179 lines
7.5 KiB
Text
179 lines
7.5 KiB
Text
/-
|
||
Copyright (c) 2023 Amazon.com, Inc. or its affiliates. All Rights Reserved.
|
||
Released under Apache 2.0 license as described in the file LICENSE.
|
||
Authors: Leonardo de Moura
|
||
-/
|
||
prelude
|
||
import Init.Core
|
||
import Init.Data.Int.Basic
|
||
import Init.Data.ToString.Basic
|
||
import Init.Data.Float
|
||
|
||
-- Just show FloatSpec is inhabited.
|
||
opaque float32Spec : FloatSpec := {
|
||
float := Unit,
|
||
val := (),
|
||
lt := fun _ _ => True,
|
||
le := fun _ _ => True,
|
||
decLt := fun _ _ => inferInstanceAs (Decidable True),
|
||
decLe := fun _ _ => inferInstanceAs (Decidable True)
|
||
}
|
||
|
||
/-- Native floating point type, corresponding to the IEEE 754 *binary32* format
|
||
(`float` in C or `f32` in Rust). -/
|
||
structure Float32 where
|
||
val : float32Spec.float
|
||
|
||
instance : Nonempty Float32 := ⟨{ val := float32Spec.val }⟩
|
||
|
||
@[extern "lean_float32_add"] opaque Float32.add : Float32 → Float32 → Float32
|
||
@[extern "lean_float32_sub"] opaque Float32.sub : Float32 → Float32 → Float32
|
||
@[extern "lean_float32_mul"] opaque Float32.mul : Float32 → Float32 → Float32
|
||
@[extern "lean_float32_div"] opaque Float32.div : Float32 → Float32 → Float32
|
||
@[extern "lean_float32_negate"] opaque Float32.neg : Float32 → Float32
|
||
|
||
set_option bootstrap.genMatcherCode false
|
||
def Float32.lt : Float32 → Float32 → Prop := fun a b =>
|
||
match a, b with
|
||
| ⟨a⟩, ⟨b⟩ => float32Spec.lt a b
|
||
|
||
def Float32.le : Float32 → Float32 → Prop := fun a b =>
|
||
float32Spec.le a.val b.val
|
||
|
||
/--
|
||
Raw transmutation from `UInt32`.
|
||
|
||
Float32s and UInts have the same endianness on all supported platforms.
|
||
IEEE 754 very precisely specifies the bit layout of floats.
|
||
-/
|
||
@[extern "lean_float32_of_bits"] opaque Float32.ofBits : UInt32 → Float32
|
||
|
||
/--
|
||
Raw transmutation to `UInt32`.
|
||
|
||
Float32s and UInts have the same endianness on all supported platforms.
|
||
IEEE 754 very precisely specifies the bit layout of floats.
|
||
|
||
Note that this function is distinct from `Float32.toUInt32`, which attempts
|
||
to preserve the numeric value, and not the bitwise value.
|
||
-/
|
||
@[extern "lean_float32_to_bits"] opaque Float32.toBits : Float32 → UInt32
|
||
|
||
instance : Add Float32 := ⟨Float32.add⟩
|
||
instance : Sub Float32 := ⟨Float32.sub⟩
|
||
instance : Mul Float32 := ⟨Float32.mul⟩
|
||
instance : Div Float32 := ⟨Float32.div⟩
|
||
instance : Neg Float32 := ⟨Float32.neg⟩
|
||
instance : LT Float32 := ⟨Float32.lt⟩
|
||
instance : LE Float32 := ⟨Float32.le⟩
|
||
|
||
/-- Note: this is not reflexive since `NaN != NaN`.-/
|
||
@[extern "lean_float32_beq"] opaque Float32.beq (a b : Float32) : Bool
|
||
|
||
instance : BEq Float32 := ⟨Float32.beq⟩
|
||
|
||
@[extern "lean_float32_decLt"] opaque Float32.decLt (a b : Float32) : Decidable (a < b) :=
|
||
match a, b with
|
||
| ⟨a⟩, ⟨b⟩ => float32Spec.decLt a b
|
||
|
||
@[extern "lean_float32_decLe"] opaque Float32.decLe (a b : Float32) : Decidable (a ≤ b) :=
|
||
match a, b with
|
||
| ⟨a⟩, ⟨b⟩ => float32Spec.decLe a b
|
||
|
||
instance float32DecLt (a b : Float32) : Decidable (a < b) := Float32.decLt a b
|
||
instance float32DecLe (a b : Float32) : Decidable (a ≤ b) := Float32.decLe a b
|
||
|
||
@[extern "lean_float32_to_string"] opaque Float32.toString : Float32 → String
|
||
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
|
||
If negative or NaN, returns `0`.
|
||
If larger than the maximum value for `UInt8` (including Inf), returns the maximum value of `UInt8`
|
||
(i.e. `UInt8.size - 1`).
|
||
-/
|
||
@[extern "lean_float32_to_uint8"] opaque Float32.toUInt8 : Float32 → UInt8
|
||
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
|
||
If negative or NaN, returns `0`.
|
||
If larger than the maximum value for `UInt16` (including Inf), returns the maximum value of `UInt16`
|
||
(i.e. `UInt16.size - 1`).
|
||
-/
|
||
@[extern "lean_float32_to_uint16"] opaque Float32.toUInt16 : Float32 → UInt16
|
||
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
|
||
If negative or NaN, returns `0`.
|
||
If larger than the maximum value for `UInt32` (including Inf), returns the maximum value of `UInt32`
|
||
(i.e. `UInt32.size - 1`).
|
||
-/
|
||
@[extern "lean_float32_to_uint32"] opaque Float32.toUInt32 : Float32 → UInt32
|
||
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
|
||
If negative or NaN, returns `0`.
|
||
If larger than the maximum value for `UInt64` (including Inf), returns the maximum value of `UInt64`
|
||
(i.e. `UInt64.size - 1`).
|
||
-/
|
||
@[extern "lean_float32_to_uint64"] opaque Float32.toUInt64 : Float32 → UInt64
|
||
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
|
||
If negative or NaN, returns `0`.
|
||
If larger than the maximum value for `USize` (including Inf), returns the maximum value of `USize`
|
||
(i.e. `USize.size - 1`). This value is platform dependent).
|
||
-/
|
||
@[extern "lean_float32_to_usize"] opaque Float32.toUSize : Float32 → USize
|
||
|
||
@[extern "lean_float32_isnan"] opaque Float32.isNaN : Float32 → Bool
|
||
@[extern "lean_float32_isfinite"] opaque Float32.isFinite : Float32 → Bool
|
||
@[extern "lean_float32_isinf"] opaque Float32.isInf : Float32 → Bool
|
||
/-- Splits the given float `x` into a significand/exponent pair `(s, i)`
|
||
such that `x = s * 2^i` where `s ∈ (-1;-0.5] ∪ [0.5; 1)`.
|
||
Returns an undefined value if `x` is not finite.
|
||
-/
|
||
@[extern "lean_float32_frexp"] opaque Float32.frExp : Float32 → Float32 × Int
|
||
|
||
instance : ToString Float32 where
|
||
toString := Float32.toString
|
||
|
||
@[extern "lean_uint64_to_float32"] opaque UInt64.toFloat32 (n : UInt64) : Float32
|
||
|
||
instance : Inhabited Float32 where
|
||
default := UInt64.toFloat32 0
|
||
|
||
instance : Repr Float32 where
|
||
reprPrec n prec := if n < UInt64.toFloat32 0 then Repr.addAppParen (toString n) prec else toString n
|
||
|
||
instance : ReprAtom Float32 := ⟨⟩
|
||
|
||
@[extern "sinf"] opaque Float32.sin : Float32 → Float32
|
||
@[extern "cosf"] opaque Float32.cos : Float32 → Float32
|
||
@[extern "tanf"] opaque Float32.tan : Float32 → Float32
|
||
@[extern "asinf"] opaque Float32.asin : Float32 → Float32
|
||
@[extern "acosf"] opaque Float32.acos : Float32 → Float32
|
||
@[extern "atanf"] opaque Float32.atan : Float32 → Float32
|
||
@[extern "atan2f"] opaque Float32.atan2 : Float32 → Float32 → Float32
|
||
@[extern "sinhf"] opaque Float32.sinh : Float32 → Float32
|
||
@[extern "coshf"] opaque Float32.cosh : Float32 → Float32
|
||
@[extern "tanhf"] opaque Float32.tanh : Float32 → Float32
|
||
@[extern "asinhf"] opaque Float32.asinh : Float32 → Float32
|
||
@[extern "acoshf"] opaque Float32.acosh : Float32 → Float32
|
||
@[extern "atanhf"] opaque Float32.atanh : Float32 → Float32
|
||
@[extern "expf"] opaque Float32.exp : Float32 → Float32
|
||
@[extern "exp2f"] opaque Float32.exp2 : Float32 → Float32
|
||
@[extern "logf"] opaque Float32.log : Float32 → Float32
|
||
@[extern "log2f"] opaque Float32.log2 : Float32 → Float32
|
||
@[extern "log10f"] opaque Float32.log10 : Float32 → Float32
|
||
@[extern "powf"] opaque Float32.pow : Float32 → Float32 → Float32
|
||
@[extern "sqrtf"] opaque Float32.sqrt : Float32 → Float32
|
||
@[extern "cbrtf"] opaque Float32.cbrt : Float32 → Float32
|
||
@[extern "ceilf"] opaque Float32.ceil : Float32 → Float32
|
||
@[extern "floorf"] opaque Float32.floor : Float32 → Float32
|
||
@[extern "roundf"] opaque Float32.round : Float32 → Float32
|
||
@[extern "fabsf"] opaque Float32.abs : Float32 → Float32
|
||
|
||
instance : HomogeneousPow Float32 := ⟨Float32.pow⟩
|
||
|
||
instance : Min Float32 := minOfLe
|
||
|
||
instance : Max Float32 := maxOfLe
|
||
|
||
/--
|
||
Efficiently computes `x * 2^i`.
|
||
-/
|
||
@[extern "lean_float32_scaleb"]
|
||
opaque Float32.scaleB (x : Float32) (i : @& Int) : Float32
|
||
|
||
@[extern "lean_float32_to_float"] opaque Float32.toFloat : Float32 → Float
|
||
@[extern "lean_float_to_float32"] opaque Float.toFloat32 : Float → Float32
|