"""Implement the documented contracts. There is deliberately no answer fallback.

RLHF: dpo_loss, dpo_gradient. LoRA: lora_forward, merge, quantize.
GRPO: advantages, surrogate. See README.md and the topic-specific tests.
"""
import math


def dpo_loss(policy_gap, reference_gap, beta):
    """Stable softplus of -beta*(policy_gap-reference_gap); reject nonfinite/beta<=0."""
    raise NotImplementedError("Implement the stable preference loss")


def dpo_gradient(theta, beta):
    """Derivative of dpo_loss(theta, 0, beta); validate finite inputs and beta>0."""
    raise NotImplementedError("Differentiate the two-response loss")


def lora_forward(W, A, B, x, alpha):
    """Compatible finite shapes: W out×in, A rank×in, B out×rank. Do not mutate."""
    raise NotImplementedError("Compute Wx + alpha/rank * B(Ax)")


def merge(W, A, B, alpha):
    """Same shape contract as forward; return NEW W + alpha/rank * BA."""
    raise NotImplementedError("Merge into a new matrix")


def quantize(values, bits):
    """Return integer codes,scale. 4/8 bits, ties-to-even, narrow signed range.
    Reject empty/nonfinite input. All-zero input uses scale=1.
    """
    raise NotImplementedError("Quantize using the maximum absolute value")


def advantages(rewards):
    """Population std per prompt. Equal rewards→zeros; invalid groups→ValueError."""
    raise NotImplementedError("Normalize one group")


def surrogate(ratios, advantage, mask, epsilon=0.2):
    """Mean min(r*A,clip(r)*A) over valid completion tokens for one response.
    Binary mask must match ratios and include a token. Valid ratios positive/finite;
    advantage finite; epsilon finite in [0,1). Reject invalid input with ValueError.
    Masked ratios do not enter the calculation. No KL term.
    """
    raise NotImplementedError("Mask, clip with the correct sign, then reduce")