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@ -7,18 +7,14 @@ use algebra::PrimeField; |
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use core::{cmp::Ordering, marker::PhantomData};
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use core::{cmp::Ordering, marker::PhantomData};
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use r1cs_core::{ConstraintSystem, SynthesisError};
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use r1cs_core::{ConstraintSystem, SynthesisError};
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pub struct CmpGadget<ConstraintF: PrimeField> {
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constraint_field_type: PhantomData<ConstraintF>,
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}
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impl<ConstraintF: PrimeField> CmpGadget<ConstraintF> {
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fn process_cmp_inputs<CS: ConstraintSystem<ConstraintF>>(
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impl<F: PrimeField> FpGadget<F> {
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fn process_cmp_inputs<CS: ConstraintSystem<F>>(
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mut cs: CS,
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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a: &FpGadget<F>,
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b: &FpGadget<F>,
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ordering: Ordering,
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ordering: Ordering,
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should_also_check_equality: bool,
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should_also_check_equality: bool,
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) -> Result<(FpGadget<ConstraintF>, FpGadget<ConstraintF>), SynthesisError> {
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) -> Result<(FpGadget<F>, FpGadget<F>), SynthesisError> {
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let left;
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let left;
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let right;
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let right;
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match ordering {
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match ordering {
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@ -35,7 +31,7 @@ impl CmpGadget { |
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},
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},
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};
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};
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let right_for_check = if should_also_check_equality {
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let right_for_check = if should_also_check_equality {
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right.add_constant(cs.ns(|| "plus one"), &ConstraintF::one())?
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right.add_constant(cs.ns(|| "plus one"), &F::one())?
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} else {
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} else {
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right.clone()
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right.clone()
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};
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};
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@ -43,31 +39,31 @@ impl CmpGadget { |
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Ok((left.clone(), right_for_check))
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Ok((left.clone(), right_for_check))
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}
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}
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fn check_smaller_than_mod_minus_one_div_two<CS: ConstraintSystem<ConstraintF>>(
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fn check_smaller_than_mod_minus_one_div_two<CS: ConstraintSystem<F>>(
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mut cs: CS,
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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a: &FpGadget<F>,
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) -> Result<(), SynthesisError> {
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) -> Result<(), SynthesisError> {
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let a_bits = a.to_bits(cs.ns(|| "a to bits"))?;
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let a_bits = a.to_bits(cs.ns(|| "a to bits"))?;
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Boolean::enforce_smaller_or_equal_than::<_, _, ConstraintF, _>(
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Boolean::enforce_smaller_or_equal_than::<_, _, F, _>(
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cs.ns(|| "enforce smaller than modulus minus one div two"),
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cs.ns(|| "enforce smaller than modulus minus one div two"),
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&a_bits,
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&a_bits,
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ConstraintF::modulus_minus_one_div_two(),
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F::modulus_minus_one_div_two(),
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)?;
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)?;
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Ok(())
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Ok(())
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}
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}
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/// this function verifies a and b are <= (p-1)/2
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/// this function verifies a and b are <= (p-1)/2
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pub fn enforce_cmp<CS: ConstraintSystem<ConstraintF>>(
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pub fn enforce_cmp<CS: ConstraintSystem<F>>(
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&self,
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mut cs: CS,
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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b: &FpGadget<F>,
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ordering: Ordering,
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ordering: Ordering,
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should_also_check_equality: bool,
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should_also_check_equality: bool,
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) -> Result<(), SynthesisError> {
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) -> Result<(), SynthesisError> {
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let (left, right) = Self::process_cmp_inputs(
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let (left, right) = Self::process_cmp_inputs(
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cs.ns(|| "process cmp inputs"),
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cs.ns(|| "process cmp inputs"),
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a,
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&self,
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b,
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b,
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ordering,
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ordering,
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should_also_check_equality,
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should_also_check_equality,
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@ -76,16 +72,16 @@ impl CmpGadget { |
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}
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}
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/// this function assumes a and b are known to be <= (p-1)/2
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/// this function assumes a and b are known to be <= (p-1)/2
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pub fn enforce_cmp_unchecked<CS: ConstraintSystem<ConstraintF>>(
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pub fn enforce_cmp_unchecked<CS: ConstraintSystem<F>>(
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&self,
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mut cs: CS,
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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b: &FpGadget<F>,
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ordering: Ordering,
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ordering: Ordering,
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should_also_check_equality: bool,
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should_also_check_equality: bool,
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) -> Result<(), SynthesisError> {
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) -> Result<(), SynthesisError> {
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let (left, right) = Self::process_cmp_inputs(
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let (left, right) = Self::process_cmp_inputs(
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cs.ns(|| "process cmp inputs"),
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cs.ns(|| "process cmp inputs"),
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a,
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&self,
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b,
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b,
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ordering,
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ordering,
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should_also_check_equality,
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should_also_check_equality,
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@ -94,16 +90,16 @@ impl CmpGadget { |
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}
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}
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/// this function verifies a and b are <= (p-1)/2
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/// this function verifies a and b are <= (p-1)/2
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pub fn is_cmp<CS: ConstraintSystem<ConstraintF>>(
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pub fn is_cmp<CS: ConstraintSystem<F>>(
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&self,
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mut cs: CS,
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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b: &FpGadget<F>,
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ordering: Ordering,
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ordering: Ordering,
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should_also_check_equality: bool,
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should_also_check_equality: bool,
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) -> Result<Boolean, SynthesisError> {
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) -> Result<Boolean, SynthesisError> {
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let (left, right) = Self::process_cmp_inputs(
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let (left, right) = Self::process_cmp_inputs(
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cs.ns(|| "process cmp inputs"),
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cs.ns(|| "process cmp inputs"),
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a,
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&self,
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b,
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b,
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ordering,
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ordering,
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should_also_check_equality,
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should_also_check_equality,
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@ -112,16 +108,16 @@ impl CmpGadget { |
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}
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}
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/// this function assumes a and b are known to be <= (p-1)/2
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/// this function assumes a and b are known to be <= (p-1)/2
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pub fn is_cmp_unchecked<CS: ConstraintSystem<ConstraintF>>(
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pub fn is_cmp_unchecked<CS: ConstraintSystem<F>>(
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&self,
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mut cs: CS,
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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b: &FpGadget<F>,
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ordering: Ordering,
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ordering: Ordering,
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should_also_check_equality: bool,
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should_also_check_equality: bool,
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) -> Result<Boolean, SynthesisError> {
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) -> Result<Boolean, SynthesisError> {
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let (left, right) = Self::process_cmp_inputs(
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let (left, right) = Self::process_cmp_inputs(
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cs.ns(|| "process cmp inputs"),
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cs.ns(|| "process cmp inputs"),
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a,
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&self,
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b,
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b,
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ordering,
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ordering,
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should_also_check_equality,
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should_also_check_equality,
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@ -130,10 +126,10 @@ impl CmpGadget { |
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}
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}
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/// this function verifies a and b are <= (p-1)/2
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/// this function verifies a and b are <= (p-1)/2
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fn is_smaller_than<CS: ConstraintSystem<ConstraintF>>(
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fn is_smaller_than<CS: ConstraintSystem<F>>(
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mut cs: CS,
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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a: &FpGadget<F>,
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b: &FpGadget<F>,
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) -> Result<Boolean, SynthesisError> {
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) -> Result<Boolean, SynthesisError> {
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Self::check_smaller_than_mod_minus_one_div_two(cs.ns(|| "check a in range"), a)?;
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Self::check_smaller_than_mod_minus_one_div_two(cs.ns(|| "check a in range"), a)?;
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Self::check_smaller_than_mod_minus_one_div_two(cs.ns(|| "check b in range"), b)?;
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Self::check_smaller_than_mod_minus_one_div_two(cs.ns(|| "check b in range"), b)?;
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@ -141,24 +137,24 @@ impl CmpGadget { |
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}
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}
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/// this function assumes a and b are known to be <= (p-1)/2
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/// this function assumes a and b are known to be <= (p-1)/2
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fn is_smaller_than_unchecked<CS: ConstraintSystem<ConstraintF>>(
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fn is_smaller_than_unchecked<CS: ConstraintSystem<F>>(
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mut cs: CS,
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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a: &FpGadget<F>,
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b: &FpGadget<F>,
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) -> Result<Boolean, SynthesisError> {
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) -> Result<Boolean, SynthesisError> {
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let two = ConstraintF::one() + ConstraintF::one();
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let two = F::one() + F::one();
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let d0 = a.sub(cs.ns(|| "a - b"), b)?;
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let d0 = a.sub(cs.ns(|| "a - b"), b)?;
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let d = d0.mul_by_constant(cs.ns(|| "mul 2"), &two)?;
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let d = d0.mul_by_constant(cs.ns(|| "mul 2"), &two)?;
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let d_bits = d.to_bits_strict(cs.ns(|| "d to bits"))?;
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let d_bits = d.to_bits(cs.ns(|| "d to bits"))?;
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let d_bits_len = d_bits.len();
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let d_bits_len = d_bits.len();
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Ok(d_bits[d_bits_len - 1])
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Ok(d_bits[d_bits_len - 1])
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}
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}
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/// this function verifies a and b are <= (p-1)/2
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/// this function verifies a and b are <= (p-1)/2
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fn enforce_smaller_than<CS: ConstraintSystem<ConstraintF>>(
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fn enforce_smaller_than<CS: ConstraintSystem<F>>(
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mut cs: CS,
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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a: &FpGadget<F>,
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b: &FpGadget<F>,
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) -> Result<(), SynthesisError> {
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) -> Result<(), SynthesisError> {
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Self::check_smaller_than_mod_minus_one_div_two(cs.ns(|| "check a in range"), a)?;
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Self::check_smaller_than_mod_minus_one_div_two(cs.ns(|| "check a in range"), a)?;
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Self::check_smaller_than_mod_minus_one_div_two(cs.ns(|| "check b in range"), b)?;
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Self::check_smaller_than_mod_minus_one_div_two(cs.ns(|| "check b in range"), b)?;
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@ -166,21 +162,29 @@ impl CmpGadget { |
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}
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}
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/// this function assumes a and b are known to be <= (p-1)/2
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/// this function assumes a and b are known to be <= (p-1)/2
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fn enforce_smaller_than_unchecked<CS: ConstraintSystem<ConstraintF>>(
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fn enforce_smaller_than_unchecked<CS: ConstraintSystem<F>>(
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mut cs: CS,
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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a: &FpGadget<F>,
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b: &FpGadget<F>,
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) -> Result<(), SynthesisError> {
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) -> Result<(), SynthesisError> {
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let is_smaller_than = Self::is_smaller_than_unchecked(cs.ns(|| "is smaller than"), a, b)?;
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let is_smaller_than = Self::is_smaller_than_unchecked(cs.ns(|| "is smaller than"), a, b)?;
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cs.enforce(
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cs.enforce(
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|| "enforce smaller than",
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|| "enforce smaller than",
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|_| is_smaller_than.lc(CS::one(), ConstraintF::one()),
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|lc| lc + (ConstraintF::one(), CS::one()),
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|lc| lc + (ConstraintF::one(), CS::one()),
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|_| is_smaller_than.lc(CS::one(), F::one()),
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|lc| lc + (F::one(), CS::one()),
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|lc| lc + (F::one(), CS::one()),
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);
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);
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Ok(())
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Ok(())
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}
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}
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}
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pub struct CmpGadget<ConstraintF: PrimeField> {
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constraint_field_type: PhantomData<ConstraintF>,
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}
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impl<ConstraintF: PrimeField> CmpGadget<ConstraintF> {
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}
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}
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#[cfg(test)]
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#[cfg(test)]
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@ -189,7 +193,6 @@ mod test { |
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use rand_xorshift::XorShiftRng;
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use rand_xorshift::XorShiftRng;
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use std::cmp::Ordering;
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use std::cmp::Ordering;
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use super::CmpGadget;
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use crate::{
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use crate::{
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alloc::AllocGadget, fields::fp::FpGadget, test_constraint_system::TestConstraintSystem,
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alloc::AllocGadget, fields::fp::FpGadget, test_constraint_system::TestConstraintSystem,
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};
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};
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@ -222,17 +225,15 @@ mod test { |
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match a.cmp(&b) {
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match a.cmp(&b) {
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Ordering::Less => {
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Ordering::Less => {
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CmpGadget::<Fr>::enforce_cmp(
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a_var.enforce_cmp(
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cs.ns(|| "smaller than test"),
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cs.ns(|| "smaller than test"),
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&a_var,
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&b_var,
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&b_var,
|
|
|
Ordering::Less,
|
|
|
Ordering::Less,
|
|
|
false,
|
|
|
false,
|
|
|
)
|
|
|
)
|
|
|
.unwrap();
|
|
|
.unwrap();
|
|
|
CmpGadget::<Fr>::enforce_cmp(
|
|
|
|
|
|
|
|
|
a_var.enforce_cmp(
|
|
|
cs.ns(|| "smaller than test 2"),
|
|
|
cs.ns(|| "smaller than test 2"),
|
|
|
&a_var,
|
|
|
|
|
|
&b_var,
|
|
|
&b_var,
|
|
|
Ordering::Less,
|
|
|
Ordering::Less,
|
|
|
true,
|
|
|
true,
|
|
@ -240,17 +241,15 @@ mod test { |
|
|
.unwrap();
|
|
|
.unwrap();
|
|
|
},
|
|
|
},
|
|
|
Ordering::Greater => {
|
|
|
Ordering::Greater => {
|
|
|
CmpGadget::<Fr>::enforce_cmp(
|
|
|
|
|
|
|
|
|
a_var.enforce_cmp(
|
|
|
cs.ns(|| "smaller than test"),
|
|
|
cs.ns(|| "smaller than test"),
|
|
|
&a_var,
|
|
|
|
|
|
&b_var,
|
|
|
&b_var,
|
|
|
Ordering::Greater,
|
|
|
Ordering::Greater,
|
|
|
false,
|
|
|
false,
|
|
|
)
|
|
|
)
|
|
|
.unwrap();
|
|
|
.unwrap();
|
|
|
CmpGadget::<Fr>::enforce_cmp(
|
|
|
|
|
|
|
|
|
a_var.enforce_cmp(
|
|
|
cs.ns(|| "smaller than test 2"),
|
|
|
cs.ns(|| "smaller than test 2"),
|
|
|
&a_var,
|
|
|
|
|
|
&b_var,
|
|
|
&b_var,
|
|
|
Ordering::Greater,
|
|
|
Ordering::Greater,
|
|
|
true,
|
|
|
true,
|
|
@ -275,17 +274,15 @@ mod test { |
|
|
|
|
|
|
|
|
match b.cmp(&a) {
|
|
|
match b.cmp(&a) {
|
|
|
Ordering::Less => {
|
|
|
Ordering::Less => {
|
|
|
CmpGadget::<Fr>::enforce_cmp(
|
|
|
|
|
|
|
|
|
a_var.enforce_cmp(
|
|
|
cs.ns(|| "smaller than test"),
|
|
|
cs.ns(|| "smaller than test"),
|
|
|
&a_var,
|
|
|
|
|
|
&b_var,
|
|
|
&b_var,
|
|
|
Ordering::Less,
|
|
|
Ordering::Less,
|
|
|
false,
|
|
|
false,
|
|
|
)
|
|
|
)
|
|
|
.unwrap();
|
|
|
.unwrap();
|
|
|
CmpGadget::<Fr>::enforce_cmp(
|
|
|
|
|
|
|
|
|
a_var.enforce_cmp(
|
|
|
cs.ns(|| "smaller than test 2"),
|
|
|
cs.ns(|| "smaller than test 2"),
|
|
|
&a_var,
|
|
|
|
|
|
&b_var,
|
|
|
&b_var,
|
|
|
Ordering::Less,
|
|
|
Ordering::Less,
|
|
|
true,
|
|
|
true,
|
|
@ -293,17 +290,15 @@ mod test { |
|
|
.unwrap();
|
|
|
.unwrap();
|
|
|
},
|
|
|
},
|
|
|
Ordering::Greater => {
|
|
|
Ordering::Greater => {
|
|
|
CmpGadget::<Fr>::enforce_cmp(
|
|
|
|
|
|
|
|
|
a_var.enforce_cmp(
|
|
|
cs.ns(|| "smaller than test"),
|
|
|
cs.ns(|| "smaller than test"),
|
|
|
&a_var,
|
|
|
|
|
|
&b_var,
|
|
|
&b_var,
|
|
|
Ordering::Greater,
|
|
|
Ordering::Greater,
|
|
|
false,
|
|
|
false,
|
|
|
)
|
|
|
)
|
|
|
.unwrap();
|
|
|
.unwrap();
|
|
|
CmpGadget::<Fr>::enforce_cmp(
|
|
|
|
|
|
|
|
|
a_var.enforce_cmp(
|
|
|
cs.ns(|| "smaller than test 2"),
|
|
|
cs.ns(|| "smaller than test 2"),
|
|
|
&a_var,
|
|
|
|
|
|
&b_var,
|
|
|
&b_var,
|
|
|
Ordering::Greater,
|
|
|
Ordering::Greater,
|
|
|
true,
|
|
|
true,
|
|
@ -320,10 +315,9 @@ mod test { |
|
|
let mut cs = TestConstraintSystem::<Fr>::new();
|
|
|
let mut cs = TestConstraintSystem::<Fr>::new();
|
|
|
let a = rand_in_range(&mut rng);
|
|
|
let a = rand_in_range(&mut rng);
|
|
|
let a_var = FpGadget::<Fr>::alloc(cs.ns(|| "a"), || Ok(a)).unwrap();
|
|
|
let a_var = FpGadget::<Fr>::alloc(cs.ns(|| "a"), || Ok(a)).unwrap();
|
|
|
CmpGadget::<Fr>::enforce_cmp(
|
|
|
|
|
|
|
|
|
a_var.enforce_cmp(
|
|
|
cs.ns(|| "smaller than test"),
|
|
|
cs.ns(|| "smaller than test"),
|
|
|
&a_var,
|
|
|
&a_var,
|
|
|
&a_var,
|
|
|
|
|
|
Ordering::Less,
|
|
|
Ordering::Less,
|
|
|
false,
|
|
|
false,
|
|
|
)
|
|
|
)
|
|
@ -336,10 +330,9 @@ mod test { |
|
|
let mut cs = TestConstraintSystem::<Fr>::new();
|
|
|
let mut cs = TestConstraintSystem::<Fr>::new();
|
|
|
let a = rand_in_range(&mut rng);
|
|
|
let a = rand_in_range(&mut rng);
|
|
|
let a_var = FpGadget::<Fr>::alloc(cs.ns(|| "a"), || Ok(a)).unwrap();
|
|
|
let a_var = FpGadget::<Fr>::alloc(cs.ns(|| "a"), || Ok(a)).unwrap();
|
|
|
CmpGadget::<Fr>::enforce_cmp(
|
|
|
|
|
|
|
|
|
a_var.enforce_cmp(
|
|
|
cs.ns(|| "smaller than or equal to test"),
|
|
|
cs.ns(|| "smaller than or equal to test"),
|
|
|
&a_var,
|
|
|
&a_var,
|
|
|
&a_var,
|
|
|
|
|
|
Ordering::Less,
|
|
|
Ordering::Less,
|
|
|
true,
|
|
|
true,
|
|
|
)
|
|
|
)
|