1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221

//! `f32` extension providing various arithmetic approximations and polyfills
//! for `std` functionality.

mod abs;
mod acos;
mod asin;
mod atan;
mod atan2;
mod ceil;
mod copysign;
mod cos;
mod exp;
mod floor;
mod fract;
mod hypot;
mod inv;
mod invsqrt;
mod ln;
mod log;
mod log10;
mod log2;
mod powf;
mod round;
mod sin;
mod sqrt;
mod tan;
mod trunc;
mod utils;

/// `f32` extension providing various arithmetic approximations and polyfills
/// for `std` functionality.
pub trait F32Ext: Sized {
    /// Compute absolute value with a constant-time, data-independent
    /// implementation.
    fn abs(self) -> f32;

    /// Approximate `asin(x)` in radians in the range `[-pi/2, pi/2]`.
    fn asin(self) -> f32;

    /// Approximate `acos(x)` in radians in the range `[0, pi]`
    fn acos(self) -> f32;

    /// Approximate `atan(x)` in radians with a maximum error of `0.002`.
    fn atan(self) -> f32;

    /// Approximate `atan(x)` normalized to the `[−1,1]` range with a maximum
    /// error of `0.1620` degrees.
    fn atan_norm(self) -> f32;

    /// Approximate the four quadrant arctangent `atan2(x)` in radians, with
    /// a maximum error of `0.002`.
    fn atan2(self, other: f32) -> f32;

    /// Approximate the four quadrant arctangent.
    /// Normalized to the `[0,4)` range with a maximum error of `0.1620` degrees.
    fn atan2_norm(self, other: f32) -> f32;

    /// Approximate floating point ceiling.
    fn ceil(self) -> f32;

    /// Approximate cosine in radians with a maximum error of `0.002`.
    fn cos(self) -> f32;

    /// Approximate floating point floor.
    fn floor(self) -> f32;

    /// Approximate the length of the hypotenuse of a right-angle triangle given
    /// legs of length `x` and `y`.
    fn hypot(self, other: f32) -> f32;

    /// Approximate `1/x` with an average deviation of ~8%.
    fn inv(self) -> f32;

    /// Approximate inverse square root with an average deviation of ~5%.
    fn invsqrt(self) -> f32;

    /// Approximate sine in radians with a maximum error of `0.002`.
    fn sin(self) -> f32;

    /// Approximate square root with an average deviation of ~5%.
    fn sqrt(self) -> f32;

    /// Approximate `tan(x)` in radians with a maximum error of `0.6`.
    fn tan(self) -> f32;

    /// Retrieve whole number part of floating point with sign.
    fn trunc(self) -> f32;

    /// Round the number part of floating point with sign.
    fn round(self) -> f32;

    /// Retrieve the fractional part of floating point with sign.
    fn fract(self) -> f32;

    /// Copies the sign from one number to another and returns it.
    fn copysign(self, sign: f32) -> f32;

    /// Approximate `ln(x)`.
    fn ln(self) -> f32;

    /// Approximate `e^x`.
    fn exp(self) -> f32;

    /// Approximate `log` with an arbitrary base.
    fn log(self, base: f32) -> f32;

    /// Approximate `log2`.
    fn log2(self) -> f32;

    /// Approximate `log10`.
    fn log10(self) -> f32;

    /// Approximate `self^n`.
    fn powf(self, n: f32) -> f32;
}

impl F32Ext for f32 {
    fn abs(self) -> f32 {
        self::abs::abs(self)
    }

    fn asin(self) -> f32 {
        self::asin::asin_approx(self)
    }

    fn acos(self) -> f32 {
        self::acos::acos_approx(self)
    }

    fn atan(self) -> f32 {
        self::atan::atan_approx(self)
    }

    fn atan_norm(self) -> f32 {
        self::atan::atan_norm_approx(self)
    }

    fn atan2(self, other: f32) -> f32 {
        self::atan2::atan2_approx(self, other)
    }

    fn atan2_norm(self, other: f32) -> f32 {
        self::atan2::atan2_norm_approx(self, other)
    }

    fn ceil(self) -> f32 {
        self::ceil::ceil(self)
    }

    fn cos(self) -> f32 {
        self::cos::cos_approx(self)
    }

    fn floor(self) -> f32 {
        self::floor::floor(self)
    }

    fn hypot(self, other: f32) -> f32 {
        self::hypot::hypot_approx(self, other)
    }

    fn inv(self) -> f32 {
        self::inv::inv_approx(self)
    }

    fn invsqrt(self) -> f32 {
        self::invsqrt::invsqrt_approx(self)
    }

    fn sin(self) -> f32 {
        self::sin::sin_approx(self)
    }

    fn sqrt(self) -> f32 {
        self::sqrt::sqrt_approx(self)
    }

    fn tan(self) -> f32 {
        self::tan::tan_approx(self)
    }

    fn trunc(self) -> f32 {
        self::trunc::trunc_sign(self)
    }

    fn round(self) -> f32 {
        self::round::round(self)
    }

    fn fract(self) -> f32 {
        self::fract::fract_sign(self)
    }

    fn copysign(self, sign: f32) -> f32 {
        self::copysign::copysign(self, sign)
    }

    fn ln(self) -> f32 {
        self::ln::ln_1to2_series_approximation(self)
    }

    fn exp(self) -> f32 {
        self::exp::exp_ln2_approximation(self, 4)
    }

    fn log(self, base: f32) -> f32 {
        self::log::log_ln_approx(self, base)
    }

    fn log2(self) -> f32 {
        self::log2::log2_ln_approx(self)
    }

    fn log10(self) -> f32 {
        self::log10::log10_ln_approx(self)
    }

    fn powf(self, n: f32) -> f32 {
        self::powf::powf_exp_ln_approx(self, n)
    }
}