Performs raw subtraction of scalar element ( say b ) from another one ( say a ),<br />without any reduction i.e. r = a - b<br /><br />Expected stack state<br /><br />[a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, ...]<br /><br />Final stack state<br /><br />[c, r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, ...]<br /><br />Note, if c == 0xffff_ffff, overflow has occurred during subtraction<br />else c == 0, no overflow occurred during subtraction.<br /><br />Adapted from equivalent Rust implementation https://github.com/itzmeanjan/miden/blob/e7038e45865a7032a0629346921a77010e82862d/miden/tests/integration/stdlib/math/ext5_scalar.rs#L56-L74<br />
## std::math::ecgfp5::scalar_field
| Procedure | Description |
| ----------- | ------------- |
| mont_mul | Montgomery multiplication of two radix-2^32 scalar field elements s.t. each<br />number can be represented using 10 limbs, each of 32 -bit width, returning<br /><br />r = (a * b) / 2^320 (mod N) \| N = 319 -bit prime ( See https://github.com/itzmeanjan/miden/blob/6a611e693601577864da3e43e745525b83c0030d/miden/tests/integration/stdlib/math/ext5_scalar.rs#L24-L35 )<br /><br />Expected stack state<br /><br />[a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, ...]<br /><br />Final stack state<br /><br />[r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, ...]<br /><br />Adapted from equivalent Rust implementation https://github.com/itzmeanjan/miden/blob/6a611e693601577864da3e43e745525b83c0030d/miden/tests/integration/stdlib/math/ext5_scalar.rs#L92-L132<br /> |
| to_mont | Given a scalar field element in radix-2^32 form, this routine converts it to<br />Montgomery representation, by multiplying input scalar by R2 = ((2 ^ 320) ^ 2) % N \| N = scalar field prime<br /><br />Expected stack state<br /><br />[a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, ...]<br /><br />Final stack state<br /><br />[r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, ...]<br /><br />Adapted from equivalent Rust implementation https://github.com/itzmeanjan/miden/blob/6a611e693601577864da3e43e745525b83c0030d/miden/tests/integration/stdlib/math/ext5_scalar.rs#L134-L139<br /> |
| from_mont | Given a scalar field element in Montgomery representation, this routine converts it to<br />standard radix-2^32 form, by multiplying input by 1 ( in radix-2^32 form )<br /><br />Expected stack state<br /><br />[a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, ...]<br /><br />Final stack state<br /><br />[r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, ...]<br /><br />Adapted from equivalent Rust implementation https://github.com/itzmeanjan/miden/blob/6a611e693601577864da3e43e745525b83c0030d/miden/tests/integration/stdlib/math/ext5_scalar.rs#L141-L146<br /> |
| inv | Given an element ( say a ) of scalar field, this routine computes multiplicative inverse ( say a' )<br />of that element s.t. a * a' = 1 ( mod N ) \| N = Scalar field prime<br /><br />Expected stack state<br /><br />[a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, ...] \| a[0..10] is a 319 -bit number, represented in radix-2^32 form<br /><br />Final stack state<br /><br />[b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, ...] \| b[0..10] is a 319 -bit number s.t. b = a^-1 ( mod N ), represented in radix-2^32 form<br /><br />Note, if input operand is 0, then multiplicative inverse can't be computed, which is why output result is also 0.<br /><br />Adapted from equivalent Rust implementation https://github.com/itzmeanjan/miden/blob/6a611e693601577864da3e43e745525b83c0030d/miden/tests/integration/stdlib/math/ext5_scalar.rs#L162-L176<br /> |