; |
| 72 | + abs_result |= dst_nan_code |
| 73 | + & ((a_abs & src_nan_code) >> (F::SIGNIFICAND_BITS - R::SIGNIFICAND_BITS)).cast(); |
| 74 | + } else if a_abs >= overflow { |
| 75 | + // a overflows to infinity. |
| 76 | + abs_result = (dst_inf_exp << R::SIGNIFICAND_BITS).cast(); |
| 77 | + } else { |
| 78 | + // a underflows on conversion to the destination type or is an exact |
| 79 | + // zero. The result may be a denormal or zero. Extract the exponent |
| 80 | + // to get the shift amount for the denormalization. |
| 81 | + let a_exp: u32 = (a_abs >> F::SIGNIFICAND_BITS).cast(); |
| 82 | + let shift = src_exp_bias - dst_exp_bias - a_exp + 1; |
| 83 | + |
| 84 | + let significand = (a.repr() & src_significand_mask) | src_min_normal; |
| 85 | + |
| 86 | + // Right shift by the denormalization amount with sticky. |
| 87 | + if shift > F::SIGNIFICAND_BITS { |
| 88 | + abs_result = dst_zero; |
| 89 | + } else { |
| 90 | + let sticky = if (significand << (src_bits - shift)) != src_zero { |
| 91 | + src_one |
| 92 | + } else { |
| 93 | + src_zero |
| 94 | + }; |
| 95 | + let denormalized_significand: F::Int = significand >> shift | sticky; |
| 96 | + abs_result = |
| 97 | + (denormalized_significand >> (F::SIGNIFICAND_BITS - R::SIGNIFICAND_BITS)).cast(); |
| 98 | + let round_bits = denormalized_significand & round_mask; |
| 99 | + // Round to nearest |
| 100 | + if round_bits > halfway { |
| 101 | + abs_result += dst_one; |
| 102 | + } |
| 103 | + // Ties to even |
| 104 | + else if round_bits == halfway { |
| 105 | + abs_result += abs_result & dst_one; |
| 106 | + }; |
| 107 | + } |
| 108 | + } |
| 109 | + |
| 110 | + // Apply the signbit to the absolute value. |
| 111 | + R::from_repr(abs_result | sign.wrapping_shr(src_bits - dst_bits).cast()) |
| 112 | +} |
| 113 | + |
| 114 | +intrinsics! { |
| 115 | + #[aapcs_on_arm] |
| 116 | + #[arm_aeabi_alias = __aeabi_d2f] |
| 117 | + pub extern "C" fn __truncdfsf2(a: f64) -> f32 { |
| 118 | + trunc(a) |
| 119 | + } |
| 120 | + |
| 121 | + #[cfg(target_arch = "arm")] |
| 122 | + pub extern "C" fn __truncdfsf2vfp(a: f64) -> f32 { |
| 123 | + a as f32 |
| 124 | + } |
| 125 | +} |
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