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fn test_atanh() { let a = FixedTrait::new(58982, false); assert_precise(atanh(a), 96483, 'invalid 0.9', Option::None(())); let a = FixedTrait::new(HALF, false); assert_precise(atanh(a), 35999, 'invalid half', Option::None(())); let a = FixedTrait::ZERO(); assert(ata...
use orion::numbers::fixed_point::implementations::fp16x16::core::ONE; fn msb(whole: u32) -> (u32, u32) { if whole < 256 { if whole < 2 { return (0, 1); } if whole < 4 { return (1, 2); } if whole < 8 { return (2, 4); } if w...
f exp == 14 { return 16384; } if exp == 15 { return 32768; } if exp == 16 { return 65536; } } 65536 } fn sin(a: u32) -> (u32, u32, u32) { let slot = a / 402; if slot < 128 { if slot < 64 { if slot < 32 { ...
; } } else { if slot == 16 { return (6434, 6424, 6824); } if slot == 17 { return (6836, 6824, 7224); } if slot == 18 { ...
return (13270, 13180, 13573); } if slot == 34 { return (13672, 13573, 13966); } if slot == 35 { return (14074, 13966, 14359); } if slot == 36 { ...
return (20508, 20175, 20557); } if slot == 52 { return (20910, 20557, 20939); } if slot == 53 { return (21313, 20939, 21320); } if slot == 54 { ...
} if slot == 69 { return (27747, 26925, 27291); } if slot == 70 { return (28149, 27291, 27656); } if slot == 71 { return (28551, 27656, 28020); ...
} if slot == 87 { return (34985, 33347, 33692); } if slot == 88 { return (35387, 33692, 34037); } if slot == 89 { return (35789, 34037, 34380); ...
return (41821, 39040, 39362); } if slot == 105 { return (42223, 39362, 39683); } if slot == 106 { return (42625, 39683, 40002); } if slot == 107 { ...
return (49059, 44604, 44898); } if slot == 123 { return (49461, 44898, 45190); } if slot == 124 { return (49863, 45190, 45480); } if slot == 125 { ...
return (55895, 49361, 49624); } if slot == 140 { return (56297, 49624, 49886); } if slot == 141 { return (56699, 49886, 50146); } if slot == 142 { ...
ot == 157 { return (63133, 53812, 54040); } if slot == 158 { return (63536, 54040, 54267); } if slot == 159 { return (63938, 54267, 54491); } ...
, 57607); } if slot == 175 { return (70372, 57607, 57798); } } else { if slot == 176 { return (70774, 57798, 57986); } if slot == 177 { ...
224 { if slot < 208 { if slot == 192 { return (77208, 60547, 60700); } if slot == 193 { return (77610, 60700, 60851); } if slot == 194 { ...
turn (84044, 62830, 62943); } if slot == 210 { return (84446, 62943, 63054); } if slot == 211 { return (84848, 63054, 63162); } if slot == 212 { ...
if slot == 227 { return (91282, 64501, 64571); } if slot == 228 { return (91684, 64571, 64639); } if slot == 229 { return (92086, 64639, 64704); } ...
} if slot == 245 { return (98520, 65387, 65413); } if slot == 246 { return (98922, 65413, 65436); } if slot == 247 { return (99325, 65436, 65457); ...
} if slot == 13 { return (5964, 5947, 6402); } if slot == 14 { return (6423, 6402, 6856); } if slot == 15 { return (6881, 6856, 7310); } if slot == 16 { return (7340, 7310, 7762); } if slot == 17 { return (7799, 7762, 8214); } if slot =...
return (20644, 19999, 20416); } if slot == 46 { return (21103, 20416, 20830); } if slot == 47 { return (21561, 20830, 21243); } if slot == 48 { return (22020, 21243, 21655); } if slot == 49 { return (22479, 21655, 22064); } if slot == 50 { ...
return (35324, 32398, 32753); } if slot == 78 { return (35783, 32753, 33105); } if slot == 79 { return (36241, 33105, 33455); } if slot == 80 { return (36700, 33455, 33804); } if slot == 81 { return (37159, 33804, 34150); } if slot == 82 { ...
if x <= 12451 { if x <= 6553 { return 7370; } if x <= 7208 { return 8101; } if x <= 7864 { return 8831; } if x <= 8519 { return 9559; } if x <= 9175 { return 10285; } if x ...
n 29325; } if x <= 28180 { return 29942; } if x <= 28835 { return 30554; } if x <= 29491 { return 31161; } if x <= 30146 { return 31762; } if x <= 30801 { return 32358; } ...
return 46606; } if x <= 49807 { return 47024; } if x <= 50462 { return 47436; } if x <= 51118 { return 47841; } if x <= 51773 { return 48241; } } if x <= 58327 { if x <= 52428 { ...
{ return 57234; } if x <= 71434 { return 57462; } } if x <= 77987 { if x <= 72089 { return 57685; } if x <= 72744 { return 57903; } if x <= 73400 { return 58116; } if x <= ...
408; } if x <= 92405 { return 62511; } if x <= 93061 { return 62611; } if x <= 93716 { return 62708; } if x <= 94371 { return 62802; } if x <= 95027 { return 62894; } ...
<= 113377 { return 64590; } if x <= 114032 { return 64627; } if x <= 114688 { return 64662; } if x <= 115343 { return 64696; } if x <= 115998 { return 64729; } if x <= 116654 { ...
return 65509; } if x <= 170393 { return 65520; } if x <= 176947 { return 65527; } if x <= 183500 { return 65531; } if x <= 190054 { return 65533; } if x <= 196608 { return 65534; ...
use core::integer; use orion::numbers::fixed_point::implementations::fp16x16::math::lut; use orion::numbers::fixed_point::implementations::fp16x16::core::{ HALF, ONE, TWO, FP16x16, FP16x16Impl, FP16x16Add, FP16x16Sub, FP16x16Mul, FP16x16Div, FP16x16IntoFelt252, FixedTrait }; const TWO_PI: u32 = 411775; const...
let r2 = r3 * at; let mut res = (r2 + FixedTrait::new(65536, false)) * at; if (shift) { res = res + FixedTrait::new(34315, false); } if (invert) { res = res - FixedTrait::new(HALF_PI, false); } FixedTrait::new(res.mag, a.sign) } fn atan_fast(a: FP16x16) -> FP16x16 { ...
edTrait::new(partial_rem - start, false) / FixedTrait::new(402, false); let res = partial_step * (FixedTrait::new(high, false) - FixedTrait::new(low, false)) + FixedTrait::<FP16x16>::new(low, false); FixedTrait::new(res.mag, a.sign ^ partial_sign && res.mag != 0) } fn tan(a: FP16x16) -> FP16x16 { ...
fn test_acos() { let error = Option::Some(84); let a = FixedTrait::ONE(); assert(acos(a).into() == 0, 'invalid one'); let a = FixedTrait::new(ONE / 2, false); assert_relative(acos(a), 68629, 'invalid half', error); let a = FixedTrait::ZERO(); assert_relative(...
fn test_acos_fast() { let error = Option::Some(84); let a = FixedTrait::ONE(); assert(acos_fast(a).into() == 0, 'invalid one'); let a = FixedTrait::new(ONE / 2, false); assert_relative(acos_fast(a), 68629, 'invalid half', error); let a = FixedTrait::ZERO(); a...
fn test_acos_fail() { let a = FixedTrait::new(2 * ONE, true); acos(a); }
fn test_atan_fast() { let error = Option::Some(84); let a = FixedTrait::new(2 * ONE, false); assert_relative(atan_fast(a), 72558, 'invalid two', error); let a = FixedTrait::ONE(); assert_relative(atan_fast(a), 51472, 'invalid one', error); let a = FixedTrait::new(ONE ...
fn test_atan() { let a = FixedTrait::new(2 * ONE, false); assert_relative(atan(a), 72558, 'invalid two', Option::None(())); let a = FixedTrait::ONE(); assert_relative(atan(a), 51472, 'invalid one', Option::None(())); let a = FixedTrait::new(ONE / 2, false); assert_relat...
fn test_asin() { let error = Option::Some(84); let a = FixedTrait::ONE(); assert_relative(asin(a), HALF_PI.into(), 'invalid one', Option::None(())); let a = FixedTrait::new(ONE / 2, false); assert_relative(asin(a), 34315, 'invalid half', error); let a = FixedTrait::Z...
fn test_asin_fail() { let a = FixedTrait::new(2 * ONE, false); asin(a); }
fn test_cos() { let a = FixedTrait::new(HALF_PI, false); assert(cos(a).into() == 0, 'invalid half pi'); let a = FixedTrait::new(HALF_PI / 2, false); assert_relative(cos(a), 46341, 'invalid quarter pi', Option::None(())); let a = FixedTrait::new(PI, false); assert_relat...
fn test_cos_fast() { let error = Option::Some(84); let a = FixedTrait::new(HALF_PI, false); assert(cos_fast(a).into() == 0, 'invalid half pi'); let a = FixedTrait::new(HALF_PI / 2, false); assert_precise(cos_fast(a), 46341, 'invalid quarter pi', error); let a = Fixed...
fn test_sin() { let a = FixedTrait::new(HALF_PI, false); assert_precise(sin(a), ONE.into(), 'invalid half pi', Option::None(())); let a = FixedTrait::new(HALF_PI / 2, false); assert_precise(sin(a), 46341, 'invalid quarter pi', Option::None(())); let a = FixedTrait::new(PI, fal...
fn test_sin_fast() { let error = Option::Some(84); let a = FixedTrait::new(HALF_PI, false); assert_precise(sin_fast(a), ONE.into(), 'invalid half pi', error); let a = FixedTrait::new(HALF_PI / 2, false); assert_precise(sin_fast(a), 46341, 'invalid quarter pi', error); ...
fn test_tan() { let a = FixedTrait::new(HALF_PI / 2, false); assert_precise(tan(a), ONE.into(), 'invalid quarter pi', Option::None(())); let a = FixedTrait::new(PI, false); assert_precise(tan(a), 0, 'invalid pi', Option::None(())); let a = FixedTrait::new_unscaled(17, false); ...
mod core; mod math; mod helpers;
use core::debug::PrintTrait; use orion::numbers::{fixed_point::core::FixedTrait, FP16x16}; use orion::numbers::fixed_point::implementations::fp16x16wide::math::{ core as core_math, trig, hyp, erf }; use orion::numbers::fixed_point::utils;
struct FP16x16W { mag: u64, sign: bool } const TWO: u64 = 131072; const ONE: u64 = 65536; const HALF: u64 = 32768; const MAX: u64 = 2147483648; impl FP16x16WImpl of FixedTrait<FP16x16W, u64> { fn ZERO() -> FP16x16W { FP16x16W { mag: 0, sign: false } } fn HALF() -> FP16x16W { ...
FP16x16W { core_math::floor(self) } fn exp(self: FP16x16W) -> FP16x16W { core_math::exp(self) } fn exp2(self: FP16x16W) -> FP16x16W { core_math::exp2(self) } fn ln(self: FP16x16W) -> FP16x16W { core_math::ln(self) } fn log...
} } impl FP16x16WPrint of PrintTrait<FP16x16W> {
fn print(self: FP16x16W) { self.sign.print(); self.mag.print(); } } impl FP16x16WIntoFelt252 of Into<FP16x16W, felt252> { fn into(self: FP16x16W) -> felt252 { let mag_felt = self.mag.into(); if self.sign { mag_felt * -1 } else { mag_felt * 1 ...
} } impl FP16x16WTryIntoU8 of TryInto<FP16x16W, u8> { fn try_into(self: FP16x16W) -> Option<u8> { if self.sign { Option::None(()) } else { (self.mag / ONE).try_into() } } } impl FP16x16WPartialEq of PartialEq<FP16x16W> { fn eq(lhs: @FP16x16...
fn add_eq(ref self: FP16x16W, other: FP16x16W) { self = Add::add(self, other); } } impl FP16x16WSub of Sub<FP16x16W> { fn sub(lhs: FP16x16W, rhs: FP16x16W) -> FP16x16W { core_math::sub(lhs, rhs) } } impl FP16x16WSubEq of SubEq<FP16x16W> {
fn sub_eq(ref self: FP16x16W, other: FP16x16W) { self = Sub::sub(self, other); } } impl FP16x16WMul of Mul<FP16x16W> { fn mul(lhs: FP16x16W, rhs: FP16x16W) -> FP16x16W { core_math::mul(lhs, rhs) } } impl FP16x16WMulEq of MulEq<FP16x16W> {
fn mul_eq(ref self: FP16x16W, other: FP16x16W) { self = Mul::mul(self, other); } } impl FP16x16WDiv of Div<FP16x16W> { fn div(lhs: FP16x16W, rhs: FP16x16W) -> FP16x16W { core_math::div(lhs, rhs) } } impl FP16x16WDivEq of DivEq<FP16x16W> {
fn div_eq(ref self: FP16x16W, other: FP16x16W) { self = Div::div(self, other); } } impl FP16x16WPartialOrd of PartialOrd<FP16x16W> { fn ge(lhs: FP16x16W, rhs: FP16x16W) -> bool { core_math::ge(lhs, rhs) } fn gt(lhs: FP16x16W, rhs: FP16x16W) -> bool { core_math::gt(lhs...
use core::debug::PrintTrait; use orion::numbers::fixed_point::implementations::fp16x16wide::core::{ HALF, ONE, TWO, FP16x16W, FP16x16WImpl, FP16x16WSub, FP16x16WDiv, FixedTrait, FP16x16WPrint }; const DEFAULT_PRECISION: u64 = 7; // 1e-4 // To use `DEFAULT_PRECISION`, final arg is: `Option::None(())`. // To use `...
mod core; mod comp; mod lut; mod trig; mod hyp; mod erf;
use orion::numbers::fixed_point::implementations::fp16x16wide::core::{ FP16x16W, FixedTrait, FP16x16WImpl, FP16x16WPartialOrd, FP16x16WPartialEq }; fn max(a: FP16x16W, b: FP16x16W) -> FP16x16W { if a >= b { a } else { b } } fn min(a: FP16x16W, b: FP16x16W) -> FP16x16W { if a <= b {...
fn test_max() { let a = FixedTrait::new_unscaled(1, false); let b = FixedTrait::new_unscaled(0, false); let c = FixedTrait::new_unscaled(1, true); assert(max(a, a) == a, 'max(a, a)'); assert(max(a, b) == a, 'max(a, b)'); assert(max(a, c) == a, 'max(a, c)'); asse...
fn test_min() { let a = FixedTrait::new_unscaled(1, false); let b = FixedTrait::new_unscaled(0, false); let c = FixedTrait::new_unscaled(1, true); assert(min(a, a) == a, 'min(a, a)'); assert(min(a, b) == b, 'min(a, b)'); assert(min(a, c) == c, 'min(a, c)'); asse...
fn test_bitwise_and() { let a = FixedTrait::new(225280, false); let b = FixedTrait::new(4160843776, true); let c = FixedTrait::new(94208, false); assert(bitwise_and(a, b) == c, 'bitwise_and(a,b)') }
fn test_bitwise_xor() { let a = FixedTrait::new(225280, false); let b = FixedTrait::new(4160843776, true); let c = FixedTrait::new(4160880640, true); assert(bitwise_xor(a, b) == c, 'bitwise_xor(a,b)') }
fn test_bitwise_or() { let a = FixedTrait::new(225280, false); let b = FixedTrait::new(4160843776, true); let c = FixedTrait::new(4160974848, true); assert(bitwise_or(a, b) == c, 'bitwise_or(a,b)') } }
use core::integer; use orion::numbers::fixed_point::implementations::fp16x16wide::core::{ HALF, ONE, MAX, FP16x16W, FP16x16WImpl, FP16x16WAdd, FP16x16WAddEq, FP16x16WSub, FP16x16WMul, FP16x16WMulEq, FP16x16WTryIntoU128, FP16x16WPartialEq, FP16x16WPartialOrd, FP16x16WSubEq, FP16x16WNeg, FP16x16WDiv, FP16x16...
10, false)) * frac; let r5 = (r6 + FixedTrait::new(87, false)) * frac; let r4 = (r5 + FixedTrait::new(630, false)) * frac; let r3 = (r4 + FixedTrait::new(3638, false)) * frac; let r2 = (r3 + FixedTrait::new(15743, false)) * frac; let r1 = (r2 + FixedTrait::new(45426, false)) * fr...
ue)) * norm; let r5 = (r6 + FixedTrait::new(172935, false)) * norm; let r4 = (r5 + FixedTrait::new(394096, true)) * norm; let r3 = (r4 + FixedTrait::new(608566, false)) * norm; let r2 = (r3 + FixedTrait::new(655828, true)) * norm; let r1 = (r2 + FixedTrait::new(534433, false)) * ...
zero(ONE)); if (HALF <= rem) { FixedTrait::new_unscaled(div + 1, a.sign) } else { FixedTrait::new_unscaled(div, a.sign) } } fn sqrt(a: FP16x16W) -> FP16x16W { assert(a.sign == false, 'must be positive'); let root = integer::u64_sqrt(a.mag.into() * ONE.into()); FixedTrait::n...
fn test_into() { let a = FixedTrait::<FP16x16W>::new_unscaled(5, false); assert(a.mag == 5 * ONE, 'invalid result'); }
fn test_try_into_u128() { let a = FixedTrait::<FP16x16W>::new_unscaled(5, false); assert(a.try_into().unwrap() == 5_u128, 'invalid result'); let b = FixedTrait::<FP16x16W>::new(5 * ONE, false); assert(b.try_into().unwrap() == 5_u128, 'invalid result'); ...
fn test_negative_try_into_u128() { let a = FixedTrait::<FP16x16W>::new_unscaled(1, true); let _a: u128 = a.try_into().unwrap(); }
fn test_acos() { let a = FixedTrait::<FP16x16W>::ONE(); assert(a.acos().into() == 0, 'invalid one'); }
fn test_asin() { let a = FixedTrait::ONE(); assert_precise(a.asin(), HALF_PI.into(), 'invalid one', Option::None(())); }
fn test_atan() { let a = FixedTrait::new(2 * ONE, false); assert_relative(a.atan(), 72558, 'invalid two', Option::None(())); }
fn test_ceil() { let a = FixedTrait::new(190054, false); assert(ceil(a).mag == 3 * ONE, 'invalid pos decimal'); }
fn test_floor() { let a = FixedTrait::new(190054, false); assert(floor(a).mag == 2 * ONE, 'invalid pos decimal'); }
fn test_round() { let a = FixedTrait::new(190054, false); assert(round(a).mag == 3 * ONE, 'invalid pos decimal'); }
fn test_sqrt_fail() { let a = FixedTrait::new_unscaled(25, true); sqrt(a); }
fn test_sqrt() { let mut a = FixedTrait::new_unscaled(0, false); assert(sqrt(a).mag == 0, 'invalid zero root'); a = FixedTrait::new_unscaled(25, false); assert(sqrt(a).mag == 5 * ONE, 'invalid pos root'); }
fn test_msb() { let a = FixedTrait::<FP16x16W>::new_unscaled(100, false); let (msb, div) = lut::msb(a.mag / ONE); assert(msb == 6, 'invalid msb'); assert(div == 64, 'invalid msb ceil'); }
fn test_pow() { let a = FixedTrait::new_unscaled(3, false); let b = FixedTrait::new_unscaled(4, false); assert(pow(a, b).mag == 81 * ONE, 'invalid pos base power'); }
fn test_pow_frac() { let a = FixedTrait::new_unscaled(3, false); let b = FixedTrait::new(32768, false); assert_relative( pow(a, b), 113512, 'invalid pos base power', Option::None(()) ); }
fn test_exp() { let a = FixedTrait::new_unscaled(2, false); assert_relative(exp(a), 484249, 'invalid exp of 2', Option::None(())); }
fn test_exp2() { let a = FixedTrait::new_unscaled(5, false); assert(exp2(a).mag == 2097152, 'invalid exp2 of 2'); }
fn test_exp2_int() { assert(exp2_int(5).into() == 2097152, 'invalid exp2 of 2'); }
fn test_ln() { let mut a = FixedTrait::new_unscaled(1, false); assert(ln(a).mag == 0, 'invalid ln of 1'); a = FixedTrait::new(178145, false); assert_relative(ln(a), ONE.into(), 'invalid ln of 2.7...', Option::None(())); }
fn test_log2() { let mut a = FixedTrait::new_unscaled(32, false); assert(log2(a) == FixedTrait::new_unscaled(5, false), 'invalid log2 32'); a = FixedTrait::new_unscaled(10, false); assert_relative(log2(a), 217706, 'invalid log2 10', Option::None(())); }
fn test_log10() { let a = FixedTrait::new_unscaled(100, false); assert_relative(log10(a), 2 * ONE.into(), 'invalid log10', Option::None(())); }
fn test_eq() { let a = FixedTrait::new_unscaled(42, false); let b = FixedTrait::new_unscaled(42, false); let c = eq(@a, @b); assert(c, 'invalid result'); }
fn test_ne() { let a = FixedTrait::new_unscaled(42, false); let b = FixedTrait::new_unscaled(42, false); let c = ne(@a, @b); assert(!c, 'invalid result'); }
fn test_add() { let a = FixedTrait::new_unscaled(1, false); let b = FixedTrait::new_unscaled(2, false); assert(add(a, b) == FixedTrait::new_unscaled(3, false), 'invalid result'); }
fn test_add_eq() { let mut a = FixedTrait::new_unscaled(1, false); let b = FixedTrait::new_unscaled(2, false); a += b; assert(a == FixedTrait::<FP16x16W>::new_unscaled(3, false), 'invalid result'); }
fn test_sub() { let a = FixedTrait::new_unscaled(5, false); let b = FixedTrait::new_unscaled(2, false); let c = a - b; assert(c == FixedTrait::<FP16x16W>::new_unscaled(3, false), 'false result invalid'); }
fn test_sub_eq() { let mut a = FixedTrait::new_unscaled(5, false); let b = FixedTrait::new_unscaled(2, false); a -= b; assert(a == FixedTrait::<FP16x16W>::new_unscaled(3, false), 'invalid result'); }
fn test_mul_pos() { let a = FP16x16W { mag: 190054, sign: false }; let b = FP16x16W { mag: 190054, sign: false }; let c = a * b; assert(c.mag == 551155, 'invalid result'); }
fn test_mul_neg() { let a = FixedTrait::new_unscaled(5, false); let b = FixedTrait::new_unscaled(2, true); let c = a * b; assert(c == FixedTrait::<FP16x16W>::new_unscaled(10, true), 'invalid result'); }
fn test_mul_eq() { let mut a = FixedTrait::new_unscaled(5, false); let b = FixedTrait::new_unscaled(2, true); a *= b; assert(a == FixedTrait::<FP16x16W>::new_unscaled(10, true), 'invalid result'); }
fn test_div() { let a = FixedTrait::new_unscaled(10, false); let b = FixedTrait::<FP16x16W>::new(190054, false); let c = a / b; assert(c.mag == 225986, 'invalid pos decimal'); }
fn test_le() { let a = FixedTrait::new_unscaled(1, false); let b = FixedTrait::new_unscaled(0, false); let c = FixedTrait::<FP16x16W>::new_unscaled(1, true); assert(a <= a, 'a <= a'); assert(!(a <= b), 'a <= b'); assert(!(a <= c), 'a <= c'); assert(b <= a, 'b <=...
fn test_lt() { let a = FixedTrait::new_unscaled(1, false); let b = FixedTrait::new_unscaled(0, false); let c = FixedTrait::<FP16x16W>::new_unscaled(1, true); assert(!(a < a), 'a < a'); assert(!(a < b), 'a < b'); assert(!(a < c), 'a < c'); assert(b < a, 'b < a');...
fn test_ge() { let a = FixedTrait::new_unscaled(1, false); let b = FixedTrait::new_unscaled(0, false); let c = FixedTrait::<FP16x16W>::new_unscaled(1, true); assert(a >= a, 'a >= a'); assert(a >= b, 'a >= b'); assert(a >= c, 'a >= c'); assert(!(b >= a), 'b >= a'...
fn test_gt() { let a = FixedTrait::new_unscaled(1, false); let b = FixedTrait::new_unscaled(0, false); let c = FixedTrait::<FP16x16W>::new_unscaled(1, true); assert(!(a > a), 'a > a'); assert(a > b, 'a > b'); assert(a > c, 'a > c'); assert(!(b > a), 'b > a'); ...
fn test_cos() { let a = FixedTrait::<FP16x16W>::new(HALF_PI, false); assert(a.cos().into() == 0, 'invalid half pi'); }