Numeric traits and functions for generic mathematics.
These are implemented for the primitive numeric types in std::{u8, u16, u32, u64, uint, i8, i16, i32, i64, int, f32, f64, float}.
FPCategory - Used for representing the classification of floating point numbersAlgebraicBitCountBitwise - Collects the bitwise operators under one trait.BoundedCheckedAddCheckedDivCheckedMulCheckedSubExponentialFloat - Primitive floating point numbersFractionalFromStrRadixHyperbolicInt - A collection of traits relevant to primitive signed and unsigned integersIntConvertibleIntegerNum - The base trait for numeric typesNumCast - An interface for casting between machine scalarsOneOrderablePrimitive - Specifies the available operations common to all of Rust's core numeric primitivesReal - Defines constants and methods common to real numbersRealExt - Methods that are harder to implement and not commonly used.RoundSaturating - Saturating math operationsSignedTimes - Times traitToStrRadixTrigonometricUnsignedZeroof ::std::cmp::Eq for FPCategory - Automatically derived.of NumCast for u8of NumCast for u16of NumCast for u32of NumCast for u64of NumCast for uintof NumCast for i8of NumCast for i16of NumCast for i32of NumCast for i64of NumCast for intof NumCast for f32of NumCast for f64of NumCast for floatof Zero for @mut T where <T: Zero + 'static>of Zero for @T where <T: Zero + 'static>of Zero for ~T where <T: Zero>of Saturating for T where <T: CheckedAdd + CheckedSub + Zero + Ord + Bounded>of CheckedAdd for i8of CheckedAdd for i16of CheckedAdd for i32of CheckedAdd for i64of CheckedAdd for intof CheckedAdd for u8of CheckedAdd for u16of CheckedAdd for u32of CheckedAdd for u64of CheckedAdd for uintof CheckedSub for i8of CheckedSub for i16of CheckedSub for i32of CheckedSub for i64of CheckedSub for intof CheckedSub for u8of CheckedSub for u16of CheckedSub for u32of CheckedSub for u64of CheckedSub for uintof CheckedMul for i8of CheckedMul for i16of CheckedMul for i32of CheckedMul for intof CheckedMul for u8of CheckedMul for u16of CheckedMul for u32of CheckedMul for uintabsabs_subacosacoshasinasinhatanatan2atanhcast - Cast from one machine scalar to anothercbrtclampcoscoshexpexp2exp_m1gcdhypotlcmlnln_1ploglog10log2maxminmul_addonepowpow_with_uint - Calculates a power to a given radix, optimized for uint pow and radix.rsqrtsignumsinsin_cossinhsqrttantanhzeronum::strconvFPCategoryUsed for representing the classification of floating point numbers
FPNaN - "Not a Number", often obtained by dividing by zero
FPInfinite - Positive or negative infinity
FPZero - Positive or negative zero
FPSubnormal - De-normalized floating point representation (less precise than FPNormal)
FPNormal - A regular floating point number
Algebraicpowfn pow(&self, n: &Self) -> Selfsqrtfn sqrt(&self) -> Selfrsqrtfn rsqrt(&self) -> Selfcbrtfn cbrt(&self) -> Selfhypotfn hypot(&self, other: &Self) -> SelfBitCountpopulation_countfn population_count(&self) -> Selfleading_zerosfn leading_zeros(&self) -> Selftrailing_zerosfn trailing_zeros(&self) -> SelfBitwiseCollects the bitwise operators under one trait.
Boundedmin_valuefn min_value() -> Selfmax_valuefn max_value() -> SelfCheckedAddchecked_addfn checked_add(&self, v: &Self) -> Option<Self>CheckedDivchecked_divfn checked_div(&self, v: &Self) -> Option<Self>CheckedMulchecked_mulfn checked_mul(&self, v: &Self) -> Option<Self>CheckedSubchecked_subfn checked_sub(&self, v: &Self) -> Option<Self>Exponentialexpfn exp(&self) -> Selfexp2fn exp2(&self) -> Selflnfn ln(&self) -> Selflogfn log(&self, base: &Self) -> Selflog2fn log2(&self) -> Selflog10fn log10(&self) -> SelfFloatPrimitive floating point numbers
NaNfn NaN() -> Selfinfinityfn infinity() -> Selfneg_infinityfn neg_infinity() -> Selfneg_zerofn neg_zero() -> Selfis_NaNfn is_NaN(&self) -> boolis_infinitefn is_infinite(&self) -> boolis_finitefn is_finite(&self) -> boolis_normalfn is_normal(&self) -> boolclassifyfn classify(&self) -> FPCategorymantissa_digitsfn mantissa_digits(unused_self: Option<Self>) -> uintdigitsfn digits(unused_self: Option<Self>) -> uintepsilonfn epsilon() -> Selfmin_expfn min_exp(unused_self: Option<Self>) -> intmax_expfn max_exp(unused_self: Option<Self>) -> intmin_10_expfn min_10_exp(unused_self: Option<Self>) -> intmax_10_expfn max_10_exp(unused_self: Option<Self>) -> intldexpfn ldexp(x: Self, exp: int) -> Selffrexpfn frexp(&self) -> (Self, int)exp_m1fn exp_m1(&self) -> Selfln_1pfn ln_1p(&self) -> Selfmul_addfn mul_add(&self, a: Self, b: Self) -> Selfnext_afterfn next_after(&self, other: Self) -> SelfFractionalrecipfn recip(&self) -> SelfFromStrRadixfrom_str_radixfn from_str_radix(str: &str, radix: uint) -> Option<Self>Hyperbolicsinhfn sinh(&self) -> Selfcoshfn cosh(&self) -> Selftanhfn tanh(&self) -> Selfasinhfn asinh(&self) -> Selfacoshfn acosh(&self) -> Selfatanhfn atanh(&self) -> SelfIntA collection of traits relevant to primitive signed and unsigned integers
IntConvertibleto_intfn to_int(&self) -> intfrom_intfn from_int(n: int) -> SelfIntegerdiv_remfn div_rem(&self, other: &Self) -> (Self, Self)div_floorfn div_floor(&self, other: &Self) -> Selfmod_floorfn mod_floor(&self, other: &Self) -> Selfdiv_mod_floorfn div_mod_floor(&self, other: &Self) -> (Self, Self)gcdfn gcd(&self, other: &Self) -> Selflcmfn lcm(&self, other: &Self) -> Selfis_multiple_offn is_multiple_of(&self, other: &Self) -> boolis_evenfn is_even(&self) -> boolis_oddfn is_odd(&self) -> boolNumThe base trait for numeric types
NumCastAn interface for casting between machine scalars
fromfn from<T: NumCast>(n: T) -> Selfto_u8fn to_u8(&self) -> u8to_u16fn to_u16(&self) -> u16to_u32fn to_u32(&self) -> u32to_u64fn to_u64(&self) -> u64to_uintfn to_uint(&self) -> uintto_i8fn to_i8(&self) -> i8to_i16fn to_i16(&self) -> i16to_i32fn to_i32(&self) -> i32to_i64fn to_i64(&self) -> i64to_intfn to_int(&self) -> intto_f32fn to_f32(&self) -> f32to_f64fn to_f64(&self) -> f64to_floatfn to_float(&self) -> floatOneonefn one() -> SelfOrderableminfn min(&self, other: &Self) -> Selfmaxfn max(&self, other: &Self) -> Selfclampfn clamp(&self, mn: &Self, mx: &Self) -> SelfPrimitiveSpecifies the available operations common to all of Rust's core numeric primitives. These may not always make sense from a purely mathematical point of view, but may be useful for systems programming.
bitsfn bits(unused_self: Option<Self>) -> uintbytesfn bytes(unused_self: Option<Self>) -> uintRealDefines constants and methods common to real numbers
pifn pi() -> Selftwo_pifn two_pi() -> Selffrac_pi_2fn frac_pi_2() -> Selffrac_pi_3fn frac_pi_3() -> Selffrac_pi_4fn frac_pi_4() -> Selffrac_pi_6fn frac_pi_6() -> Selffrac_pi_8fn frac_pi_8() -> Selffrac_1_pifn frac_1_pi() -> Selffrac_2_pifn frac_2_pi() -> Selffrac_2_sqrtpifn frac_2_sqrtpi() -> Selfsqrt2fn sqrt2() -> Selffrac_1_sqrt2fn frac_1_sqrt2() -> Selfefn e() -> Selflog2_efn log2_e() -> Selflog10_efn log10_e() -> Selfln_2fn ln_2() -> Selfln_10fn ln_10() -> Selfto_degreesfn to_degrees(&self) -> Selfto_radiansfn to_radians(&self) -> SelfRealExtMethods that are harder to implement and not commonly used.
lgammafn lgamma(&self) -> (int, Self)tgammafn tgamma(&self) -> Selfj0fn j0(&self) -> Selfj1fn j1(&self) -> Selfjnfn jn(&self, n: int) -> Selfy0fn y0(&self) -> Selfy1fn y1(&self) -> Selfynfn yn(&self, n: int) -> SelfRoundfloorfn floor(&self) -> Selfceilfn ceil(&self) -> Selfroundfn round(&self) -> Selftruncfn trunc(&self) -> Selffractfn fract(&self) -> SelfSaturatingSaturating math operations
saturating_addfn saturating_add(self, v: Self) -> SelfSaturating addition operator. Returns a+b, saturating at the numeric bounds instead of overflowing.
saturating_subfn saturating_sub(self, v: Self) -> SelfSaturating subtraction operator. Returns a-b, saturating at the numeric bounds instead of overflowing.
Signedabsfn abs(&self) -> Selfabs_subfn abs_sub(&self, other: &Self) -> Selfsignumfn signum(&self) -> Selfis_positivefn is_positive(&self) -> boolis_negativefn is_negative(&self) -> boolTimesTimes trait
use num::Times;
let ten = 10 as uint;
let mut accum = 0;
do ten.times { accum += 1; }timesfn times(&self, it: &fn())ToStrRadixto_str_radixfn to_str_radix(&self, radix: uint) -> ~strTrigonometricsinfn sin(&self) -> Selfcosfn cos(&self) -> Selftanfn tan(&self) -> Selfasinfn asin(&self) -> Selfacosfn acos(&self) -> Selfatanfn atan(&self) -> Selfatan2fn atan2(&self, other: &Self) -> Selfsin_cosfn sin_cos(&self) -> (Self, Self)UnsignedZerozerofn zero() -> Selfis_zerofn is_zero(&self) -> bool::std::cmp::Eq for FPCategoryAutomatically derived.
eqfn eq(&self, __arg_0: &FPCategory) -> ::boolnefn ne(&self, __arg_0: &FPCategory) -> ::boolNumCast for u8fromfn from<N: NumCast>(n: N) -> u8to_u8fn to_u8(&self) -> u8to_u16fn to_u16(&self) -> u16to_u32fn to_u32(&self) -> u32to_u64fn to_u64(&self) -> u64to_uintfn to_uint(&self) -> uintto_i8fn to_i8(&self) -> i8to_i16fn to_i16(&self) -> i16to_i32fn to_i32(&self) -> i32to_i64fn to_i64(&self) -> i64to_intfn to_int(&self) -> intto_f32fn to_f32(&self) -> f32to_f64fn to_f64(&self) -> f64to_floatfn to_float(&self) -> floatNumCast for u16fromfn from<N: NumCast>(n: N) -> u16to_u8fn to_u8(&self) -> u8to_u16fn to_u16(&self) -> u16to_u32fn to_u32(&self) -> u32to_u64fn to_u64(&self) -> u64to_uintfn to_uint(&self) -> uintto_i8fn to_i8(&self) -> i8to_i16fn to_i16(&self) -> i16to_i32fn to_i32(&self) -> i32to_i64fn to_i64(&self) -> i64to_intfn to_int(&self) -> intto_f32fn to_f32(&self) -> f32to_f64fn to_f64(&self) -> f64to_floatfn to_float(&self) -> floatNumCast for u32fromfn from<N: NumCast>(n: N) -> u32to_u8fn to_u8(&self) -> u8to_u16fn to_u16(&self) -> u16to_u32fn to_u32(&self) -> u32to_u64fn to_u64(&self) -> u64to_uintfn to_uint(&self) -> uintto_i8fn to_i8(&self) -> i8to_i16fn to_i16(&self) -> i16to_i32fn to_i32(&self) -> i32to_i64fn to_i64(&self) -> i64to_intfn to_int(&self) -> intto_f32fn to_f32(&self) -> f32to_f64fn to_f64(&self) -> f64to_floatfn to_float(&self) -> floatNumCast for u64fromfn from<N: NumCast>(n: N) -> u64to_u8fn to_u8(&self) -> u8to_u16fn to_u16(&self) -> u16to_u32fn to_u32(&self) -> u32to_u64fn to_u64(&self) -> u64to_uintfn to_uint(&self) -> uintto_i8fn to_i8(&self) -> i8to_i16fn to_i16(&self) -> i16to_i32fn to_i32(&self) -> i32to_i64fn to_i64(&self) -> i64to_intfn to_int(&self) -> intto_f32fn to_f32(&self) -> f32to_f64fn to_f64(&self) -> f64to_floatfn to_float(&self) -> floatNumCast for uintfromfn from<N: NumCast>(n: N) -> uintto_u8fn to_u8(&self) -> u8to_u16fn to_u16(&self) -> u16to_u32fn to_u32(&self) -> u32to_u64fn to_u64(&self) -> u64to_uintfn to_uint(&self) -> uintto_i8fn to_i8(&self) -> i8to_i16fn to_i16(&self) -> i16to_i32fn to_i32(&self) -> i32to_i64fn to_i64(&self) -> i64to_intfn to_int(&self) -> intto_f32fn to_f32(&self) -> f32to_f64fn to_f64(&self) -> f64to_floatfn to_float(&self) -> floatNumCast for i8fromfn from<N: NumCast>(n: N) -> i8to_u8fn to_u8(&self) -> u8to_u16fn to_u16(&self) -> u16to_u32fn to_u32(&self) -> u32to_u64fn to_u64(&self) -> u64to_uintfn to_uint(&self) -> uintto_i8fn to_i8(&self) -> i8to_i16fn to_i16(&self) -> i16to_i32fn to_i32(&self) -> i32to_i64fn to_i64(&self) -> i64to_intfn to_int(&self) -> intto_f32fn to_f32(&self) -> f32to_f64fn to_f64(&self) -> f64to_floatfn to_float(&self) -> floatNumCast for i16fromfn from<N: NumCast>(n: N) -> i16to_u8fn to_u8(&self) -> u8to_u16fn to_u16(&self) -> u16to_u32fn to_u32(&self) -> u32to_u64fn to_u64(&self) -> u64to_uintfn to_uint(&self) -> uintto_i8fn to_i8(&self) -> i8to_i16fn to_i16(&self) -> i16to_i32fn to_i32(&self) -> i32to_i64fn to_i64(&self) -> i64to_intfn to_int(&self) -> intto_f32fn to_f32(&self) -> f32to_f64fn to_f64(&self) -> f64to_floatfn to_float(&self) -> floatNumCast for i32fromfn from<N: NumCast>(n: N) -> i32to_u8fn to_u8(&self) -> u8to_u16fn to_u16(&self) -> u16to_u32fn to_u32(&self) -> u32to_u64fn to_u64(&self) -> u64to_uintfn to_uint(&self) -> uintto_i8fn to_i8(&self) -> i8to_i16fn to_i16(&self) -> i16to_i32fn to_i32(&self) -> i32to_i64fn to_i64(&self) -> i64to_intfn to_int(&self) -> intto_f32fn to_f32(&self) -> f32to_f64fn to_f64(&self) -> f64to_floatfn to_float(&self) -> floatNumCast for i64fromfn from<N: NumCast>(n: N) -> i64to_u8fn to_u8(&self) -> u8to_u16fn to_u16(&self) -> u16to_u32fn to_u32(&self) -> u32to_u64fn to_u64(&self) -> u64to_uintfn to_uint(&self) -> uintto_i8fn to_i8(&self) -> i8to_i16fn to_i16(&self) -> i16to_i32fn to_i32(&self) -> i32to_i64fn to_i64(&self) -> i64to_intfn to_int(&self) -> intto_f32fn to_f32(&self) -> f32to_f64fn to_f64(&self) -> f64to_floatfn to_float(&self) -> floatNumCast for intfromfn from<N: NumCast>(n: N) -> intto_u8fn to_u8(&self) -> u8to_u16fn to_u16(&self) -> u16to_u32fn to_u32(&self) -> u32to_u64fn to_u64(&self) -> u64to_uintfn to_uint(&self) -> uintto_i8fn to_i8(&self) -> i8to_i16fn to_i16(&self) -> i16to_i32fn to_i32(&self) -> i32to_i64fn to_i64(&self) -> i64to_intfn to_int(&self) -> intto_f32fn to_f32(&self) -> f32to_f64fn to_f64(&self) -> f64to_floatfn to_float(&self) -> floatNumCast for f32fromfn from<N: NumCast>(n: N) -> f32to_u8fn to_u8(&self) -> u8to_u16fn to_u16(&self) -> u16to_u32fn to_u32(&self) -> u32to_u64fn to_u64(&self) -> u64to_uintfn to_uint(&self) -> uintto_i8fn to_i8(&self) -> i8to_i16fn to_i16(&self) -> i16to_i32fn to_i32(&self) -> i32to_i64fn to_i64(&self) -> i64to_intfn to_int(&self) -> intto_f32fn to_f32(&self) -> f32to_f64fn to_f64(&self) -> f64to_floatfn to_float(&self) -> floatNumCast for f64fromfn from<N: NumCast>(n: N) -> f64to_u8fn to_u8(&self) -> u8to_u16fn to_u16(&self) -> u16to_u32fn to_u32(&self) -> u32to_u64fn to_u64(&self) -> u64to_uintfn to_uint(&self) -> uintto_i8fn to_i8(&self) -> i8to_i16fn to_i16(&self) -> i16to_i32fn to_i32(&self) -> i32to_i64fn to_i64(&self) -> i64to_intfn to_int(&self) -> intto_f32fn to_f32(&self) -> f32to_f64fn to_f64(&self) -> f64to_floatfn to_float(&self) -> floatNumCast for floatfromfn from<N: NumCast>(n: N) -> floatto_u8fn to_u8(&self) -> u8to_u16fn to_u16(&self) -> u16to_u32fn to_u32(&self) -> u32to_u64fn to_u64(&self) -> u64to_uintfn to_uint(&self) -> uintto_i8fn to_i8(&self) -> i8to_i16fn to_i16(&self) -> i16to_i32fn to_i32(&self) -> i32to_i64fn to_i64(&self) -> i64to_intfn to_int(&self) -> intto_f32fn to_f32(&self) -> f32to_f64fn to_f64(&self) -> f64to_floatfn to_float(&self) -> floatZero for @mut T where <T: Zero + 'static>zerofn zero() -> @mut Tis_zerofn is_zero(&self) -> boolZero for @T where <T: Zero + 'static>zerofn zero() -> @Tis_zerofn is_zero(&self) -> boolZero for ~T where <T: Zero>zerofn zero() -> ~Tis_zerofn is_zero(&self) -> boolSaturating for T where <T: CheckedAdd + CheckedSub + Zero + Ord + Bounded>saturating_addfn saturating_add(self, v: T) -> Tsaturating_subfn saturating_sub(self, v: T) -> TCheckedAdd for i8checked_addfn checked_add(&self, v: &i8) -> Option<i8>CheckedAdd for i16checked_addfn checked_add(&self, v: &i16) -> Option<i16>CheckedAdd for i32checked_addfn checked_add(&self, v: &i32) -> Option<i32>CheckedAdd for i64checked_addfn checked_add(&self, v: &i64) -> Option<i64>CheckedAdd for intchecked_addfn checked_add(&self, v: &int) -> Option<int>CheckedAdd for u8checked_addfn checked_add(&self, v: &u8) -> Option<u8>CheckedAdd for u16checked_addfn checked_add(&self, v: &u16) -> Option<u16>CheckedAdd for u32checked_addfn checked_add(&self, v: &u32) -> Option<u32>CheckedAdd for u64checked_addfn checked_add(&self, v: &u64) -> Option<u64>CheckedAdd for uintchecked_addfn checked_add(&self, v: &uint) -> Option<uint>CheckedSub for i8checked_subfn checked_sub(&self, v: &i8) -> Option<i8>CheckedSub for i16checked_subfn checked_sub(&self, v: &i16) -> Option<i16>CheckedSub for i32checked_subfn checked_sub(&self, v: &i32) -> Option<i32>CheckedSub for i64checked_subfn checked_sub(&self, v: &i64) -> Option<i64>CheckedSub for intchecked_subfn checked_sub(&self, v: &int) -> Option<int>CheckedSub for u8checked_subfn checked_sub(&self, v: &u8) -> Option<u8>CheckedSub for u16checked_subfn checked_sub(&self, v: &u16) -> Option<u16>CheckedSub for u32checked_subfn checked_sub(&self, v: &u32) -> Option<u32>CheckedSub for u64checked_subfn checked_sub(&self, v: &u64) -> Option<u64>CheckedSub for uintchecked_subfn checked_sub(&self, v: &uint) -> Option<uint>CheckedMul for i8checked_mulfn checked_mul(&self, v: &i8) -> Option<i8>CheckedMul for i16checked_mulfn checked_mul(&self, v: &i16) -> Option<i16>CheckedMul for i32checked_mulfn checked_mul(&self, v: &i32) -> Option<i32>CheckedMul for intchecked_mulfn checked_mul(&self, v: &int) -> Option<int>CheckedMul for u8checked_mulfn checked_mul(&self, v: &u8) -> Option<u8>CheckedMul for u16checked_mulfn checked_mul(&self, v: &u16) -> Option<u16>CheckedMul for u32checked_mulfn checked_mul(&self, v: &u32) -> Option<u32>CheckedMul for uintchecked_mulfn checked_mul(&self, v: &uint) -> Option<uint>absfn abs<T: Signed>(value: T) -> Tabs_subfn abs_sub<T: Signed>(x: T, y: T) -> Tacosfn acos<T: Trigonometric>(value: T) -> Tacoshfn acosh<T: Hyperbolic>(value: T) -> Tasinfn asin<T: Trigonometric>(value: T) -> Tasinhfn asinh<T: Hyperbolic>(value: T) -> Tatanfn atan<T: Trigonometric>(value: T) -> Tatan2fn atan2<T: Trigonometric>(x: T, y: T) -> Tatanhfn atanh<T: Hyperbolic>(value: T) -> Tcastfn cast<T: NumCast, U: NumCast>(n: T) -> UCast from one machine scalar to another
let twenty: f32 = num::cast(0x14);
assert_eq!(twenty, 20f32);cbrtfn cbrt<T: Algebraic>(value: T) -> Tclampfn clamp<T: Orderable>(value: T, mn: T, mx: T) -> Tcosfn cos<T: Trigonometric>(value: T) -> Tcoshfn cosh<T: Hyperbolic>(value: T) -> Texpfn exp<T: Exponential>(value: T) -> Texp2fn exp2<T: Exponential>(value: T) -> Texp_m1fn exp_m1<T: Float>(value: T) -> Tgcdfn gcd<T: Integer>(x: T, y: T) -> Thypotfn hypot<T: Algebraic>(x: T, y: T) -> Tlcmfn lcm<T: Integer>(x: T, y: T) -> Tlnfn ln<T: Exponential>(value: T) -> Tln_1pfn ln_1p<T: Float>(value: T) -> Tlogfn log<T: Exponential>(value: T, base: T) -> Tlog10fn log10<T: Exponential>(value: T) -> Tlog2fn log2<T: Exponential>(value: T) -> Tmaxfn max<T: Orderable>(x: T, y: T) -> Tminfn min<T: Orderable>(x: T, y: T) -> Tmul_addfn mul_add<T: Float>(a: T, b: T, c: T) -> Tonefn one<T: One>() -> Tpowfn pow<T: Algebraic>(value: T, n: T) -> Tpow_with_uintfn pow_with_uint<T: NumCast + One + Zero + Div<T, T> +
Mul<T, T>>(radix: uint, pow: uint) -> TCalculates a power to a given radix, optimized for uint pow and radix.
Returns radix^pow as T.
Note: Also returns 1 for 0^0, despite that technically being an undefined number. The reason for this is twofold: - If code written to use this function cares about that special case, it's probably going to catch it before making the call. - If code written to use this function doesn't care about it, it's probably assuming that x^0 always equals 1.
rsqrtfn rsqrt<T: Algebraic>(value: T) -> Tsignumfn signum<T: Signed>(value: T) -> Tsinfn sin<T: Trigonometric>(value: T) -> Tsin_cosfn sin_cos<T: Trigonometric>(value: T) -> (T, T)sinhfn sinh<T: Hyperbolic>(value: T) -> Tsqrtfn sqrt<T: Algebraic>(value: T) -> Ttanfn tan<T: Trigonometric>(value: T) -> Ttanhfn tanh<T: Hyperbolic>(value: T) -> Tzerofn zero<T: Zero>() -> T